GTA

All Springer/NP/PCP Air Gun Discussion General => "Bob and Lloyds Workshop" => Topic started by: lloyd-ss on January 10, 2016, 01:21:18 AM

Title: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on January 10, 2016, 01:21:18 AM
EDIT on February 19, 2016 by Lloyd-ss. 
Could be that the velocity bar for HPA has just been raised.  If you wish, skip on down to Reply # 133.
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EDIT on March 22, 2016 by Lloyd-ss. 
And the bar has been raised again.  If you wish, skip on down to Reply # 241.
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EDIT on March 31, 2016 by Lloyd-ss. 
And the bar has been raised again.  If you wish, skip on down to Reply # 387.
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Note- This thread will be replacing the Maximum Velocity thread in this same gate that was started months and months ago.  I think a fresh approach might be helpful.   :D

I am very skeptical off things that don’t make intuitive sense to me.  And my intuition seldom lets me down.  I have been building and refining an internal ballistics spreadsheet for PCPs for several years and it is close, but not exactly right. That bothers me.  Its tendency is to predict too high a velocity with higher pressures and/or longer barrels.

There has also been a lot of talk about how the speed of sound affects maximum velocities and how sonic choke can severely hinder high velocities , to the point of developing some sort of phenomenon where the velocities might be clipped in a very noticeable manner.  That is extremely counter intuitive to me so I am obviously starting off with a bias.

So I decided to go back to the basic physics of a pellet propelled by HPA from a reservoir of limited volume.
Please, please, I don’t want to hear about a bunch of esoteric theories of what might be happening, unless they can be backed up with REAL data that is relevant to this thread. That means relevant to the working parameters of the usual PCP.

This will be more of an empirical model, rather a theoretical model.  A chicken and egg thing.  Our data is the chicken, and I think we can work backwards to clone an egg that will reproduce the same chicken, over, and over, again.

I wanted to start out with clean data.  What is the maximum velocity that can be obtained from a “clean” set-up that doesn’t have any porting or choke point or U-turns, etc, etc.  I ended up with a 22 cal barrel 23.3” long (it has a 14.5 cc volume) and a reservoir, also of 14.5 ccs, that dumps directly into the barrel.  The projectiles are special, 10.2 grains, with a sealing o-ring, and a cam operated release mechanism that will provide repeatable full-pressure release. Admittedly, this is a special case dump gun, very different from the complicated PCPS we use, but this will give a clear picture of the basic physics.
Here are some pictures of the set-up.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MV-1_zpsvgywmatf.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MV-1_zpsvgywmatf.jpg.html)

(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/CrossShaftDetails-8a_zpsntarzwba.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/CrossShaftDetails-8a_zpsntarzwba.jpg.html)
 
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MV-2_zpslhqcneab.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MV-2_zpslhqcneab.jpg.html)


Pretty self explanatory.  One thing worth noting is that there are four different bushing  (call them T-ports if you wish) for the breech, one at 100% full bore area, and one each at 24%, 48%, and 74% of the bore area.


This graph shows the data from the first round of testing.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MV5_zpsy0dk1dl9.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MV5_zpsy0dk1dl9.jpg.html)


 A total of 20 shots were taken, 4 at each pressure of 1800, 2500, 3300, 3750, and 4500 psi.  At each pressure, one shot was taken using  each of the 4 different bushings.  I think this gives a full, broad, set of data, covering extremes of pressure and of port sizes.

One thing that really stands out in this graph, is that even though many of the velocities ranged well into the supersonic range, there is absolutely no evidence of any clipping or steps or anomalies in the velocities. Sonic Joke, maybe. Or maybe I am just missing the entire point   ??????  Prove me wrong with real data.


This next graph is a bit more theoretical, but still well grounded in our pragmatic world. It shows the actual velocities of the 20 shots, displayed as a percentage of the theoretical maximum velocity for that set-up with a full bore T  port.  Notice how all of the strings track identically with each other, indicating a definite consistency of performance.  Again, no visible  steps or choking or anomalies. 

(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MV6_zpsh6qfvgv1.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MV6_zpsh6qfvgv1.jpg.html)

But still none of the shots reach 100% of theoretical, and they all drop off with the smaller T-ports.  The idea of this exercise is to come up with an empirical mode that can predict real-world results.  So what is messed up?  First, here is what is right: 1)The model uses declining pressure behind the projectile as the air expands into the barrel.  Remember, the barrel is 14.5 ccs and the reservoir is 14.5 ccs.  2) Pellet drag and breakaway are accounted for. 3) The force needed to accelerate the column  of compressed air behind the pellet is accounted for.
Those compensations have the model working consistently, but  there are some obvious problem areas.

So what needs to be fixed?
1) Compensate for T-port sizes. 
2) Compensate for the length of the barrel. 
3) Compensate for pressure drop in the barrel as the velocity increases.

And, there are more variables to be dealt with : valve, porting, port length and dia, dwell, etc, etc.  Some require linear compensation, some geometric, and some need a single- instance adjustment.  But before we tackle all of that, let’s get this simple version of one barrel and a dump reservoir  working first.
Title: Re: Sonic Choke or Sonic Joke
Post by: Bill G on January 10, 2016, 10:50:56 AM
Brilliant approach Lloyd.   In you instance, That TP is more like an orifice. As you know, I too have been working on a modeling tool for internal ballistics of the air gun for probably going on 7yrs now (I'm not as smart as I wish I was) :-[. I have theorized that perhaps what we are depicting as sonic choke is basicly the difference of flow through a pipe vs orifice.  Traditional PCP being a pipe flow profile and your test rig being more akin to orifice flow.  I have altered a version of my model to look at this in the same way you are with regard to dump performance. The amount of volume that can flow through an orifice has a pretty dramatic increase when the length of the tiny flat (throat) approaches zero.  The dead space created by the distance between the projectile and poppet has a larger effect than what I would have thought too.  I think that I am missing some connection between the capacity of a given porting at a given psi to flow a volume.  This could be the source of my deviation of velocity when predicting vs testing.  I can get a given caliber to be very predictable but when the caliber and of course porting change, then some "tweaking" has to occur. I am unfortunate enough not to have a variety of platforms to test and that makes it fairly difficult to compare data to computation.  Nor do I have the resources, to build a test rig to conduct such tests as you are doing, readily available.  It take some planning to get the access to the resources for building these things.  (I'm working on that).
Not to contaminate your line of thought but perhaps help us both stumble down a path of further understanding, I'll pose this question/questions.  Do you think that how quickly the pressure spike occurs at the base of the projectile, has a net gain in velocity, by the end of the shot cycle?  maybe better said as, harder acceleration resulting in higher velocity even though the volume and pressure flux are the same.  In a traditional valve the time it takes for the poppet to reach the certain area for max flow and then the duration that the poppet in in the "less than certain area" during closing results in lower net fps.  Your test rig looks to do away with all of that.                   
Title: Re: Sonic Choke or Sonic Joke
Post by: Bill G on January 10, 2016, 12:18:03 PM
Lloyd.  I put the information that you published about your rig into my modeler.  I used some friction information that I had collected from trials that I had performed in the past.  I have a break away friction of 7# as an average of all the .22cal barrels that I have measured with various pellets, so that is want I am using for breakaway friction.  My returned predicted velocity is 1269.5fps.  That looks fairly close to your graph.  This was based on 1800 psi with 100% porting.  I'm gonna input the other variations to see how close they are. 
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 10, 2016, 12:30:26 PM
Bill G,
You make some very good points and I tend to agree with most of what you said, and my thoughts are that as I accumulate data, it will show us where the "unknown" or "problem" areas are that might need more specialized testing. Like you, and a bunch of others, I have a bunch of ideas and possibilities floating around in my head that need to be dealt with in a somewhat methodical manner ( like Bob does, definitely!) so that a bunch of test time isn't wasted. 

Yes, I agree, this setup is more like flow through an orifice  into a pipe, but please be aware, that one of the orifices is bore diameter so the orifice restriction should not be a factor.  Without getting to far ahead and confusing the issue, a way to look at the conventional valve and T-port setup might be like a tank flowing into a short length of small diameter pipe, and then into a longer piece of slightly larger diamete pipe.  Maybe a scheme like "equivalent pipe diameters" could be investigated?  When you think about it, a barrel is only about 100 diameters long.  Flow calculations in normal air piping  might be more in the range of 1000 diameters or more.  But then again, our pressures are more like 20 or 30 times the "normal" pressures.

I am looking at introducing a factor into my spreadsheet  that utilizes the fact that the pressure drop in the pipe increases as the square of the velocity.  This is looking quite promising, but I am having to learn and apply this on a "pay-as-you-go" basis, ha, ha, because I really don't have sufficient background to dive in with full confidence.

I think your thoughts about sluggish valve action is right on the money.  There is no square wave airgun valve that I am aware of. Maybe something like a ceramic disk faucet valve would give a "squarer" cycle.  But on top of the sluggish valve, you have to add the startup of the pellet.  That has to come into play, but maybe not that much.  I have fiddled with some big bore barrels in the past where I played with the number of grease grooves on the bullet, and their fit into the bore in hopes  of getting more of a snap-action release, but honestly, the chrony data was pretty inconclusive.  But I could see where it might be more of a concern with smaller caliber, lighter pellets.  But, with all that rambling, yes, I think my test rig does give a snap-action release which eliminates at least a couple of variables.

I have some more data to present shortly that views this from yet another angle!
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 10, 2016, 12:32:17 PM
Lloyd.  I put the information that you published about your rig into my modeler.  I used some friction information that I had collected from trials that I had performed in the past.  I have a break away friction of 7# as an average of all the .22cal barrels that I have measured with various pellets, so that is want I am using for breakaway friction.  My returned predicted velocity is 1269.5fps.  That looks fairly close to your graph.  This was based on 1800 psi with 100% porting.  I'm gonna input the other variations to see how close they are. 

Bill G, That will definitely be helpful.
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 10, 2016, 04:46:14 PM
Lloyd, you can bet I'll be following this thread with interest.... The first thing I noticed is that I see an inflection in the curves at about the 50% TP area point, with the slope down to 25% being much steeper than that going up to 100%.... The inflection point seems to be related to TP area, and NOT to velocity.... It is possible that the "kink" in the curve at 50% is due to insufficient data points, and we may be looking at a section of a parabola (or other polynomial) going through 0-0.... In case you don't have the data (it's not easy to find), here is the speed of sound vs. high pressures for air and Nitrogen....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/SpeedofSound20C_zpsa0791bdb.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/SpeedofSound20C_zpsa0791bdb.jpg.html)

It may or may not be significant that the inflection points of your curves is occurring at just below the speed of sound in air from the above.... but following the same general trend.... Is it possible that as you restrict the TP area, the pressure drop due to Bernoulli's principle, reduces the speed of sound to values very close to your inflection points from above?.... All I'm saying is, that there may be some correlation between the inflection point when the TP area is 50% to the pressure related speed of sound at the TP....

As you know, my feelings on "Sonic Choking" is that it doesn't suddenly happen at a given air velocity, but takes place gradually as the flow velocity approaches the speed of sound at the pressure involved.... and it takes place as a limit to the "Mass Flow", ie the mass of air that can flow through the orifice at that upstream pressure.... When the velocity at the TP (restriction) is well below the local speed of sound there, the flow rate is dependant on the pressure.... but as the velocity approaches the local speed of sound there, the rate of flow increase slows, until eventually (when the orifice chokes) a mass flow limit is reached.... What effect that mass flow limit has on the acceleration of the pellet, of course, is another matter.... Is it possible that the steeper slope of the curve when the TP is smaller than 50% is a result of mass-flow limiting?....

One final point, I agree that to compare calibers, you need to think of the barrel length in calibers, the way Naval guns are measured.... Double the caliber, you need twice the barrel length to get the same situation....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 10, 2016, 06:23:23 PM
Bob,
We are going to have to agree to disagree on part of this one. What you might be seeing as an inflection point, I think is just excel trying to make a "best fit" of the data points, and nothing more.  There are only 4 data points in each line so the "curve" could be drawn a number of different ways.  As I get farther into this I hope to find what truly does make the predicted and actual data agree.  But at this time I do not wish to force the data to fit any particular theories that may or may not be applicable.

As far as anything on the second graph indicating some sort of mass limiting related to the 50% port area or the speed of sound, I definitely do not think that is the case.  There are 5 sets of data points, with pressures of 1800 psi, 2500, 3300, 3750, and 4500 psi.  The velocity through the 50% port will be extremely different at each pressure.  The 1800 psi shots might be subsonic through the port, but the 4500 psi air through the ports are probably quite a bit above the speed of sound.  The point is that the air through a 50% port could have a wide range of velocities  and there is probably no relevant inflection point associated with the 50% area of the port. 

As I do more testing and collect more data, the controlling factors will surface, but at this time, I am still saying "no"  to sonic choking.  If there is data to support it, I could be persuaded to consider it, but not based on the data so far.

Lloyd



Title: Re: Sonic Choke or Sonic Joke
Post by: Bill G on January 10, 2016, 07:57:02 PM
As I've been working on this today, I think that it may be better referred to as mass chocking not sonic chocking.  Lots of math to do but it seems that the higher the pressure the less mass can flow.  The air seems to be able to move at sonic speed.  I'd love to see data above 4500psi.  I'm going to theorize that sonic chocking can happen but not at the pressures we are dealing with. 
Bob has mentioned a phenomenon that occurs when trying to gain shot count by filling to extreme pressures(above 4500psi) What ever that psi is, I'm gonna theorize, that and above, is where we are most likely to experience anything close to sonic choking.

Lloyd, I glad you dredged this one up again I've been pondering it for a couple of months now.  Good to have guys to bounce it off of.   

I've got to go find some more dry erase markers.  these are about dry and I think I'm getting a buzz. >:( ;D

Bill

     
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 10, 2016, 08:57:17 PM
Short barrel vs long barrel
I collected 10 more data points today in a manner that I have been wanting to do for years!
The previous 20 data points were all done with a 23.3" long barrel, but this second batch of 10 points were all done with an 8.2" long barre!
Everything else was the same.  At each pressure I took one shot with the .22 cal 100% port.  For the second shot at that pressure I used the small 24% of bore area port.

The short barrel is 35% of the length of the long barrel, but in general, the 8" barrel achieves about 80% of the velocity of the 23" barrel.
This data is just presented as a table.  As far as the percentages look, it seems that the higher pressure shots achieve a very slightly higher percentage of their initial velocity in the short barrel than at lower pressures.  And it also seems that the smaller ports might achieve a very slightly higher percentage of their velocity in the short barrel compared to a 100% port.



(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/23and8barrels_zps7utycahs.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/23and8barrels_zps7utycahs.jpg.html)

Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 10, 2016, 10:44:53 PM
Ok, Lloyd, we'll agree to disagree, but I only see one fair curve in your original data, that for 3750 psi, the others I see a change in slope at the 50% point.... Take the smoothing out of Excel (have it plot straight lines, point to point, it will be much more obvious....

BillG, the phenomenon you are referring to regarding shot count not being linear above 3000 psi is not mass choking, but the VanDerWaals effect, which means that at extreme pressures the molecules are bouncing off each other more frequently, and hence the pressure rises more quickly than predicted by Boyle's Law.... For example, if you had a 1 litre container at 3000 psi (207 bar) and it holds 207 L of air, Boyle would predict that at 4500 psi the same container would hold 310 L of air (50% more).... but in fact it will only hold about 91% of that (281 L) at 4500 psi.... Here is the graph for that....

(http://i378.photobucket.com/albums/oo221/rsterne/Important/IdealGases_zps796cc652.jpg) (http://s378.photobucket.com/user/rsterne/media/Important/IdealGases_zps796cc652.jpg.html)

Lloyd, that is great data using the 8.2 barrel compared to the 23".... I can't resist the temptation to balance your spreadsheet using the 23.3" barrel, and then change only to the 8.2" and see what it predicts.... I used 1 lb. drag and 5 lbs. breakaway, air mass included.... Numbers below are PSI / TP % / Efficiency to get your spreadsheet to output your 23.3" velcocity / Velocity predicted by your spreadsheet with 8.2" barrel....

1800 psi / 100% - 0.726 efficiency - 933 fps
1800 psi / 24% - 0.485 - 753 fps

3300 psi / 100% - 0.688 - 1131 fps
3300 psi / 24% -  0.463 - 922 fps

4500 psi / 100% - 0.704 - 1263 fps
4500 psi / 24% - 0.457 - 1012 fps

I can draw two conclusions from that.... Your 100% TP shots are about 70% efficient, and your 24% TP shots are less than 50% efficient.... Your spreadsheet underestimates the velocity with an 8.2" barrel, which means the efficiency is greater with the shorter barrel, or worse with the longer barrel.... I think this is what you are trying to test, is it not?....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Rocker1 on January 11, 2016, 06:31:20 AM
  I need Tylenol  aspirin , you guys do it to me everytime but yet I come back for more.  David
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 11, 2016, 10:43:57 AM
  I need Tylenol  aspirin , you guys do it to me everytime but yet I come back for more.  David
Ha ha David. You are a real sucker for punishment, LOL.
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 11, 2016, 11:33:58 AM
Bob,
Thanks for looking at the new numbers.  Yes, taking the same shot with different length barrels really tells the true story of the internal ballistics and how the acceleration of the pellet varies in the barrel.   

You are correct that the intent of this exercise is to make the spreadsheet more accurate in its performance predictions, and it looks like I have enough data to start working on that.
Checking the efficiencies (on the spreadsheet)  of this raw data does give us some clues on what needs to be fixed.

But here is something that I think is very exciting (serious geek stuff, ha, ha).  Let's just look at two particular shots.  3300psi, 100% T-port, and 23.3 and 8.2" barrels.  Both shots use the entire 14.5cc dump shot.  23.3" vel is 1421fps actual (1786 theo), and the 8.2" barrel is 1176fps actual (1376fps theo). Using the current spreadsheet, 23.3" barrel dumpshot and .63 eff,  we get the 1421fps of the actual shot.  For the 8.2" barrel .73 eff to get the 1176 velocity.  (I am using zero breakaway and doing some rounding.)
The pellet exits the 8.2" barrel at .00094 seconds.  If we switch to the 23.3" barrel (63% eff) and close the valve at .00094 sec we end up with 1364fps (down from the actual of 1421) but the ending pressure in the tank is 2550psi, instead of zero.  Shot eff is a mediocre .92, but not bad.  So you get 96% of the original velocity but using only 23% of the air.  So as we have always said, closing the valve too late just wastes a bunch of air. (Bob- I think my 23% calc is correct, but not positive.)

I think i have enough data to add some new velocity and length dependent variables to the spreadsheet. Head scratching, number crunch time!
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: Kailua on January 11, 2016, 02:17:04 PM
I for one is that stupid guy which would raise my hand in class asking stupid questions.  Also not knowing if this question pertains truly to this discussion.  My question is there a pressure lost between the lands and grooves of the barrel?  Could it be part of the equation also on different barrel lengths?
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 11, 2016, 03:17:53 PM
I for one is that stupid guy which would raise my hand in class asking stupid questions.  Also not knowing if this question pertains truly to this discussion.  My question is there a pressure lost between the lands and grooves of the barrel?  Could it be part of the equation also on different barrel lengths?
I don't think that there is much, if any, pressure lost as leakage past the pellets.  At least, there isn't supposed to be.
Take a look at this first pic.  The 2 pellets on the right were just pushed through the barrel with  1/8" wood dowel.  The 2 pellets on the left were shot through the barrel and retrieved.  Look at the difference in the skirts.  The fired pellets swelled up from the air pressure and sealed very well.
(http://i226.photobucket.com/albums/dd79/loyd500/22J-SB-exact-jumbo.jpg) (http://s226.photobucket.com/user/loyd500/media/22J-SB-exact-jumbo.jpg.html)

Here is a pic of the special barrel and bullets I used for these tests.  They seal with a o-ring, and are retained by the cam in the half-moon cutout until  full pressure is built up and the cam releases them.  They definitely have no air leakage.
Lloyd
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/20160111_134656_zpsnstiwvj7.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/20160111_134656_zpsnstiwvj7.jpg.html)
Title: Re: Sonic Choke or Sonic Joke
Post by: Gertrude on January 11, 2016, 03:31:30 PM
  I need Tylenol  aspirin , you guys do it to me everytime but yet I come back for more.  David
I'm with you Dave, and adding in a fifth of whisckskie to boot.  ;)
 if my brain's gunna hurt that bad, then it should be for good reason  ;D
Title: Re: Sonic Choke or Sonic Joke
Post by: Airsnipe on January 11, 2016, 11:33:51 PM
This reminds me of something I saw not long ago. Can't remember where but if it comes to me I will post it. Anyway, someone came up with an idea that using a physical object (long pole) to communicate over long distances, would be faster than the speed of light since the message would be felt on the other end at the same time the message was being sent. This theory already doesn't hold water as inertia is not being considered. But what got me thinking, was the idea brought up that the object carrying the message, can't move faster than the speed at which sound can travel through the material it's made of. And sound does not travel through anything faster than the speed of light.

I don't know if this is relevant to this topic (or even truth) but sound does travel at different speeds through different things though I had not heard that a material can't be moved any faster than sound can travel through it.

Not that we don't have enough things to account for already :o
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 11, 2016, 11:51:42 PM
Airsnipe, if you are saying you should be able to drive a bullet faster if the speed of sound in the bullet material is faster.... I don't see it....

Lloyd.... Just as an aside, how far from the muzzle is the Chrony?.... Those bullet's don't exactly look very aerodynamic, and once transonic (>Mach 0.8 ), let alone supersonic, the bullet slows down in a real rush.... I've seen losses of >100 fps in 5 yards at 1200+ fps....

Yes, no question, dump shots are very inefficient, particularly when the dump volume is greater than 50% of the barrel volume.... let alone at 100% (or 286%)....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Airsnipe on January 12, 2016, 12:05:04 AM
Bob, I'm thinking more to do with the air in the barrel in front of the projectile. I'm thinking the forces needed to move the air out of the way of the projectile increases (not linearly) as the projectile speeds up nearing the speed of sound through air. So the energy needed to move the air at say double the speed requires more than double the energy making a curve in force needed.
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 12, 2016, 11:27:37 AM
Bob, I'm thinking more to do with the air in the barrel in front of the projectile. I'm thinking the forces needed to move the air out of the way of the projectile increases (not linearly) as the projectile speeds up nearing the speed of sound through air. So the energy needed to move the air at say double the speed requires more than double the energy making a curve in force needed.
Airsnipe, The mass of the air in the barrel in front of the bullet is really insignificant and can be disregarded.  With this .22 cal 23.3" barrel, which holds 14.5 cc of air, the weight of that air is only .27 grains (I did indeed slip a decimal point, 0.27 grains is correct)(unless I slipped a decimal point), so it pushes out of the way pretty easy.  However, the weight of the air that is accelerating BEHIND the bullet IS significant and is included in the calculation. That 14.5 cc barrel filled with 3500 psi air is about 60 grains of air.  So instead of us driving a 10.2 grain projectile out of the barrel, we are really driving something more like a 70 grain projectile.

Bob, The chrony is set about 2 feet in front of the barrel, so I don't think the velocity has fallen off very much.  You are right, they a little wad cutters.  I used that shape because I am shooting them into a cardboard tube that is stuffed tightly with plastic grocery bags.  Those bags stop the bullets in about 6" and they are easy to retrieve and have no damage. That way I can get several shots with each "bullet." However, they have to be retrieved after every single shot and that does take a lot of time.

Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 12, 2016, 04:33:16 PM
Yeah, 2 ft. is not an issue....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 12, 2016, 09:49:39 PM
Lloyd,

I read through this thread. I'm away from my desk and on my iPhone so not prepared to back up much of what I say until I'm back home.

You said that the actual velocities are coming out less than predicted. I don't know what was predicted but I did see (1786 theo). Anytime I see much over 1640fps for air at room temperature,  it raises a red flag.

If you slipped a decimal on your air density and mass calculations, it could account for the difference.

I looked into it a while back, and there is no way to get much over 1640fps. The mass of the highly compressed air eventually uses all of it's available energy just to accelerate itself.

Recheck the mass of air (14.5cc and 3500psi).
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 12, 2016, 10:01:10 PM
Scott.... You need to read the thread that started this project.... http://www.gatewaytoairguns.org/GTA/index.php?topic=94054.0 (http://www.gatewaytoairguns.org/GTA/index.php?topic=94054.0)

The theoretical velocity is based on the force created by the pressure times the bore area over the barrel length.... As to the 1640 fps maximum with air at room temperature you quoted, that is based on the RMS velocity of air molecules, but that is a distribution of velocities, and some of the molecules will be moving several times that fast.... Velocities of over 1700 fps have been recorded with air, and in fact some of the mid 1500 velocities in a rather famous video were taken far enough from the muzzle, and with light enough (plastic) "bullets" that with their terrible BC from their shape and low SD, they would have lost a lot of velocity by the time they got to the Chrony, and would have been over 1700 fps at the muzzle....

I too initially used the 1640 fps molecular velocity to propose that was the highest velocity for air from a PCP.... only to have it proven wrong....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Bill G on January 12, 2016, 10:55:06 PM
I've had velocity numbers higher than what you are getting.  My theoretical numbers are very close (10fps rounded).  I had the thought that I am not using any flow calculations for the air flowing through the barrel.  This brings me to the questions. Does it matter since it is pushing a pellet and the air wouldn't flow as if it were in a pipe with no obstruction?  Would this flow dynamic be the reason for the "fudge factor" that is used?.  Another thing that I have noticed while working with the listed pressures vs TP area.  as the psi goes up and the tp remains the same, There appears to be a variance in the percentage of efficiency.  Nothing new, we all know higher psi + higher efficiency.  But it makes me wonder if the same hold true to variance in TP?  The mass of air that moves through at various pressures indicates a loss in efficiency as the psi goes up.  That is contrary to what I had expected so I'm force to audit what I'm doing. 

Lloyd!!!!! why you make me think so hard! ;D ;D   I need the exercise believe me.   
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 12, 2016, 11:08:06 PM
Scott, Don't place too much on what we are throwing around as theoretical maximum velocities.  Personally, I think that most of the arguments that there ARE theoretical maximums are flawed. :P  What I am really trying to do in this particular thread is to collect enough data to improve the internal ballistics calculator that I have been working on for years so that it can make a fairly accurate estimate of an airguns probable performance.  This will all be based on real data, using only the basic laws of physics like F=ma, etc., and what I learn in this drawn out experiment.  I think getting wrapped around the axle with too much heavy theory about molecular speed and such are counterproductive to the goal of this thread, and to actually finding out what the "maximum" might really be.  :-\ 

Scott, I have indeed taken into account the substantial mass of the compressed air as it accelerates behind the pellet,  along with the barrel friction, and the falling pressure behind the pellet caused by the expansion of the air inside the closed system.  My current spreadsheet does predict too high of a velocity, but I am fixing the spreadsheet via analysis of the collected data, not adjusting it because a theory says I need to.   ;)

Regarding the general area of 1640 fps being the max velocity for PCPs, I am not ready to accept that.  As Bob said there have been some verifiable instances of velocities in the 1700 fps realm.  If you look at Reply # 8 in this thread, you will see that I achieved 1605 fps    :D  with a 22 cal 10.2gn "bullet", in a 23.3" long barrel, at 4500 psi.  That is darn close to that 1640fps max and there is plenty of room to play to get some more velocity.  A little more pressure, or a longer barrel, or a lighter "bullet."  Or all three of those.

The real point is, just because somebody says that there are theoretical limitations on airgun velocities, it is our choice whether or not to believe it, or whether you want to find out if it is real or not.
As for now, I think the maximum velocity is up for grabs.  ;D
Lloyd 

Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 12, 2016, 11:38:52 PM
Bill G,
I think you are up to the task, right?
We are coming to the same conclusions from different directions and that is a good thing.

I hate to mention it again, but I charted my actual velocities against my predicted velocities (I don't want to call them theoretical, because the predictions are all backed up by basic physics).  I was specifically looking at what I will call the velocity loss, the delta V, between predicted and actual. Everything I looked at was with a 100% bore dia T-port.  I used data from the 8.2" barrel and the 23.3" barrel, and at all 5 pressures.

First I plotted delta V against barrel distance and got some interesting results.   Similar curves at the 5 different pressures but I got to thinking (dangerous) that the velocities in the barrel varied tremendously base on the pressure that the bullet was fired at.  So, taking a different approach, I again looked for the umpteenth time at numerous empirical formulas for air flow in pipes and the big hitters as far as affecting flow and pressure drop were 1) velocity, and 2) pressure.  Bill, sound familiar? 
So I tried plotting the delta V against the actual velocity.  Hmmm, better, but still the lines for the different pressures didn't track that closely with each other.  So I went back to what I knew was correct and plotted delta V against the "predicted" velocity.  Bingo! The lines at the 5 different pressures almost laid on top of each other, but there was a slight change in the shape of the lines based on the pressure. So, going strictly on empirical data, I put a correction factor into my spreadsheet that reduces the actual velocity based on the variable of the predicted velocity, dependent upon the starting pressure in the gun.  Basically, the correction was a second order polynomial based on the velocity and the pressure.  It worked.   The spreadsheet now puts out data that agrees with the actual test shots.  Of course, when I add in the reductions for smaller T-ports it all might fall apart again. But what the heck.  Fix it again.
Lloyd
P.S.  I will try to post the graphs in a way that makes sense, but that will take a little prep work to get them to that point.
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 12, 2016, 11:53:34 PM
I'm not considering the RMS velocity of air molecules. I'm just looking at the physics of accelerating a mass with a constant force. Using room temp air at 3500psi.

F=ma

That mass includes the pellet AND the column of air behind the pellet.

I'm talking about 3500psi air at room temperature.

I'm not saying that 1640fps is a hard limit. But when I see velocities higher than that, I look for the reason. Non-standard conditions will allow higher than 1640fps.

If we switch to Helium, or higher temp air, or super high air pressure (van der Waal effect), then the density of the air is less of a problem.

BTW - 14.5cc, 3500psi air has a mass of about 60grains. The pellet is only 10.2gr. Most the work is simply accelerating the air.




Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 13, 2016, 12:15:43 AM
Scott,
I think we are pretty much on the same page in that getting above 1640fps takes some special actions.  And they are usually enough of a bother that they will only be done as a fun experiment.

Thanks for pointing out that misplaced decimal on the mass of air.  You had me panicked for a minute. I had done that 6/60 gn calc (edited now, thank you) as a quickie manual thing, so I had to go back into my spreadsheet just to assure myself that I hadn't used the wrong value there.  Luckily, it is correct.
Lloyd   
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 13, 2016, 12:18:00 AM
Correction made to mass(weight)  of air, where I had misplaced a decimal point. :-[
Lloyd
And also, the weight has to be converted to mass for the acceleration calculation.  The weight and mass, and the appropriate units, are not an easy concept.
Lloyd

Bob, I'm thinking more to do with the air in the barrel in front of the projectile. I'm thinking the forces needed to move the air out of the way of the projectile increases (not linearly) as the projectile speeds up nearing the speed of sound through air. So the energy needed to move the air at say double the speed requires more than double the energy making a curve in force needed.
Airsnipe, The mass of the air in the barrel in front of the bullet is really insignificant and can be disregarded.  With this .22 cal 23.3" barrel, which holds 14.5 cc of air, the weight of that air is only .027 grains (unless I slipped a decimal point), so it pushes out of the way pretty easy.  However, the weight of the air that is accelerating BEHIND the bullet IS significant and is included in the calculation. That 14.5 cc barrel filled with 3500 psi air is about 60 grains of air.  So instead of us driving a 10.2 grain projectile out of the barrel, we are really driving something more like a 70 grain projectile. 

Bob, The chrony is set about 2 feet in front of the barrel, so I don't think the velocity has fallen off very much.  You are right, they a little wad cutters.  I used that shape because I am shooting them into a cardboard tube that is stuffed tightly with plastic grocery bags.  Those bags stop the bullets in about 6" and they are easy to retrieve and have no damage. That way I can get several shots with each "bullet." However, they have to be retrieved after every single shot and that does take a lot of time.

Lloyd

Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 13, 2016, 02:18:34 AM
Weight is a force generated by gravity. It's pretty hard to weigh air.

For these calcs, I don't care about the "weight" of air. 14.5cc at 3500psi will have that same mass on earth, moon, or deep space. I don't need gravity to determine it's mass.

Forget weight. A grain is already a unit if mass. Mass is what matters for kinetic energy. A grain is a unit of mass, and a slug is a unit if mass. Convert all masses to slugs if you are using the Imperial system.

slug = 225218 grains

A slug is a mass that will accelerate at one ft/second squared, when subjected to one lbf.

A lbm will generate a lbf when subjected to the acceleration of standard gravity. A lbm is usually used for commerce as a convenient "weight".

It gets confusing when we mix commerce and engineering terms. As many don't really know what a mass is, the term "weight" is used pretty loosely.

Mass does not depend in gravity. Weight does.

Gravity varies, so weight varies. A 10,000lbm might weigh 9995lbf.

Confused? If we are using any mass for engineering calculations in the Imperial system, always convert directly to slugs. That will bypass the unnecessary "gravity" considerations.

Sorry about rambling. But I recently spent a lot of time explaining to someone about mass and kinetic energy, and that gravity is not part of the equation.
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 14, 2016, 03:50:57 PM
Lloyd,

I ran your numbers. They are close to what I get with the same input. Now I'm thinking that I may have succumbed to a 1640fps "myth".

I have not tested the limit in practice. But so far, testing it in theory, I don't see 1640fps as any kind of limit.

I'm going to see about adding fluid friction losses to my spreadsheet. Maybe that will bring down the "theoretical" values.

If that does not bring it down to match actual values, maybe we will have to attribute it to something like "sonic choking". In which case, it's not something that I know how to deal with.

BTW - I like the design of your dump valve test bed as it mostly eliminates any restrictions or timing/dwell issues. It makes a good comparison for verification of a simple mathematical model of the process.
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 14, 2016, 04:09:03 PM
Quote
Now I'm thinking that I may have succumbed to a 1640fps "myth".
You're not the only one!!!.... It sounded like a good idea, though.... based on the velocity of air molecules and all.... Trouble is,  those molecules didn't read the speed limit sign, and a few of them insist on exceeding the RMS value of 1640 by a wide margin.... *LOL*....

At least none of us are subsrcibing to the "Sonic Horizon Theory", which IMO held no merit.... No offense to the originator of said theory intended....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 14, 2016, 06:46:33 PM
Thanks guys, for the comments.  We are like accountants trying to figure out where the lost money went.

Here is some of the data that I have collected, presented in a bit more usable format, and also presented in a few new ways that open up some questions.
First off, these shots were all taken on the test bed shown, with a full bore diameter entry port. So, no T-port restriction.  10 shots, one each with an 8.2" barrel and a 23.3" barrel, at 5 different pressures. 14.5cc of air, .22 cal, full dump shot. The reservoir was manually filled each time using a gage with a 3" dial face so the fill pressures might be +/- 50psi.

First, here is a chart of the data: the actual shot velocity, the velocity that my spreadsheet predicted, and the delta between the two velocities.  I put the delta V in there, because I think that is what we are chasing.

 (http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/Delta%20V%20chart_zpsnmr9tulo.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/Delta%20V%20chart_zpsnmr9tulo.jpg.html)

Here is a chart of delta V against the length of the barrel. Interesting. Please note that the different velocities are not evenly spaced, so that might exaggerate the visual appearance of some of the variations.
Please note that there is a mistake in the chart titles of the next 3 charts.  They say 23.3" barrel, but actually they show the data for both the 8.2" and the 23.3" barrel. Only the last chart shows just the 23.3" barrel data.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/DeltaVvsBblLen_zpssjpgwcgt.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/DeltaVvsBblLen_zpssjpgwcgt.jpg.html)

Here is delta V against the actual velocities. 
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/DeltaVvsActualV_zpsezhpstgs.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/DeltaVvsActualV_zpsezhpstgs.jpg.html)

Here is delta V against the velocity predicted by my spreadsheet.  I find this very interesting because of the way the different pressures almost lay on top of each other. (Ignore the trend line polynomial equation.)
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/DeltaaVvsPredictedV_zps0jhgcip1.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/DeltaaVvsPredictedV_zps0jhgcip1.jpg.html)

Here is delta V against the starting pressure in the gun, but only for the 23.3" barrel.  I think this is interesting because the delta V for pressures from 3300 to 4500 are all the same.  What is that?
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/DeltaVvsPSI_zps4ipkvxcq.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/DeltaVvsPSI_zps4ipkvxcq.jpg.html)

Any thoughts or comments would be appreciated.
Thanks,
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 14, 2016, 09:26:29 PM
Lloyd,

Here is what my spreadsheet predicts vs yours:

mine(yours)fps

PSI        8.2"                   23.3"
1800psi, 1113(1112)fps, 1473(1499)fps
2500psi, 1254(1253)fps, 1629(1655)fps
3300psi, 1378(1376)fps, 1761(1786)fps
3750psi, 1436(1433)fps, 1821(1845)fps
4500psi, 1519(1516)fps, 1907(1928)fps

Pretty close considering I have never seen your spreadsheet, so mine may be a little different. Ever since computers, my calculus ability has waned. I used a spreadsheet to do a numerical integration. My calculation increment is by .1" along the barrel. Even at .1" increment, there may be a small error (on the high side) in the results.

I used air = .001225g/cc.

I did not include any friction (gas or pellet).

I modeled the expansion as adiabatic which makes a small difference as the ratio of barrel/reservoir volume increases. That could account for my lower numbers with the longer barrel.
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 14, 2016, 10:30:40 PM
Scott,
This is really weird. I had a few pounds of barrel friction in the spreadsheet when I did my calcs, so I removed that and my predictions went up even a little higher than yours.  So we ended up farther apart.  But I also have a way to toggle between isothermal and adiabatic in the spreadsheet by switching an exponent in the expansion calc.  I had it set to "1" for isothermal.  I switched the exponent to "1.4" for adiabaic and here is what I got for the 23.3" lengths:

           Scott adiabatic,  (Lloyd original isothermal),  Lloyd adiabatic
1800psi,  1473  (1499)fps,    1470
2500psi,  1629  (1655)fps,   1627
3300psi,  1761  (1786)fps,   1759
3750psi,  1821  (1845)fps,   1819
4500psi,  1907  (1928)fps,   1904

I do my iterations by time, .00001 sec,  rather than by distance like you do.  I am surprised we are that close in our predictions!!!
What can I say?
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 15, 2016, 12:15:46 AM
Lloyd, to get your original predictions, I had to use zero TP volume, 1 lb. drag and 2 lbs. breakaway, isothermal expansion, and 100% efficiency.... eliminating the drag and breakaway, and using adiabatic gave your last results, so your spreadsheet and Scott's agree within 2-3 fps, I suspect just rounding errors and/or the difference in integrating using time or distance.... So we know the math works, now it's just a matter of getting the right fudge factors to figure out where that velocity is going....

Starting with those settings (no drag, adiabatic), the efficiency factor required to get your actual velocities with the 23.3" barrel is remarkably consistent at 70-73%, with no real trend vs. pressure.... although the highest efficiency was at the lowest pressure (and the lowest efficiency at the middle pressure).... With the 8.2" barrel, there WAS a trend, with the higher pressures being less efficient.... 80+% at 1800 psi dropping to 73+% at 4500 psi.... What is remarkable is that if you put in a fudge factor of, say, 73% you would be very close to actual results!....

RE your graphs, IMO the Delta's should be a percentage of theoretical.... ie DeltaV = (actual/theoretical)x100%.... Your velocity Delta's expressed as a percent of theoretical, all lie between 16-18% for the 23.3" barrel.... and between 11-15% for the 8.2% barrel.... These are using the predictions in the table; using the adiabatic, and adding some pellet drag, they would be even less.... I would like to see your graphs using percentage, I think the trends are close to linear.... Isn't it just possible to accept that the mechanical losses in the system account for about 20-30% ?.... I know the goal is to identify the sources of that loss and quantify it.... but do you not think we're chasing our tail here?....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 15, 2016, 01:19:56 AM
I put in 2 lbs. drag and 5 lbs. breakaway, left the efficiency at 100% and used adiabatic expansion, and calculated the theoretical velocity and energy for the 10 shots.... Then I calculated the DeltaV as a percentage of theoretical and actual, and plotted them vs. velocity, with the following results....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Theory%20Delta%20vs%20Velocity_zpsezpky0zk.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Theory%20Delta%20vs%20Velocity_zpsezpky0zk.jpg.html)

I then plotted the DeltaV against pressure, with the following results....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Theory%20Delta%20vs%20Pressure_zpspkdnxem4.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Theory%20Delta%20vs%20Pressure_zpspkdnxem4.jpg.html)

I then calculated the FPE obtained in the shots, as a percentage of the theoretical (ie the efficiency) and plotted that against velocity and pressure....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Theory%20Efficiency%20vs%20Velocity_zpsqu6vkgzj.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Theory%20Efficiency%20vs%20Velocity_zpsqu6vkgzj.jpg.html)


(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Theory%20Efficiency%20vs%20Pressure_zpstr3ffbad.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Theory%20Efficiency%20vs%20Pressure_zpstr3ffbad.jpg.html)

On the first two graphs, it doesn't take too much imagination to see all those lines going through zero-zero, just as they should.... The plots of DeltaV vs. velocity look like they might be linear with a cutoff as the velocity gets into the stratosphere.... The plots of DeltaV vs. pressure are curved, maybe a parabola through 0-0....

On the second two graphs, you can see how narrow a range the efficiency is running in.... better at lower velocities, and limiting out at about 70% as the velocities push over ~ 1400, regardless of barrel length.... I don't think the curve vs. pressure tells us much, IMO it is just the velocities effect on the efficiency showing up.... The only way to tell if there is a pressure effect is to do some tests with MUCH heavier bullets and plot them out the same and see if higher pressures are less efficient.... or if we are just seeing that velocities are.... The same applies to the DeltaV plot vs. Pressure....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 15, 2016, 10:09:18 AM
Lloyd,........... so your spreadsheet and Scott's agree within 2-3 fps, I suspect just rounding errors and/or the difference in integrating using time or distance.... So we know the math works, now it's just a matter of getting the right fudge factors to figure out where that velocity is going....
............... I know the goal is to identify the sources of that loss and quantify it.... but do you not think we're chasing our tail here?....
Bob

Bob,
If we are going to apply for a government DARPA grant (most of us are from the US, can you pretend to be from the US, too?) we'll have to substitute some big-time engineering and science words for things like fudge factors and chasing our tails, LOL. Instead, we will be "Deriving an empirical formula to accurately predict the internal and exit velocities of pneumatically launched projectiles, that will have a foundation based on  long established physical laws, coupled with the results of empirical test data that will be collected, documented, and integrated, during the controlled testing that will be performed according to our scientifically designed and executed sequence of laboratory experiments." 8) 
They ought to give us big bucks for something like that, don't you think?

But, plan "B", if the government isn't going to fund our playing with airguns (Darn !), maybe we can just stop chasing our tails and shoot some stuff over the chrony and crunch some numbers to come up with some fudge factors that make our spreadsheets spit out the right answers.   ;D

I think we are probably stuck with plan B, LOL.

-------------
Like you said, with the fact that Scott and I are getting exactly the same results, based on our independently built spreadsheet models, it is a pretty good bet that the basic math is solid.  So, what empirically derived fudge factors do we need.  I agree that  the data in the last couple of posts can definitely be corrected by some sort of linear compensation fudge factor.  But that is only for this particular instance of a full bore diameter T-port dump shot.  Here is the data from the same setup with various bore area T-ports.  They will need different compensations.

Actual velocities, 14.5cc dump shot directly into the barrel, .22 cal, 10.2 gn projectile.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/23and8barrels_zps7utycahs.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/23and8barrels_zps7utycahs.jpg.html)

And then what about controlling the valve closing time?  Wow, a lot to deal with!

My guess is that there need to be at least these compensation factors:
1) reductions due to breakaway and drag of the projectile.  That is already in the spreadsheet.
2) reductions based on the valve dwell time.  That is already in the spreadsheet but might require a fudge factor.
3) a factor based on reservoir volume. That is already done.
4) A reduction based on the initial pressure drop because of T-port volume. Already in place.

5) A reduction based on T-port cross sectional area and probably the length and intricacy of this restriction.  This needs to be done, and is obviously important.
6) A general factor to be applied to the output (?) that will be based on test results. It might be a polynomial correction factor that is based on velocity of the projectile within the barrel. Or maybe it will just be a simple linear factor based on something else.
7) Possibly a secondary fudge factor that has something to do with caliber or projectile S.D..  I don't know???
8 ) What we don't know that we don't know.

So, it looks like 5, 6, 7 and 8 are what the dog is chasing. Refining this to work across the entire PCP gamut is going to be tough, but I plan on living for several more years. ;)
Lloyd


Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 15, 2016, 01:44:29 PM
I agree with your assessment of items 5-8, especially #8.... *LOL*.... My thoughts?....

#5 - transfer port area - should be entirely possible to include a basic factor for that, I have a simple system I use on my maximum FPE vs pressure and barrel length spreadsheet with little to no basis in science, but it seems to agree quite well with my empirical data.... Instead of using the caliber squared for determining the bore area to calculate the acceleration and hence the maximum FPE, I use TP diameter times caliber.... Why?.... I dunno, but it seems to work, when predicting the maximum (not so good at low power) and it's pretty easy.... *LOL*.... As far as the length and wandering around of the port, I view that as a true "efficiency loss" for that particular gun.... hard to quantify, and the cross to bear of the guy that built it that way (and I'm as guilty as most).... I will comment that large ports can produce very good power even if they aren't straight, compared to what you might expect (eg. my Hayabusa compared to a Condor, very little difference when comparing apples to apples)....

#6 - a general factor based on test results - I would be more specific, and tie it somehow to the gas used and the speed of sound and molecular velocity of that gas.... Now don't jump down my throat, I'm not saying there is a limit.... just that we ALL know that the efficiency goes into the dumper when the velocity approaches or exceeds Mach 1, and we need to compensate for that.... I think your testing will be most valuable in determining the velocity factor with air.... we may have to use CO2 and Helium to find similar factors or confirm the math, however.... I don't think the length of barrel is an efficiency factor directly, I think we will find if we test enough it is the velocity at each point in the barrel we need to compensate for.... and longer barrels (at the same pressure) spend more time at higher velocities....

#7 - caliber and/or SD -  I have my doubts that any compensation is needed for these, as from my experience using your spreadsheet to both predict projectile behaviour and explain it, it already does an excellent job.... This applies to being very good at predicting the velocity when you change bullet weights, to the increased dwell required to drive them faster.... I am constantly AMAZED at how good the spreadsheet works, just the way it is....

#8 - what the heck do I know anyway?.... only that your spreadsheet works d a r n well and we have to be careful to improve it, not just change it.... I do have a general comment, though, and that is I think the expansion should be isothermal when the valve is open and adiabatic when closed, but that's just a gut feel.... Maybe we need an exponent in between 1.0 and 1.4, or a variable one?....

Bob

Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 15, 2016, 02:26:27 PM
Bob,
Thanks for your comments. Much appreciated!
Here are my responses to the 5 thru 8:
5) Agreed.  You've do a lot with that as the T-port size relates to FPE, and as you say, it works. The true essence of an empirical formula.  I would have to modify the relationship slightly because the spreadsheet predicts/models the  velocity and only does the quickie math for the FPE at the end. Probably something to back figure the velocity based on the predicted FPE and the bullet weight.
6) Yes, this general factor has to do with the speeds/velocities of the gas.  It might end up being a simple relationship with the velocity of the projectile inside the barrel.  But it would probably be an exponential relationship, maybe to the power of 1.8 or 1.9 instead of Vel squared.  As you say, testing will show that.  And it may be that this exponential "degradation" will account for a lot of those "gas" factors.
7)Cool.  If we appear to be produccing accurate results in that department, lets leave it alone.  Come to think of it, the bullet diameter and weight that are already in the spread sheet should be taking care of the S.D. ratio and other "bullet" factors.
8 ) I already have the isothermal/adiabatic option built into the spreadsheet as a toggle to exponents of  1.0 or 1.4.  I can fix that to be iso (1.0) when the valve is open and adiabatic(1.4) after the valve closes.

Sounds like we've got a plan, now we need to design some more experiments to produce clean data that covers the full operational range of PCPs. That one sentence is a precursor to a LOT of work.  My test bed can only do dump shots, so it has its limitations. Its reservoir volume can be changed, though.

Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 15, 2016, 03:21:47 PM
My thoughts:

Before considering restrictions such as the transfer port, we should get our equations to match the simplified dump valve test bed.

A general "fudge factor" might get us close for a narrow set of design parameters. But it's not a good solution.

I think that the main omission is fluid flow losses. We could use existing empirical formulas that take into account viscosity and/or Reynolds number. Instead, I'm going to attempt an empirical formula that takes into account the info pertinent to our model.

The pertinent variables might include: pipe diameter, pipe length, fluid velocity, and pressure. Based on Lloyd's test data, the goal is to come up with a formula to predict friction force of the flowing gas in the barrel.

Things to consider:

The force will be a function of swept area and shear stresses in the air, along the pipe surface.

Swept area is determined by barrel diameter and length.

Shear stresses by velocity, viscosity.

Viscosity by pressure.

Velocity at the pipe surface by velocity gradient.

Gradient by pipe radius.

I'll start with a formula such as:

lbf = Xfactor x Length x FPS x FPS x PSI

The pipe diameter seemed to cancel out, but I could be wrong in the way that it affects the gradient. We might need to put it back in there. Not sure about velocity squared. And there could be an exponential relationship, as Lloyd stated.

The lbf from the formula will be included along with pellet friction at each stage of the integration. Xfactor will be a variable that we change until calculated velocity numbers match the test data.
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 15, 2016, 04:36:39 PM
As usual, once I stopped typing, I decided to do something about it.... My solution for #5, while not elegant, is certainly better than no correction at all.... What I did was to multiply the caliber by the TP diameter, and then take the sq.rt. of that and use it in your spreadsheet for the caliber.... Here is the raw data.... If you click on it, it should be large enough to read....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Theory%20TP%20Correction%20Table_zpssjftwipx.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Theory%20TP%20Correction%20Table_zpssjftwipx.jpg.html)

OK, what it means....  Columns are for each barrel length and pressure.... At the top left, you can see how I came up with the "Caliber" number to put in your spreadsheet.... The top row, with the numbers in bold, is what you get without any correction for the diameter of the transfer port.... The next row down is for the 3/16" TP, next down for the 5/32" TP, and below that for the 7/64" TP (which is what I got for diameters working back from your areas).... So, that top section is what the predicted velocities would be using 1 lb. drag, 2 lb. breakaway, 100% efficiency, and adiabatic expansion (I forgot to change it back, which would have made the predicted velocities higher, me bad).... I ran all the data again, using Isothermal, no real changes noted in any trends....

The next section down is your measured velocities for each combination.... The section below that is the "efficiency", which is how your measured velocity compares to my prediction.... It is (actual/theory)x100%.... The bottom section is the same thing, but without the TP diameter correction.... ie it is how your measured velocity compares to your existing spreadsheet velocity prediction (the bold numbers are the divisor).... So then I graphed out some of the data, as below.... Here is the uncorrected data, plotted against TP diameter....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Theory%20Efficiency%20vs%20TP%20Diam%20Uncorrected_zpsldh1fsj7.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Theory%20Efficiency%20vs%20TP%20Diam%20Uncorrected_zpsldh1fsj7.jpg.html)

As you can see, the shots with the smaller transfer ports are a long way from your spreadsheet predictions.... Next, here is the efficiency plotted using my predictions....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Theory%20Efficiency%20vs%20TP%20Diam%20Corrected_zpsvccufsdj.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Theory%20Efficiency%20vs%20TP%20Diam%20Corrected_zpsvccufsdj.jpg.html)

Other than the data for the 8.2" barrel at 1800 psi, all the shots fall between 79-90% of the velocity predicted by a simple multiplication of bore x TP diameter, and then using that as the base for the area (by using the sq.rt. of that as the caliber).... I then plotted the corrected data against velocity, instead of TP diameter....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Theory%20Efficiency%20vs%20Velocity%20TP%20Corrected_zpsqiengfuj.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Theory%20Efficiency%20vs%20Velocity%20TP%20Corrected_zpsqiengfuj.jpg.html)

If you take out the smallest TP size, you see something interesting....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Theory%20Efficiency%20vs%20Velocity%20TP%20Uncorrected_zpskfrihpmf.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Theory%20Efficiency%20vs%20Velocity%20TP%20Uncorrected_zpskfrihpmf.jpg.html)

It looks to me that all the data follows a pretty even curve, slightly less efficient as the velocity increases.... If we can get a velocity correction that works, it might end up  a straight line at "some" value of efficiency.... ie a constant fudge factor.... What about the small size ports?....Well, they were much less efficient, so back to what I saw in the first graphs you posted, with that inflection point in the lines, indicating some form of "choking" with the smallest size ports.... I dunno, just a guess....

Anyway, see what you think of the idea of using sq.rt (bore x transfer port) as the caliber in your spreadsheet.... Play with it for a while and see if you think it has any merit.... The way I think it might work is actually pretty simple.... The force on the bullet is pressure x (bore^2) x PI/4.... If you run that air through a TP smaller than the bore, the pressure drops off (drag from passing through the port? I dunno), so the force is less.... On the other hand, if you take a constant sized TP and make the bore larger, you get more power.... They seem to me to be roughly equal in importance, so I just multiplied them together instead of using bore^2 in my force calculations... Seems to work in the spreadsheet I use to predict maximum FPE based on pressure, caliber, TP diameter, and barrel length !!!

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 15, 2016, 04:37:58 PM
I played with a fluid resistence formula a little bit. The xfactor multiplier came out to be much less than zero, so I turned it into a divisor instead.

I included a 2 lbf pellet drag and the following fluid friction force in my spread sheet:

lbf = (Length x PSI x FPS)/Xfactor

Xfactor = 450000

Results:

calculated (test results)

PSI,   V23.3,   V8.2
1800psi   1233(1254)fps   993(989)fps
2500psi   1355(1373)fps   1114(1086)fps
3300psi   1456(1465)fps   1219(1176)fps
3750psi   1501(1521)fps   1268(1219)fps
4500psi   1564(1605)fps   1338(1291)fps

The calculated velocities are now within 3% of actual test data in every case. I think if we apply an exponent of .9 or .95 to the velocity and adjust the Xfactor a tiny amount, we can get within about 1% of test data. That's within the tolerance of the chronograph.

I'm using drag over distance. If Lloyd uses drag over time, he might need a velocity squared function.

It's interesting that the 450000 is very close to (2 x 225,218). I'm going to investigate if it's merely a coincidence, or because we are dealing with mass flow rate and we could be using slugs somewhere in the fluid friction formula. It does not really matter in actual use, as long as the factor is correct and the formula works.
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 15, 2016, 04:45:15 PM
Scott, while I admire your approach, it amounts to Computational Fluid Dynamics.... I won't even pretend to understand the math, because I don't, and I certainly don't have a computer capable of running a CFD program.... I'm just trying to come up with some patches that will make your excellent spreadsheet match test results better.... Call it the redneck approach to PCP Internal Ballistics, if you like.... but it's something I can understand that may work.... even if I can't explain exactly why....

I'd love to KNOW why.... I just don't.... at least not yet....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 15, 2016, 05:03:20 PM
Scott, while the overall results are impressive for a first attempt, I notice that the predicted velocities for the 23.3" barrel are now lower than the test results, whereas the predictions for the 8.2" barrel remain higher.... I guess that means it is "overcompensating" for the losses as they relate to barrel length?....

Bo
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 15, 2016, 05:11:27 PM
Scott, while the overall results are impressive for a first attempt, I notice that the predicted velocities for the 23.3" barrel are now lower than the test results, whereas the predictions for the 8.2" barrel remain higher.... I guess that means it is "overcompensating" for the losses as they relate to barrel length?....

Bo
Actually, I just found what could be a big error in my application of the fluid friction in the spreadsheet. I'll report back when I work it out.
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 15, 2016, 07:03:28 PM
I fixed one big error and then added an exponent to each of the pertinent variables. That will allow me to vary the affect of each independently. This is the best solution I arrived at in about two hours of doing manual iterations of the variables:

Xfactor = 25000
lbf = (Length^0.2 x PSI^1.0 x FPS^0.75)/(Xfactor x Diameter^1.0)

Results:

calculated (test results)

PSI, V23.3, V8.2
1800psi 1237(1254) 989(989)
2500psi 1366(1373) 1112(1086)
3300psi 1471(1465) 1217(1176)
3750psi 1519(1521) 1266(1219)
4500psi 1586(1605) 1335(1291)

The calculated velocities are still within about 3% of actual in every case. Most are closer than 2%.

I'm not saying it will work in every case. I need more test data to refine the formula. The .2 exponent on the length factor is suspect as I think it should really be 1, but .2 worked. I don't know why. Once we get more data, I'll play with the numbers some more to very/modify the exponents and factors.

This is the "redneck approach" to CFD. I'm only loosely aware of the relationships of the variables to the flow friction, so it's hit or miss until I stumble on combination that works empirically.

I will play with the pressure and diameter exponents and see if it looks any better.


Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 15, 2016, 08:14:18 PM
I am enjoying watching for the time being.  Scott, I think it will be great if you get your  xFactor fluid flow compensation to produce results that are reasonably close to the actual test shots.  That way, any additional compensation factors that are necessary might be gun-specific.
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 15, 2016, 09:30:12 PM
I am enjoying watching for the time being.  Scott, I think it will be great if you get your  xFactor fluid flow compensation to produce results that are reasonably close to the actual test shots.  That way, any additional compensation factors that are necessary might be gun-specific.
Lloyd
I just reposted some info (check my update to prior post). It is reasonable close to the test data, but I have no idea if it will hold up under further use.
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 15, 2016, 09:49:45 PM
Scott,
Are you using inches or feet for the length?  What about the diameter?  PSI and FPS are instantaneous, correct?
Thanks,
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 16, 2016, 12:42:18 AM
Perhaps we are looking too hard for the answer, when a linear function would give us the correction we need.... I used the actual velocities from Lloyds tests with all the transfer port sizes and two barrel lengths.... and plotted them vs. the velocities I calculated in the table in Post #41 above, using the product of the caliber and transfer port diameter.... with the following results....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Theoretical%20vs%20Actual%20Velocity_zpszaoivzkp.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Theoretical%20vs%20Actual%20Velocity_zpszaoivzkp.jpg.html)

I had Excel add the trendline for the 23.3" barrel, which pretty much gives a linear efficiency of just about 83%, over the 20 data points.... Even when I added the 10 data points for the 8.2" barrel they aren't far off....  :o

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 16, 2016, 12:46:38 AM
That looks very promising Bob. And you certainly can't beat the simplicity of the correction.
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 16, 2016, 12:48:11 AM
What did you think of the data in Post #41?.... I think the relatively simple TP correction works quite well....

BTW, I should mention that if the velocity corrects by 83%, the efficiency factor needed for your spreadsheet is about 69%, as it affects the FPE, not the fps.... 0.83^2 = 0.69....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 16, 2016, 01:19:44 AM
Lloyd,

I'm using inches for barrel length, but converting to feet when calculating FPS and checking FPE. I'm using inches for area and caliber. PSI and FPS are instantaneous and taken at the midpoint of the incremental length used in the integral. It should not matter if it's feet or inches in the empirically derived friction formula. Those conversions are taken care of by the Xfactor.

It would have been something if the switch to metric in the 1980's had succeeded. We would not be mixing and converting centimeters, inches, cc, ci, grams, pounds, slugs, etc.

----------------------------------------------------------

I dropped out everything that did not seem to bring it closer to the test data.

The following empirically derived formula ends up looking almost too simple but it seems to work. It's missing what I originally considered to be a couple of key variables. Since I only have .22 caliber data to work with, the current Xfactor may only work with .22 caliber.

Xfactor = 100000
lbf = (PSI x FPS)/Xfactor

Results:

calculated (test results), % difference

PSI, V23.3, V8.2
1800psi 1255(1254) +0.1%,  988(989)   -0.1%
2500psi 1379(1373) +0.4%,  1106(1086) +1.8%
3300psi 1480(1465) +1.0%,  1205(1176) +2.4%
3750psi 1525(1521) +0.3%,  1251(1219) +2.6%
4500psi 1587(1605) -1.1%,  1316(1291) +1.9%

---------------------------------------------------------------------------------------
Bob,

I think a linear function may also get us close enough. But I wanted to see if we could "figure out where the lost money went". I think that most of the "lost money" is from fluid friction.

PS: if we use a 100cc, 4500psi chamber rather than 14.5cc, my spreadsheet shows us breaking the mythical 1650fps with the 10.2gr, .22 pellet at 23.3". And hitting 1750fps at 36".
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 16, 2016, 01:28:45 AM
It would certainly explain why multiplying the bore by the TP diameter seems to work.... The TP being smaller than the port adds more "fluid friction", if only at one point in the system.... How does your formula work when you apply it to the data with the restricted TPs?....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 16, 2016, 01:33:01 AM
I have not added in any transfer port restrictions or any dead space between the valve and pellet. I want to get the simplified (unrestricted dump) version working correctly first.

PS: if we use a 100cc, 4500psi chamber rather than 14.5cc, my spreadsheet shows us hitting the mythical 1650fps with the 10.2gr, .22 pellet at 23.3". And hitting 1750fps at 36".
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 16, 2016, 01:42:53 AM
Using Lloyd's spreadsheet, with 100 cc, I get 1660 fps with 23.3", and 1802 at 36".... *LOL*.... (10.2 gr., 4500 psi, full size ports, same 70% efficiency as the 1605 fps shot Lloyd already did with 14.5 cc)....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 16, 2016, 02:11:39 AM
I would like to see a test with a 1/4" smoothbore, maybe using DOM tubing. 36" long. And run tests at calculated 1700fps and 1750fps.

We might be able to dispel the 1640fps myth with repeatable data. Or we may encounter some unknown (to us) barrier. Either way, it could verify our mathematical model.
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 16, 2016, 02:23:01 AM
C'mon, where's your spirit of adventure.... a quarterbore Delrin pellet at 7 gr., 100 cc of 4500 psi air in a 36" barrel should break 2000 fps.... *grin*.... I mean the theoretical is over 2400....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 16, 2016, 11:05:31 AM
Bob and Scott,
I stopped posting for maybe 18 hours and so much has been presented that it feels like I have been away for a week, LOL.

We've got guests coming tomorrow so likely I will be giving my support in prep for that, so my participation until Monday in this thread might be kinda slim.

Bob, I have not studied you data yet, but here is what I want to do:
Make a couple of new versions of my spreadsheet.  One will have your correction methodology, and one will have Scott's, and another will have mine.  No competition, just working to see how the compensations track during further testing.  I already have a version of mine that tracks perfectly with the current 100% port area data, but it drifts off with the non-dumpshot examples. (Your monocoque, for example).

As far as getting more data, I am excited about trying that, but had a couple of failures last night.  I think our 3 heads might be tied together on this one, but I was trying to get a shot much faster than the current 1605fps that is my max (.22, 23.3", 10.2 gn, 14.5 cc dump, 4500 psi).  Running some numbers thru the spreadsheet, for me, the easiest way to get more velocity will be to reduce the mass of the projectile. 
The current projectiles weigh 10.2 grains so I tried making one out of Delrin.  Delrin has a 8700 psi tensile, and the way I do the o-ring, it looked like it was barely strong enough to work at 4500 psi.  I made a 7.4 grain Delrin projectile and based on the 10.2 going 1605, the 7.4 should have gone 1721. But unfortunately that was not going to happen.  I guess yield is much lower than the tensile.  I was filling the gun from a Shoebox to get to 4500 and it let go at 3000; the head popped off and because the bore was still plugged at the release cam, it went out at 378fps. Major fail. Darn.

So then I made a new aluminum one and managed to get it down to 8.0 grains. Predicted vel = 1693 fps.  It was getting too late and I turned the gland that the o-ring fits into at .120, instead of .115 like all the previous projectiles had been.  It was off the lathe before I really discovered the mistake so I thought I'd try it anyway (one of those bad decisions you make when too tired.). I FORCED it into the barrel. How much difference can a tight o-ring make, anyway.  Well, instead of 1693, I got 1576. Double darn.  I didn't think the .005 difference in the gland depth would have made that big a difference, but doing the math, that is a 23% difference in the o-ring compression.  Very significant.

I think my best option at this point is to modify a .25 cal barrel (or as Scott suggested, a piece of DOM tube)  to fit my test bed so that I can make a light and strong projectile to push the velocity limit.   I'd like to go to .30 cal, but 25 cal is about as big as I can fit into it.  My .22 cal setup just has too many limitations for serious max vel testing.
Lloyd

(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/20160115_212625_zpskyhl2pos.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/20160115_212625_zpskyhl2pos.jpg.html)

(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/20160115_232816_zpsh0nzjbae.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/20160115_232816_zpsh0nzjbae.jpg.html)

(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/20160115_225103_zpsyvnkrysk.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/20160115_225103_zpsyvnkrysk.jpg.html)

Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 16, 2016, 01:27:42 PM
So you pulled the nose right off that Delrin bullet, parting it at the O-ring groove?.... Maybe PEEK would be strong enough?.... I'm sure you will figure it out, possibly drilling the aluminum one for a hollow nose and tail?.... (just stay away from the O-ring groove) *LOL*.... If you can get the weight down to 7.8 gr. you should be able to break 1700 fps with your current setup....

Lloyd, when you build a spreadsheet with my {square root (bore diam. x transfer port diam.) } used in the calculations, please send me a copy, I'd love to run some of the data I have and see how it tracks.... I have one gun here (my Disco Double) that has a variable barrel port (the bolt retracts and I can control how far quite accurately), so it is easy to get data....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 16, 2016, 03:09:54 PM
I thought I would try to see how my idea of using the "area" of the bore x transfer port diameters would work over the entire range of TP diameters, from 0-100% of bore size.... I used Lloyd's spreadsheet, input .25 cal, 25" barrel, 3000 psi, infinite reservoir volume and no losses except the mass of the air, and used TP diameters every 10%, to calculate the velocity and FPE with 25 gr., 100 gr., and 400 gr. bullets (to get various speed ranges).... Here are the results....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Lloyds%20Spreadsheet%20Bob%20TP_zpsetcskwuy.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Lloyds%20Spreadsheet%20Bob%20TP_zpsetcskwuy.jpg.html)

There was obviously something strange going on.... I expected to see the velocity parabolic and the FPE linear, but all three graphs had a discontinuity at about 450 fps.... That made no sense, so I went looking for a cause.... It turns out that the J4 version of Lloyd's spreadsheet I was using stopped integrating at 891 lines, which with the barrel length and pressure I chose worked out to about 450 fps.... so any velocity below that gave an incorrect result ::) .... There is a definite smooth curve relationship between velocity and TP diameter, but I don't know yet if that is an accurate model of what happens in the real world....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 16, 2016, 03:27:35 PM
I went to sleep thinking about the 1640fps limit.

Where did it come from?

I speculated that it was from the calculated velocity that freely expanding air might achieve. Instead of a cylindrical expansion that is restricted to a barrel, imagine a spherical expansion. I did a little internet research and that's where I now think it came from.

We are concentrating the flow in a cylindrical barrel, so it seems velocities higher than 1640fps should be predictable and doable.

I looked into supersonic wind tunnels. They use a dump tank similar to Lloyd's experiments. Speeds of mach 4 are obtainable without additional heating.

https://en.wikipedia.org/wiki/Ludwieg_tube

https://upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Supersonic-en.svg/2000px-Supersonic-en.svg.png
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 16, 2016, 03:47:57 PM
Bob,
Check that again. 
Each iteration is .00001 sec, so with the arbitrary limitation of 891 iterations, any locktime over approx .0089 sec will be truncated.  The truncation is time related, not velocity or distance related.  That happens with the 400gr .25 cal because it is too slow to get out of the barrel in .0089 sec, but the other combinations you have presented should be correct.  The .0089 maximum lock time covers all plausible caliber/weight combinations. That is what my Rev J4 version is doing, anyway.
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 16, 2016, 04:03:53 PM
Scott, That is very interesting and certainly gives hope to achieving much higher velocities. 

There is something funny in the Wiki article, though:
"As always when a diaphragm ruptures, a shock wave propagates into the low-pressure region (here the dump tank) and an expansion wave propagates into the high-pressure region (here the nozzle and the long tube). "
Quoted from : https://en.wikipedia.org/wiki/Ludwieg_tube

They are calling the dump tank the low pressure region.  Isn't that backwards?  For there to be flow, the air has to move from a high pressure area to a lower pressure area, hence, from the tank to  the nozzles/exit.  It can still be from a low velocity area to a high velocity area, but the pressures have to go from high to low.  Am I missing something?
Lloyd

 
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 16, 2016, 04:55:39 PM
Scott, That is very interesting and certainly gives hope to achieving much higher velocities. 

There is something funny in the Wiki article, though:
"As always when a diaphragm ruptures, a shock wave propagates into the low-pressure region (here the dump tank) and an expansion wave propagates into the high-pressure region (here the nozzle and the long tube). "
Quoted from : https://en.wikipedia.org/wiki/Ludwieg_tube (https://en.wikipedia.org/wiki/Ludwieg_tube)

They are calling the dump tank the low pressure region.  Isn't that backwards?  For there to be flow, the air has to move from a high pressure area to a lower pressure area, hence, from the tank to  the nozzles/exit.  It can still be from a low velocity area to a high velocity area, but the pressures have to go from high to low.  Am I missing something?
Lloyd
 
After further reading, the Ludwieg tube appears to use a vacuum chamber. Different than a typical supersonic wind tunnel which uses a pressurized chamber. The following might be more typical:

(https://upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Supersonic-en.svg/780px-Supersonic-en.svg.png)
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 16, 2016, 05:11:27 PM
Lloyd, using the 100 gr, and reducing the "caliber" number I get the following for the last few lines in the spreadsheet....

100% - .25 cal - 1012.1 fps (constant)
60% - .15 cal - 662.2 fps (constant)
50% - .125 cal - 561.8 fps (constant)
40% - .1 cal - line 880 - 446.3; line 885 - 447.6; line 890 - 448.6; line 891 - 448.8
30% - .075 cal - line 880 - 259.4; line 885 - 260.9; line 890 - 262.3; line 891 - 262.6

As you can see, the velocity is still increasing in the last two examples, so the integration is not complete.... This is version J4.... Even the 25 gr. pellet runs out of lines at the 20% TP size (cal = 0.05).... 448.8 fps and still increasing....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 16, 2016, 05:17:47 PM
OK, so one uses a big vacuum tank and the other a HPA tank, but both use flow thru a converging-diverging nozzle to drop the pressure and increase the air velocity on the down stream side of the nozzle.  They are using what amounts to an open ended system to create high velocity air, but without regard to the pressure drop..... maybe? I don't know.
We have a closed system (until the bullet exits the muzzle) and want maximum pressure behind the bullet until it exits.  But there must be a pressure drop (lower pressure directly behind the bullet) to make the air flow in the barrel.  So, the hypersonic tubes want maximum air velocity in the tube and we want maximum velocity of the projectile.  Are this goals common, or mutually exclusive.  I don't know.
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 16, 2016, 05:19:17 PM
Lloyd, using the 100 gr, and reducing the "caliber" number I get the following for the last few lines in the spreadsheet....

100% - .25 cal - 1012.1 fps (constant)
60% - .15 cal - 662.2 fps (constant)
50% - .125 cal - 561.8 fps (constant)
40% - .1 cal - line 880 - 446.3; line 885 - 447.6; line 890 - 448.6; line 891 - 448.8
30% - .075 cal - line 880 - 259.4; line 885 - 260.9; line 890 - 262.3; line 891 - 262.6

As you can see, the velocity is still increasing in the last two examples, so the integration is not complete.... This is version J4.... Even the 25 gr. pellet runs out of lines at the 20% TP size (cal = 0.05).... 448.8 fps and still increasing....

Bob
Bob, OK, I think I see what you mean.  Let me change the time increment and make a J5 version and send that to you in a few minutes.  This is curious.
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 16, 2016, 05:42:19 PM
I tried Version K1 and got the same results.... The maximum lock time on both is 0.00878 sec.... That is occurring before the bullet reaches the muzzle if the velocity is less than about 450 fps....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 16, 2016, 05:52:48 PM
I tried Version K1 and got the same results.... The maximum lock time on both is 0.00878 sec.... That is occurring before the bullet reaches the muzzle if the velocity is less than about 450 fps....

Bob
Correct, 450-500 fps is about the low limit with a 25" barrel  with the way I have the time increments set.  The J5 version I just sent should handle really slooooooow bullets.   ;)

The barrel toggle in column O should switch from zero to 1 when the pellet leaves the muzzle.
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: Bill G on January 16, 2016, 05:56:26 PM
I left my jump drive in my desk at work so I don't have my newest iteration of spread sheet.  So, without it in front of me, I'll try to convey some findings.  I discovered that when I compared the possible flow through the specified port, at a specified pressure, to the chamber size at the same pressure, I could derive an "efficiency factor" (Better term welcome). It is expressed as a percentage.  What I discovered is that I can alter that percentage based on the pressure, proportionally, and it smooths the velocity differences from pressure to pressure or port area to port area.  It appears linear. Trying to change both port area and pressure just makes me get lost. 

I'll try to get back on once I get the jump drive in hand and have the numbers in front of me.  I may just have to follow along in the near future due to having to travel for work in the near future and I won't be able to keep up with the conversation in a meaningful way. You guys are all over this thing at the ragged edge of my ability.  I gotz sum lernnin to do. 

Bill
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 16, 2016, 06:46:48 PM
Lloyd, that worked just fine.... Here are the new graphs....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Lloyds%20Spreadsheet%20Bob%20TP_zpsypb0moz7.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Lloyds%20Spreadsheet%20Bob%20TP_zpsypb0moz7.jpg.html)

You will notice an overall difference in shape of the velocity curve as well.... because in the first set I used the TP diameter, instead of sq.rt.(bore x TP)....  :-[ .... These curves are smooth right down to the point where the TP is only 10% of the bore (0.025"), not surprising they go in to the dumper after that....  ::) .... Remember, that without the TP correction, the predicted velocity and energy would be a constant, not falling off as the TP gets smaller.... Note that for the light bullet, the velocity curve is more horizontal at the top end, as it should be.... while for the heavy bullet it is straighter.... This is consistent with reality.... Also note that although all the criteria are the same in every case with the exception of the bullet weight, the maximum FPE drops off dramatically for the light bullet going supersonic, just as we find in the real world.... For the 400 gr. bullet, wide open ports, we get 280 FPE, for the 100 gr. it is 230, but for the 25 gr. it is only 140 FPE (half the power for 1/16th the bullet weight).... That is a function of your calculator (there is no TP correction when wide open).... and one of the reasons I like it so much - it really works well....

Bob

Title: Re: Sonic Choke or Sonic Joke
Post by: Airsnipe on January 16, 2016, 06:47:09 PM
I'm not sure if this has been accounted for (or is significant) but I don't know if the pressure on the atmosphere side of the projectile is being considered. There is 14.whatever psi on the low pressure side of the projectile. I was thinking you have this somewhere in one of those formulas? But I would imagine that as the projectile speeds up, the low pressure side of the pellet also increases in pressure. Is that force being considered in these formulas? Or is this just as insignificant as the weight of air in the barrel?   
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 16, 2016, 06:55:05 PM
The weight of the air in front of the bullet is insignificant, and the molecules can get away from the bullet at an average of 1650 fps anyway.... The weight of the HP air DRIVING the bullet, however is VERY significant, not only is it dense (~200-300 x normal), but it must be accelerated out the muzzle.... It MUST be included or the calculations are wayyyyyyyyyyyyy off.... That was mentioned earlier in this discussion....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Airsnipe on January 16, 2016, 07:12:31 PM
OK but what about the atmospheric pressure? There is one atmosphere of pressure countering the HP side. This is a very low value (once again maybe not significant) but the lower the HPA side the more significant it becomes. Say at 1400psi the atmospheric pressure is countering about 1% of the pressure accelerating the pellet.
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 16, 2016, 07:33:52 PM
.............................. You guys are all over this thing at the ragged edge of my ability.  I gotz sum lernnin to do. 

Bill
Bill G, ha, ha, I think we are all on the ragged edge of our abilities.  This is definitely pay as you go!

Bob, Please email me how you think the T-port compensation should be added into the spreadsheet, because I am not 100% positive.  I want to make sure I understand so that I might get it right the first time.  Or at least close  ;)  )

Airsnipe, I think the force of the air on the atmospheric side of the pellet is still pretty insignificant.  At rest, the atmospheric air exerts about .55 pounds of force on the pellet.  Lets say the pellet is fired and by the time it is a half inch shy of the muzzle, 3/4 of the air in front of it has flowed out the muzzle and the remaining 1/4 has become pressurized (stacked up) in front of the pellet, that is about 3.3 pounds of force, but that is only in the zone very close to the muzzle.  That is equivalent to about 90psi.  So maybe not totally insignificant depending on how the air in front of the bullet does move.  This is kind of in the realm of pellet drag values.
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 16, 2016, 07:45:02 PM
OK but what about the atmospheric pressure? There is one atmosphere of pressure countering the HP side. This is a very low value (once again maybe not significant) but the lower the HPA side the more significant it becomes. Say at 1400psi the atmospheric pressure is countering about 1% of the pressure accelerating the pellet.
When we specify tank pressure, it is the pressure over and above air pressure.  1400 PSIG gauge is really 1414.7 PSIA, so the ambient air pressure is accounted for.
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 16, 2016, 08:02:54 PM
The TPort affects the flow from the start so flow restriction during the iteration is really required. But maybe not really needed to get a good enough answer.

For Transfer Port compensation, at the backend of the calculation, what about something like:

If TParea2/TParea1 = .XX

FPS2/FPS1 = .XX^(1/8)
FPE2/FPE1 = .XX^(1/4)

It seems about right.
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 17, 2016, 02:02:55 PM
I got the new version of Lloyd's spreadsheet this morning (J7) and right after breakfast I used some data I had for a Disco with various size transfer ports to test it.... The data was taken a few years ago, in a stock .22 cal Disco with 14.3 gr. pellets, at 3 pressures, 1600, 1200, and 850 psi.... with no adjustments to the gun between shots (ie same hammer spring preload), just the different size TPs.... I did six tests at 1600 psi, but only three at the lower pressures.... I tested larger size transfer ports as well, but since the barrel port and valve ports were stock, they did not increase the velocity to any significant degree, so I deleted them from this data as they were not a true test of the port diameter....

I set up Lloyd's new J7 spreadsheet using the criteria for a Disco.... .22 cal, 14.3 gr, 135 cc reservoir, 0.02CI transfer volume, 24" barrel, 0.140" TP diameter, 1 lb. drag and 2 lb. breakaway, air mass included, and 0.70 efficiency.... I used Isothermal expansion while the valve was open and Adiabatic after it closed.... I then adjusted the dwell until I got the same velocity as with the test results with the stock 0.140" port at each pressure.... and then changed the port size (only) to get the predicted velocities with the smaller ports.... Here are the results....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Transfer%20Port%20Theory_zpsn3hoygrf.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Transfer%20Port%20Theory_zpsn3hoygrf.jpg.html)

I was pretty disappointed, as the method I had Lloyd put into the spreadsheet, which works well for maximum FPE (essentially a dump shot) predicts too low a velocity with the smaller transfer ports.... ie it overcorrects for them.... Just for the record, here are the dwells I used for the three pressures to get the actual Disco velocities with the 0.140" TP, and the resulting predicted FPE/CI....

1600 psi - 0.0018 sec - 1.13 FPE/CI
1200 psi - 0.0025 sec - 1.02 FPE/CI
850 psi - 0.0035 sec - 0.90 FPE/CI

Those efficiency numbers are slightly low, but certainly in the ballpark for a stock Disco at those pressures.... so my guess of using 0.70 for the "fudge factor" in the J7 spreadsheet was pretty close, and not the reason for the divergence of the spreadsheet predicitions from reality.... Sorry, Lloyd, but what seemed to work pretty well for your "wide open" dump shot test gun doesn't work very well for a typical (low pressure) PCP.... Realistically, it predicts velocities on the low side about as much as no compensation would on the high side (which would predict no loss in velocity as the TP changed - ie straight lines at the maximum velocity)....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: sixshootertexan on January 17, 2016, 02:24:20 PM
Scott, That is very interesting and certainly gives hope to achieving much higher velocities. 

There is something funny in the Wiki article, though:
"As always when a diaphragm ruptures, a shock wave propagates into the low-pressure region (here the dump tank) and an expansion wave propagates into the high-pressure region (here the nozzle and the long tube). "
Quoted from : https://en.wikipedia.org/wiki/Ludwieg_tube (https://en.wikipedia.org/wiki/Ludwieg_tube)

They are calling the dump tank the low pressure region.  Isn't that backwards?  For there to be flow, the air has to move from a high pressure area to a lower pressure area, hence, from the tank to  the nozzles/exit.  It can still be from a low velocity area to a high velocity area, but the pressures have to go from high to low.  Am I missing something?
Lloyd

Great reading as usual guys. Here's a video of a supersonic ping pong ball.  Hope it helps. https://www.youtube.com/watch?v=YYNCGZCul1Q (https://www.youtube.com/watch?v=YYNCGZCul1Q)
Title: Re: Sonic Choke or Sonic Joke
Post by: Bill G on January 17, 2016, 04:17:28 PM
After working on another copy of my sheet based on an older version, I reproduced what I left at my desk, at work.  first off, this is based on a dump valve setup.  It appears that there is an applicable set of polynomials that are required.  One of them will pertain to the PSI and the other will pertain to the port area.  My calculus if far too weak to try and derive a combination so brute force math will have to do.  I have a gut feeling that the port calculations will be really close to linear and that the pressure calculations will be much more curved.  I'm currently working on developing the best regression model for the two and then find a way to employ them at the same time.   I gotta find my Ti-83.  Kids were using it and they never put thing back where they find them. >:(  Just based on Lloyd's data, It appears that there is an optimal flow for a 14.5cc plenum at 1750psi.  As the psi increases the velocity increases but not at a velocity that would be expected.  The predicted velocity, with my sheet, is much greater than what Lloyd has achieved with his test rig.  for the sake of simplicity, I will depict the flow efficiency as a percentage.  What I have done is take the 14.5cc at an established psi and calculated the velocity. At 1800 psi, I had to use 97% of the plenum to achieve a velocity that matches the actual velocity.  if I modeled it to use 100% of plenum, the psi used would be 1746. 
For lack of a better way of expressing this it goes as follows.

psi               Flow efficiency     Lolyd's published velocity     my predicted velocity
1746                  100%                       N/A                                      1241.7
1800                    97%                     1254                                      1257
2500                 57.2%                     1373                                      1375
3300                   38%                      1465                                      1466.3
3750                 33.3%                     1521                                      1524
4500                 27.4%                     1605                                      1602
just for hmmmm factor.
17503                     1%                     N/A                                        850

This is based on 100% bore area. 

Once I find my Ti-83, I'll work on the regression for both psi and port area. 

The flow efficiency % is simply a percentage of the plenum.  But if it is a dump valve, then the whole volume is used at what ever psi is applied. This got me to thinking about what Bob says about improving efficiency by closing the valve before the projectile leaves the bore. Perhaps as the psi increases, the flow of air molecules just cant fit in the valve/ bore quickly enough.  But the force from the psi is obviously high enough to improve the velocity, just not linear.  The fudge factor could be what I am dubbing flow efficiency.  My gut tells me that the velocity change from porting will be nearly linear(at least on a dump valve with orifice TP).  The flow efficiency plays well into Bob's lessons of closing the valve before the Elvis is gone.  It also makes since from the stand point of Boyl's law too.  At 4500 psi is requires a much smaller dump plenum to attain the same velocity.  According to what I've presented, 14.5cc at 1746 gets 1241fps and  ~4cc at 4500psi will get 1602fps.     
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 17, 2016, 07:32:43 PM
.......... Sorry, Lloyd, but what seemed to work pretty well for your "wide open" dump shot test gun doesn't work very well for a typical (low pressure) PCP........

Bob


Gee Bob, I hope you don't feet tooooo bad about making me jump thru hoops on all the dead end revisions, ha ha.    ;)
I've been thinking about it too, and one thing that happens early in each time iteration of the bullets progress in the barrel, is the actual amount of air that is used for that iteration.  The actual amount of force that that amount of air applies to the bullet might be adjusted, but still, the air volume consumed must be correct.  If it isn't, then the total amount of air used for the shot will be wrong, and then the actual efficiency of the shot (FPE/std-cuin) won't be right, and the ability to predict follow-on shots will be futile.  I think I will try and draw a flow chart of the spreadsheet to help locate where the "force" losses, and air flow reductions are most likely occurring.

Does anybody know if there is an easy flowchart application in Excel or Word?  I think Visio was pretty good, but I don't have that.  I can write the flow chart  out by hand but an interactive app would  be nice because of the multiple layers of conditional statements in the spreadsheet.

Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: Bill G on January 17, 2016, 10:02:18 PM
Found my Ti-84..  Looks like the best fitting regression model is a cubic regression.  y=ax^3+bx^2+cx+d

R^2 =.9999.  Of course this fit is based on the pressures and velocities published by Lloyd

a= -5.0332^-11
b= 5.8976 E-7
c= -.002349
d= 3.46759

Now, I have no idea how to integrate that into my sheet :-[. 
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 17, 2016, 10:06:02 PM
I understand that the correct amount of air needs to be used in each iteration, or the total air consumption will be in error.... However, if you restrict the transfer port, you WILL use less air, in fact generally the FPE/CI goes up, not down.... When you included ALL the air in the shot with the smaller transfer port, not only was the air consumption the same as if the TP was bore size.... but that massive amount of air reduced the velocity of the shot even more than the J7 version.... and as you can see, it is too slow....

I really thought I was onto something, because the system worked well for your dump shots, and I have used is successfully to predict the MAXIMUM FPE in quite a few PCPs before they were built.... It generally overestimates the power by about 10% compared to what mere mortals can get.... but at least it gives a "lofty goal".... When applied to the data I had for the Disco, the predictions were quite a bit below what I measured....

and, yes, I feel TERRIBLE about all the work I caused you, especially when you were trying to duck company to do it....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 19, 2016, 12:34:14 PM
I took another diversion from all the math stuff, and wanted to try shooting  something faster than my previous best of 16.5fps. Since bigger cal and lighter weight seemed the best approach, I slightly modified the test bed to use a 30 cal air barrel from Mike Sayers (Bob's design, BTW).  It barely fit in, using the 7/16-20 barrel retention  thread in the breech.  Increased the dump tank to 26.1cc. Made a couple of 30 cal o-ring bullets out of aluminum and necked them down to reduce the weight.  One is 17.1 gn, the other 14.7.

30 cal O-ring bullets 17.1 gn and 14.7 gn
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/30cal-17-1and14-7_zpsq6u6mtag.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/30cal-17-1and14-7_zpsq6u6mtag.jpg.html)

I was expecting great things. Based on the 1605fps I got with the 10.2gn 22 cal at 4500, the 17.1 gn 30 cal had the potential to do better than 1700fps.  So, I set the video cam up, got the gun all loaded and ready to shoot, filled to 4500psi, pulled the trip cord to fire, and darn, it was totally jammed.  I guess my effort to reduce the bullet weight weakened it too much and it bent under the pressure and wedged tight between the release cam and the barrel.  I hadn't done the math and now realize the aluminum bullet had 318 pounds of force on it. So anyway, when it totally jammed,  I stopped the recording and had to get a hammer to tap the trip lever hard several times (including replacing a bent screw) to fire the gun.  The bullet went over the chrony at a disappointing 1655fps.  Plus, the bullet ended up going thru the grocery bag soft trap and went into the heavy steel trap where I can't retrieve it to see what really happened.  I might try the 14.7 gn bullet at a lower pressure in hopes that it won't bend and jam. I need to figure out a light weight bullet that is still sturdy, plus, a more robust rotating mechanism for the cam.
Still, I guess 1655fps from a failed attempt isn't too bad.
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 19, 2016, 01:36:30 PM
Pretty funny when the mechanical strength of the bullet becomes a limiting factor instead of the RMS velocity of the air molecules.... *grin*.... but even with a "failed attempt" it looks like you surpassed that number (1650 fps @ 70*F)....

Looks to me like you can eliminate almost all of the O-ring land on the back side of the groove (just enough for loading)?.... no force in that direction, as the O-ring "pulls" the bullet through the barrel.... use that material to replace that where the bullet is so thin on the bottom (which is where I'm guessing it bent)....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 19, 2016, 01:52:50 PM
Bob, I have a small rod of Grade 5 TiAlloy. About 60% heavier than the aluminum, but 3 times the yield strength. Might try a more robust aluminum bullet first and save the Ti as a fall back position.
1700 is in sight.  BTW, my shop is attached to the house and I always warn my wife when a big boomer is coming.  She said the 30 cal was way louder than the .22 stuff.  The residual muzzle pressure was similar, but the volume of air was a lot greater I guess.
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on January 19, 2016, 01:57:58 PM
Yeah, I started doing that with my wife as well.... My garage/shop isn't attached, but as soon as I go supersonic she can easily hear it in the house.... Can't you get an aluminum bullet in .22 cal down under 8 gr?....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on January 19, 2016, 03:42:50 PM
Bob, I have a small rod of Grade 5 TiAlloy. About 60% heavier than the aluminum, but 3 times the yield strength. Might try a more robust aluminum bullet first and save the Ti as a fall back position.
1700 is in sight.  BTW, my shop is attached to the house and I always warn my wife when a big boomer is coming.  She said the 30 cal was way louder than the .22 stuff.  The residual muzzle pressure was similar, but the volume of air was a lot greater I guess.
Lloyd
Lloyd,

You did not give the barrel length, so I put the info in my spreadsheet and went down the FPS column until I reached 1655fps. That
was at 15.3".

The 14.7gr shows 1714fps at the same 15.3" length.

What is the actual length of the .308 caliber barrel?

Edit: I used the wrong PSI initially. At 3300psi, it shows about the same velocities with a 23.8" barrel.
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 19, 2016, 05:33:32 PM
Scott,
Here is my data:
Previous highest vel shot was .22 cal, 10.2 gn, 4500 psi, 14.5cc tank, 23.3" barrel, dump shot, full bore port, 1605fps actual velocity.

Based on that actual data, for the .300 cal, 17.1 gn, 4500 psi, 26.1cc tank, 27.3" barrel, dump shot, full bore port, I estimated an actual of 1735fps.  But after the bullet got all hung up in the release cam, it probably dragged all the way down the barrel and only got 1655fps.

Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on January 19, 2016, 07:17:26 PM
...................... Can't you get an aluminum bullet in .22 cal down under 8 gr?....

Bob
Bob, you are right, I think I can.  This is from my reply #59 in this thread. 
"So then I made a new aluminum one and managed to get it down to 8.0 grains. Predicted vel = 1693 fps.  It was getting too late and I turned the gland that the o-ring fits into at .120, instead of .115 like all the previous projectiles had been.  It was off the lathe before I really discovered the mistake so I thought I'd try it anyway (one of those bad decisions you make when too tired.). I FORCED it into the barrel. How much difference can a tight o-ring make, anyway.  Well, instead of 1693, I got 1576. Double darn.  I didn't think the .005 difference in the gland depth would have made that big a difference, but doing the math, that is a 23% difference in the o-ring compression.  Very significant."

I found the 8gn one in my tin full of dead soldiers and it is in rough shape but I think I can do a better job at it this time.
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: Bill G on February 04, 2016, 12:18:39 AM
Lloyd, not to bother you but I was wondering what your course of data collection is going to be? 

multiple calibers
multiple dump volumes
various barrel lengths
???
It would be interesting to see the data on various plenum volumes as % of bore volume.  Kinda like you did with the port sizes.

Thanks
Bill
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on February 04, 2016, 11:30:43 PM
Lloyd, not to bother you but I was wondering what your course of data collection is going to be? 

multiple calibers
multiple dump volumes
various barrel lengths
???
It would be interesting to see the data on various plenum volumes as % of bore volume.  Kinda like you did with the port sizes.

Thanks
Bill
Hi Bill,
Thanks for putting a bug in my ear.  I seem to work on projects serially, not in parallel.  I've be hitting some that I need to get out the door and this one has set idle.  Plus, I am working on a 13' long oak dining table that my wife asked for about 3 years ago.

The first item when I get back on this project is to try and get some shots above 1700 fps.  Its just something that needs to be done.

For collecting some meaningful test data, the number of variables needs to be limited.  With the dump shot setup that I am using, each shot takes about 10 minutes, not including making the bullets. But for a single caliber and a single bullet weight, I think 2 or 3 barrel lengths should be used; 3 or 4 pressures; and 3 or 4 port sizes.  Instead of orifice plates to simulate T-ports, I think that short tubes should be used to more closely simulate the effect of smaller valves and T-ports.  Plenum volume would be a nice variable, but the number of shots needed is getting unmanageable. The dump valve setup I have is good for max velocity shots, but it isn't practical testing that requires a large number of shots. 
A more "test friendly" setup is needed.
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: jeff76 on February 05, 2016, 09:30:34 AM
in theory.  if there was a way to seal the muzzle and create a vacuum in the barrel, and break that seal at the same time or a few milliseconds after the pellet begins to move, that the pellet would be pushed as well as pulled at the same time?  kind of like when you go to push a door open at the same time someone on the other side is pulling it open and you "dang" near rip it off at the hinges.
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on February 05, 2016, 03:19:50 PM
The additional force created by the vacuum (15 psi) would be tiny, compared to the 4500 psi available pushing the bullet.... increasing the force on the bullet by only 1/3%.... IMO, not worth the bother.... True, you wouldn't have to push the air out of the way in front of the bullet, inside the barrel, but Lloyd already addressed that earlier in the thread with some numbers.... again, not worth the trouble....

In your analogy with the door, you are doubling the force because the pushing and pulling forces are roughly equal, no so in this case, the pushing force is 300x greater....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Bill G on February 06, 2016, 12:57:28 AM
Lloyd,  The tube idea is a good idea toward the traditional valve set-up.  personally I'm trying to move away from the passages toward an orifice or even CD nozzle. As to the data variable of plenum volume,  A max plenum size of what ever you were to choose altered by a series of progressively shorter spacers to take up volume.  But like you said, that's a bunch more shooting with 10min intervals for every shot.  This is a very large undertaking when you really start thinking about it.  With regard to the method you are using, it is about as instantaneous as I could imagine.  I can see where loading can be difficult and time consuming, not to mention how involved making the test projectiles can be.  You sir have chosen to carry a large burden. I thank you for the undertaking and the exchange of data. 

Bill     
Title: Re: Sonic Choke or Sonic Joke
Post by: Michael Loar on February 06, 2016, 01:24:29 AM
I was lost on the first page along with Rocker1 but still manage to pickup the overall theory and reason for the testing and learning all the time form you guys so it does help me improve my projects more than not and always follow with great enthusiasm even if I don't post as I tend to lurk and learn at my own slow pace.

Thanks as always for great thinking material but time for that whiskey and icepack. LOL

Mike 
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on February 06, 2016, 10:17:52 AM
Lloyd,  The tube idea is a good idea toward the traditional valve set-up.  personally I'm trying to move away from the passages toward an orifice or even CD nozzle. As to the data variable of plenum volume,  A max plenum size of what ever you were to choose altered by a series of progressively shorter spacers to take up volume.  But like you said, that's a bunch more shooting with 10min intervals for every shot.  This is a very large undertaking when you really start thinking about it.  With regard to the method you are using, it is about as instantaneous as I could imagine.  I can see where loading can be difficult and time consuming, not to mention how involved making the test projectiles can be.  You sir have chosen to carry a large burden. I thank you for the undertaking and the exchange of data. 

Bill     

We've really got about three topics going in this thread, but that is about par for this group, LOL.

One is the project of trying to shoot something with compressed air as fast as possible.  For that, the instantaneous release cam seems to be a good set-up. 

Then there is the data collection/data base development, for  shot velocity/fpe with all the various variables.

And finally, the ongoing development of an algorithm for predicting the internal ballistics of a PCP.  Several of us are working on that and getting decent results, but are still looking for further refinements.

So all in all, that's a whole 'nother Cardew book, LOL.

Bill G, please help me out with your mention of the CD nozzle in the path between the valve and bullet.  If the goal is to keep maximum force on the bullet all the way down the barrel (I think that is the goal, correct?), how does the CD nozzle come into play? I know that it can increase the velocity of the airstream, but will it increase the force on the bullet in this closed system? I am having trouble wrapping my head around that question.
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on February 06, 2016, 01:15:27 PM
As I understand it, a CD nozzle is used to create a situation where the velocity of the gas reaches Mach 1 at the narrowest part of the restriction.... That allows the gas to continue to accelerate beyond Mach 1 downstream of the restriction.... By definition, the flow is choked, and you must get a pressure reduction of 1.89:1 across the system.... ie the outlet pressure cannot exceed 53% of the inlet pressure.... and in addition, there is a maximum mass flow that occurs once Mach 1 is reached in the nozzle.... The only way you can increase the amount of gas flowing through the system after choking occurs is to increase the upstream pressure.... Reading through this thread may help refresh your memory....  http://www.gatewaytoairguns.org/GTA/index.php?topic=66737.0 (http://www.gatewaytoairguns.org/GTA/index.php?topic=66737.0)

Since the goal is to maintain the greatest force against the bullet, and that requires pressure and air mass.... we should be avoiding restrictions in the system.... However, trying to understand how those restrictions affect the results is a sensible goal, because we use that as part of the tuning process sometimes....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on February 06, 2016, 01:30:21 PM
As I understand it, a CD nozzle is used to create a situation where the velocity of the gas reaches Mach 1 at the narrowest part of the restriction.... That allows the gas to continue to accelerate beyond Mach 1 downstream of the restriction.... By definition, the flow is choked, and you must get a pressure reduction of 1.89:1 across the system.... ie the outlet pressure cannot exceed 53% of the inlet pressure.... and in addition, there is a maximum mass flow that occurs once Mach 1 is reached in the nozzle.... The only way you can increase the amount of gas flowing through the system after choking occurs is to increase the upstream pressure.... Reading through this thread may help refresh your memory....  http://www.gatewaytoairguns.org/GTA/index.php?topic=66737.0 (http://www.gatewaytoairguns.org/GTA/index.php?topic=66737.0)

Since the goal is to maintain the greatest force against the bullet, and that requires pressure and air mass.... we should be avoiding restrictions in the system.... However, trying to understand how those restrictions affect the results is a sensible goal, because we use that as part of the tuning process sometimes....

Bob
I could imagine some benefits to the CD nozzle and maybe limit barrel length to about 50 x bore diameter.

If "sonic choking" is not an issue, than no CD nozzle and no limit on barrel length. But I think it may an issue if trying to reliably exceed 1700fps.

I would like to see a reliable configuration the yeilds >1700fps. Just to show that it is not an absolute limit.

My spreadsheet does not take into account "sonic choking". I'd rather that we not need to worry about that phenomenon, but we might have to once we are velocity constrained.
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on February 06, 2016, 01:50:42 PM
50 x bore diameter is basically a pistol barrel for an airgun.... 12.5" in .25 cal.... or a naval gun eg. 16"/50 cal on a battleship (puts our long barrels I context, no?).... Artillery pieces are usually only 22-23 calibers long !!!

I played with Lloyd's spreadsheet trying to reduce the pressure by 47% to emulate choking, and had zero success.... Yet how can it NOT be happening when we are shooting well above Mach 1, even at high pressures.... The speed of sound in air at 4500 psi and 20*C is ~ 1550 fps, and we are beyond that.... At 3300 psi it is ~ 1400, and we are also beyond that....

Bob

Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on February 06, 2016, 09:53:42 PM
   ( Bob, you know how to yank my chain, don't you, LOL.  ;)   )

IF sonic choke occurs in PCPs, and I say again, IF it occurs, it has to be a progressive phenomenon, that builds up very slowly after the air velocity exceeds Mach1.  So slowly in fact, that I have yet to see that anyone has shown hard evidence that it requires special consideration in our calculations.  It seems that the normal losses from increasing velocity (which we have not been able to wrap our heads around yet, anyway), will be enough to deal with the subtle effects of sonic choke at normal PCP pressures and velocities, even when we are pushing the limits of their performance.

I will again present this chart from earlier in the thread to back up my argument against sonic choking.

These shots are all .22 cal, 10.2 gn 14.5 cc dump shots.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/23and8barrels_zps7utycahs.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/23and8barrels_zps7utycahs.jpg.html)

In particular, look at the last 2 columns regarding the 8" barrel.  In all of these shots, the MV from the 8" barrel is below (or at)  Mach1.  But looking at those identical shots from a 23" barrel several of the shots are well above Mach 1.  But still, all of the shots from the 8" barrel are about 80% (within margin of error for the experiment) of the velocity from the three-times-longer 23" barrel.  My contention is, that if sonic choking WAS occurring,   that the highest velocities from the 23" barrel would be degraded enough that the velocities from the 8" barrel would be a noticeably higher percentage than the 80% measured during the actual experiment.  For example, the 4500 psi shot with 100% port area did 1605fps. That is certainly well above Mach1, but the 80% is still constant.  If sonic choking had started to occur, maybe the 23" velocity would have been 1470fps and the percentage would have been 88%.  But it wasn't. 
For the 4500 psi shot with the 24% port area, you might say that the 83% is an indication of something starting to degrade.  Maybe yes, but I seriously doubt it.  Again, I think that 3% is within the margin of error for the experiment.  If someone wants to present data that actually shows the effects of sonic choking, I would love to see it and be proven wrong.  I am always eager to learn new things, but I appreciate the evidence.
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on February 06, 2016, 10:19:15 PM
As you know, I think I see an inflection in the curve below the 50% area TP, with the 25% port velocity depressed somewhat.... but I know you disagree.... I do agree that any solid evidence of sonic choking is lacking and/or hidden within the margin of error.... Further, I have tried introducing the 47% loss in pressure that must occur in sonic choking into your spreadsheet, and it makes no sense, basically that reduction in pressure would result in much lower velocities, as you say....

However, I am drawn back to the data presented previously by Jim_HBar about what a sonic choke is, and what it does to the pressure across the choke.... I don't think Jim figured that chokes were likely to occur, but at the time, we weren't working with velocities high enough to exceed Mach 1 at the pressures involved.... Now, we are.... Some of your shots are exceeding Mach 1 at 4500 psi, and a few at lower pressures as well.... That being the case, unless the pellet is moving faster than the air in the barrel, must we not have supersonic flow in the barrel, at least right behind the pellet?....

Waitttttttttt a minute.... Look at what I just said (in bold above).... Is that possible?.... Maybe that is the key to the whole "Sonic Joke".... Could it be that he air in the barrel is staying below Mach 1 at the pressure it is at (eg. ~1550 fps @ 4500 psi).... but enough of the molecules of air are moving fast enough (some are way beyond the 1650 RMS velocity), and colliding with the base of the bullet, to maintain the pressure, and hence the force needed to continue the acceleration to the 1605 fps (or beyond) muzzle velocity?....

Now THERE is a way out thought to ponder....  ??? .... Is there a velocity gradient in the air in the barrel, with the air at the breech (or in the valve) essentially stationary, and ONLY the air touching the pellet going the same speed as the pellet (at any given instant)?....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Matt15 on February 06, 2016, 10:23:24 PM
This post is very interest. However I do not understand much of it. Hope you guys can solve the mystery.  ;D
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on February 06, 2016, 10:25:31 PM
Matt, it's a work in progress.... unknown if it will be solved in my lifetime....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Bill G on February 06, 2016, 11:19:31 PM
My rational for the CD is not for achieving sonic speed of the air but to allow a volume to pass as quickly as possible.  The projectile allows a back pressure due to restriction.  In fact other than looking like a CD nozzle it probably isn't.  Essentially I am taking a vessel of compressed are that is 1"_ in diameter and narrowing it down to bore diameter.  So .22cal with 100% porting is obviously the highest flow we can get but the volume flow can be higher the shorter the pipe.  The "nozzle is to allow a restriction without a restriction if you will.  Since there is no pipe, the volume of flow is higher and that will allow me to use a smaller port, which in turn requires less force to pop it open.  My thinking is that the projectile is going to disallow the super sonic flow until it is likely 50% of the way down the bore.  (Barrel length can have a considerable effect on the flow since it is effectively a pipe)  By the time that the projectile has reached this point, the initial volume has expanded enough that the pressure at that point is inadequate to achieve the affect of choking and the projectile will have been able to maintain the highest pressure possible applied throughout the cycle.  The CD nozzle was originally intended for hot exhaust gas and the pressure would be continuous as long as fuel is being burned.  That isn't us.  We have a diminishing pressure which brings me to the theory of no choking is occurring unless we go really small with the nozzle or have a really large plenum.  Ideally, I would see this being applied to a valve that uses a plenum of 30% of bore volume(if viewed from the aspect of dump chamber.  But instead of being a dump chamber, there is a transfer between the chamber and reservoir that has a port that can dramatically exceed bore diameter.  The idea is to allow, as close as possible, zero force drop at the projectile for the first 3rd of the bore while having the volume flow at the highest speed possible.  The result would be 1/3 bore volume expanding from a decided psi with the projectile already moving at a substantial velocity.  If we are lucky, this could result in a very short lived super sonic flow applied, to an already fast projectile, just before the valve begins the close cycle.  This may already be occurring which could explain why we are getting velocities above sonic from a system that this isn't supposed to be possible.  For all I know an orifice is better but either way not having a pipe flow is even better. 

With regard to flow, 1800 psi, 23.3' barrel, 14.5cc plenum and 100% bore porting.  The possible flow under those conditions is .6099ci (9cc).  That would indicate the remainder of the 14.5cc is being unused.  Under the said conditions, my calculator returns a velocity of 1706.9fps.  But when I adjust the "used" volume to match what possible, I get 1553.27fps.  that's pretty close to Lloyds results.. Next, I will look at the other test pressures comparatively to see if this was a coincidence, I hope not.  I did some comparison with the port data and it seems that the flow becomes more efficient but tops out at .30. what I'm seeing based on the presented data is that, although the velocity is increasing with increased pressure, the efficiency of flow is decreasing as the port tightens. This makes me think that if we are using 100% bore porting, the efficiency of flow will increase as the caliber increases.  I did a regression for this and it indicates that 100% flow efficiency is reached once the caliber reaches .30.  This only raises the question of how does the plenum size has an affect on this flow efficiency. It also make me think that there is an optimal volume dump chamber for the caliber and barrel length, which makes since really.

Yea, this is bordering on a hijack. I'm just very interested in the information that you collect as it helps me and just thought that it may be useful to see my line of thought and how it flirts with the data. 

Bill                 
Title: Re: Sonic Choke or Sonic Joke
Post by: Bill G on February 06, 2016, 11:27:15 PM
As you know, I think I see an inflection in the curve below the 50% area TP, with the 25% port velocity depressed somewhat.... but I know you disagree.... I do agree that any solid evidence of sonic choking is lacking and/or hidden within the margin of error.... Further, I have tried introducing the 47% loss in pressure that must occur in sonic choking into your spreadsheet, and it makes no sense, basically that reduction in pressure would result in much lower velocities, as you say....

However, I am drawn back to the data presented previously by Jim_HBar about what a sonic choke is, and what it does to the pressure across the choke.... I don't think Jim figured that chokes were likely to occur, but at the time, we weren't working with velocities high enough to exceed Mach 1 at the pressures involved.... Now, we are.... Some of your shots are exceeding Mach 1 at 4500 psi, and a few at lower pressures as well.... That being the case, unless the pellet is moving faster than the air in the barrel, must we not have supersonic flow in the barrel, at least right behind the pellet?....

Waitttttttttt a minute.... Look at what I just said (in bold above).... Is that possible?.... Maybe that is the key to the whole "Sonic Joke".... Could it be that he air in the barrel is staying below Mach 1 at the pressure it is at (eg. ~1550 fps @ 4500 psi).... but enough of the molecules of air are moving fast enough (some are way beyond the 1650 RMS velocity), and colliding with the base of the bullet, to maintain the pressure, and hence the force needed to continue the acceleration to the 1605 fps (or beyond) muzzle velocity?....

Now THERE is a way out thought to ponder....  ??? .... Is there a velocity gradient in the air in the barrel, with the air at the breech (or in the valve) essentially stationary, and ONLY the air touching the pellet going the same speed as the pellet (at any given instant)?....

Bob

Yes I think that is possible Bob.  that is what I was trying to covey in my previous post.  I think that if there is a sonic choke occurring, it is very short lived and that it is enough of a kinetic punch to get us above sonic.  And beyond that, there could be a fine line of sonic flow at the center.  This is evident in the exhaust gas of jet and rocket engines.  (shock cones). Which is what we may be able to achieve with CD valve.  Using that shock could result in the use of less volume which gets us more efficiency.
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on February 07, 2016, 12:13:15 AM
Bill, if the idea of a velocity gradient is correct, then there can never be sonic choking in the transfer port unless it is TINY.... When the pellet is just starting out, there is no significant air velocity.... As the pellet moves down the barrel, the air behind it is constantly expanding, but is also being replace/augmented by additional air exiting the valve.... If there was truly a significant velocity gradient, the air at the transfer port, which is near the valve, would never reach Mach 1, unless the port was very small....

The idea that we could get more power by restricting the flow is counter-intuitive to me.... Rocket engines are PRODUCING large quantiies of hot gasses under enormous pressures, a far cry from the meager expansion of already compressed air in a PCP.... I'm sorry, but I see no similarities at all....

Quote
The possible flow under those conditions is .6099ci (9cc).
I have no idea how you arrived at that conclusion, so can't comment....


Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: match on February 07, 2016, 01:07:04 AM
not sure if this will help but I found a very interesting paper on this

http://www.aft.com/documents/AFT-CE-Gasflow-Reprint.pdf (http://www.aft.com/documents/AFT-CE-Gasflow-Reprint.pdf)
Title: Re: Sonic Choke or Sonic Joke
Post by: Bill G on February 07, 2016, 05:40:12 AM
Bob,I suppose I'm not articulating it as I intended.  The point is that even though the port is restricted it has nearly no length and that will allow a higher flow rate.  With a typical PCP set up, there is likely an 1" or better of piping from the poppet to the base of projectile. I was interrupted earlier and mis-stated the .6099(9cc) volume.  It was an incomplete statement.  9cc is what can flow through a 1" long porting under those conditions.  I suspect that it the longest porting/ barrel length combination that can achieve what Lloyd is achieving. With a dump configuration like Lloyd is using, I have to show a .334ci(5.47cc) volume to get 1254fps. The barrel, at 23.3" looks to be able to flow up to .6099ci (9cc) with his projectile and a 1" long porting.  Looking at my acceleration profile, it looks like the highest point of acceleration occurs at ~ .279" down the bore.  The rate of acceleration decreases from there.  What I'm wondering is, Is the projectile getting a boost of acceleration due to a shockwave forming for the briefest of moments at some distance down the bore?  Based on the force applied over the distance of the barrel the velocity should be much higher.  If a shockwave is forming and giving acceleration beyond what force is applying, if only for the briefest of moments, then  the projectile would essentially outrun the volume of expanding air, thus resulting in a diminished velocity.  The .6099 volume through a 1" long porting when compared to the .335ci volume that I purpose is fairly close to 50% rule (choked air at 50%pressure drop).  If this is true, then there may be a shockwave formation at ~5.7" down the bore. Perhaps pushing the projectile to sonic speed just to end up decelerating just until the force from pressure catches up and gives a final push resulting in a muzzle velocity of just over sonic in this case.  This could explain why smaller calibers are so much less efficient. Hard to tell when they are using different projectile weights but I think if we were to analyze it based on the projectile SD it would likely scale pretty well.  The smaller the porting / bore the more likely we are to experience this choking if it exists at all.  According the the regression models that I toyed with, the efficiency of flow increases as the caliber increases until .30.  The larger the caliber the less likely we are to have any choking.  Of course this hasn'r even covered the other pressures used. :(.    This could work in our favor with short barrels and smaller volumes.  In theory, we could achieve near sonic velocities if the barrel length and volume were matched to produce the shock wave say 1" from exiting the bore.

This is becoming compulsive at times.   :-[

Bill G
               

     
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on February 07, 2016, 02:25:50 PM
Quote
The barrel, at 23.3" looks to be able to flow up to .6099ci (9cc) with his projectile and a 1" long porting.
Sorry, I still don't understand this.... Over what period of time, is the first question (of many) that comes to mind (and that is assuming the "9cc" is at 1800 psi).... The barrel volume is the same as the valve (14.5 cc), so at the point the pellet leaves the muzzle, of the 14.5 cc of 1800 psi air that was in the valve, half (or more) is still in the valve, and half (or less) is now in the barrel, and the maximum pressure at the base of the pellet will be 900 psi.... It won't matter to the pellet if the valve closes at that instant, or continues to dump all the rest of the air.... so in reality the most air that can be "used" is 7.25 cc (of 1800 psi air), the rest is "wasted".... although without it being in the valve to start with, the pressure drop would be greater, so it still contributes to the FPE of the shot.... However, the fact remains that you could close the valve at that instant, trapping 14.5 cc at 900 psi, and double the efficiency....

I won't even pretend to understand shock waves, and the effect they may or may not have on a pellet preceeding them down the bore.... They definitely cannot exceed the local Mach speed at the pressure of their location, precisely why you see a supersonic jet pass overhead before the shock wave hits you.... My gut tells me that anything to do with restricting the flow, and/or choking it, and/or creating a shock wave, uses up energy that could be used in accelerating the pellet if that didn't occur.... It would take hard evidence to the contrary to convince me otherwise....

My guess is that you are trying to explain something way above my head, and it's simply not soaking in....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on February 08, 2016, 12:16:42 AM
.... but enough of the molecules of air are moving fast enough (some are way beyond the 1650 RMS velocity), and colliding with the base of the bullet, to maintain the pressure, and hence the force needed to continue the acceleration to the 1605 fps (or beyond) muzzle velocity?....

Now THERE is a way out thought to ponder....  ??? .... Is there a velocity gradient in the air in the barrel, with the air at the breech (or in the valve) essentially stationary, and ONLY the air touching the pellet going the same speed as the pellet (at any given instant)?....

Bob
There may also be a radial component to the velocity gradient. The purpose of the CD nozzle would be to accentuate that. The center of the stream could be >>>mach 1, while closer to the barrel inner surface, velocity is much less. More of the "molecules of air" pushing the pellet to a higher velocity, without increasing the average velocity.

(https://upload.wikimedia.org/wikipedia/commons/thumb/8/84/Development_of_fluid_flow_in_the_entrance_region_of_a_pipe.jpg/660px-Development_of_fluid_flow_in_the_entrance_region_of_a_pipe.jpg)

I'm just speculating, not stating any of this as fact.
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on February 08, 2016, 12:27:29 AM
It makes perfect sense that there would be a radial distribution to the velocity of the air down the barrel, due to friction with the barrel itself.... at least in the subsonic region, where flow is incompressible.... That is why pipes have to be oversize.... I have no idea what happens to that profile, however, when you approach Mach 1, and the flow is now compressible.... Does it get more "pointed" in the middle, or the opposite, flattening out until you get a shock wave forming at Mach 1?.... I have no idea....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Bill G on February 15, 2016, 10:33:54 PM
.... but enough of the molecules of air are moving fast enough (some are way beyond the 1650 RMS velocity), and colliding with the base of the bullet, to maintain the pressure, and hence the force needed to continue the acceleration to the 1605 fps (or beyond) muzzle velocity?....

Now THERE is a way out thought to ponder....  ??? .... Is there a velocity gradient in the air in the barrel, with the air at the breech (or in the valve) essentially stationary, and ONLY the air touching the pellet going the same speed as the pellet (at any given instant)?....

Bob
There may also be a radial component to the velocity gradient. The purpose of the CD nozzle would be to accentuate that. The center of the stream could be >>>mach 1, while closer to the barrel inner surface, velocity is much less. More of the "molecules of air" pushing the pellet to a higher velocity, without increasing the average velocity.

(https://upload.wikimedia.org/wikipedia/commons/thumb/8/84/Development_of_fluid_flow_in_the_entrance_region_of_a_pipe.jpg/660px-Development_of_fluid_flow_in_the_entrance_region_of_a_pipe.jpg)

I'm just speculating, not stating any of this as fact.

This is How I imagine it in my mind.  The question to me is does the center region cause an unexpected acceleration?
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on February 15, 2016, 10:59:27 PM
Thinking about the idea of a velocity profile once more.... That diagram is for the free flow of a fluid in a pipe.... without a bullet plugging it.... Once you put a bullet in the airflow, and the molecules of air are bouncing of it (which is what creates the pressure -ie force- to accelerate the bullet).... surely the velocity profile, at best, would be something in between the first two diagrams.... ie no profile, to one with just a slight lag in velocity along the edges.... no?....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on February 16, 2016, 01:25:40 AM
Sorry guys, I totally missed this last series of replies.  A lot of food for thought, obsessive and otherwise.  The diagram that Scott introduced brings up a number of thoughts.  Even the wording at the left hand entrance end is provocative.  Hydrodynamic..... air is compressible and velocity AND pressure gradients are always changing, both radially and axially in the barrel.  And Bob, yes, I tend to agree that the air velocity in most of the barrel might be lower than the velocity of the projectile.  After all, it is the pressure/force on the bullet that accelerates it, not the velocity of the air that is behind it.
But, back to Scott's diagram, keeping in mind that that diagram is for a system with an open exit, I think.  A pellet barrel is a closed system, with a pellet acting like a cork in a pipe.  The first profile at the left: the flat fronted one, looks like what I'd expect from a big fat 500gn .458 lumbering through the barrel at 600fps.  That 500gn bullet really is a cork in the barrel.  Lighter projectiles must certainly behave differently.

But thinking about the velocity and pressure profiles of a compressible fluid within the barrel, it seems like many different things could possibly happen.  Bill G, you may have already said this, but I am struggling with the concepts and might totally miss the point on some of the things that are said.   So, with that slow moving bullet, the pressure on the back end of the bullet might remain almost constant all the way down the barrel.  And the velocity might also.  But with light weight projectiles things change.
The profiles in those diagrams are for velocity, as it increases in the pipe.  But we are trying to push a cork out of the barrel.  Isn't pressure what is important, not velocity? I realize that they are related, but air can stack up behind a projectile and the pressure can increase (or at least not decrease).  And what about the density of the air? That ties the relationship between velocity and pressure/force together, doesn't it?  With that same heavy bullet, you've got low velocity, but high pressure and high density.  With a light,fast pellet, at the end of the barrel you might have high velocity but low pressure (after all, air will only move from a high pressure area to a lower pressure area).  I know Bill G has mentioned this continuum of changes of velocity and pressure in the barrel before.  So maybe we can maintain high pressure against the back of the bullet, with actually having all of the air at the same high velocity.  This is difficult.  I wish I had actually "learned " this stuff, instead of having just "passed" it. 
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on February 17, 2016, 01:18:56 AM
I see our friend Steve in NC is still hyping his "Sonic Horizon Theory".... he put up a link to it tonight....  http://www.network54.com/Forum/79537/message/1188078593 (http://www.network54.com/Forum/79537/message/1188078593)

Here is the chart he uses....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/valveineffect_zpsow04p5s5.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/valveineffect_zpsow04p5s5.jpg.html)

along with this statement....
Quote
Any propellant that leaves the valve after the pellet crosses the Sonic Horizon can make no contribution whatsoever to muzzle energy - and is therefore totally wasted.
So according to that, with Lloyd's shot at 1600 fps, any air that exits the valve after the pellet has moved 5% of the way down the barrel (about 1") cannot affect the muzzle velocity.... Does anybody have any idea how we can work that into our spreadsheets?.... No, seriously?....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Michael Loar on February 17, 2016, 02:16:17 AM
Bob
I am by no means at or near any level of knowledge that you and Lloyd are at in the theory of HPA and its effects in a barrel or gun, But Steve's post on the 54 and graph of the full dump system just makes no sense to me in that the valve is charged and fires, then the poppet closes and stops the pressure discharge into the barrel.

Then he shows the high pressure air following the pellet down the barrel with a invisible wall behind it at the point the poppet closed shutting off discharge of HPA behind the pellet so would the pressurized expanding air not only follow behind the pellet pushing it down the barrel, but also start to expand rearwards back towards the valve poppet seat so that in effect the energy pushing on the pellet would be diminished more so than if the full charge of air in the valve had been released to fully expand behind the pellet and leave the valve empty ready for the next charging cycle.

I just cannot see where that invisible wall that traps the pressure expanding behind the pellet comes from much less how it can even be considered to exist at all.

But I am only a retired auto/cycle technician that can fix anything that rolls down a road and no college graduate but what he says and shows makes no sense to me at all.

Mike   
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on February 17, 2016, 02:03:17 PM
Bingo!.... In the case of Lloyd's 1600 fps shot in a (let's call it a 24") barrel, according to Steve you could close the valve when the bullet has travelled 5% (ie 1.2 inch) and nothing after that matters.... As I see it, that 1.2" long volume of 4500 psi air now has to expand to 20 times that, with the pressure dropping to just (4500/20) = 225 psi by the time the bullet reaches the muzzle.... The bullet, therefore, sees a continually decreasing force as it travels down the barrel.... If we use .22 cal, at 4500 psi the force starts at 170 lbs.... The way I see it, the force decreases like this, if you close the valve at the 5% point of bullet travel down the barrel....

Bullet travel and force:
1.2" = 170 lbs.
2.4" = 85 lbs.
6" = 34 lbs.
12" = 17 lbs.
24" = 8.5 lbs.

If we leave the valve open, air continues to flow from the reservoir (let's assume for a moment that is infinite volume), and keeps the pressure at 4500 psi, and the force at (nearly) 170 lbs., for the entire 24" of travel.... Tell me again how those could possibly have the same result?.... It may be possible that the air exiting the valve can't reach the bullet after the 5% point.... but each increment of air being released can effect the increment of air released previously, pushing it along the barrel and making it exert the same pressure on the one in front, and ultimately on the bullet.... You can think of it as 20 "chunks" of air, each one pushing the one in front of it if you wish.... but the net result is that the bullet sees a (fairly) constant 170 lbs. of force all the way to the muzzle....

Incidently, if you run the numbers through Lloyd's spreadsheet for a 10.2 gr. bullet in a 23.3" barrel, using 14.5 cc of 4500 psi air, and close the valve at 5% of the barrel length, even with setting the pellet drag and breakaway at zero, not including the air mass, and the efficiency at 100%, you only get about 1300 fps as a result.... Add 1 lb. of pellet drag, 2 lbs. of breakaway, and include the mass of air and that drops to about 1150 fps.... Drop the efficiency down to 70%, which is more realistic, and you get under 1000 fps.... However, increase the dwell to a dump shot, where the valve is still open when the pellet leaves the barrel, and the predicted velocity jumps to 1609 fps.... Lloyd got 1605 in his test.... Note that with a 14.5 cc reservoir, the muzzle pressure ends up 2250 psi, and the force drops to 85 lbs. (or less), because the barrel volume is the same size.... A larger reservoir would produce a higher velocity....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Michael Loar on February 17, 2016, 05:21:35 PM
Bob

Thanks for confirming what I felt I knew to be true but just don't have the math background to be able to prove it on paper in theory. I have however in 45 years of repairing air, hydraulic, electrical, mechanical and all other systems used in todays ultra high tech vehicles gained a wealth of real world knowledge and what Steve shows and states just does not make sense much less even plausible.

Yours and Lloyds explanations and numbers to me are spot on as to what and how thing happen and occur in a HPA gun when fired be it a PCP or Pumper.

Just simple plain common sense if you ask me but then I guess there are some that never opened that door to absorb that common sense when growing up.

Mike
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on February 17, 2016, 09:00:56 PM
Bob and Mike,
Thanks for stirring the pot again, and making the big chunks float to the top.   ;)

I certainly have a hard time believing such things on faith, and require some empirical evidence to back up statements that don't seem intuitive.  My on collected data goes contrary to any sort of hard limits on velocity.  Here is one example from data that was collected from shots taken back in January. Yes, it is a rehash of previous data, but presented in a slightly different manner.  The purpose is to show that continuing to add HPA to the barrel as the pellet/projectile travels through the barrel, despite the rapidly diminishing returns,  will always add some additional velocity to the pellet.  There might be a point where the velocity ceases to increase, but I have yet to see evidence of that happening.

Although no conventional valve was used, here is evidence to demonstrate the continuing increase in velocity.  This consists of data from several shots that has been averaged and normalized to yield a comparison between a low volume shot (representing an early valve closure) and a high volume dump shot (representing a late valve closure).

SET-UP INFORMATION-
Constants between the 2 shots:
.22 cal, 23.3" barrel, 10.2 gn projectile, 2100 psi, dump shot.
Variables between the 2 shots:
Shot 1 = 6.2cc dump reservoir (volume equivalent of 43% of the barrel length)
Shot 2 = 14.5cc dump reservoir (volume equivalent of 100% of the barrel length)

DATA-
Shot 1, 2100 psi,  6.2 cc dump shot, .22 cal 10.2 gn, 1183 fps
  Calculated residual muzzle pressure 629 psi

Shot 2, 2100 psi, 14.5 cc dump shot, .22 cal 10.2 gn, 1300 fps 
  Calculated residual muzzle pressure 1050 psi

DISCUSSION-
As shown in the graph from a few posts before this one, another discussion had suggested that when the MV was in the 1200fps range, that additional HPA introduced into the barrel breech after the projectile was more that 15% of the distance down the barrel (3.5") would not increase the MV.  This "ineffectiveness of additional HPA" was extrapolated over a broad velocity range, and this is only an example of data from the 1200fps range.
These two example shots seem to show that additional HPA will increase the MV, no matter how late in the shot cycle it is introduced.  Both of the example shots are at or above the mentioned 1200fps MV, yet, the second shot, with the additional HPA, is 117fps faster (9.9%) than first shot.    Despite the diminishing returns (the first shot used only 43% as much HPA as the 2nd shot),  the increase in velocity of almost 10% is significant, and certainly beyond the margin of error for the experiment.   
Therefore, I suggest that as of yet, any upper limits on velocity increases to be gained from increased valve dwell have yet to be proven.

BACKUP INFORMATION-
Shot 1 is the average velocity of 4 shots (1203, 1175, 1182, 1171), all taken at 2100 psi, 10.3 gn, 23.3" barrel, .22 cal, 6.2cc dump.
Shot 2 is normalized to 2100 psi and 10.3 gn from these 2 shots:
shot 2a- 1800 psi, 10.2gn, 23.3" barrel, 14.5cc dump, 1254 fps.
shot 2b- 2500 psi, 10.2gn, 23.3" barrel,  14.5cc dump, 1373 fps.

Lloyd-ss
 

Title: Re: Sonic Choke or Sonic Joke
Post by: Michael Loar on February 17, 2016, 09:37:50 PM
Lloyd
It all makes very clear and common sense to me as I said I am not a numbers cruncher but understand how air and fluids work and essentially air is a fluid in the sense that it moves and react to forces applied to it like a fluid does just not as fast or dramatic as a solid fluid such as oil does but it does react none the less.

So for me it only makes sense if you add more air ( fluid ) behind an object in a closed system before it leaves the end of the barrel ( the closed system ) it will continue to accelerate to the end of the barrel albeit maybe only marginal for the added air but none the less it will continue to increase until the added force is removed or the pellet exits the barrel out of the closed system.

The key and I believe the main point of this post is where is that point is where added air is no longer any benefit to increasing the pellets velocity so as to reach the point of maximum velocity with as little air as possible thereby gaining the maximum efficiency possible from our PCP guns with the highest power for the air used per shot.

Mike 
Title: Re: Sonic Choke or Sonic Joke
Post by: Michael Loar on February 17, 2016, 09:39:48 PM

Lloyd
It all makes very clear and common sense to me as I said I am not a numbers cruncher but understand how air and fluids work and essentially air is a fluid in the sense that it moves and reacts to forces applied to it like a fluid does just not as fast or dramatic as a solid fluid such as oil does but it does react none the less.

So for me it only makes sense if you add more air ( fluid ) behind an object in a closed system before it leaves the end of the barrel ( the closed system ) it will continue to accelerate to the end of the barrel albeit maybe only marginally for the added air but none the less it will continue to increase in velocity until the added force is removed or the pellet exits the barrel out of the closed system.

The key and I believe the main point of this post is where is that point where added air is no longer of any benefit to increasing the pellets velocity so as to reach the point of maximum velocity with as little air as possible thereby gaining the maximum efficiency possible from our PCP guns with the highest power for the air used per shot.

Mike
Title: Re: Sonic Choke or Sonic Joke
Post by: Michael Loar on February 17, 2016, 09:44:28 PM
Sorry for the dual post and the first one can be deleted

Mike
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on February 17, 2016, 09:49:02 PM
................................
The key and I believe the main point of this post is where is that point is where added air is no longer any benefit to increasing the pellets velocity so as to reach the point of maximum velocity with as little air as possible thereby gaining the maximum efficiency possible from our PCP guns with the highest power for the air used per shot.

Mike 
Mike,
I agree 100% that that is the real goal of all this effort, but at the same time we are going to have a whole lot of fun wasting air to find out what the upper limits are, too!  ;D
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on February 17, 2016, 10:30:00 PM
There is no question that closing the valve earlier in the cycle is more efficient.... and that smaller benefits occur the later you close the valve.... In many PCPs, closing the valve when the pellet is 50% of the way to the muzzle only loses about 3% of the maximum velocity you can get with that PCP setup with a dump shot.... yet is uses roughly half the air....

BTW, Lloyd, who you callin' a big chunk?....  ???

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on February 17, 2016, 11:01:02 PM
Bob, ha, ha.  Its good to be among friends where we can keep it fun.  Heck, maybe the big chunks are ideas, LOL.   
We certainly have one specific goal of making more efficient airguns, but also, and I think this fits most of us, just learning more about how these PCPs work is enough reward in itself.
   
Also, I want to add about Steve's sonic horizon, even though I don't agree with him on that topic, he is incredibly smart when it comes to airgun theory and practical application, and I will never dismiss offhand what he has to offer.  I have learned quite a bit from the wealth of information that he has shared over the years.
Lloyd-ss
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on February 18, 2016, 12:17:42 AM
^X2....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Michael Loar on February 18, 2016, 02:46:55 AM
................................
The key and I believe the main point of this post is where is that point is where added air is no longer any benefit to increasing the pellets velocity so as to reach the point of maximum velocity with as little air as possible thereby gaining the maximum efficiency possible from our PCP guns with the highest power for the air used per shot.

Mike 
Mike,
I agree 100% that that is the real goal of all this effort, but at the same time we are going to have a whole lot of fun wasting air to find out what the upper limits are, too!  ;D
Lloyd


Lloyd and Bob
I agree that if there is no fun in the efforts put forth in this post then it would soon lose it appeal and following as I know I have contributed little to nothing in the way of knowledge or insight and actually only gained by leaps and bounds from it due to both of you with your dedication and passion for the hobby and for that I am grateful.

I also am not discounting any of the very little I have seen or read about Steves contributions to this hobby but just that his theory about sonic horizon sounded more like a scene out the new start wars movie than any dealings with air guns and still seems to not hold up to common practice or theory IMO.

Big chunks are not bad especially if they are dark chocolate with bunny ears. LOL  Yes the whole expanding our knowledge and hobby together is by far the most rewarding and enjoyable part of the hobby/sport , well next to actually shooting the guns I guess.

Mike 
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on February 18, 2016, 01:37:19 PM
I just ran across this post by Steve in NC, and while it is not precisely on topic, it certainly is interesting....  http://www.network54.com/Forum/79537/message/1211671778 (http://www.network54.com/Forum/79537/message/1211671778)

If you read through, you will see that the absolute maximum energy in a given quantity of air (at 1 bar) is 3.875 FPE/CI.... To achieve that, the temperature of the air at the muzzle would be absolute zero, and with no molecular motion, there would be no pressure, and hence no report....  :o

Just out of curiosity, I ran the numbers for the 5% barrel distance from Steve's graph above for 1600 fps, for Lloyd's 1605 fps test shot.... The bore is .22 cal, and 5% of the barrel length is (just under) 1.2".... so the volume is 0.0456 CI.... The reservoir was 14.5 cc (0.8847 CI), and the pressure was 4500 psi so when the 10.2 gr. bullet has moved that far, the pressure has dropped to 4500 x (0.8847/(0.8847+0.0456)) = 4500 x 0.8847/0.9303 = 4279 psi / 14.5 = 295 bar x 0.0456 = 13.46 CI at 1 bar.... If we multiply that by 3.875 we get a maximum energy of 52.1 FPE.... Since according to the Sonic Horizon Theory, nothing that happens at the valve after the bullet has moved 5% of the barrel length can generate more FPE in the bullet, it would follow that is the LIMIT for the energy possible in Lloyd's test gun....

However, Lloyd achieved 1605 fps with the 10.2 gr. bullet, which is 58.4 FPE.... a theoretical impossiblilty if the Sonic Horizon Theory (and Steve's calculation of the maximum energy in one CI of air) are correct.... Could someone please check my numbers and see if/where I made an error?.... Perhaps the graph is just drawn in error, as I don't have the math/logic Steve used to develop it.... Still, it is an interesting anomaly....

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on February 18, 2016, 02:36:35 PM
The difference between 52.1fpe theoretical (one theory anyway) and a single 58.4fpe test result is not enough prove/disprove anything.

Weighing errors, velocity reading errors, rounding errors, atmospheric conditions, etc.

Empirical "proof" from testing would require the ability to consistently exceed the "theoretical" limits.

A repeatable test that would regularly produce over 1700fps would definitely swing me. As it is, I'm not committing either way to the "sonic" limitations.

However, knowing that a mach 2.5 wind tunnel is possible using a dump chamber makes me believe that it should be possible to drive a pellet at higher velocities than 1640fps.

Can a "pellet" comprised of a single lead molecule riding the mach 2.5 peak of the velocity gradient exceed 1700fps? What about a pellet composed of a reasonable number of molecules?
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on February 18, 2016, 03:06:11 PM
You're right, of course.... I just thought it interesting that the theoretical maximum yielded "solid air" out the muzzle at zero pressure and zero report.... so the achieveable FPE would be of course much less than 52.1 FPE.... On the other hand, any transfer of heat from the barrel to the expanding air would rule out 100% Adiabatic expansion, which was assumed in the calculations.... and it would be pretty hard for that not to occur (even in the short time frame of a shot).... which would raise the maximum FPE, wouldn't it?.... Too many conflicting things happening for the 3.875 FPE/CI maximum to really mean anything, IMO....

A while back I used an online calculator for the energy contained in a given volume of compressed air that is expanded to 1 bar to create this graph....

(http://i378.photobucket.com/albums/oo221/rsterne/Important/MaxEfficiencyFPE-CI.jpg) (http://s378.photobucket.com/user/rsterne/media/Important/MaxEfficiencyFPE-CI.jpg.html)

There are two interesting things about this chart, compared to the 3.875 FPE/CI number.... First, the maximum FPE/CI depends on pressure, it isn't constant.... Secondly, that 3.875 number lies in between the two curves.... Here is the calculator I used.... http://www.tribology-abc.com/abc/thermodynamics.htm (http://www.tribology-abc.com/abc/thermodynamics.htm)

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on February 19, 2016, 01:35:11 AM
Here are two more shots in the series of shots that I have been taking with my max vel dump shot gun.
Again, .22 cal, 23.3" barrel, 4500 psi, dump reservoir increased from 14.5cc to 26cc.
Two matched projectiles of 7.5 gn each.  Size 004 o-ring stretched over a .115 dia centerpost.  A little more attention to detail this time.  The fits were good, and the projectiles were just strong enough to hold up for the shots. The barrel was cleaned and lightly lubed with silicone chamber oil.

Here's a pic of the 2 matched projectiles being weighed together.  7.5 grains each:
 (http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/7pt5gn-proj_zpsk9sfoqiy.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/7pt5gn-proj_zpsk9sfoqiy.jpg.html)

Here is the set-up. Same as before, but this time with a heftier lever for the release cam, and a leather lanyard to trip it. The chrony is only a foot and a half away. The HPA is coming in thru the black microbore tube at the middle center.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/1745SetUp1_zpsora9na1y.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/1745SetUp1_zpsora9na1y.jpg.html)

Here is the chrony after the first shot.  1745 FPS
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/Vel1745Shot-1_zpsrbn3ajlk.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/Vel1745Shot-1_zpsrbn3ajlk.jpg.html)

And here is the chrony after the second shot.  1714 FPS
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/Vel1714Shot-2_zpsjs9vdvwu.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/Vel1714Shot-2_zpsjs9vdvwu.jpg.html)

Based on my previous fastest shot of 1605fps with a 10.2 gn projectile and 14.5cc dump reservoir, the calculator showed that the velocity for this set-up, using the same system loss percentages, and with the 7.5 gn and 26cc reservoir, would be about 1736 fps.  The two shots of 1745fps and 1714 are right there!
I think it is important to note that there is nothing extraordinary about these two shots.  They fall right in line with the usual efficiencies of HPA shots.  No magic, just light weight projectiles, plenty of HPA, and an efficient air delivery system.

I think there is a need for someone to come to my place and serve as a witness to a repeat performance of these shots.

Lloyd-ss
Title: Re: Sonic Choke or Sonic Joke
Post by: rsterne on February 19, 2016, 02:10:52 AM
So much for a speed limit.... *grin*.... My only comment is....

WOO HOO !!!

Bob
Title: Re: Sonic Choke or Sonic Joke
Post by: lloyd-ss on February 19, 2016, 02:19:00 AM
Thanks Bob!
Attention to detail is what did it.  My previous attempts were a bit hurried, but this time the shots got the effort they deserved.  And thanks to you guys for prodding me along on this.
Lloyd
Title: Re: Sonic Choke or Sonic Joke
Post by: Scotchmo on February 19, 2016, 03:07:55 AM
Thanks Bob!
Attention to detail is what did it.  My previous attempts were a bit hurried, but this time the shots got the effort they deserved.  And thanks to you guys for prodding me along on this.
Lloyd
Great work Lloyd!!!!

My spreadsheet shows a predicted velocity of 1724fps, ignoring pellet friction.

With one pound of dynamic friction, it predicts 1716fps.

My spreadsheet currently makes no account of "sonic choke" or "sonic horizon".

I can't mathematically disprove a sonic horizon theory as I don't really understand what it's affect might be. Our spreadsheet models use proven engineering principals and no hypothetical theories. Results jive with their predictions so far. Even when exceeding 1640fps by a significant amount.

One more thing to check next time - the temperature of the dump chamber before firing. Just to make sure. Hopefully close to ambient so as not to introduce another variable.

At this point, I'm leaning HEAVILY toward: 1640fps limit = MYTH = sonic joke

I was hoping that our prodding would work ;). Thanks for all the work. Your test should be an episode of Mythbusters.

BTW: The spreadsheet I'm using is from my last iteration and includes an empirically derived fluid friction of the form:
Xfactor = 100000
lbf = (PSI x FPS)/Xfactor
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on February 19, 2016, 10:00:49 AM
Scott,
I think it is important, and reassuring, that at least 3 of us have independently, and using different methodologies, come up spreadsheets/calculators/models, that all predict very, very similar results.  The GTA has provided a great meeting place for us to explore this hobby and freely exchange ideas with each other.  Personally, this is very exciting and I am having a great time!  Of course, I am not doing some of the things that I really need to be doing, but I will get back to them shortly.  Those activities happen during my silent periods, LOL.

I was able to retrieve the two projectiles, one is in good condition, the other is in fair, so I can hopefully get 2 more shots, but probably not until the first of next week.  I have a good temperature probe that I can tape to the dump reservoir as you suggested.   The reservoir is just about exactly one pound, almost entirely aluminum, with a few stainless parts, so it has significant heat capacity.  I have a CF fill tank and a shoe box mainifolded to the gun, and I first fill to about 3700 from the tank and then close that off and finish the fill with the shoebox, using the CF tank gauge to read the dump reservoir pressure..  The shoebox takes about 2 minutes to top it up to a solid 4500, it clicks off, and I fire.  I never have checked the temp of the aluminum before, but do not remember it feeling particularly warm or cold.  I will record some readings with the next shots.  I will also see if I can check the final barrel temp after I am satisfied with validity of the dump reservoir readings.

Regarding your fluid friction Xfactor, I am assuming that you use that to reduce the force in the F=ma calculation of each iteration, correct?

Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Michael Loar on February 19, 2016, 10:26:57 AM
Bob
I read thru the last link you posted to Steve's 54 post on velocities and all the ensuing comments from others but found his comment in his original post somewhat contradictory to his Sonic horizon theory in that it states the expanding air is now trapped between the valve and pellet as shown below between the quotation marks, so what happened to that invisible wall of the sonic horizon in his theory. He seems to not stay true to his beliefs except only when it suits his purposes.

"" In phase 2, the valve is closed. So the fixed charge of air now " trapped between the valve and pellet expands as it continues to accelerate the pellet ", causing both its pressure and temperature to drop. Because the expansion is so rapid that no significant heat can transfer from the barrel to the air, the only energy available to push the pellet is the initial thermal energy of the molecules in the charge. This means that the sum of the energy of the pellet and the molecules is constant, as one speeds up at the expense of the other slowing down. ""

Lloyd
I second Bobs " WOO HOO" as in now we are moving on up and getting into the extremes of just what is actually capable with the proper equipment and can only say I want/feel that you can get it even faster with just a bit more tinkering like say over 2000 fps or close to Mach 2 with a lighter projectile and even more volume of air. Just a thought on my end as I cannot crunch any numbers but just base it on land speed records at Bonneville where it has been stated many times you cannot go any faster and yet they continue to do so quite often.

Keep your head down and nose to the grind stone and anything is possible IMO.

Mike
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Airsnipe on February 19, 2016, 12:05:18 PM
Lloyd, In the two shots you had a 31fps difference. This setup is meant to eliminate variables and make things consistent and predictable. So is this 31 fps seem within expectations? I guess it's only like 1.8% variance.

I'm not criticizing your setup or your efforts in any way. With all things considered, it seems your setup should offer closer shot variance? Am I just picking at stupid details or is this 31fps good for the speed of the projectile and I'm really just seeing nothing out of the ordinary?
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on February 19, 2016, 12:24:48 PM
Lloyd, In the two shots you had a 31fps difference. This setup is meant to eliminate variables and make things consistent and predictable. So is this 31 fps seem within expectations? I guess it's only like 1.8% variance.

I'm not criticizing your setup or your efforts in any way. With all things considered, it seems your setup should offer closer shot variance? Am I just picking at stupid details or is this 31fps good for the speed of the projectile and I'm really just seeing nothing out of the ordinary?

Happy to answer, no offense taken at all.  I think 1.8% is actually very good for this project.  1.8% is generally considered pretty decent on an airgun, correct?   On a 900 fps gun that is only +/- 8fps.

Think of these numbers.  For the air pressure, I am relying on the compressor shut off, but also reading the gage. With markings every 100 psi, reading to +/-30 psi is good, and that is a total of 1.3%.  The gauge itself might have a 0.5% repeatability.  With the weight of the projectile, the scale I have has a resolution of .1 gn.  With a 7.5 gn projectile, there is another 1.3%.  On the machining of the projectile itself, the center core that controls the o-ring compression is .115 in diameter.  If I am off .001, that is almost 1% which will affect the velocity somehow.  So if you add up the percentages that I have mentioned, 1.3 + .5 + 1.3 +.8 =   3.9%.  So yes, I am very happy with a 1.8% variation, especially since it spanned the high and low side of my spreadsheet calculations.

Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on February 19, 2016, 12:53:56 PM
IMO, this disproves the idea that the velocity of a PCP is limited by the RMS velocity of air molecules, which is ~ 1650 fps at 70*F....That is, after all, an average velocity, and some of the molecules in fact are travelling many times that fast.... Ever since I saw a video of a .177 Condor shooting a 1.7 gr. plastic Sabot at 1705 fps, I pretty much discarded the concept of a hard speed limit.... I just double checked the 1605 fps shot that Lloyd had previously at 4500 psi with a 14.5 cc chamber and 10.2 gr. bullet, and using 1 lb. drag and 2 lbs. breakaway, the spreadsheet balances at 70% efficiency, which is quite remarkable.... Changing the bullet weight to 7.5 gr. and the reservoir to 26 cc, and leaving the efficiency at 70%, the velocity prediction is 1745 fps.... To me this indicates that we are not approaching any particular limit, or you would expect the efficiency "fudge factor" to be dropping off rapidly.... Lowering it to 68% predicts 1719 fps.... so the average of the 2 shots is 69%....

My thoughts are that if a bullet can be made with a lower Sectional Density.... or by using a larger reservoir or longer barrel.... the velocity can be pushed even higher.... We are approaching velocities where increasing the chamber size pays very small dividends.... Using the average efficiency of 69%, I get the following....

26 cc = 1732 fps
100 cc = 1752 fps
400 cc = 1758 fps

On the other hand,  lightening the bullet is more productive.... using the current 26 cc reservoir and 69%....

7.5 cc = 1732 fps
7.0 gr. = 1756 fps
6.5 gr. = 1782 fps
6.0 gr. = 1809 fps

The most productive method for increasing velocity, however, is a longer barrel.... using the current 7.5 gr. with a 26 c reservoir at 69%....

23.3" = 1732 fps
30.0" = 1810 fps
36.0" = 1865 fps
42.0" = 1907 fps

It would take a 6 gr. bullet, using a 100 cc reservoir, and a 42" barrel, to break 2000 fps, assuming the efficiency could be held to 69%.... Incidently, if you hold the SD constant, the caliber doesn't affect the results.... The only benefit of going to a larger caliber is if it would be easier to make a bullet with a lower SD.... or if the efficiency increases because of lower air resistance in the barrel (or other reasons)....

BTW, I agree that 1.8% ES is pretty good for such a test, particularly when the results agree with theory.... Once again. Lloyd, congratulations on a job well done !!!

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on February 19, 2016, 01:37:29 PM
Bob,
You are teasing me with the numbers, so why stop now, huh?  :P
It looks like I can get some smooth bore .245 I.D. tubing in long lengths for a whole lot less than a barrel, so I might try that. Hopefully it won't need to much polishing in the I.D.   A 9.3 gn projectile in .245 would have the same S.D. as the 7.5 gn in .22, so I would have to make  a projectile lighter than 9.3 gn.  I think that is possible. 
The plot thickens, he, he, he.  8)
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on February 19, 2016, 02:11:48 PM
Lloyd, for a constant SD, with a cylinder, the length stays constant.... If the cross-groove remains the same diameter, you should be able to shorten the length.... Of course you can always bevel the base, it looks like there is material on the back, on the side opposite the notch, that is just going along for the ride and not required for strength....

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Airsnipe on February 19, 2016, 02:21:43 PM
Lloyd, thanks for the explanation. I knew it was very good for a normal airgun. Thinking of all the variables you eliminated in the setup, I was just shooting expectations to high in my mind. Like you explained, there are still several variables you are contending with.

Great job on the whole project and I can't wait to see more. This topic is fascinating to say the least. I'm glad this community has such great and talented people to discover and share this info.

Lets see Mach 2  ;D I have faith  8)
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Scotchmo on February 19, 2016, 03:56:39 PM
Scott,
...

Regarding your fluid friction Xfactor, I am assuming that you use that to reduce the force in the F=ma calculation of each iteration, correct?

Lloyd

Exactly.

At zero pellet friction:

If I look at the 23.0" position in the spreadsheet, the remaining pressure is 2431psi, and velocity is 1721.0. At that point, the empirically derived fluid friction is:

2436 x 1721/100000 = 41.9 lbf.

For 26cc chamber volume, the fluid friction peaks at about 7"-8" down the barrel and then slowly falls off. Pressure is falling, and velocity is increasing only marginally. A larger dump chamber results in more pressure farther down the barrel, but also more fluid friction and more air mass.

At .22 caliber and 23", not a lot to be gained with a larger dump chamber. I'm assuming that 4500psi is about the limit of your equipment.

We need a longer barrel, and/or lighter pellet to get explore 1800fps, 1900fps, and 2000fps.

My spreadsheet predict 1888 FPS if you increase the barrel length to 48" and change nothing else.

40cc dump, 4500psi, 48", .25 caliber, 9.2gr = 2006 FPS according to my spreadsheet.

My fluid friction formula was derived from your .22 caliber barrel, and barrel diameter is not factored in (yet), but hopefully it's close enough.

Drawn over mandrel tubing might have a consistent enough internal diameter to use as a smoothbore barrel.

In the interest of advancing the knowledge, I'm willing to help fund the 48" "barrel blank". It will be about $74 shipped. Anybody else want to chip in?
https://www.speedymetals.com/pc-3423-8242-58-od-x-0188-wall-dom-steel-tube.aspx (https://www.speedymetals.com/pc-3423-8242-58-od-x-0188-wall-dom-steel-tube.aspx)
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on February 19, 2016, 04:07:32 PM
I'll throw in $25 towards that.... just give me a PayPal address...

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Scotchmo on February 19, 2016, 04:13:48 PM
Lloyd, thanks for the explanation. I knew it was very good for a normal airgun. Thinking of all the variables you eliminated in the setup, I was just shooting expectations to high in my mind. Like you explained, there are still several variables you are contending with.

Great job on the whole project and I can't wait to see more. This topic is fascinating to say the least. I'm glad this community has such great and talented people to discover and share this info.

Lets see Mach 2  ;D I have faith  8)
Mach 2 (2232fps) is a tall order. For 7.5gr, .22, we'll need to increase the dump chamber to 300cc and barrel length to 16 feet.

A lighter pellet would help a lot but may be tough given the restraining/releasing mechanism and limits on material strength. Next step should probably be a 48", .25 smoothbore. And a more modest goal of 2000fps.

Lloyd, I'll throw in $25 as well. PayPal address?
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Scotchmo on February 19, 2016, 04:26:28 PM
Here is an interesting conundrum:

No matter how long of a barrel, or how much pressure, or how light a pellet. I can't reach Mach 3 (3300fps) in the spreadsheet.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on February 19, 2016, 05:52:39 PM
There is no backing down now is there?   I am up for it. But i am in the airport now and won't be home till monday. Not really necessary for anyone to chip in,but if you do, it is lloyd500 @hotmail.com
Thanks for the generous offers. This is one of those projects that just Needs to be done.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Hobbyman2007 on February 19, 2016, 05:58:40 PM
Congrats Lloyd on your achievement. I have been reading this since the beginning and know how much work went into it. cant wait to see what a smooth bore and bigger caliber might bring.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on February 19, 2016, 06:27:47 PM
Done.... have a good trip !!!!

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Bill G on February 20, 2016, 01:45:50 AM
Man!  Nicely done Lloyd.  I'll be off the grid as of Monday.  I have to travel for work and its a pain in the rear to keep up on the smart phone.  Now this is getting over the top interesting and I'll be all torn up in suspense.  My numbers aren't as close as you and Scott with out fudging the efficiency manually.  I'm working on integrating a regression that will adapt the efficiency based on Port, psi and Barrel length.  Still rolling the ideas around in my head as too how it all influences each other.  Based on the models that I've run, the port and psi seem to have the largest influence with regard to flow efficiency.  I'm really at the limit of my mathematical ability so it slow going.  LOL I had some old text books out doing remedial learning the other day.  I might be getting too old for this. :-[   Scott thanks for the lead on the flow friction, I'll see about implementing that.  Looking forward to what the future offers.   

Great job!
Bill
Bill   
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: K.O. on February 23, 2016, 06:51:16 PM
Hi Lloyd I have been thinking about this but have not read thru this thread yet...

but

I have a theory that no this does not disprove sonic choking but it shows how sonic choking can be beneficial by inducing Sonic packing...using the shock wave that is produced by supersonic flow...

post #123 in the below thread about theoretical max velocity (rather than copy and paste)...


http://www.gatewaytoairguns.org/GTA/index.php?topic=94054.msg994804#new (http://www.gatewaytoairguns.org/GTA/index.php?topic=94054.msg994804#new)

?
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: K.O. on February 23, 2016, 08:04:16 PM
ok just read the thread and  Bills explanation of sonic packing is what I was trying to explain... I think...
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Bill G on February 24, 2016, 06:23:20 PM
My lack of terminology leaves me wanting when it comes to articulating my thoughts on the subject.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on February 24, 2016, 06:58:31 PM
OK folks, with our feet back on the ground, we are gearing up for the next round of testing with a
                      8)    Version 2 Really Really Fast Pellet Gun     8)

The previous, kinda clunky test bed, now dubbed Version 1, got us to 1745 fps, so a job well done. It had an offset cam to clamp the projectile on one side until the reservoir was at full pressure, and then the projectile was released.
That was .22 cal, 7.5 gn, 4500 psi air, 26cc dump tank, 23.3" barrel.  End result, 1714 and 1745 fps.

Version 2 uses a projectile that resembles a conventional pellet with a pinched waist, but again, has an o-ring for sealing. The clamping in Ver 2 is balanced and clamps from both sides on the waist of the pellet.  Release should not be so sluggish, LOL, and should be clean and crisp, and as my father used to say, the pellet should "take of like a ruptured rubber duck". Another advantage of Version 2 is that the pellets are a lot easier to make without the milled notch.  Also, they should be less susceptible to damage during launch.

The picture at the end of this post shows how the clamping will work.  The little levers will be external to the block, and the two rotating cam clamps will be made from 5/16 dia rod, similar to the single one in Version 1.  The levers might be switched to the forward position for "pinch them together to clamp", "release them to launch."

Here are the specs, as of this moment.
Barrel, smooth bore DOM steel tubing with a nominal I.D. of  .245". 
Barrel length TBD, but starting at approx 47" for maximum go power.  But that might be too long. There will also be a 36" barrel so that the gains from 36" to 48" can be determined. That barrel will probably be progressively shortened to collect additional internal ballistic data.
Pressure, up to 4500 psi air.
Pellet weight, approximately 6.5 grains, made of 7075 aluminum, with size 005 70 duro Buna-N o-ring.
Dump reservoir volume TBD, but at least 36cc, to equal 100% of the barrel volume.

Predictions
Based on the 1745 fps shot, if the new Version 2 shot were as follows:
.245 cal
6.5 gn
4500 psi
36cc dump shot

With a 24" barrel, I would be somewhat confident in predicting something over 1850 fps, although the spreadsheet shows 1882fps.
With the 47" barrel, the spreadsheet shows 2081 fps with the 36cc reservoir, but I wouldn't bet much money on that.
We'll just have to wait and see.   ;)

I will say one thing, if Version 2 works as expected, I will bring it to the Funshoot in Kentucky this May.  ;D
 
Here is the Version 2 pellet.


(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MaxVel%20Ver2/Ver2-25Pel-sm-a_zpsuvor9bbo.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MaxVel%20Ver2/Ver2-25Pel-sm-a_zpsuvor9bbo.jpg.html)

Here is a sketch of the mechanical set up for Version 2.


(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MaxVel%20Ver2/Ver2-Mech-a_zps9stx8ygc.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MaxVel%20Ver2/Ver2-Mech-a_zps9stx8ygc.jpg.html)
 
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Michael Loar on February 24, 2016, 07:11:19 PM
Lloyd

I have faith you will indeed get to 2000 fps with version 2 and beyond.

Let the suspense begin !!!

Mike
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Scotchmo on February 24, 2016, 08:03:28 PM
Right now, I'm on the deck of a cruise ship off of Catalina Island. Mai tai's, burgers, now I need a nap. I can't run Lloyds next configuration through my spreadsheet simulation. At least not until Saturday. But his planned setup should break 2000fps by a comfortable margin.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on February 24, 2016, 08:57:22 PM
I agree.... 2000 fps will soon be in the mirrors....

and I can't wait !!!

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Michael Loar on February 24, 2016, 08:58:50 PM
Scott
Have a burger and Mai Tai for me and don't get sunburned.

Mike
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on February 24, 2016, 10:04:57 PM
I'll always take a good burger over a mediocre steak.   ;D

------------------------------------

I need some help with o-ring material selection, please.   :P

This is fitting in a smooth bore  (.245 dia) and I plan on using what might be called a "too small" o-ring. I want to stretch it over the over-sized center post of the projectile so that the O.D. of the o-ring is tight and will resist rolling over.  I might have to experiment with fit, but probably about 7 to 9% compression,  which has worked so far in this experiment. Normal compressions are closer to 20%.

Size 005 o-ring .101 I.D. x .241 O.D.  over a .118 center post will give about .0635 gland depth in a .245 bore.  Compression will be approx 8% after accounting for the thinning due to stretching on the over-sized center post.
But the fit is an experimental thing, and I can putz with that.

Now, for the material selection and I am hoping you folks know more than I do about this.  This o-ring needs to do things that o-rings were never intended to do, but these are one-shot usages, so they can get smoked out the barrel.  :o

The O-Ring material needs to be:
Low friction for sliding along the smooth wall.
Heat resistant.  The friction will probably burn or melt it.
Stretchy. So that it can be stretched over the head of the pellet.
Abrasion/wear resistant so that it will hold a seal all the way to the end of the barrel.
Must be available  in small qtys (100 or so) without a $$$$ minimum order. It doesn't do any good if I can't buy it.
What do you think? Help!  :(

Edit--
After some research, am leaning toward Aflas (FEPM) or Viton (FKM, Fluorocarbon).  Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on February 24, 2016, 10:16:00 PM
 :o  :o  :-[  :-[  ???  ???

I got nuthin'....

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Michael Loar on February 24, 2016, 11:50:24 PM
With you there Lloyd and if its going to be steak its got to be a Ribeye or better yet Prime Rib.

Mike
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: match on February 25, 2016, 11:36:20 AM
viton?

but you may need to make teflon rings and press them on....
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Michael Loar on February 25, 2016, 11:57:24 AM
I will second the Viton or polyurethane o rings.

Or buy some delrin round bar from Mcmaster Carr and machine what you need.

Here is a link to 005 urethane o rings on ebay .

http://www.ebay.com/itm/Captain-O-Ring-Polyurethane-Oring-005-90A-Durometer-25-Pack-/171804395797 (http://www.ebay.com/itm/Captain-O-Ring-Polyurethane-Oring-005-90A-Durometer-25-Pack-/171804395797)

Mike
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on February 25, 2016, 11:59:04 AM
viton?

but you may need to make teflon rings and press them on....
Match, thanks for your thoughts on this.
For the 1745fps, I just used the standard 70 duro Buna-N, but looking at them under magnification, they show wear from the rifling, but they are still intact after a single shot. Definitely not good enough for a second shot, though.

Viton is a Fluorocarbon and is good for heat, but fair for wear.  I don't know about friction.  In a 90 duro it might work.  You have some doubts about the Viton? Please let me know if you think they are not worth trying.

The Aflas looks good for heat, wear, and friction, so it seems like a good choice, but McMaster doesn't have them in size 005.

The teflon would be great for heat, friction, and wear, but I have never had good luck getting Teflon to seal when used as a standard o-ring, and I have my doubts about it sealing at 4500psi.   I think the pellet would have to be a 2-piece configuration to get the teflon ring installed, and I wanted to simplify the construction because of the number of shots I will be taking.

So, do you think the 90 duro Viton are not up to the task?
Thanks,
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: I_like_Irons on February 25, 2016, 12:01:25 PM
I have dealt with larger o-rings that have a PTFE sleeve, but nothing that small. 

What about a normal Buna-N o-ring.  Just lubricate the bore first.  I'd use a barrel cleaning mop with a silicone oil, or grease.

ETA:  The advantage going this route is that you lower the friction (which will be something that all o-rings) will have.  Also, the coating on the o-ring will tend to absorb heat. 

The Buna-N o-rings are inexpensive enough that you can change them for each shot easily.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on February 25, 2016, 12:32:18 PM
The Buna-N are certainly cheap enough and I have plenty of them on hand.  For the 1745 shot, I did lube the bore with Crosman silicone chamber oil. Maybe I should just try that first before making it more complicated than it needs to be.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on February 25, 2016, 02:09:25 PM
K.I.S.S.... and cheap!....

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on February 25, 2016, 03:42:57 PM
Dupont Krytox may be a suitable lubricant for you to run a patch down the barrel.... GPL 205, or possibly another one....

http://www2.dupont.com/Lubricants/en_US/assets/downloads/K-17456-3,%20Automotive%20Product%20Guide.pdf (http://www2.dupont.com/Lubricants/en_US/assets/downloads/K-17456-3,%20Automotive%20Product%20Guide.pdf)

Non-flammable, good to 200*C....

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on February 25, 2016, 04:05:24 PM
I just happen to have a bit of the Krytox! I'll give it a try.
Title: A few questions
Post by: rgb1 on February 26, 2016, 09:28:24 AM
Lloyd, for the shots mentioned in reply 123, what was the
calculated residual pressure? How are real gas effects
being taken into account?

Lloyd or Bob, in reply 141, how is efficiency being calculated?

                                                              Ron
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: match on February 26, 2016, 01:05:08 PM

So, do you think the 90 duro Viton are not up to the task?


90 duro viton is exactly what I was thinking - the question mark was because I was not sure if they were available that hard in that size... but found it: https://www.globaloring.com/o-rings/specialty-o-rings/rgd-o-rings/v90rgd005-005-viton-rgd-o-ring.html (https://www.globaloring.com/o-rings/specialty-o-rings/rgd-o-rings/v90rgd005-005-viton-rgd-o-ring.html)

75 duro may be good enough in a smooth-bore

Viton is little more expensive than buna-n - you should try the 90 duro buna-n if available and just use them once.

My only concern with buna-n is combustion of the surface in the barrel - leaving residue and messing up the measurements.... this may not be an issue with a lubed smooth-bore.

Be careful of what you use in the bore - I would tend toward moly or graphite but lithium grease may even be an option.... don't know.

Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on February 26, 2016, 04:30:35 PM
Lloyd, for the shots mentioned in reply 123, what was the
calculated residual pressure? How are real gas effects
being taken into account?

Lloyd or Bob, in reply 141, how is efficiency being calculated?

                                                              Ron
Ron, I am guessing that you mean the shots in reply# 133. 
The residual pressure calculates to 2888 psi for both the 1745and 1714fps shots.

I am not sure what you are asking in the question about the real gas effects, but if you clarify a bit I'll see what answers I can supply.

The efficiency mentioned in reply #141 is the "system efficiency factor" used in the spreadsheet that equates to the rather nebulous system losses for any unique PCP set-up at a particular power and velocity.  That is applied in the force equation in the spreadsheet after the other effects of pellet weight, expanding volume, declining pressure, etc, are all accounted for.  It is the illusive part of the calculation that much of this effort is focused on finding.  The efficiency factor mentioned is NOT the same as the usual air efficiency which is "FPE produced per standard cubic inch of air that is used by the shot".

Lloyd

Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on February 26, 2016, 04:43:40 PM

So, do you think the 90 duro Viton are not up to the task?


90 duro viton is exactly what I was thinking - the question mark was because I was not sure if they were available that hard in that size... but found it: https://www.globaloring.com/o-rings/specialty-o-rings/rgd-o-rings/v90rgd005-005-viton-rgd-o-ring.html (https://www.globaloring.com/o-rings/specialty-o-rings/rgd-o-rings/v90rgd005-005-viton-rgd-o-ring.html)

75 duro may be good enough in a smooth-bore

Viton is little more expensive than buna-n - you should try the 90 duro buna-n if available and just use them once.

My only concern with buna-n is combustion of the surface in the barrel - leaving residue and messing up the measurements.... this may not be an issue with a lubed smooth-bore.

Be careful of what you use in the bore - I would tend toward moly or graphite but lithium grease may even be an option.... don't know.


John,
Thanks for that link to the o-ring site and the other suggestions. 
I have tried the size 005 90 duro Buna-N o-ring and wasn't able to fit it over the head of the pellet without it breaking.  The 90 duro in the small sizes are not very stretchy.  I wonder if the 90 duro Viton in 005 is more stretchy.  I haven't used any Viton o-rings before, except in carburetors, and that was a long time ago.

I remember talking to an application engineer from Seal Science several years ago, who has since retired.  He said that material compatibility is much more important in dynamic o-ring applications than most people think.  I am sure that is true in this application, but given the one-shot nature of the application, getting "close" will hopefully be good enough, but I am sure that the FPS difference between a "close" application, and a "perfect" application would be significant.
Lloyd
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rgb1 on February 26, 2016, 06:45:49 PM
Lloyd , regarding gas expansion what equation of state is being used?
There are at least a half a dozen cubic versions, van der Waals being
the most notable.


                                                                                      Ron
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on February 26, 2016, 06:53:13 PM
Ron, the "efficiency factor" is simply a "fudge factor" present in Lloyds PCP Internal Ballistics spreadsheet that allows it to balance with empirical data.... Once you determine that number (by trial and error) for one set of conditions in a given gun, it tends to work for other conditions, within reason.... For the most part, PCPs run about 60-75% efficiency, and the surprising thing is that Lloyd's test gun isn't that far off.... I see Lloyd explained it already....

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: match on February 26, 2016, 09:56:35 PM
 
I have tried the size 005 90 duro Buna-N o-ring and wasn't able to fit it over the head of the pellet without it breaking.  The 90 duro in the small sizes are not very stretchy.  I wonder if the 90 duro Viton in 005 is more stretchy. 


did you try heat?

drop it in a pot of boiling hot water for a few minutes....
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Scotchmo on February 26, 2016, 10:46:22 PM
I'm home from the cruise. I'm looking forward to reading about the next test:

.245 cal
6.5 gn
4500 psi
36cc dump shot
47"

My spreadsheet shows about 2060fps using the .22 caliber fluid friction formula and 1 lb. pellet friction. My best guess is that fluid friction will also be proportional to caliber. Doing so yields about 2020fps in the spreadsheet. If the .245 caliber is later tested at different barrel lengths and pressures, we can see if it holds true. Either way, if we see a little over 2000fps, we should be able to predict about what's needed for 2200fps, 2500fps, or 3000fps. And it won't be pretty.

As far as efficiency, there are many ways to calculate it. Instead of using a "fudge factor", I'm trying to account for all losses.
Overall efficiency (pellet energy/air energy) is very low.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on February 27, 2016, 10:52:17 AM
Lloyd , regarding gas expansion what equation of state is being used?
There are at least a half a dozen cubic versions, van der Waals being
the most notable.


                                                                                      Ron
Ron,
Nothing very sophisticated.  My spreadsheet model calculates in .00001 second increments, outputting a delta V for the increment, after accounting for pellet break-away and dynamic friction, volume increase, T-port volume, accelerating the mass of air that is behind the pellet, closing point of the valve, etc. 
The new volume for each increment is calculated from the delta d of the barrel length, which is derived from the delta V of the previous increment.  Then the new pressure in the tank is calculated.  After the valve closes, the volume in the calculation changes to just the volume inside the barrel and T-port and the continuing expansion within the barrel.
My original spreadsheet used a simple P2= P1*(V1/V2).   Later, at Bob's suggestion, I incorporated an exponent into the equation to account for isothermal vs adiabatic expansion. The new equation is P2=P1*((V1/V2)^exp) , with the ability of the spreadsheet user to choose the exp, i.e., 1.0 for isothermal, and 1.4 for adiabatic, or anything in between. Different exponents can be chosen for the expansion period when the valve is open, and for the period after the valve has closed. Honestly, the changes attributable to changing the exponent are rather modest.   For the 1745fps shot in question, the calculated velocities are 1745 vs 1732, with all other parameters left the same. (Edit- it seems like the difference ought to greater than that, doesn't it? Lloyd)

Here is a chart of the calculated internal ballistics of the 1745 shot.
The X axis is the length along the barrel.  Y axis on the left is the FPE, shown in red. Y axis on the right PSI in the barrel, shown in blue,
and the velocity of the projectile, shown in green.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/1745fps-chart_zpsvt5yenrr.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/1745fps-chart_zpsvt5yenrr.jpg.html)


And here is a chart of a more typical PCP shot where the valve closes very early in the cycle. The .65 efficiency in the chart title is for the system efficiency of the gun.  The efficiency of the system for the 1745 shot was .70.
(http://i226.photobucket.com/albums/dd79/loyd500/V8-1.jpg) (http://s226.photobucket.com/user/loyd500/media/V8-1.jpg.html)

I hope this helps clarify things a bit.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Michael Loar on February 27, 2016, 02:25:31 PM
I'm home from the cruise. I'm looking forward to reading about the next test:

.245 cal
6.5 gn
4500 psi
36cc dump shot
47"

My spreadsheet shows about 2060fps using the .22 caliber fluid friction formula and 1 lb. pellet friction. My best guess is that fluid friction will also be proportional to caliber. Doing so yields about 2020fps in the spreadsheet. If the .245 caliber is later tested at different barrel lengths and pressures, we can see if it holds true. Either way, if we see a little over 2000fps, we should be able to predict about what's needed for 2200fps, 2500fps, or 3000fps. And it won't be pretty.

As far as efficiency, there are many ways to calculate it. Instead of using a "fudge factor", I'm trying to account for all losses.
Overall efficiency (pellet energy/air energy) is very low.

Scott

How was the burger and Mai Tai you had for us on the cruise.

Mike
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Scotchmo on February 27, 2016, 03:21:45 PM
I'm home from the cruise. I'm looking forward to reading about the next test:

.245 cal
6.5 gn
4500 psi
36cc dump shot
47"

My spreadsheet shows about 2060fps using the .22 caliber fluid friction formula and 1 lb. pellet friction. My best guess is that fluid friction will also be proportional to caliber. Doing so yields about 2020fps in the spreadsheet. If the .245 caliber is later tested at different barrel lengths and pressures, we can see if it holds true. Either way, if we see a little over 2000fps, we should be able to predict about what's needed for 2200fps, 2500fps, or 3000fps. And it won't be pretty.

As far as efficiency, there are many ways to calculate it. Instead of using a "fudge factor", I'm trying to account for all losses.
Overall efficiency (pellet energy/air energy) is very low.

Scott

How was the burger and Mai Tai you had for us on the cruise.

Mike
The burger and drink that I had for you was very good. A week of indulging and I gained 5 lbs. Now I have to go into subsistence mode to lose it.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Tomg on February 27, 2016, 06:30:22 PM
I was thinking about lightweight bullets, instead of o-ring over metal projectile. Why not machine a delrin jacket that fits over a metal core? Cheap, repeatable and easy to make.

 
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on February 27, 2016, 06:32:33 PM
I think releasing a Delrin bullet would be the problem.... Lloyd's test "gun" has full pressure against the bullet prior to release, so the loads are very high.... See post #156 on page 8....

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rgb1 on February 27, 2016, 08:34:55 PM
Lloyd, thanks for the explanation, that's what I was looking for, and more.

                                                                                      Ron
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Michael Loar on February 27, 2016, 08:51:45 PM
Scott
Yea that's the problem with vacations we always over eat but at least you did not get a sunburn Right ?

I have never had any luck in subsistence modes, no will power I guess. LOL

Mike
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on February 27, 2016, 10:44:24 PM
Lloyd, I think the reason for the small difference between Isothermal and Adiabatic expansion for your 4500 psi dump shot is that the expansion is not very great.... Your residual muzzle pressure is 63% of the starting pressure.... so you get very little cooling.... It makes a much bigger difference in a PCP where the valve closes early with a much lower residual muzzle pressure.... I am currently using Isothermal while the valve is open (assuming a large reservoir), and then Adiabatic while the valve is closed....

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on February 28, 2016, 02:07:30 AM
Bob, that makes sense.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: phoebeisis on February 29, 2016, 10:34:01 AM
Is the 1745 fps a smooth bore?
I seem to remember seeing a comment that mentioned rifling marks on the o-ring.
Thanks
Charlie
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on February 29, 2016, 05:50:01 PM
No, the .22 cal barrel was rifled.... the new .25 cal will be a smoothbore....

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: phoebeisis on February 29, 2016, 09:00:16 PM
Bob
Thanks
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on March 02, 2016, 10:08:54 PM
The material for the new Version 2 barrel and "pellets" arrived today.  Thanks guys!

One piece of 5/8" O.D. x .25 I.D. x 48" long DOM A513 steel.  I need to prep the ends and take a close look inside and try pushing a few lead pellets thru to see how consistent the I.D. feels and figure how much work it will need.  Just peeking thru the sawed ends, it doesn't look too bad.

The other piece is the 1/4" 7075 Aluminum rod to make the pellets out of.

And, I had to get this in to show what I do during my free time  ;) .  The airgun parts are setting on a 13 foot long dining table I am in the midst of making.  Still have to make the base and put a Danish oil finish on it.  The outer frame  is 2" white oak cut from our property and the field is heart pine from my mother-in-laws 1910 house.  I found them in the attic and it looks like the plasterers used them for walk boards.  Even with a lot of hand scraping ahead of time, they were death on the planer blades.

(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MaxVel%20Ver2/MV-Ver2Barrel-a_zpsr7dhe8pb.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MaxVel%20Ver2/MV-Ver2Barrel-a_zpsr7dhe8pb.jpg.html)
Here is the "before" of the pine boards.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/DRTable-1a_zpskqkyhrzb.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/DRTable-1a_zpskqkyhrzb.jpg.html)

If you look at the pictures in reply # 133 you'll see that I am also putting that pine and oak to good airgun usage, LOL.

Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on March 02, 2016, 10:18:02 PM
Hey, Lloyd.... slide me the gravy, will ya!.... Nice job on the table....

You have a new goal to beat.... 2043 fps with a .22 cal tinfoil bullet.... http://www.gatewaytoairguns.org/GTA/index.php?topic=104752.20 (http://www.gatewaytoairguns.org/GTA/index.php?topic=104752.20)

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on March 02, 2016, 10:53:01 PM
Hey, Lloyd.... slide me the gravy, will ya!.... Nice job on the table....

You have a new goal to beat.... 2043 fps with a .22 cal tinfoil bullet.... http://www.gatewaytoairguns.org/GTA/index.php?topic=104752.20 (http://www.gatewaytoairguns.org/GTA/index.php?topic=104752.20)

Bob
Sorry Bob, I don't do tin foil.    ;)  Need some FPE to go with the FPS.   :D
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: 39M on March 02, 2016, 10:58:40 PM
I'll always take a good burger over a mediocre steak.   ;D

------------------------------------

I need some help with o-ring material selection, please.   :P

This is fitting in a smooth bore  (.245 dia) and I plan on using what might be called a "too small" o-ring. I want to stretch it over the over-sized center post of the projectile so that the O.D. of the o-ring is tight and will resist rolling over.  I might have to experiment with fit, but probably about 7 to 9% compression,  which has worked so far in this experiment. Normal compressions are closer to 20%.

Size 005 o-ring .101 I.D. x .241 O.D.  over a .118 center post will give about .0635 gland depth in a .245 bore.  Compression will be approx 8% after accounting for the thinning due to stretching on the over-sized center post.
But the fit is an experimental thing, and I can putz with that.

Now, for the material selection and I am hoping you folks know more than I do about this.  This o-ring needs to do things that o-rings were never intended to do, but these are one-shot usages, so they can get smoked out the barrel.  :o

The O-Ring material needs to be:
Low friction for sliding along the smooth wall.
Heat resistant.  The friction will probably burn or melt it.
Stretchy. So that it can be stretched over the head of the pellet.
Abrasion/wear resistant so that it will hold a seal all the way to the end of the barrel.
Must be available  in small qtys (100 or so) without a $$$$ minimum order. It doesn't do any good if I can't buy it.
What do you think? Help!  :(

Edit--
After some research, am leaning toward Aflas (FEPM) or Viton (FKM, Fluorocarbon).  Lloyd
I don't know if it would be too heavy. But if you had a mold that the pellet head would fit in face down, you could put a tiny drop of lead to form a ring.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: 39M on March 02, 2016, 11:20:03 PM
Or I'm not sure if teflon can be melted, but it would seem the harder, slicker materials would be easier to install in a liquid form. Unless you had a tiny roll of teflon tape.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on March 02, 2016, 11:24:47 PM
Or I'm not sure if teflon can be melted, but it would seem the harder, slicker materials would be easier to install in a liquid form. Unless you had a tiny roll of teflon tape.
Thank you for the suggestions.
Whatever I use, it has to able to hold 4500psi in a static state so that full pressure can be built up behind the pellet before it is released.  I will try some conventional o-ring materials first before getting to exotic.  Pat of it also is that will need a lot ( a few hundred) of these and they need to be easy to make.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: 39M on March 02, 2016, 11:28:47 PM
Or another thought.

The pellet really doesn't need the ring around the top to hold the seal in place, only the one behind the seal. So without the forward ring, a teflon seal could be easily pressed on. Plus, it would slightly lower the SD.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: 39M on March 02, 2016, 11:32:43 PM
Or another thought.

The pellet really doesn't need the ring around the top to hold the seal in place, only the one behind the seal. So without the forward ring, a teflon seal could be easily pressed on. Plus, it would slightly lower the SD.
I guess I forgot the pressure from behind would blow the seal off in this case. Disregard.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on March 03, 2016, 09:31:21 PM
I got the barrel material a day or so ago, and today I machined both ends of the DOM tube to form a bit of a crown at each end and then slugged it with a .25 cal pellet.  To make a long story short, the bore is .278   :(  instead of the .249 advertised (supposed to be 5/8" O.D. x .188 wall x .249 I.D.).  I had to flare the skirt of the pellet to get it to drag in the bore so that I'd have something to measure.  It looks like all of the industry standard manufacturing tolerances for DOM tubing were taken advantage of...... and then some.   Actual size is .626 O.D. x .278 I.D. x .174 wall, not the .249 I.D. it was supposed to be.

Oh well, no big deal on the I.D. since the projectiles are custom made, except that now the .250 dia 7075 aluminum rod I bought  is too small.  I need about a .274 projectile O.D. to prevent o-ring extrusion at 4500 psi.  Worst part is that the I.D., although smooth, is bumpy, i.e., chattery.   Pushing the pellet all the way thru requires fairly uniform force (a good thing), but you can feel the pellet go bump, bump, bump,  >:( ...... all the way thru.  A bad artifact of the drawing process, I guess.  I can't tell how high the bumps really are, and I will probably just live with them and see how the testing goes.  I pushed the pellets in thru both ends of the tube, but it felet the same both ways.    I could resort to making a barrel lap out of a piece of brass, but not yet.
Anyway, minor annoyance, but certainly nothing that can't be dealt with.  The plus side is that the slightly larger I.D. has the potential of slightly higher velocities if I can keep the pellet weight down. Lemonade out of lemons.  :P
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on March 03, 2016, 10:01:46 PM
In case anyone is interested.... I just substituted Helium for air in Lloyd's spreadsheet, still using the .25 cal setup with 7.5 gr. bullet.... With no other changes, it goes from 2043 fps to 3538 fps....  :o

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: I_like_Irons on March 03, 2016, 10:15:10 PM
Now instead of helium, how about trying it with hydrogen.  It is cheaper stuff to get.  Just don't mix it with an oxidizer around heat, sparks or flame.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on March 03, 2016, 11:22:05 PM
Bob,
The Version 2 setup is .278 cal, with hopefully a 6.5 gn projectile. The helium gets down right silly  :P , even at pressures well below 4500psi.

David, I think the ~2000 fps projectile is going to make plenty of heat to see what the hydrogen will do.  I once shot a short wooden dowel from a long barreled test bed and the rifling put scorch marks on the dowel. Had a burnt smell, too.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on March 03, 2016, 11:27:14 PM
.278 cal, using a 48 cc reservoir (1 barrel volume) and a 6.5 gr projectile I get 2170 fps at 70% efficiency.... that jumps to 4001 on Helium.... LOVE IT !!!.....

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on March 03, 2016, 11:36:25 PM
Makes me a little giddy, he, he.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Scotchmo on March 04, 2016, 12:31:45 AM
I played with my spreadsheet some and attempted to take barrel dimensions into account for fluid friction. I'm now starting to think that 48" may be longer than optimal. And the optimal velocity for the next .245, 6.5gr test might be in the mid 1800fps range and under 30" barrel.

My fluid friction estimates are far from close but the trend shows that velocity maxes out at some barrel length, even while pressure remains high.

Fluid friction in a pipe causes an apparent pressure loss that increases with flow rate and barrel length. We may need an even lighter pellet to break 2000fps.

We may not see the 2000fps velocity that we originally expected. It will be interesting to see what happens as we cut the barrel length a little at a time. I wont' be too surprised if it velocity increases as we cut the barrel.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on March 04, 2016, 02:13:20 AM
I just love conflicting theories.... soooooooooooo much to learn for everyone.... *grin*....

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: phoebeisis on March 04, 2016, 08:21:48 AM
Slight aside-well big aside ballistics  by the inch- 45 cap various rounds-5 of 10 slow down going 17 to 18"-and many give practically no gain after 11 inches-the numbers spread A LOT- so commercial loads aren't great-but the idea-
  the 45acp roughly .5 gram powder/gas  10-12 gram bullet     
your .22     10 grams air  .5 gram bullet
the firearm-less mass of much faster propellant-not unlike helium and could be a *(&^ of a lot like hydrogen if anyone is brave enough to use hydrogen
Similar to a springer  my 460-100mg air 1 gram pellet- hot fast gas but not  very much

18"   1450   1309   1189   1065   1220   1251   1195   1062   888   937
17"   1419   1316   1201   1080   1195   1200   1229   1038   866   955
16"   1443   1362   1237   1117   1229   1304   1225   1116   919   994
15"   1430   1319   1212   1095   1214   1284   1226   1070   932   972
14"   1413   1301   1268   1098   1213   1267   1191   1072   915   973
13"   1423   1289   1184   1093   1199   1188   1186   1076   917   971
12"   1402   1281   1179   1090   1184   1235   1169   1077   926   953
11"   1396   1279   1212   1074   1200   1260   1185   1116   948   980
10"   1373   1266   1171   1098   1204   1246   1172   1077   924   976
9"   1379   1262   1172   1077   1179   1235   1154   1081   934   967
8"   1367   1236   1150   1069   1148   1174   1136   1080   903   951
7"   1313   1228   1145   1069   1142   1174   1105   1063   906   931
6"   1283   1183   1102   1043   1117   1138   1061   1012   874   897
5"   1238   1149   1067   1015   1102   1131   1033   1002   843   895

Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on March 04, 2016, 09:53:55 AM
Scott, Yes, we might max out before the full 48" of the barrel is used.  If the velocity is trending the same as the .22 did ( 1745fps, 7.5gn, .22, 23.3", 26cc, 4500psi,  70% system eff) then the identical trend in the .278 barrel ( 6.5gn, .278, 47.4", 48cc, 4500psi, 70% system eff) should be about  2166 fps.  I also doubt it will be that fast, because I think the system efficiency will start dropping quickly in relation to the velocity.  My fudge factor, or your fudge factor? They are pretty close, so it might be a coin toss.
Scott, try running your numbers with a .278 bore and see what you get.

Charles, yes, kinda off topic.  Shows me the 45 acp is behaving like a pistol cartridge should.

Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on March 04, 2016, 01:56:36 PM
I agree, you would expect a .45 ACP, with its fast burning powder intended for short barrels, to not gain velocity after a certain length.... You see the same thing with a .22LR, limited gains after 18-20" of barrel length.... and a .22 Short (or CB Cap) even more so.... It's a matter of the pressure profile compared to the total volume of gas produced....

Try the same thing with a .50 cal BMG, and I'm betting you're still gaining with a 36" barrel (and could gain even more with a slower powder).... Think of a PCP as having a VERY slow burning powder (actually worse than that, cooling of the charge as it expands).... As long as the pressure at the base of the bullet exceeds the drag of the bullet in the bore, it should keep accelerating, the way I see it.... The only question is at what point does the fluid friction (including any possible sonic effects) in the barrel reduce the net force on the bullet to zero?....

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Scotchmo on March 04, 2016, 02:22:11 PM
Scott, Yes, we might max out before the full 48" of the barrel is used.  If the velocity is trending the same as the .22 did ( 1745fps, 7.5gn, .22, 23.3", 26cc, 4500psi,  70% system eff) then the identical trend in the .278 barrel ( 6.5gn, .278, 47.4", 48cc, 4500psi, 70% system eff) should be about  2166 fps.  I also doubt it will be that fast, because I think the system efficiency will start dropping quickly in relation to the velocity.  My fudge factor, or your fudge factor? They are pretty close, so it might be a coin toss.
Scott, try running your numbers with a .278 bore and see what you get.

Charles, yes, kinda off topic.  Shows me the 45 acp is behaving like a pistol cartridge should.

Lloyd

I ran it with the .278.

Using the my old (wrong) friction formula, I get 2078 fps at 47.4".

Using a maybe better formula, I get a max velocity of about 1978 fps at about 23" and falling off to 1851fps at 47.4".

I think the trends are correct. But the constants and exponents that I'm using are best guesses at this time from limited data. I'll need more data to refine them.

After some thought, I'm realizing that increasing barrel length will become detrimental at some point. The best way to get velocity up is to lighten the pellet.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Scotchmo on March 04, 2016, 02:25:17 PM
.... As long as the pressure at the base of the bullet exceeds the drag of the bullet in the bore, it should keep accelerating, the way I see it.... The only question is at what point does the fluid friction (including any possible sonic effects) in the barrel reduce the net force on the bullet to zero?....

Bob

The longer the "pipe" the greater the "pressure" loss. So yes. There is probably a point where a longer barrel results in  lower velocity. Even if the 4500psi chamber volume is infinite.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: K.O. on March 04, 2016, 05:54:16 PM
Sorry guys but after a certain point there is no mechanism for the charge to transmit its force to the back of the pellet... so while estimates as a % of total efficiency may get you a good estimate it is wrong... ;)


Take Lloyds graph of the 1745 fps shot in post # 180 and at the bottom add  what the psi is at is at each two inches down the barrel...


then add a line that is the falling speed of sound of the charge it will meet up with the acceleration about 9.5"-10" down the barrel...

this is where you guys have it breaking Newtonian physics and keep accelerating so what is the bridge to quantum effects that allows this to happen..?

for my model the zero point property of a gas molecule(quantum effect) and maybe an electrostatic property of the ordered flow (a molecular beam) takes over and the pellet starts giving back kinetic energy to the charge... the zero point property(and maybe electrostatic of the charge) of the molecules then causes the vacuum that would be felt at the head of the charge to be felt at the back of the charge...this creates supersonic flow (not for the column but at the throat of the chamber)....it is supersonic for the pressure of the chamber... so over scavenging happens until the pressure differential at the throat/in the chamber is great enough to cause a a thermodynamic event...a super sonic shockwave which then may or may not get turned into a supersonic stem in the barrel... either way it compresses the molecular beam in front of it back to the point that the speed of sound(by raising psi) is at least a 1745fps....

I have been studying trying to find a way to predict the timing of these events... also to take a look for a mechanism that allows your models to be an actual representation of what is happening rather than a good educated guess educated by the overall trends in efficiency...

my point is the acceleration of the pellet is a macroscopic effect so to transmit force to the back of the pellet you can not break the speed at which a molecule can travel and at any given pressure that is the speed of sound. unless the pellet and the charge create some sort of quantum tunnel (by clearing a way thru space-time) that allows the lower state charge to beat the speed of sound and have an additive effect to the charge...

quantum inter molecular forces of gasses is what make mine much more plausible... classic kinetics say there is no attractive repulsive force to gasses

but look at  the section on "Effects of Intermolecular Forces" in the link...

http://chemwiki.ucdavis.edu/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A_Chem1_(Lower)/06._Properties_of_Gases/6.6%3A_Real_Gases_and_Critical_Phenomena (http://chemwiki.ucdavis.edu/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A_Chem1_(Lower)/06._Properties_of_Gases/6.6%3A_Real_Gases_and_Critical_Phenomena)
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on March 04, 2016, 06:37:34 PM
Quote
you can not break the speed at which a molecule can travel and at any given pressure that is the speed of sound
Sorry, that is incorrect.... The speed of sound in air at NTP is 1126 fps.... However, the RMS average speed of an air molecule at the same conditions is 1650 fps.... nearly 50% faster....

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c4 (http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c4)

Take a look at the Maxwell Speed Distribution in that link, and you will see that some molecules are going MUCh faster than 1650.... if the graph is to scale about 4000 fps.... Not many, for sure.... but if most of the flow is going in one direction, those few won't have much to bounce off to lose speed until they reach the back of the pellet....

I think good ol' Newton can explain this just fine.... IMHO....

Bob

Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on March 04, 2016, 07:49:49 PM
Let me propose a thought experiment, to do with the average RMS molecular velocity of air.... Take a basketball full of air at 70*F.... The average molecular SPEED is 1650 fps, in random directions, bouncing off each other and the inside of the basketball, causing the pressure to hold it stretched tight.... The average VELOCITY of all the molecules, put together, must be ZERO, however, or the basketball would be moving / rolling / oscillating.... I am using velocity here as a VECTOR, and the vector sum is zero at any given instant....

Now take the ball to the top of the Empire State building and toss it off.... Let's assume it reaches a terminal velocity of 150 fps.... The molecules, relative to the ball, still have an average SPEED of 1650 fps, and an average VELOCITY of zero.... but relative to the ground, they have an average VELOCITY of 150 fps.... That means that the average velocity of the molecules, relative to the ground, is 1800 fps....

Now drop that basketball down a pipe.... in a vacuum.... accelerated by gravity (or the vacuum, or external pressure) to a velocity, relative to the pipe of 2000 fps.... If the velocity of the molecules cannot exceed 1650 fps absolute, relative to the pipe, then once the ball reaches that velocity, there should be a net force slowing the ball, applied by the air molecules inside the ball.... I submit, just using simple logic, that is not the case....

Now line up many basketballs in the pipe.... same thing, right?.... You now have a whole bunch of air molecules, travelling at 2000 fps relative to the pipe....

Now take away the shell of the balls.... Is it reasonable to assume that suddenly there is a limit to the flow of 1650 fps, imposed by the random motion of the molecules?.... I would suggest that is not the case, because the SPEED of the molecules, relative to their center of mass may be 1650 fps.... but the mass itself is moving, so the pressure those molecules can exert in the forward direction is greater than what they exert in the backwards direction.... That force can come from gravity, a vacuum, or pressure.... and in the case of our barrels, it comes from a pressure differential between the reservoir and the air in front of the bullet.... The force accelerates the bullet, AND THE MASS OF THE GAS, while not breaking the 1650 fps "speed limit" of individual molecules, because that speed MUST be measured relative to the center of mass of the expanding gas column....

As I said, I think you can explain all this with Newtonian Physics.... and I submit that the above is very likely why the "old idea" of a speed limit to air in a pipe is 1650 fps has been so easily broken.... In fact, if the air is expanding (as in driving a bullet), I would suggest that the limiting speed of the bullet may be TWICE the 1650 fps random SPEED of the molecules.... because the center of mass of the expanding air can reach 1650 fps, with the average molecule expanding away from that center of mass at 1650 fps.... The ones at the closed end have zero velocity.... and the ones behind the bullet reach 3300 fps.... Now I realize that friction losses would prevent us from ever reaching that.... but isn't the concept valid?.... and this for EXPANDING air....

Taking it further, then, if you are continually adding air (pressure, ie a force acting on the molecules at the breech end), giving them additional VELOCITY toward the muzzle (ie adding a vectored energy).... you should be able to approach the above state even easier.... because you are doing it continuously.... At some point, yes the FLOW velocity will reach the speed of sound, but even then, the molecules against the bullet will be flying away from the center of mass (which is travelling very quickly) at 1650 fps (or nearly).... I may not have described the sequence of events perfectly.... but I think RELATIVE motion of the molecules to the center of mass of the air is the key....

After all, Relativity is only a limit when you approach "C", not Mach 1....

Bob

Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: K.O. on March 04, 2016, 08:32:02 PM
Well my mistake in math in the other thread gave to much freedom of movement and the correct smaller (1.09 diameters) mean free path freedom just strengthens my argument that speeds even out with the conditions in the chamber

ok so in the closed dynamic system... the air chamber at 4500 psi... the collisions happen very often because freedom of movement is so limited... so the mean speed is a tighter closer average...

and the ripples in the pond die out very quickly to the average that is the speed of sound of psi@ temp of the system...

4500 psi at 70f is a much different system  than 70f at 14.3 psi (near ntp) things happen slower when the mean free path is approaching 350 diameters in open air...

simply the closed high pressure system balances itself much, much quicker... and closed systems do want to balance...

so what is the mechanism that's  causing the speeding back up..?

we should probably take this back to the thread with my math mistakes... ;)... and hey I was distracted  two ways by a bunch of twenty year ols and by diving into The rabbit hole of trying to understand some of the subjects brought up by thinking about molecular beams...
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: K.O. on March 04, 2016, 08:40:34 PM
Let me propose a thought experiment, to do with the average RMS molecular velocity of air.... Take a basketball full of air at 70*F.... The average molecular SPEED is 1650 fps, in random directions, bouncing off each other and the inside of the basketball, causing the pressure to hold it stretched tight.... The average VELOCITY of all the molecules, put together, must be ZERO, however, or the basketball would be moving / rolling / oscillating.... I am using velocity here as a VECTOR, and the vector sum is zero at any given instant....

Now take the ball to the top of the Empire State building and toss it off.... Let's assume it reaches a terminal velocity of 150 fps.... The molecules, relative to the ball, still have an average SPEED of 1650 fps, and an average VELOCITY of zero.... but relative to the ground, they have an average VELOCITY of 150 fps.... That means that the average velocity of the molecules, relative to the ground, is 1800 fps....

Now drop that basketball down a pipe.... in a vacuum.... accelerated by gravity (or the vacuum, or external pressure) to a velocity, relative to the pipe of 2000 fps.... If the velocity of the molecules cannot exceed 1650 fps absolute, relative to the pipe, then once the ball reaches that velocity, there should be a net force slowing the ball, applied by the air molecules inside the ball.... I submit, just using simple logic, that is not the case....

Now line up many basketballs in the pipe.... same thing, right?.... You now have a whole bunch of air molecules, travelling at 2000 fps relative to the pipe....

Now take away the shell of the balls.... Is it reasonable to assume that suddenly there is a limit to the flow of 1650 fps, imposed by the random motion of the molecules?.... I would suggest that is not the case, because the SPEED of the molecules, relative to their center of mass may be 1650 fps.... but the mass itself is moving, so the pressure those molecules can exert in the forward direction is greater than what they exert in the backwards direction.... That force can come from gravity, a vacuum, or pressure.... and in the case of our barrels, it comes from a pressure differential between the reservoir and the air in front of the bullet.... The force accelerates the bullet, AND THE MASS OF THE GAS, while not breaking the 1650 fps "speed limit" of individual molecules, because that speed MUST be measured relative to the center of mass of the expanding gas column....

As I said, I think you can explain all this with Newtonian Physics.... and I submit that the above is very likely why the "old idea" of a speed limit to air in a pipe is 1650 fps has been so easily broken.... In fact, if the air is expanding (as in driving a bullet), I would suggest that the limiting speed of the bullet may be TWICE the 1650 fps random SPEED of the molecules.... because the center of mass of the expanding air can reach 1650 fps, with the average molecule expanding away from that center of mass at 1650 fps.... The ones at the closed end have zero velocity.... and the ones behind the bullet reach 3300 fps.... Now I realize that friction losses would prevent us from ever reaching that.... but isn't the concept valid?.... and this for EXPANDING air....

Taking it further, then, if you are continually adding air (pressure, ie a force acting on the molecules at the breech end), giving them additional VELOCITY toward the muzzle (ie adding a vectored energy).... you should be able to approach the above state even easier.... because you are doing it continuously.... At some point, yes the FLOW velocity will reach the speed of sound, but even then, the molecules against the bullet will be flying away from the center of mass (which is travelling very quickly) at 1650 fps (or nearly).... I may not have described the sequence of events perfectly.... but I think RELATIVE motion of the molecules to the center of mass of the air is the key....

After all, Relativity is only a limit when you approach "C", not Mach 1....

Bob

sorry Bob after a couple days of trying to understand what is going on I decided to have a couple  charged ;)  wisk/cokes and relax...

will read  again when more capable... 8) my above response was written before reading your last reply and the cokes...
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: 39M on March 04, 2016, 09:00:27 PM
I'd guess that multiple restrictions would increase pressure and speed. Maybe chop one of those .278 barrels short, and restrict it down after a foot or a few inches to a .177 with an even lighter pellet.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: K.O. on March 04, 2016, 09:32:13 PM
got any good abrasives you could just fire lap and it might help...

"
 Pushing the pellet all the way thru requires fairly uniform force (a good thing), but you can feel the pellet go bump, bump, bump,  >:( ...... all the way thru.  A bad artifact of the drawing process, I guess.  I can't tell how high the bumps really are, and I will probably just live with them and see how the testing goes.  I pushed the pellets in thru both ends of the tube, but it felet the same both ways.    I could resort to making a barrel lap out of a piece of brass, but not yet.
"
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: match on March 04, 2016, 10:50:26 PM
Bob -

Great thought experiment. Well done.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: K.O. on March 04, 2016, 11:42:16 PM
diversion or truth yet to be examined..?

That's what is so cool about Lloyd beating the speed of sound of the original charge... no matter what it require a bridge between the quantum and macroscopic Bob is suggesting a brute force method mine is more subltle... at least that is how it seems with a bit of the irish unbalancing my perceptions.. ;)

both methods require a Quantum- Newtonian bridge I think... Hamiltonian physics bridge..? sorry to many charged sodas........... ;)

but to me this has not been studied directly yet and the use of lighter and heavier projectiles along with a gradual shortening of the barrel will provide a better model either way...

the way particle-molecular beams beams have been studied can give guidance but in the end it has to follow emphirical evidence that proves it one way or the other...

the inspiration of the right now  is deeply thought provoking... ;D ;D ;D ;D ;D ;D ;D ;D ;D ;D ;D ;D ;D ;D ;D ;D ;D ;D

a look at physics from a previously ignored view...for me any ways...
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on March 05, 2016, 12:05:48 AM
got any good abrasives you could just fire lap and it might help...

"
 Pushing the pellet all the way thru requires fairly uniform force (a good thing), but you can feel the pellet go bump, bump, bump,  >:( ...... all the way thru.  A bad artifact of the drawing process, I guess.  I can't tell how high the bumps really are, and I will probably just live with them and see how the testing goes.  I pushed the pellets in thru both ends of the tube, but it felet the same both ways.    I could resort to making a barrel lap out of a piece of brass, but not yet.
"

I have made bullets out of Craytex and fired them with air thru a barrel.  It takes a bunch of shots to make a difference.  It is good for polishing.  I know people who swear by fire lapping.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on March 05, 2016, 12:35:54 AM
Bob, thought provoking.  Similar to cannon fire from a supersonic fighter.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Scotchmo on March 05, 2016, 12:37:09 AM
I prefer to view the subject of the test as a contiguous, viscous fluid. Velocity creates drag near the inner perimeter that pulls back on the flow (drag or fluid friction). It takes more and more force as the barrel length increases, and you shear more and more fluid. The drag is along the entire inner surface of the barrel (pipe). The higher the velocity, higher the pressure, and longer the pipe, the more the drag. There is also a lightweight pellet going along for the ride.

Until that model proves inadequate, I will avoid considering individual molecules, rms velocity, sonic thresholds, etc.

(http://www.intechopen.com/source/html/43434/media/image1.jpeg)

At some barrel length, the total drag will match (psi x pi x R^2). At that point, acceleration is zero and max velocity has been achieved.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on March 05, 2016, 01:03:52 AM
Scott, I understand your idea.... I assume it will predict a maximum velocity for any given caliber and pressure, and from that the optimum barrel length to achieve that?.... It appears your conclusion for the .278 cal was that 2000 fps was too high, and 23" was the optimum barrel length?.... Are you assuming an infinite reservoir (ie constant pressure), or reducing pressure from the 48cc (one barrel volume at 48") reservoir as it expands?.... How would you adjust for the mass of the gas, ie using Helium?.... Do you use the VanDerWaals corrections that reduce the number of molecules/atoms as the pressure increases?.... Air, for example, has about 9% fewer molecules (less density) per unit volume at 4500 psi than it should using Boyle's Law....

The thought experiment was to explain why a gas where the molecular velocity is 1650 fps can push a projectile faster than that.... Lloyd, your mention of cannon-fire from a supersonic jet is a perfect example of the concept, bravo.... When you disprove what sounds to be a sensible theory (the 1650 fps limit), I think coming up with an alternate theory is a good idea.... This was just one attempt at that.... I must admit to being pleased it wasn't shot down (by Lloyd's supersonic cannon) immediately....  ;D

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Scotchmo on March 05, 2016, 01:26:45 AM
Scott, I understand your idea.... I assume it will predict a maximum velocity for any given caliber and pressure, and from that the optimum barrel length to achieve that?.... It appears your conclusion for the .278 cal was that 2000 fps was too high, and 23" was the optimum barrel length?.... Are you assuming an infinite reservoir (ie constant pressure), or reducing pressure from the 48cc (one barrel volume at 48") reservoir as it expands?.... How would you adjust for the mass of the gas, ie using Helium?.... Do you use the VanDerWaals corrections that reduce the number of molecules/atoms as the pressure increases?.... Air, for example, has about 9% fewer molecules (less density) per unit volume at 4500 psi than it should using Boyle's Law....

The thought experiment was to explain why a gas where the molecular velocity is 1650 fps can push a projectile faster than that.... Lloyd, your mention of cannon-fire from a supersonic jet is a perfect example of the concept, bravo.... When you disprove what sounds to be a sensible theory (the 1650 fps limit), I think coming up with an alternate theory is a good idea.... This was just one attempt at that.... I must admit to being pleased it wasn't shot down (by Lloyd's supersonic cannon) immediately....  ;D

Bob
I can't predict any specific fps at this point. Only that there is a limit to the acceleration and that is when (air drag) = (air pressure x area), even with an infinite reservoir.

The best approach to higher velocity would be to accelerate the pellet as fast as possible. Rather than use a very long barrel. So use a very light pellet. I think 48" in .278 may be sufficient to start slowing the pellet down. Larger calibers should be able to utilize longer barrels.

I don't think we can maintain the % efficiency into a longer barrel. We will need more data to plot the falling off efficiency vs barrel length and go from there.

And I could be wrong :)

My fluid friction formula is crude and does not use VanDerWaals correction.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: phoebeisis on March 05, 2016, 12:52:02 PM
Slight aside-spending your $$
but if you want a smoothbore .550  42" barrel  $189+ shipping
Might be hard to smooth current barrel(this is the smallest smooth bore barrel I could find-other than .22lr)
With the bigger bore you might try to put the O-ring into the breech chamber instead of on the pellet-might save some friction-
The 2000 fps  3500 psi foil ball from a not very  long barrel seems to indicate-as Scotchmo suggested -that the weight of the pellet matters more than anything else-including a good seal- when you are using room temp air-which is kinda slow -most of it is slower than your 1745 shot
Big bore means lighter pellet is easier to make grab  drill out  etc-
 you could even insert a tiny magnet-get time/speed  readings down the barrel-
granted lotta' work but I am very free with your time and $$-
I'm that kind of guy!( all this is  just thinking out loud-not terribly serious about it)

TRACK OF THE WOLF
Our 28 gauge barrel is smooth .550" cylinder bore, 1" octagon at the breech, threaded for our 3/4-16 plug, with .550" thread depth. The tapered octagon breech is over 12" long, with the front 4" fading to 16 sides. A double wedding band, at the transition to round, is followed by a single wedding band 3" forward. Muzzle is .815" diameter. In-the-white, the barrel is not marked with our brand or caliber stamp. Any flat may be top, to simplify plug installation. See our #LABOR-BP breech plug installation labor option, which includes do-it-yourself instructions.

Weight is about 5 pounds, before you install plug, lugs, or sights.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on March 05, 2016, 03:52:28 PM
Scott, I would assume the key number in determining the optimum would be the barrel length IN CALIBERS....

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on March 05, 2016, 05:23:35 PM
Extending my thought experiment from yesterday, I have a question for you all to ponder.... At what point is the airflow in the barrel Supersonic?....

When an object such as a plane, or a bullet, passes through a body of air, it is an easy concept to understand.... The OBJECT is supersonic when it is penetrating the air at a velocity higher than Mach 1.... The classic description of the "Sound Barrier" was that some magical signal (a sound wave?) proceeded in front of the object at the speed of sound, telling the air molecules to get out of the way.... Sounds plausible to a twelve year old, but is that what is really happening?.... I still don't know.... At rest, at 70*F, the air molecules are impacting the object at an average of 1650 fps.... As the object accelerates, surely they must be impacting at a higher velocity, in simple terms, the velocity of the object plus 1650 fps.... This causes an increase in drag on the object, and as it approaches Mach 1 the air starts to compress in front of the object as we enter into the region of "Compressible Flow".... Using the common definition, that starts at Mach 0.8 (lets use 900 fps), and the average air molecules at that velocity would be impacting the object at ~ 2550 fps.... As the impact velocity exceeds that, we start seeing Compressibility Effects.... and eventually a Shockwave forms.... At Mach 1, that shockwave is perpendicular to the direction of travel of the object, and then gradually bends back becoming an acute angle, as Mach 1 is exceeded by greater amounts....

Now look at Scott's diagram of the velocity gradient.... It is postuated on the idea that the flow velocity at the edges (ie in contact with the barrel) is less than in the middle.... So let's assume that the flow velocity where the molecules are actually HITTING anything (the barrel) is less than 900 fps, and no compressibility is occurring, because the average molecules aren't hitting anything at over 2550 fps.... like our plane at Mach 0.8.... OK, so we can go faster than that.... and already the average molecular velocity in the center of the pipe (barrel) is greater than 2550 fps.... How about if we could get the flow at the edges to Mach 0.99 (1100 fps).... We are still subsonic, and no shockwave needs to form, right?.... The molecules at the edge of the flow are now averaging 2750 fps, and those in the center are, yep, faster still.... The way I see it, conditions are such that no shockwave must yet form.... I would say the flow is, therefore, still subsonic.... even though the velocity of the leading edge of the flow in the center of the barrel is now travelling above Mach 1.... Nothing to hit, no compressibility, no shockwave, no supersonic flow....

OK, you say, but there is a bullet in front of that, so now the molecules have something to hit.... Yes, but is it moving away from the air at high velocity.... at 900 fps?.... 1200 fps?.... 1745 fps?.... Even at 1745 fps, the molecules are still impacting the back of the bullet at over 1000 fps, and even more if there is a velocity gradient.... Lot's of "pressure" there to still cause acceleration.... Yet the average molecule has not yet collided with anything at greater than 2750 fps, which is the same as an object penetrating a body of air at Mach 0.99....

Now, increase the speed of sound to 1300 fps, like it is in air at 2500 psi (about the value in Lloyd's test gun just before the bullet leaves the muzzle).... Now you can increase the velocity at the edges of the flow (against the barrel) to 2950 fps and still you are into the same average collision velocity (in Mach) that occurs against an object penetrating a body of air at Mach 0.99 (no shockwave yet).... How fast is the velocity in the center of the gradient?.... I'm betting we could be getting close to that 3300 fps number I tossed out yesterday in my thought experiment.... for an expanding body of air....

So, I ask you again?.... At what point is the airflow in the barrel Supersonic, ie it has to generate Shockwaves, and hence enter the realm of Choked Flow?....

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Scotchmo on March 05, 2016, 06:24:10 PM
As soon as the pellet exceeds mach 1, I am certain that at least some of the air is supersonic.

Shock wave? So what. It's hard to imagine a tiny sonic shock wave so strong that it overrides any additional force applied.

Any molecule can travel up to near the speed of light if you are able accelerate is continuously.

The flow velocity at the edges is near zero, even when the center is supersonic.

We can speculate about sonic, super sonic, chokes, thresholds, etc. It can be fun.

But all the affects we see to this point can be explained by less exotic causes.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on March 05, 2016, 07:51:23 PM
I guess the point I was trying to make is that there is a difference between the molecular speed, and the compressibility it creates, which leads to shockwaves.... and "some part of the air being supersonic"....

I do agree that the simple explanations will likely win out....

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: phoebeisis on March 06, 2016, 11:57:16 AM
This rolled foil .22 cylindrical pellet(with effort fits -would fit - in  my Crosman .22 phantom-muzzle end-maybe I will shoot it-check penetration-sound etc)
3.3 grains
It is 11mm long
 if it was a .22 5.5mm ball- it would be  1.5 grains-  in any case   1-2 grains
Not sure how the 2000 fps shooter rolled his foil pellet-but under 2 grains
Not wanting to start a fight-just curious about that 2000 fps-

OP setup-pellet having to be pretty sturdy to be held while being pushed 150 lbs or so-
 ends up  pretty heavy-and it needs a seal -o-ring added friction all the way down the barrel
the 2000 fps PCP foil pellet-probably is just 1.5 grains- no seal o-ring - instant open valve
( pellet self seals  from the blast to some extent)
The bigger bore -.270 will mitigate the "sturdy heavy pellet" to some degree-different release too-claws-should help
maybe there is a way to put the O-Ring JUST in the chamber-not drag it all the way down the barrel-
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on March 16, 2016, 09:29:01 AM
Been a little while since I posted here and  reported any progress.  Springtime always lures me outside with a ton of stuff to do, and I am whipped by the time evening rolls around, so I have to wait for rainy  days to get any airgun time.

But..... I've got the breech block and end plug mostly finished and here are a few pics.  The block is 2" square x 4" long with a 1.312 air chamber I.D.
The plug is 1-3/8 O.D. with 1-3/8-16 thread and a 1" hole in it to add air volume.  I haven't decided on the final volume,  but with the .278 bore 48" long, maybe start at about 50cc?

The pair of .257 dia holes in the front of the block are for 2 pins that will slip into side-notches in the barrel to orient it angularly and lock it firmly into place.  Because the pellet has to be loaded into the breech end of the barrel, the two pins, joined together, will give  quick disconnect feature to the barrel.  The two larger .375 holes are for the cams that will clamp the pellet into place prior to release. 

I haven't done any work on the .278 barrel bore, and plan on seeing how it shoots first before messing with it.  The bore is pretty smooth despite the minor (.0005 maybe ?) diametral  variations along its length.  Hopefully the o-ring seal on the pellet will deal with that without too much fuss.

Lloyd

Here are a few pics:
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MaxVel%20Ver2/MV-breech-4b_zpsbya4ombj.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MaxVel%20Ver2/MV-breech-4b_zpsbya4ombj.jpg.html)

 (http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MaxVel%20Ver2/MV-breech-2b_zpsfeqqhoml.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MaxVel%20Ver2/MV-breech-2b_zpsfeqqhoml.jpg.html)

(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MaxVel%20Ver2/MV-breech-1b_zpsnuhuyxvt.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MaxVel%20Ver2/MV-breech-1b_zpsnuhuyxvt.jpg.html)

(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MaxVel%20Ver2/MV-breech-3b_zpsuvagdvuk.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MaxVel%20Ver2/MV-breech-3b_zpsuvagdvuk.jpg.html)

Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: madeInLV on March 18, 2016, 06:31:04 PM
Iloyd-ss,

compliments on the setup. I see you have a machine shop set up...boy i wish i had that:)

Just my 2 cents on the topic.

What is the purpose of the experiment? If it is to achieve MAX  velocity POSSIBLE on AIR, then the setup (as great as it is) will NOT do that. Your projectile is also a structural element demanding rigidity/strength, thus inevitably WEIGHT. The LIGHTER the projectile the the closer you get to the free stream/escape velocity of the gas flow.

To further  reduce weight and friction you might consider using TEFLON (PTFE) rings for the initial seal. They are a bit harder to work with but work just as fine+they are very light and way more slippery. The rubber O-ring on the other hand will produce significant friction.

FYI when sealing something with a Teflon ring tolerances must be tighter and the initial fill must be somewhat rapid to get that initial seal for the rest of the pressure to build up. A simple square cross-section ring should do the trick. Once it seals, it's just as good as an o-ring (for your application).

Now....if the intent is to reach the max velocity attainable with our pressures than a BURST disc is the best way to go. Material from regular soda cans should be consistent enough. Just make sure you calculate the cross section of the bore for the desired burst pressure.


BUT!!!!!:) Your rig as it is, is very good for RELATIVE comparison of the efficiency figures for different configurations as well as other efficiency related measurements.
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: Michael Loar on March 19, 2016, 02:12:26 AM
Alex
I am not sure if you have read this entire thread but Lloyd is indeed considering all aspects of the variables in this test with projectile weight being a prime consideration to achieve the intended goals of which he has succeed very well to this point.

If you have not read all of this thread I would recommend you do as the goal at this point is to achieve Mach 2 or better with a .257 caliber projectile in a full dump test gun of which I myself have no doubts that he will indeed achieve that velocity and then some before he is done.

Mike
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on March 19, 2016, 05:18:23 PM
Alex,
The purpose of the experiment is to achieve very high velocity with something that bears some resemblance to a PCP gun, but with various self imposed constraints.  First, the data collected and knowledge gained should have some direct application to real-world PCPs, in particular, improving on the knowledge we have regarding  the various dependencies within the PCP system.
The test rig will be powered by compressed air at no higher than 4500 psi.  Firing should be by some sort of mechanical means where the only expendable part on each shot is, at worst case, the projectile. The projectile must have some amount of reasonable mass.  With a .278 bore, 6.5 gns is certainly very light, but not ridiculous.  Super light weight projectiles might go a little faster, but might not add much useful information.  I plan on firing many shots while collecting data, so repeatably needs to be reasonable and the set-up for each shot needs to fairly convenient.  Burst disks go counter to that.

I agree that the pellet/projectile is a structural element and haven't figured a way around that yet.  I like the idea of a Teflon seal, but that will require a two-piece construction of the pellet to get the seal onto the projectile, unless the tail of the projectile has a reduced diameter.  But that might complicate the stability of the projectile, but maybe not to an unreasonable level.  Maybe there is another way to do that.  Teflon is  a funny material to machine with the way it pushes around, and  making rings that are consistent not only in dimension, but in how the edges are shaped and how they seal can be difficult.  Definitely a learning curve in machining Teflon.  And lastly because I need to make multiple projectiles, their construction needs to be simple. 
That's the plan.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on March 19, 2016, 05:45:41 PM
For machining Teflon, I found that a HSS steel cutter shaped somewhat like a Scimitar blade, with a very sharp point and pretty extreme undercuts works well.... Basically a sturdy knife blade.... Of course you have to take small cuts to prevent it digging in.... The same type of blade works on UHMW Poly.... and can be used to take a fine finishing cut on Delrin, too, on a poppet face, for example....

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: I_like_Irons on March 19, 2016, 08:28:08 PM
With regards to machining soft plastics, you don't even need HSS.  Mild steel works just as well and is a lot less expensive.  You do have to do something about preventing/removing burrs and getting the edges sharp.

UHMW is a weird stuff to machine.  You get it to size and  ten minutes later is has grown to something significantly bigger (or smaller with hole sizes).  Teflon or PTFE generally holds size after machining if you can figure out how to measure it without squishing it.

Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on March 19, 2016, 09:43:10 PM
I agree about the Teflon and UHMW, guys.  Machining it is more an art than a science. One of those were learning the "tricks" makes all the difference. I can make one part, but not 10 identical parts!  I gotta learn them tricks!
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: rsterne on March 19, 2016, 09:48:31 PM
Yes, extremely sharp tools are the key for soft plastics....

IIRC, UHMW is sensitive to humidity, and swells when it absorbs water from the air (which is does, it is hygroscopic, isn't it?)....  been a long time since I machined it....

Bob
Title: Re: Sonic Choke or Sonic Joke - 1745 FPS
Post by: lloyd-ss on March 22, 2016, 01:50:26 AM
OK guys.  I did it.
2031 fps, 9.1 gn, .278 cal, 47.5" barrel, 55 cc dump chamber, 4000 psi

There is more velocity to be achieved.  I still have yet to see any sort of limit at the velocities and pressures we are, or could be, using in our PCPs.

Here's the video.  I also put up a blurb in the PCP gate.
Lloyd

http://www.youtube.com/watch?feature=player_embedded&v=JWt5DnfYH3I # (http://www.youtube.com/watch?feature=player_embedded&v=JWt5DnfYH3I#)
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 22, 2016, 02:03:37 AM
WOW!.... Slightly better in relative terms than you did with the .22 cal @ 1745 fps....

GREAT JOB !!!

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 22, 2016, 02:13:47 AM
Thanks Bob.  I lubed the barrel with a little silicone oil and it left a pleasant burnt smell like at a race track.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Michael Loar on March 22, 2016, 03:46:15 AM
WooHoo Lloyd
I knew it could be done and at only 4000 psi so you still have another 500 psi to go up to your stated max of 4500 psi for another test and I believe you will break 2300 fps with ease.

Great job and superb results for all the nay sayers. Never a doubt in my mind.

Mike 
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Matt15 on March 22, 2016, 10:02:17 AM
Congrats Lloyd!!!
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 22, 2016, 11:02:21 AM
Thanks very much guys.  It is a lot more fun when you can share it.

This video was actually the 4th shot from this gun.  The very first shot was with a 15.3 gn projectile and went very well, the second was with an 8.5 gn and the o-ring extruded and popped.  The third shot was again with an 8.5 gn, but the projectile popped apart at the waist at approx 4000psi while still being clamped. I think about 7gns of it got launched, but because it was just the tip, it might have ended up cockeyed in the bore, PLUS, the air was effectively being flowed thru a .155 T-port which was the portion of the projectile that was still being held in the clamp.  I had drilled out the center to reduce the weight, but I guess I thinned the wall a tad too much.

Here is the data on all those shots.  I am comparing them to the previous 1745fps shot to see how they track based on my spreadsheet calculator's predictions.

Previous fastest shot:
1745fps,   7.5gn, .22 cal, 23.3", 4500psi, 26cc,  50.7fpe (full bore dia direct port)

1802 fps, 15.3gn, .278 cal, 47.5", 4500psi, 55cc, 110.3fpe (full bore dia direct port) (Predicted vel was 1804fps)

1778 fps, 7.0gn, .278 cal, 47.5", 4000psi, 55cc, 49.1fpe (.155 dia direct port, 31% of bore area) Projectile pulled apart and accidental release. (Prediced vel at full bore port was 2108fps, so this shot was at 84% velocity with a 31% port)

2031 fps, 9.1gn, .278 cal, 47.5", 4000psi, 55cc, 83.4fpe (full bore dia direct port) (Predicted vel was 2025fps, but if I misread the pressure gauge, 4100psi is a perfect velocity match. )

Looking at the numbers, I see absolutely no tapering off of the velocities.  No sort of ceiling or major speed reductions.  I would guess that we are working at velocities that are still well below anything that would cause such anomalies.

Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 22, 2016, 11:39:29 AM
I agree.... It appears we are lonely limited by barrel length and air pressure at these velocities....

Of course Helium would roughly triple the FPE.... *grin*....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 22, 2016, 11:50:34 AM
Lucky for me, I do not have any helium available.   ;)
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 22, 2016, 11:52:45 AM
Titanium pellet to stand the heat of 3500 fps and the strain of the firing mechanism?....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 22, 2016, 12:00:54 PM
Well, I do have some 110ksi yield titanium rod.   :P
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 22, 2016, 12:05:04 PM
Hollowpoint it to reduce the weight further?.... *grin*.... Mach 2 on air (~2250 fps), here we come !!!

Bob
Title: WOW! - except....
Post by: Scotchmo on March 22, 2016, 03:32:46 PM
as soon as you said "burnt smell" - red flag.

In order to make this a stick, there must be no question about combustion contributing to the exceptionally high velocity.

That is higher than I thought it would go after taking into account fluid friction. I'll adjust my model and am willing/desiring to see this new record stand. But the burning smell makes me suspicious of the results.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 22, 2016, 05:27:03 PM
Scott,
The burnt smell was very mild, and from the o-ring friction in the barrel.  Like I said, burnt rubber smell like the burnout box at a drag strip, but faint.  The breech block itself is 1 lb 10 ozs of aluminum and absorbs most of the heat out of the air as the reservoir is filled.  I did not feel the aluminum with my hand specifically for heat during the fill, but I can do that next time I take a shot.  The only lube I used was a 30wt certified silicone shock oil made by LOSI for RC cars.  Given that information, I still hold that the smell was from a simple friction burn from the o-ring.  After all, o-rings are rated to maybe 10 fps in reciprocating applications, and this was 200 times that fast, so the o-ring is sacrificial.  I do not see how any combustion could be contributing to the shot.

I've shot wooden dowels out of barrels and there were scorch marks on the dowels from the lands, and a burnt wood smell, but certainly nothing that contributed to the energy in those shots either.  I see the same situation here, just rubber instead of wood. 

Scott, Give me your thoughts on this, in particular what you think might alleviate your concerns. 
Lloyd

P.S.  I could try fabbing a projectile with a Teflon seal, which shouldn't leave a smell from the friction burn.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 22, 2016, 07:17:45 PM
I would think that the Silicone lube would be pushed ahead of the O-ring, and the likely cause of the smell was the O-ring itself, smoking after leaving the barrel.... but anything is possible.... Interestingly, when I run the numbers through Lloyd's spreadsheet, leaving the efficiency at 70% like the 1745 fps shot, I get 2024 fps, which is within 0.3% of the results.... ie it is right where it should be, IMO.... The first shot with the new barrel, at 3500 psi with a 15.3 gr. pellet was within 0.1% of predicted....

I think any temperature effects will cancel out.... If the temperature is higher after the fill and before the shot, the molecular velocity would be higher, but only until the shot occurs.... Then Adiabatic cooling would drop the temperature of the air in the barrel and chamber by 53*C for a 2:1 expansion of the air.... I suspect if you could average out the molecular velocity throughout the shot it would be less than 1650 fps is anything, not more....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 22, 2016, 07:36:23 PM
Scott,
The burnt smell was very mild, and from the o-ring friction in the barrel.  Like I said, burnt rubber smell like the burnout box at a drag strip, but faint.  The breech block itself is 1 lb 10 ozs of aluminum and absorbs most of the heat out of the air as the reservoir is filled.  I did not feel the aluminum with my hand specifically for heat during the fill, but I can do that next time I take a shot.  The only lube I used was a 30wt certified silicone shock oil made by LOSI for RC cars.  Given that information, I still hold that the smell was from a simple friction burn from the o-ring.  After all, o-rings are rated to maybe 10 fps in reciprocating applications, and this was 200 times that fast, so the o-ring is sacrificial.  I do not see how any combustion could be contributing to the shot.

I've shot wooden dowels out of barrels and there were scorch marks on the dowels from the lands, and a burnt wood smell, but certainly nothing that contributed to the energy in those shots either.  I see the same situation here, just rubber instead of wood. 

Scott, Give me your thoughts on this, in particular what you think might alleviate your concerns. 
Lloyd

P.S.  I could try fabbing a projectile with a Teflon seal, which shouldn't leave a smell from the friction burn.
That's a tough one.

The heat sopurce is probably friction. Whether it's enough to ignite anything, I don't know.

With high oxygen content, anything that can burn can act as fuel. Silicon oil might have combustible carriers. Whether high pressure air and polymer or rubber o-rings would be adequate to add additional propellant, I don't know.

Conditions such as these make me think of a hybrid rocket motor.
https://en.wikipedia.org/wiki/Hybrid_rocket

2050fps gives 30fpe more than some sonic threshold proponents thought possible. If the process is being fueled by the o-ring, than the o-ring would deteriorate rapidly as percentages of it get consumed with each shot. If the velocity is repeatable using the same o-ring, that might rule that out as a source of combustion.

I'd use no lube for starters. Swab with dry patches.

If the same o-ring can repeatably shoot at anywhere near that velocity, without deterioration, and without lubes, that would eliminate any combustion products that I would have flagged.

Another option would be to use nitrogen instead of air. Similar properties as far as density/heat-content/compressing/expanding but it does not support combustion. Nitrogen would have about the same sonic threshold (if the threshold exists), as air. Then lubes/o-rings are fine as is, since they won't burn in pure nitrogen.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 22, 2016, 08:00:10 PM
Scott,
I think I can assure that a Buna-N o-ring is not going to be in any kind of condition to work for a second shot.  That amount of friction will wear the surface of the o-ring off to a degree that it won't seal for a second shot.  Whether or not the amount of o-ring that gets scrubbed off actually burns at all or burns fast enough to contribute any force, is anybody's guess, and I find it rather a stretch to think that it would contribute to the velocity.  I don't have nitrogen to use, so that change is not a possibility.  About all I can change might be to use a dry barrel and a Teflon seal. 
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 22, 2016, 08:56:55 PM
Scott,
I think I can assure that a Buna-N o-ring is not going to be in any kind of condition to work for a second shot.  That amount of friction will wear the surface of the o-ring off to a degree that it won't seal for a second shot.  Whether or not the amount of o-ring that gets scrubbed off actually burns at all or burns fast enough to contribute any force, is anybody's guess, and I find it rather a stretch to think that it would contribute to the velocity.  I don't have nitrogen to use, so that change is not a possibility.  About all I can change might be to use a dry barrel and a Teflon seal. 
Lloyd
A single Nitrogen test that matched the air test would seal the deal. If it gave approximately the same result, than I would have more confidence when using air for further data collection.

Outside of that, there will always be a question of combustion, even if minor. You would be surprised at what can act as fuels under the right conditions. I'm not sure if Teflon would be safer from a combustion standpoint.

Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 22, 2016, 10:17:13 PM
Unfortunately, I see no way to dismiss the fear of combustion-controlled assist without using Nitrogen.... If we see the same, or slightly increased velocity (which we should) then we could revert to air.... Otherwise, people will always doubt the results (even though I am 100% comfortable with them)....

Old ideas die hard.... Just look at the continuous arguments about dieseling in Springers.... No amount of "no lube" or "dry lube" or "non-combustible lube" experiments will satisfy those who believe the only way to disprove the Cardew's experiment of filling and firing a Springer in dry Nitrogen is to duplicate it.... BTW, I'm not saying they didn't obvserve controlled combustion in their experiments.... but I still find the idea that it can be so consistent over hundreds or thousands of shots to be mind-boggling.... Please don't let these observations drag this thread off course, I was just making the obvious comparison....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 22, 2016, 10:39:40 PM
Scott,
I think I can assure that a Buna-N o-ring is not going to be in any kind of condition to work for a second shot.  That amount of friction will wear the surface of the o-ring off to a degree that it won't seal for a second shot.  Whether or not the amount of o-ring that gets scrubbed off actually burns at all or burns fast enough to contribute any force, is anybody's guess, and I find it rather a stretch to think that it would contribute to the velocity.  I don't have nitrogen to use, so that change is not a possibility.  About all I can change might be to use a dry barrel and a Teflon seal. 
Lloyd
A single Nitrogen test that matched the air test would seal the deal. If it gave approximately the same result, than I would have more confidence when using air for further data collection.

Outside of that, there will always be a question of combustion, even if minor. You would be surprised at what can act as fuels under the right conditions. I'm not sure if Teflon would be safer from a combustion standpoint.


Scott, like I said, I can not test with nitrogen.  You loan me the gauge set and I will see what I can do.
 
Regarding the Teflon, Teflon does not support combustion and is mandated as wire insulation in most aircraft and naval installations requiring maximum fire resistance.  I am not aware of any seal material that is more non-combustible than Teflon.  A few tests done with a Teflon seal, in my opinion, should eliminate the argument about combustion.
That's as good as I can do with what I have.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 23, 2016, 12:34:26 AM
Scott,
I think I can assure that a Buna-N o-ring is not going to be in any kind of condition to work for a second shot.  That amount of friction will wear the surface of the o-ring off to a degree that it won't seal for a second shot.  Whether or not the amount of o-ring that gets scrubbed off actually burns at all or burns fast enough to contribute any force, is anybody's guess, and I find it rather a stretch to think that it would contribute to the velocity.  I don't have nitrogen to use, so that change is not a possibility.  About all I can change might be to use a dry barrel and a Teflon seal. 
Lloyd
A single Nitrogen test that matched the air test would seal the deal. If it gave approximately the same result, than I would have more confidence when using air for further data collection.

Outside of that, there will always be a question of combustion, even if minor. You would be surprised at what can act as fuels under the right conditions. I'm not sure if Teflon would be safer from a combustion standpoint.


Scott, like I said, I can not test with nitrogen.  You loan me the gauge set and I will see what I can do.
 
Regarding the Teflon, Teflon does not support combustion and is mandated as wire insulation in most aircraft and naval installations requiring maximum fire resistance.  I am not aware of any seal material that is more non-combustible than Teflon.  A few tests done with a Teflon seal, in my opinion, should eliminate the argument about combustion.
That's as good as I can do with what I have.
Lloyd

If we get the same results with no lube and various seal materials, we are probably good (but still a small doubt). I was thinking that we could weigh the seal before and after, but a rough calc shows that it only takes about .02gr of combustion (rubber) to yield 30fpe. Too small of a difference to measure accurately.

For nitrogen, would this do the job?:
http://www.ebay.com/itm/Paintball-airgun-fill-station-6000-psi-CGA677-/222056548928 (http://www.ebay.com/itm/Paintball-airgun-fill-station-6000-psi-CGA677-/222056548928)

Do you have tank access?
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: 39M on March 23, 2016, 01:14:03 AM
I might try graphite as a lube for the bore. It's very slick and very difficult to ignite.

Of course with a teflon seal no lubricant would be needed. Maybe something as simple as a .278 teflon tube with a hole just large enough for an aluminum rivet, to give it some weight(fpe), would be the ideal projectile.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: 39M on March 23, 2016, 01:18:15 AM
To get to the top of the mountain might require a barrel with a super slick coating inside the bore.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Michael Loar on March 23, 2016, 03:46:03 AM
My two cents worth tell me that if indeed the o ring is burning at all even very slightly and contributing to the velocity by the time that minuscule amount of 30 fps had a chance to have any effect at all on the projectiles velocity it would be out of the barrel far ahead of that combustion and therefore the combustion would have little if any effect on its velocity. That little bit of suspected combustion would not propagate any where fast enough to create any added pressure or push to the pellet since it is already moving far faster then the combustion can propagate behind it and it has to be behind it to have any effect.

The fuel/air combustion in an automotive engine is a slow moving flame front in comparison to the milliseconds the projectile is in the barrel so I see no reason to believe that the heating of the o ring as it moves down the barrel could ever be sufficient to add to the velocity at all as it would be in front of the projectile not behind it where it would need to be to have any effect.

I see it as a non issue IMO.

Mike   
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 23, 2016, 08:07:24 AM
Scott,
I think I can assure that a Buna-N o-ring is not going to be in any kind of condition to work for a second shot.  That amount of friction will wear the surface of the o-ring off to a degree that it won't seal for a second shot.  Whether or not the amount of o-ring that gets scrubbed off actually burns at all or burns fast enough to contribute any force, is anybody's guess, and I find it rather a stretch to think that it would contribute to the velocity.  I don't have nitrogen to use, so that change is not a possibility.  About all I can change might be to use a dry barrel and a Teflon seal. 
Lloyd
A single Nitrogen test that matched the air test would seal the deal. If it gave approximately the same result, than I would have more confidence when using air for further data collection.

Outside of that, there will always be a question of combustion, even if minor. You would be surprised at what can act as fuels under the right conditions. I'm not sure if Teflon would be safer from a combustion standpoint.


Scott, like I said, I can not test with nitrogen.  You loan me the gauge set and I will see what I can do.
 
Regarding the Teflon, Teflon does not support combustion and is mandated as wire insulation in most aircraft and naval installations requiring maximum fire resistance.  I am not aware of any seal material that is more non-combustible than Teflon.  A few tests done with a Teflon seal, in my opinion, should eliminate the argument about combustion.
That's as good as I can do with what I have.
Lloyd

If we get the same results with no lube and various seal materials, we are probably good (but still a small doubt). I was thinking that we could weigh the seal before and after, but a rough calc shows that it only takes about .02gr of combustion (rubber) to yield 30fpe. Too small of a difference to measure accurately.

For nitrogen, would this do the job?:
http://www.ebay.com/itm/Paintball-airgun-fill-station-6000-psi-CGA677-/222056548928 (http://www.ebay.com/itm/Paintball-airgun-fill-station-6000-psi-CGA677-/222056548928)

Do you have tank access?

Scott, 
Good find on the nitrogen fill set-up.  Last time I looked for something like that it was several hundred dollars.  That set-up is very reasonably priced and takes away my resistance to trying the shots with nitrogen.  I had checked with one local welding supplier a few months ago and they only had 2500 psi bottles, but I will call the other welding places this morning and see what they have.  Worst case scenario if I can only get a 2500 psi tank, is to reg it down to 125psi and then pump it back up to 4500 with the Shoebox.  I have a brand new 77cuin CF bottle that has been waiting to be put to use and this could be it.  Of course, a 6k psi nitrogen tank from a local house would be fantastic.
This could work.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 23, 2016, 08:15:14 AM
Buldawg, I agree with you that the o-ring probably isn't contributing to the energy more than just the tiniest bit, if at all, but if the nitrogen set-up becomes a reality, all concerns are eliminated, and honestly, that would be the best way to go.

39M, A Teflon seal is in the works!
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Michael Loar on March 23, 2016, 10:21:22 AM
Lloyd
Yea if the nitrogen can be acquired at a reasonable cost and supplied at the pressures to equal the air it will definitely eliminate that variable from the equation of combustion adding to the velocity.
I hope it is easily attainable as I know I have checked here at my local welding shop several years ago and they can get 120 CF tanks of nitrogen at 6000 psi but it has to be ordered in advance and takes a few weeks to get but thats because it is sourced from Atlanta and trucked to my local shop and it was to costly for me to use as a fill medium for everyday use.

I don't remember the cost now but it was out of my budget and turn around time for a refilled tank was not acceptable either. I would have had to reorder a month in advance and pay at the time of ordering.

Hope the Teflon seal will work also as that will eliminate the possibility of any combustion as well.

Mike
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Michael Loar on March 23, 2016, 10:34:32 AM
Lloyd
Just an FYI on the nitrogen fill setup as all you need is the CGA677 fitting and you can use your existing HPA bleed valve , gauge and fill hose you have now.

http://www.regulatortorchrepair.com/store.php/products/cga-677-nut-and-nipple (http://www.regulatortorchrepair.com/store.php/products/cga-677-nut-and-nipple)

This is only 33 bucks and will attach your fill hose assy to a nitrogen tank.

Mike
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 23, 2016, 12:20:44 PM
Mike, thanks, another good lead on the nitrogen fittings.

I am tracking down the N tanks.  I can get 2500 psi easy and cheap locally but I have to drive an hour and a half to get 6000 psi.  I am waiting on a call back for pricing on 6000, because around here the rental on the 6k tanks is in dollars a day, not dollars a month.  But like I said, I can use the shoebox to get the nitrogen up to 4500 if it comes to that.
Lloyd   
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Michael Loar on March 23, 2016, 12:43:32 PM
Lloyd
Keep us informed and that what I ran into here with the nitrogen at 6000 psi as well. Never thought about pumping up with the shoebox but then did not have one then either.

Mike
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 23, 2016, 12:51:00 PM
I wonder what the intermediate pressure of the ShoeBox is?.... could you drill and tap into the block between the cylinders, install a male Foster, and feed it with, say, 500 psi Nitrogen (or Helium) directly into the 2nd stage?....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Michael Loar on March 23, 2016, 01:13:41 PM
Bob
That's a good question as the standard shoebox get fed 85 psi ( 100 max ) and the freedom 8 shoebox get fed 125 psi ( 135 max) so what the second stage outputs would determine what you would have to feed the third stage since the second stage is fed by either the 85 or 125 psi from the oilless compressor.

You would have to bypass the second stage and feed the third what the second stage outputs to the third with nitrogen to speed up the pressure step up of the nitrogen if I am figuring on how the three stages work correctly. 

Mike
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 23, 2016, 01:22:35 PM
I meant the 2nd stage on the ShoeBox, which of course is the 3rd stage in the system.... input directly into the block after the larger cylinder on the Shoebox, and only use the smaller, HP cylinder to boost the pressure to 4500.... Should be very little load on the motor that way, you may even be able to run a bit higher pressure than the peak during operation (which would occur at 4500 psi output).... subject to the strength of the lines, fittings, and check valve between the stages, of course.... If the two stages both have about the same compression ratio, and we are going from 125 psi to 4500, which is 36:1, it is reasonable to assume each stage is 6:1, which could mean you might be able to feed the 3rd stage directly with 750 psi.... possibly just use an 850 psi paintball regulator with a shim removed?....

Of course dropping the pressure down to 125 psi would allow you to use more of the pressure in the N2 tank that you are paying for.... so I guess that would be more cost effective....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 23, 2016, 01:34:37 PM
 Bob and Mike,

What happens if you overpressurize stage one in a freedom 8?  It doesn't have that funky cutoff switch, and normally in a compressor, if you overfeed the first stage it will just blow through the check valves till it reaches an equillibrium point.  I will study that with caution in mind and see what it looks like. Would still want a regulator on the input to keep the input pressure reasonable, say, less than 800-1000 psi.

Also, If you try to feed the outside pressure directly into the second stage you'll have to put a check in the input line so it can build pressure and won't just fight with the tank pressure.

Or am I missing something?

Lloyd


 
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 23, 2016, 01:42:24 PM
OK, got a quote on the 6000 psi nitrogen.   $125 per year rental for the cylinder, and then  $140 to get the cylinder filled.  That's about 75 cents a day.  Heck, I can spend that much on toilet paper on a bad day, LOL. :P
That's for a size 300 cylinder which is 49 liters water volume.  Bob how much nitrogen is that?  I need a more accurate measurement than a "butt load."  ;D

With the reasonably priced adapters, this might be something that  I "need."  ;D

Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 23, 2016, 01:50:49 PM
I don't know what happens if you overpressurize the first (2nd) stage.... but I don't think the air can blow through to the second (3rd) stage because when the pistons are (both) at the compression end of the stroke the high pressure piston is closing off the air passage on it's inlet side (which runs through the block, no?).... I think the ports inside the block effectively work like an active inlet valve for each stage, open only when the pistons withdraw to between the two O-rings, with check valves only on the outlet side.... Therefore, I don't think you need a check valve on the line (regulator) feeding from the tank.... as it would feed the space between the two O-rings from inside the block.... The check valve on the low pressure cylinder would prevent it from disappearing backwards through there.... (I think)....

Still, makes more sense to use something like a welding regulator to drop the N2 tank pressure down to 125 psi, you get to nearly empty your N2 tank that way.... so forget everything I suggested.... *LOL*....

Bob

Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 23, 2016, 02:27:30 PM
Nitrogen density at 6000 psi is 376 kg/m^3 at 20*C.... so 49 litres would hold (49/1000) x 376 = 18.424 kg of N2.... At 1 atmosphere is it 1.166, so you would have 18.424 x (1000 / 1.166) = 15,801 litres, or 558 CF of Nitrogen.... However, at 4500 psi, the density is 310 kg/m^3, which means if you are filling to that pressure, so you would still have (49/1000) x 310 = 15.19 kg. of Nitrogen left in the tank, and would have only (18.424-15.19) = 3.234 kg. that you would actually be able to use.... That works out to 3.234 x (1000/1.166) = 2774 litres, or 98 CF you can actually use if filling to 4500 psi.... and that assumes that the tank is actually at 6000 psi when you start....

Looking at it from the point of filling your 55cc chamber to 4500 psi, to a density of 310 kg/m^3, you need (55/1000/1000) x 310 = 0.01705 kg per fill, and you have 3.234 kg. available, so that works out to 190 fills.... minus the waste bled from the hoses and fittings.... Is that closer than "a bucket load" ? ? ?

Call it a buck a fill?.... Might be way cheaper to use the lower pressure tank, regulate it down to 125 psi, and run it through your Shoebox?....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 23, 2016, 02:46:14 PM
I'm in for $50 for the Nitrogen experiment.

Lloyd, check your PayPal account. Now you are committed.   ;D
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 23, 2016, 03:00:59 PM
I'm in for $50 for the Nitrogen experiment.

Lloyd, check your PayPal account. Now you are committed.   ;D
Does that mean the men in the white coats will be showing up at my door?  ???

Ok, game on!  I think I will probably go with the 6k bottle.  If I went with a 2500 bottle, the tank rental is almost as much, but the nitrogen fill is cheaper, but then I've got the wear and tear on the shoebox, and the noise and delay of continuously topping up. 

Bob, that is a big bucket load of fills from the 6k tank and I think I will do that.  That is a big tank to hide from the wife so I've to figure that one out.  Luckily the 6k tank  can be delivered to a local welding supply place so I don't have to make the long drive to pick it up.  That's actually what tipped the balance. Like the Brown truck showing up, LOL.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 23, 2016, 03:22:04 PM
I'm in for $50 for the Nitrogen experiment.

Lloyd, check your PayPal account. Now you are committed.   ;D
Scott, Thanks again. Do you offer beer to alcoholics, too?  Seriously though, thank you.  And it does lead to another dilemma.  If you have 6000 psi available, wouldn't it be a shame not to shoot something at 6000 psi?  The problem is the current Version 2 block was designed for 4500 psi.  :-[
Its always something.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Privateer on March 23, 2016, 04:14:04 PM
Well. I tossed a FPCP into the 'Let's blow it up thing'
Send me your PayPal info by PM and I'm in for a few bucks myself.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 23, 2016, 05:23:36 PM
Lloyd,

You are heading up these groundbreaking experiments. I would like to ask your permission:

I was told of the limit of 1640fps some time ago on another forum where it seems to be accepted as fact. I accepted the reasoning given for it at the time, without too much thought. I would like to present a little info on your results, to that forum, prior to the Nitrogen tests. Are you OK with that?
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Michael Loar on March 23, 2016, 06:58:00 PM
I meant the 2nd stage on the ShoeBox, which of course is the 3rd stage in the system.... input directly into the block after the larger cylinder on the Shoebox, and only use the smaller, HP cylinder to boost the pressure to 4500.... Should be very little load on the motor that way, you may even be able to run a bit higher pressure than the peak during operation (which would occur at 4500 psi output).... subject to the strength of the lines, fittings, and check valve between the stages, of course.... If the two stages both have about the same compression ratio, and we are going from 125 psi to 4500, which is 36:1, it is reasonable to assume each stage is 6:1, which could mean you might be able to feed the 3rd stage directly with 750 psi.... possibly just use an 850 psi paintball regulator with a shim removed?....

Of course dropping the pressure down to 125 psi would allow you to use more of the pressure in the N2 tank that you are paying for.... so I guess that would be more cost effective....

Bob

Bob
Ok I misunderstood what you were referring to as the second stage so yes that would be the way to do it and you can do the math ( not my forte at all ) to determine what would be capable pressure wise of being fed into it to speed thing up.

Using only 125 psi out of the tank means more cost for the regulator to control the tanks output pressure but being able to use most all of the nitrogen in the tank is more cost effective as well so I guess to some extent its a 50/50 toss up.

Lloyd
I believe if in a freedom 8 or max shoebox over pressurizing the first (2nd) stage of it will add to the strain on the motor and increase the heat and wear on the o rings that seal the shafts as well as the plastic shaft bushing and if over pressurized enough likely would stall the shoebox completely. In any event it would not be a good idea at all as the cylinders are only held in the block by circlips and they can become projectiles in themselves if stalled at 4500 plus psi. It would IMO be better to be safe and use 125 psi fed into the shoebox as it was designed than risk damage or injury by redesigning its operation that is already a proven concept.

Mike
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 23, 2016, 07:12:23 PM
Interestingly, you don't gain much at extreme pressures with such a light projectile.... I guess the mass of the air is overwhelming the total mass.... The mass of a 9.1 gr. pellet is only 0.00004 slugs.... A 47.5" barrel full of 1600 psi air (that is what it is, starting at 3000 psi with a 55cc chamber and 47 cc barrel) is over 10 times greater, at 0.00043 slugs.... Here is what I get with Lloyd's spreadsheet using the inputs for his recent 2031 fps shot, at 70% efficiency.... pressures are before shot....

3000 psi = 1928 fps  (75 FPE)
3500 psi = 1980 fps
4000 psi = 2024 fps
4500 psi = 2063 fps
5000 psi = 2097 fps
5500 psi = 2128 fps
6000 psi = 2156 fps  (94 FPE, an increase of 25%)

Lloyd's current calculator uses Boyle's Law for air density, and once you go above 3000 psi the density actually drops off compared to an Ideal gas.... If I understand this correctly, this results in a greater pressure drop during the shot, the higher the starting pressure.... but the density will be less, which is a plus.... I don't know how those opposing factors will effect the spreadsheet results.... On the plus side, 6000 psi Nitrogen should add about 30 fps because it is ~4% less dense than air....

Interestingly, if we increase the weight of the pellet by a factor of ten, to 91 gr. (typical bullet weight for that caliber), we see a lot different situation....

3000 psi = 1083 fps (237 FPE)
6000 psi = 1349 fps (368 FPE, an increase of 55%)

It appears that in regards to barrel lengths and pressures, while we can still make small gains, they are no longer in proportion to the gains a "normal" PCP sees.....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 23, 2016, 09:18:38 PM
Lloyd,

You are heading up these groundbreaking experiments. I would like to ask your permission:

I was told of the limit of 1640fps some time ago on another forum where it seems to be accepted as fact. I accepted the reasoning given for it at the time, without too much thought. I would like to present a little info on your results, to that forum, prior to the Nitrogen tests. Are you OK with that?

Scott,
Please do. 
This is all in the interest of learning, and sharing knowledge with the entire airgun community.  There are a lot of very smart airgunners out there with provocative ideas and theories.  Sometimes we get it right; sometimes we don't.  Nothing ventured, nothing gained.  But if the theories are proven wrong, give them a dignified burial and move forward.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 23, 2016, 09:25:53 PM
Buldawg,  With yours and Bobs discussion on the shoebox, I think if I use one  to boost the nitrogen pressure, I will just reduce it to approx 120 psi first and dump it into the input in the normal fashion.  Sounds like there are too many unknowns (at this time) to do it safely any other way with the shoebox.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Michael Loar on March 23, 2016, 09:42:54 PM
Lloyd
I would tend to agree with you on the use of the shoebox to boost the pressure of the nitrogen since there are unknowns in trying to bypass its normal operation for the sake of saving a little bit of time versus risking damaged equipment or worse injury.

If you can get the 6000 psi nitrogen tank though then there should be no need for boosting pressure since you will have 190 shots worth of pressure with just the turn of a knob with the CGA677 fitting and your current fill setup.

Mike
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 23, 2016, 09:47:07 PM
Interestingly, you don't gain much at extreme pressures with such a light projectile.... I guess the mass of the air is overwhelming the total mass.... The mass of a 9.1 gr. pellet is only 0.00004 slugs.... A 47.5" barrel full of 1600 psi air (that is what it is, starting at 3000 psi with a 55cc chamber and 47 cc barrel) is over 10 times greater, at 0.00043 slugs.... Here is what I get with Lloyd's spreadsheet using the inputs for his recent 2031 fps shot, at 70% efficiency.... pressures are before shot....

3000 psi = 1928 fps  (75 FPE)
3500 psi = 1980 fps
4000 psi = 2024 fps
4500 psi = 2063 fps
5000 psi = 2097 fps
5500 psi = 2128 fps
6000 psi = 2156 fps  (94 FPE, an increase of 25%)

Lloyd's current calculator uses Boyle's Law for air density, and once you go above 3000 psi the density actually drops off compared to an Ideal gas.... If I understand this correctly, this results in a greater pressure drop during the shot, the higher the starting pressure.... but the density will be less, which is a plus.... I don't know how those opposing factors will effect the spreadsheet results.... On the plus side, 6000 psi Nitrogen should add about 30 fps because it is ~4% less dense than air....

Interestingly, if we increase the weight of the pellet by a factor of ten, to 91 gr. (typical bullet weight for that caliber), we see a lot different situation....

3000 psi = 1083 fps (237 FPE)
6000 psi = 1349 fps (368 FPE, an increase of 55%)

It appears that in regards to barrel lengths and pressures, while we can still make small gains, they are no longer in proportion to the gains a "normal" PCP sees.....

Bob
Bob, you said a lot in that post.   The variables are so interrelated that the calculated (and actual) results sometimes are not what you would expect.  Seems like a lighter projectile is the fastest way to higher velocity.  But as you pointed out, with a light projectile and a long barrel, the mass of the column of air (nitrogen) can exceed the mass of the projectile by an order of magnitude and much of the energy is spent just accelerating the air.  With heavier pellets, where the pellet is a much larger percentage of the total mass that must be accelerated, the Energy gains are more substantial.  The variables that you change for a particular test shot need to be relevant to what the goal of each unique experiment or shot really is.

Regarding the spreadsheet, I started incorporating the VanderWaals pressure vs volume vs density and got stalled half way through.  It was more difficult than I anticipated.  I need to take a fresh stab at it and complete the task, because it is one of those tasks that just needs to done.  Boyles law isn't applicable in our situation, so we will stop hanging onto it, and give it a dignified burial, and move forward.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 23, 2016, 10:38:00 PM
I was pretty shocked when I found that the velocity increase going from 4000 psi to 4500 with your current setup is only predicted to be on the order of ~ 40 fps.... It would take a full 1 gr. reduction in the weight of the bullet to get that as well.... or about 7" more barrel length.... Interestingly, even an infinite reservoir would never get us that 40 fps if we change nothing else.... We really are getting to the point of (severely) diminishing returns.... Mach 2 (2250 fps) is looking a long way away right now, without Helium, IMO.... but with it, we would be flirting with Mach 3....

It will be interesting to see which way applying the VanDerWaals corrections takes us.... ie which is more important the lower density at high pressure, or greater pressure loss during the shot, compared to an Ideal gas.... or if they pretty much cancel out?....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 23, 2016, 11:25:37 PM
Bob,
I will see if I can finish up the VanDerWaals corrections, and then a fresh look at caliber,  SD, barrel length, etc, will be in order. 
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 24, 2016, 12:54:12 AM
...
It will be interesting to see which way applying the VanDerWaals corrections takes us.... ie which is more important the lower density at high pressure, or greater pressure loss during the shot, compared to an Ideal gas.... or if they pretty much cancel out?....

Bob
Bob,

Isn't that backwards once you get over about 2000psi?

Looking at your earlier graph:
(http://i378.photobucket.com/albums/oo221/rsterne/Important/IdealGases_zps796cc652.jpg)

It will result in the model showing a higher than expected air mass at pressures over 3500psi. So that reduces the velocity estimate.

However, with the correction, air at 2000psi is wanting to take up a larger volume than an ideal gas. As the 4500psi dump chamber depletes, the pressure will not be falling off as fast as we originally predicted. So that increases the velocity estimate.

As you suggested, maybe it will still be a wash. It could end up balancing out to be the same with or without VanDerWaals correction.

Guessing what happens with an infinite or very large dump chamber should be easy:

An infinite dump of 2000psi could use an air mass multiplier of about 93%. - higher velocity than ideal gas.

An infinite dump chamber of 3500psi air needs no correction. - velocity as predicted

An infinite dump of 4500psi might need an air mass multiplier of about 109%. - velocity lower than ideal gas

An infinite dump of 6000psi might need an air mass multiplier of about 125%. - not good for performance
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 24, 2016, 01:25:47 AM
That graph is labelled incorrectly, and is pretty confusing.... I was having Nitrogen and an Ideal gas intersect at 3000 psi when I drew it, to compare what happens at 4500 psi.... In addition, the air density I used was based on the geometric average of Oxygen and Nitrogen because I couldn't find the data for air.... Here is the correct data....

(http://i378.photobucket.com/albums/oo221/rsterne/Important/Pressure%20vs%20Density_zpsp7cy6hqy.jpg) (http://s378.photobucket.com/user/rsterne/media/Important/Pressure%20vs%20Density_zpsp7cy6hqy.jpg.html)

As you can see, for an Ideal gas (as per Boyle's Law), the relationship between density and pressure is linear.... Air and Nitrogen are almost perfectly linear up to 2000 psi, and the deviation at 3000 psi is only about 4%.... However at 4500 psi, the density is about 13% less, and at 6000 psi (not shown), it is about 20% less than predicted by Boyle's Law....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: madeInLV on March 24, 2016, 06:47:18 AM
Loyd,

congratulations! Boy it's great to see when metal comes to life!

The o-ring contraversy is BS...i think. Yes, it will cause frictiona and yes it will heat up. Will it BURN and aid the expansion by increasing the mean pressure...NO. After all, the air behinf it is expanding and COOLING. The heat generated on the o-ring surface due to friction will mess up the O-ring and won't even heat up the barrel.

Still, there will be nay sayers. Do a test with NO lube and a tefon ring (making them is real easy and they can stretch and pushed back into shape). Since you are in the US (the land of e-bay) you cold try and get some PTFE coverad O-rings. Still...making a TEFLON ring is easy.

Boy, i wish i didn't have this cold/running nose...would write more clearly:)

What's more important is what do you plan on doing with the rig?

Ok...you'll make another pellet (as light as you possibly can) with a teflon ring an hopefully get it to seal, give it 4500psi and fire it, which hopefully gets to M=2.

Say the projectile end up being 6 grains. But what if it were 3 grains? Would it go twice as fast?:):):) But you can't test it....3 grain pellet won't hold up structurally.

You could make a graph : Vmax vs SD  (SD=sectional density) where you fire heavy to light and record Vmax and EXTRAPOLATE to Vmax when SD->0. Now that would be more valuable IMHO. Then you could perfrom the same set of shots and varry the pressure. The graph would then have a bunch of pressure lines representing Vmax at that partilucalar pressrue. Increase of P and it's affect on Vmax (linear, exponensial....) woul then be visible.

Stupid cold....god i feel awfull.

Ok, what I'm getting at is practical application. This rig will show us V max attainable on air which is cool. In reality when constructing a PCP we deal with other issue though...

we are limited to 300m/s (you don't wan't to be in the transonic region) which is a lot if you think about it. NOW....we can change: caliber, barrel length, pressure ,firing cahmber volume.

At what point having a longer barrel is meaningless?
How many CALIBERS long should my barrel be?
WHY do bigger caliber systems are more efficient rather than small caliber counterparts. (efficiency vs caliber)
How big should my firing chamber be? Is the a golden rule? As in V_chamber=4*V_barrel There has to be a limit.
..............................
Is the inline configuration of the vavle that much more efficient than the traditional with 2*90deg bends? If so, how much? How about the Gyrardony style port?

In an inline valve....how steep should the angle of the cone be? 45...30 deg?

I could go on and on:)

You are doing a great job. Keep it up:)
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 24, 2016, 12:36:23 PM
Scott, I see the responses over on the Yellow, completely predictable.... One thing mentioned is the cooling effect of Abiabatic expansion, to as low at 150*K.... This of course lowers the molecular velocity.... Here is the calculator for that (air is 29 AMU)....  http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c4 (http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c4)

At 150*K, the molecular velocity of air is a paltry 1177 fps, which leaves the concept of that providing a limit to the velocity of an airgun even further in the dust.... Incidently, I think that 150*K is greatly flawed.... Here is a calculator that gives the temperature (and available energy) in expanding air, for both Isothermal and Adiabatic expansion.... http://www.tribology-abc.com/abc/thermodynamics.htm (http://www.tribology-abc.com/abc/thermodynamics.htm)

Starting at 20*C (293*K) with 55 cc (0.055x10^-3 m^3) at 4000 psi (27.6 MPa), and ending at 2160 psi (14.9 MPa) that calculator gives a final temperature when the pellet exits the muzzle of 245*K, although it could drop much lower than that once the pellet exits and the pressure goes to 1 atm.... At 245*K, the molecular velocity of air is 1506 fps.... Incidently, there would be 0.6 kJ (442 FPE) of energy released by that expansion, so we are only getting about 19% of that....

Bob

Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Michael Loar on March 25, 2016, 04:18:57 AM
Ok well totally lost in the math again as usual but my gut tells me if the pellet is light enough and the pressure high enough it will reach Mach 2 given the right barrel length and firing chamber volume and pressure.

It has been said to many times in history that it cannot be done only to be proven wrong later on by someone that is not willing to take the theory and math numbers at their face values. So I say let the nay sayers be darned and let the impossible be proven like it always is by those who refuse to stand by convention.

Mike
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 25, 2016, 09:03:58 AM
....................................
Starting at 20*C (293*K) with 55 cc (0.055x10^-3 m^3) at 4000 psi (27.6 MPa), and ending at 2160 psi (14.9 MPa) that calculator gives a final temperature when the pellet exits the muzzle of 245*K, although it could drop much lower than that once the pellet exits and the pressure goes to 1 atm.... At 245*K, the molecular velocity of air is 1506 fps.... Incidently, there would be 0.6 kJ (442 FPE) of energy released by that expansion, so we are only getting about 19% of that....
Bob
Bob, I quoted just part of your previous post regarding temperature drop resulting from the expansion of the air during the shot, and as you pointed out, up to the point that the projectile leaves the muzzle. Expanding from 55cc to approx 102cc in 2.5 milliseconds. So your calcs show a total drop of 48*K, or 86*F? As we have previously discussed, there is a continuum of velocities and pressures and now,  temperatures, inside the system.  Hard to say where most of the temperature changes are localized, but I would guess at the entrance into the barrel, for what its worth. Anyway, it doesn't seem that the temperature drop will have much affect on the velocity, in the same way that the slight heating of the air from a rapid fill won't have much affect.

In upcoming shots, I will pay attention to the before and after temperatures of the breech block and barrel, even if just by hand touch, to see if anything extraordinary is happening, despite its effect, or lack of effect, on the velocity.
Lloyd 
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 25, 2016, 09:23:52 AM
New projectiles.
I just received some correct dia 7075 aluminum rod and some Teflon to make some new projectiles and seals for the upcoming Nitrogen shots. 
With the way the clam shell grips the conical rear end of the projectile, I think I can make the clamping O.D. slightly smaller (.230 dia)  than the front end (.274 dia) of the projectile.  If I also make the extreme rear end of the projectile pointed, I hopefully will be able to force the Teflon seals on from the rear of the projectile, over the .230 dia, without damaging them.  The I.D.  of the Teflon seal will be about .170, so it ought to work.

Another thought on the projectiles is to eliminate the clamshell clamping and instead have a skinny aluminum stem extending from the rear of the projectile that is secured just outside the entrance of the barrel so that it effective holds the projectile in place as the reservoir is filled.  The skinny stem would have a necked down area that would break under tension when the correct pressure is reached.   Using, as an example, a 4500 psi fill and 60ksi break for the 7075 (will have to experiment to find out), the projectile will have 277 pounds force on it. If the stem were necked to .071, break would occur at 4500 psi.  With a .070 dia stem the break would be at 4400psi.    I should be able to hold the dia (and finish) of the necked area to a .001 tolerance and a 100 psi variation is as good as I can read on the gauge anyway.  So that design is a possibility.  The problem is figuring out a retention method that doesn't interfere with the air flow.

Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: I_like_Irons on March 25, 2016, 12:53:17 PM
The breaking rod idea is a pretty good one, but there will be a bit of variability at which pressure it actually breaks.  I'd suggest making a recording pressure gauge on the receiver block so you know exactly what the pressure is when the rod lets go.   Even one of the "old school" Bordon pressure gauges with the recording needle will work.  A camera trained on the gauge should also work.  I think you want a fairly high frame rate so that you don't "blink" just before peak pressure.

One thing that happens when a rod is put into tension but before it breaks is that it necks down.  If you look at stress strain charts you will see the ultimate strength occurs at the peak of the curve while the break point is at a lower force level.  This latter half of the curve is due to the cross sectional area being reduced though the strength of the material remains pretty much constant.  Brittle materials have a very short extension to the curve, while ductile (like aluminum) have a longer curve.

The necking aspect may be put to good use, however.  If you can design the rod's  break point a bit behind the barrel opening, then you have a fairly pointed smoothly tapered "needle" which shouldn't affect the flow too much.   The actual break on the point of the "needle" will also be ~45 degrees which helps with reducing the point gradually a bit.

Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Michael Loar on March 25, 2016, 01:13:11 PM
That's what was used in the auto industry to install ignition switches so that they could not be easily removed was break away fasteners in which the head was necked down to shear at a predetermined torque thereby leaving a fastener without any means to remove except a hammer and chisel. Then of course it was located so that the chisel had to be custom ground to even reach the head to drive it loose to be removed, I hated those screws with a passion.

Luckily in your application removal will be supersonic and instant with no need for a hammer and chisel. LOL

Mike
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 25, 2016, 01:34:18 PM
I take the idea of Adiabatic expansion in PCPs with a bit of a grain of salt.... The reason is, that I have never seen an fog of ice in front of the muzzle, even though air temperature drops of over 100*C are predicted when the valve closes early in the shot cycle.... If we start at 2000 psi, and have a residual muzzle pressure of 400 psi (not unusual for a PCP), the resulting air temperature at the muzzle should be 185*K (-126*F).... In addition, if the expansion is purely Adiabatic, the maximum achievable efficiency seems too low to me, ie we are getting too close to the theoretical maximums....

(http://i378.photobucket.com/albums/oo221/rsterne/Important/MaxEfficiencyFPE-CI.jpg) (http://s378.photobucket.com/user/rsterne/media/Important/MaxEfficiencyFPE-CI.jpg.html)
(http://i378.photobucket.com/albums/oo221/rsterne/Important/MaxEfficiencybarcc.jpg) (http://s378.photobucket.com/user/rsterne/media/Important/MaxEfficiencybarcc.jpg.html)

I got the numbers for the above graphs (and the temperatures above) from this calculator.... http://www.tribology-abc.com/abc/thermodynamics.htm (http://www.tribology-abc.com/abc/thermodynamics.htm)

With a SSG installed, we are seeing some PCPs with efficiencies of over 2.0 FPE/CI at pressure under 2000 psi.... that seems too efficient (only 15% total losses) for the expansion to be purely Adiabatic, IMO.... Remember, part of the FPE released by the expansion of the air goes into accelerating its own mass.... The reasons why the expansion are nearly Isothermal may be escaping us.... but reality, to me, shows that Adiabatic isn't the best model to use.... Does some cooling occur?.... Yep, you can feel the temperature of the reservoir drop a bit with continued shooting.... However, I have never felt the barrel get as cold as the reservoir, even though that is where the majority of the expansion is taking place....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 25, 2016, 03:06:26 PM
Bob,

My thoughts on adiabatic vs isothermal model:

The reservoir air in a multi shot gun is undergoing primarily an isothermal expansion between shots. Since it usually has seconds to recover. If it were an insulated air tube, and a semi-auto, then it might be better treated as adiabatic.

Though not many processes are purely adiabatic, the shot charge expansion is primarily adiabatic. With an infinite dump chamber, there is no expansion, so it does not matter. With the large dump chamber used in the test, it is not a major factor. Though I do factor it in.

I am talking about overall affect.

There is also localized expansion, localized variations in pressure along the barrel and radially from the bore center. If there is any super low temp regions, they would be localized to a very small area. I ignore them.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 25, 2016, 06:27:45 PM
I agree that in Lloyd's most recent shot, which is a dump shot with a reservoir larger than barrel volume.... the difference between Isothermal and Adiabatic is small, on the order of about 11 fps.... However, if you look at a gun like my regulated QB79, and apply 100% Adiabatic expansion, it is difficult to come up with numbers that match the measured efficiency without having the gun end up 100% efficient, by the time you include the mass of air being accelerated.... and we know that kind of efficiency just isn't possible....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 25, 2016, 08:27:27 PM
Bob,


On the QB79, are you talking about the overall efficiency of the fill? That will definitely have an isothermal contribution to the apparent air use efficiency.

The isothermal energy contribution is happening between shots, not during the shot. At least the vast majority of it.

Unless you are able to shoot it fast enough to deplete the main tank before the temperature restabilizes. Than your efficiency would not appear to be so high.

Insulate the gun and repeat shots as fast as you can until depleted. The apparent air use efficiency will be lower than otherwise.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 25, 2016, 11:14:09 PM
Nope, I'm talking about taking the air for each shot, starting at the regulator output of only 1200 psi, and calculating the available energy in that air.... By the time you add up the FPE of the shot, plus the FPE taken to accelerate that air.... it comes out pretty darn close to the total theoretical FPE available from that amount of air if it expands Adiabatically.... too close, IMO....

I get 90 shots at 26 FPE on a fill.... That is from 3000 psi down to 1100 psi (a 1900 psi drop) on a 13 CI (213 cc) tank, running through a 1200 psi regulator.... That works out to 1900/14.5 x 213 = 27,910 bar.cc, divided by 90 = 310 bar.cc per shot.... At 1200 psi, that is 310 / (1200/14.5) = 3.75 cc per shot.... Run that through the calculator I posted, and you even if you expand it to 1 bar (which it doesn't, or it wouldn't have any report left), you get 41 FPE, and the air exiting the barrel would be only 83*K (starting to condense).... There is 26 FPE energy in the pellet, and the mass of air in the barrel is 27% that of the pellet, so now you are up to 33 FPE required to produce the shot.... Then you have to take into account that we still have a report, as the air is not fully expanded at the muzzle.... If the muzzle pressure is only 10 bar (145 psi), and we go back to the calculator, the maximum energy in the 3.75 cc of 1200 psi air is only 26 FPE if the expansion is Adiabatic.... It would be impossible to get that much energy in the pellet, and still accelerate the air in the barrel at the same time.... If you use Isothermal expansion, there is plenty of energy to go around, however.... and the efficiencies come back to what we are used to....

Going back to Lloyd's calculator, and setting it up to emulate the performance of my QB79, using Isothermal expansion, requires a efficiency factor of 72%.... If I use Adiabatic expansion, it can only work if the efficiency is set to 100%, and then only barely....  I'm not saying the expansion is 100% Isothermal.... but I'm willing to bet it's not 100% Adiabatic, either....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Bill G on March 25, 2016, 11:37:08 PM
WOW!  I go away for a few weeks and you get all kinds of crazy velocity.  Hope to catch up over this long weekend.  Lloyd that was nicely done. 

Bill G
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 26, 2016, 01:20:28 AM
....  I'm not saying the expansion is 100% Isothermal.... but I'm willing to bet it's not 100% Adiabatic, either....

Bob
It is somewhere in between. As long as it's not over 100% efficiency, I'm happy.  :D

Is the post reg volume exactly 3.75cc?

13ci, 3000psi, 70F=1.80096moles

13ci, 1100psi, 70F=0.66035moles

1.80096-0.66035=1.14061moles

3.75cc, 1200psi, 70F=0.01268moles/shot

1.14061/0.01268=90 shots

I guess you are right!
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: K.O. on March 26, 2016, 01:56:32 AM
...
It will be interesting to see which way applying the VanDerWaals corrections takes us.... ie which is more important the lower density at high pressure, or greater pressure loss during the shot, compared to an Ideal gas.... or if they pretty much cancel out?....

Bob
Bob,

Isn't that backwards once you get over about 2000psi?

Looking at your earlier graph:
(http://i378.photobucket.com/albums/oo221/rsterne/Important/IdealGases_zps796cc652.jpg)

It will result in the model showing a higher than expected air mass at pressures over 3500psi. So that reduces the velocity estimate.

However, with the correction, air at 2000psi is wanting to take up a larger volume than an ideal gas. As the 4500psi dump chamber depletes, the pressure will not be falling off as fast as we originally predicted. So that increases the velocity estimate.

As you suggested, maybe it will still be a wash. It could end up balancing out to be the same with or without VanDerWaals correction.

Guessing what happens with an infinite or very large dump chamber should be easy:

An infinite dump of 2000psi could use an air mass multiplier of about 93%. - higher velocity than ideal gas.

An infinite dump chamber of 3500psi air needs no correction. - velocity as predicted

An infinite dump of 4500psi might need an air mass multiplier of about 109%. - velocity lower than ideal gas

An infinite dump of 6000psi might need an air mass multiplier of about 125%. - not good for performance

So am I wrong in seeing a heavy powerful (low repulsive) charge tapering to a faster lighter(higher repulsive) charge leading back to a slower an lighter charge (low repulsive) as the pressure drops...

 which sets up for supersonic flow thru over scavenging right as the pressure start dropping to about 1500-1000 psi..? which may set up conditions for a shockwave once super sonic flow at the throat collapses..?

But even if that is not happening with the break away is now closer to a rupture disk; enough that the pellet is much closer to riding a shock wav..?

Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: K.O. on March 26, 2016, 02:25:24 AM
I think I will ask my daughter to take a look at this paper and see what she thinks?

http://www.sciencedirect.com/science/article/pii/S0895717709003367 (http://www.sciencedirect.com/science/article/pii/S0895717709003367)
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 26, 2016, 12:33:49 PM
The post reg. volume is about 15 cc, the 3.75 cc is the amount of 1200 psi air used per shot....

Sorry, K.O., I don't know what a high or low "repulsive force" is.... nor do I understand how a pellet can "ride a shockwave".... You did see that graph was drawn for a specific reason, to show how air density at higher pressures compares to 3000 psi, right.... and that is was mis-labelled.... The correct graph is in reply # 291....

Bob
Title: 1640fps vs 2000fps
Post by: Scotchmo on March 26, 2016, 04:40:09 PM
You guys have got me laying awake half the night trying to wrap my head around this stuff. The following is a part of a follow up post that I put over on the yellow. There are some smart people over there as well. Their discussions don't usually have the same businesslike "air" ;D, as I see on the GTA. And those discussions fall off fairly quickly on the yellow.
----------------------------------

v = 172* sqrt(Q/(m+Z*Q))

I looked into the origins of that equation. It balances. It makes sense as far as the math goes and as far as the underlying formulas. Very clean/elegant with a maximum possible velocity as a result. Presently, I can't find anything wrong with it. But, the implications are difficult to accept. In the image below, the top view represents what I imagine would need to occur.

1) The equation has no time or distance required for acceleration. All air in the tank is at V(0). Any acceleration would be in the barrel side of the transition where is must already be at 1640fps.

2) when pellet mass goes to zero, pressure and barrel length become irrelevant. The air will always reach 1640fps, even with no barrel length, and just a tiny pressure variance.

3) The three blue/red dots represents small masses of the air. They have to transition instantly from 0fps to 1640fps. How can that be possible?

(http://www.scotthull.us/photos/Misc/1640-00.jpg)

The bottom view in the prior image is my attempt at a visual representation of the tank/barrel as modeled in the spreadsheet. The air undergoes acceleration in the tank, just before entering the barrel. So we take everything else into account as best we can. Mostly driven by the same formulas as the 1640fps equation. Though using numerical integration methods. Using small divisions of the barrel in my case, and small divisions of time in other peoples models. Each (time or distance) gives approximately the same results, neither showing a hard limit as to maximum velocity. But this method also has some things with implications that don't sit well. At any moment in time there are pressure and velocity gradients throughout the system, both radially and linearly in both the tank and the barrel. To correctly model it, maybe it needs a finite element model of the fluid dynamics that are involved in the process. Way beyond me.

Zero length barrels in the spreadsheet model just causes a divide by zero error.

At this point, I'm watching test results with great interest. What happens if we eliminate all possibility of any outside energy contribution and still get air way over 1640fps? I would look for what could be wrong with the equation. My first thoughts is that we can't simply divide by 2 for the average mass of the air column. It seems the correct thing to do, but if the pressure is not homogeneous throughout the entire barrel, that can't work. Right? Who knows. I don't.

What if after taking all possible precautions, the tests stay under 1640fps? Then, I would need to resolve the fact of an air particle having instantaneous velocity of both zero and 16404fps. Maybe it really is something at the atomic/molecular level. Again - way beyond me.


Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 26, 2016, 05:33:09 PM
I saw Steve_in_NC's answer.... that the molecules are already moving at 1640 fps, and hence don't accelerate.... You are not the only one who doesn't understand this, as the logical extension of that is that if there is only 1 bar in the reservoir, when you open the valve, the molecules coming out are going at the very same speed as if there is 100 bar inside it, and don't accelerate further.... Interestingly, if you apply his formula to Lloyd's tests, they predict velocities much lower than observed.... not only for the 2031 fps test, but also for the .22 cal tests with the 23.3" barrel at over 3000 psi....

EDIT:  I had a couple of graphs posted here, and have removed them as somewhat irrelevant.... I found a thread on the Yellow that proposed Steve's equation was out by a factor of PI/4 in one term, which raises the maximum velocity to 2088 fps.... In fairness, I have therefore deleted the graphs which were based on his original equation, even though he did not choose to change it.... Here is the pertinent thread, quite brilliantly written by Herb1836....

http://www.network54.com/Forum/79537/message/1236402420/Formula+for+maximum+theoretical+muzzle+velocity+for+an+airgun- (http://www.network54.com/Forum/79537/message/1236402420/Formula+for+maximum+theoretical+muzzle+velocity+for+an+airgun-)

Steve's answer follows, and Herb1836 points out the flaw, where PI/4 is omitted from the "Q" in the numerator of the equation (but is included in the constant of 172).... thereby changing the maximum velocity to 2088 fps.... That was pointed out to Steve, and he reverted to the basic idea that 1640 fps was the absolute limit, so there could be a problem in the calculation of the average air density which he took to be Z = D/2.... The matter was left unsettled.... Therefore, I saw no point in using a flawed equation, and removed the graphs based on it.... Actually, when I work through it, I get yet another answer, of 1854 fps....  ::)

Interestingly, for that zero mass projectile, as you state, you can set the barrel length at 0.001", and the pressure to 1 psi, and you still get the same 1644 fps maximum velocity....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: K.O. on March 26, 2016, 08:23:37 PM
http://research.chem.ox.ac.uk/claire-vallance.aspx (http://research.chem.ox.ac.uk/claire-vallance.aspx)


and this says its her lecture notes...  oops pdf to large to attach.

http://vallance.chem.ox.ac.uk/pdfs/PropertiesOfGasesLectureNotes.pdf (http://vallance.chem.ox.ac.uk/pdfs/PropertiesOfGasesLectureNotes.pdf)

 Heading 5 subset compression factor
as the temp drops the pull/attractive force  gets stronger helping pull the charge out of the chamber: helps achieve supersonic flow at some point, maybe?

about riding the shock wave... and this being close to using a Rupture disk thus giving a much higher initial  acceleration... so now the chamber and pellet are acting much more like a shock tube than before...

Might have some one who reads this that understands shock tube simulators... might be close enough to do some modeling in that direction..?

Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: K.O. on March 26, 2016, 08:27:00 PM
and no did not read any but your  post(mislabeled) will go back and pay better attention... :-[  ::)
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 26, 2016, 09:37:49 PM
Another version of the thought experiment.... Start with Lloyd's test setup.... 4000 psi pushing against the back of the bullet, but assume an infinite reservoir volume.... Therefore, no matter where the bullet is in the barrel, the pressure of the reservoir remains at 4000 psi.... We will assume the temperature is a constant (initially at least)....

OK, so now put a membrane, with a mass of zero, against the back of the bullet.... release enough air to move the bullet 1% of the barrel length, and insert another mass-less membrane.... repeat this until the bullet is at the muzzle, and you have 100 packets of air, each separated by a membrane.... got the picture?....

As the bullet moves down the barrel, each packet of air, when released, will be at 4000 psi, it will be 1% long, and have the same mass.... The molecules within that packet of air will be rattling around at 1650 fps, relative to its center of mass, pushing on the membranes at 4000 psi.... However, the bullet is accelerating, and the lighter it is, the faster it accelerates.... The packet of air immediately behind it must be travelling at (nearly) the velocity of the bullet, while the one at the breech is barely moving (while it is filling).... One of two things must happen, or a combination of the two....

1. Each successive packet (which remains 1% of the barrel length long), will be filled identically, but in a shorter period of time (the flow rate out of the valve will increase)....
OR
2. If that doesn't happen then the packet of air next to the bullet must expand, and the pressure decrease (and so on, progressively, towards the breech)....
 
I would suggest that since each packet of air produced is at 4000 psi, and it is pushing on the one ahead of it (and ultimately the bullet) with that pressure, there is no reason (or mechanism) for the air in each packet to expand (at least initially).... This is condition 1.... Each packet is filled, from the reservoir, with molecules moving at 1650 fps.... As the packet in front of it accelerates away, progressively more and more of the molecules in each packet are travelling in the direction of the muzzle.... Eventually, when the bullet reaches 1650 fps, all the packets of air behind it, all still at 4000 psi, are all travelling at 1650 fps....

If the bullet has not yet reached the muzzle, now things change.... The air coming out of the valve cannot exceed the molecular velocity of 1650 fps.... In other words, the minimum time it takes to fill that 1% long packet has been reached.... However, there is still 4000 psi pushing on the bullet, accelerating it.... so as the bullet continues to accelerate, the pressure in that first packet starts to drop.... Actually, the pressure in ALL the packets starts to drop.... This is condition 2.... It's not like the valve is closed, it is still feeding air into the packet next to the breech at a constant rate.... However, the pressure between the breech and the bullet starts to decline.... It doesn't matter (for the purpose of our thought experiment) if that drop in pressure is continuous along the barrel or progressive.... The point is, that the air entering from the reservoir is NOT exceeding 1650 fps, while the force on the bullet is enough to keep accelerating it.... The air in the packet immediately behind the bullet is expanding, still being accelerated by the expanding packet behind it, and so on back to the breech.... The average pressure in the barrel is dropping, the air is entering from the reservoir at 1650 fps, and the bullet continues to accelerate well beyond that velocity, because of the expanding air behind it.... Each packet is now getting longer as the air inside it expands and the pressure drops.... The membranes are getting further apart.... The one closest to the breech is still moving 1650 fps.... so each one forward of that is moving faster than 1650 fps.... and so is the bullet, which is in front of them all, getting a push from each packet in turn.... The result is it easily surpasses 1650 fps by the time it reaches the muzzle....

If we look at the temperature of the air, since we have an infinite reservoir, the air entering the barrel stays at constant temperature.... The air in each packet, as long as it is not expanding, also stays at that temperature.... so while we are in condition 1, we have an Isothermal situation.... Once the velocity of the air exiting the valve reaches 1650 fps, we enter condition 2.... The air exiting the valve, filling the next packet, is still Isothermal.... However, the air in all the other packets is now expanding, and that is likely to be Adiabatic.... Using Lloyd's shot as the model, for the bullet to be travelling 2031 fps at the muzzle, it will be going 1650 about 28% of the way down the barrel, about 0.001 sec after launch, and will exit the muzzle at 0.0025 sec.... I would suggest only the latter part of that cycle is Adiabatic....

Now, how does this relate to reality?.... First of all, the transition from condition 1 to condition 2 will not be instantaneous but somewhat gradual.... Secondly, the velocity that the air can exit the valve may not be 1650 fps, but could be the local speed of sound (at 4000 psi about 1480 fps).... In the case of Lloyd's shot, the reservoir was not infinite, but 55 cc, so the pressure would be dropping as the bullet (and each packet of air) moves down the barrel.... The point where the pressure and speed of sound cross using Lloyd's spreadsheet is about 3500 psi, and 1400 fps, which the bullet crosses about 8" of the way down the barrel.... We could enter condition 2 at that point, and from then on, air continues to enter the barrel at the (local) speed of sound, pushing all the packets down the barrel at that velocity, and the air in each packet expands, dropping in pressure, but still accelerating the bullet to it's eventual 2013 fps.... Of course there could be other factors, such as barrel friction, fluid velocity profiles, etc.etc.... but the point of this thought experiment was to provide a mechanism whereby the velocity in each packet of air, relative to that packet, and for the first packet relative to the valve, does not exceed 1650 fps.... I think it does that rather elegantly....

Bob
Title: I think I'm on to something.
Post by: Scotchmo on March 26, 2016, 11:31:27 PM
I currently have three versions of the spreadsheet:

spreadsheet 1) - no friction losses - it generally predicts too high of a velocity

spreadsheet 2) - modest friction losses, but I know it's not quite right. It works fair for the range of values that we are working in. It is more like an "efficiency factor". - it predicts pretty close to test values

spreadsheet 3) - complete progressive friction losses - I have not been able to get this to work well. As soon as the barrel gets over about 10", it break down. I've played with constants and exponents but is always falls off too fast with longer barrels. I may have found a simultaneous solution to this and the 70F 1640fps conundrum:

Bob,

About the constant temperature air - it's not.

I have been subtracting out the fluid flow losses by reducing force on the pellet. That's fine, but where did the loss actually go? It is still in the system. It should show up as entropy production (at least the adiabatic portion). I have not modeled it yet, but I did a quick check at 3" of barrel in spreadsheet number two. The "Joke" formula predicts 1640fps at the barrel inlet, but now predicts 1687fps at three inches down the barrel. When I get time, I will attempt a new variation on the spreadsheet, with full fluid friction, and entropy production. I'll show the ever increasing 1640fps limit column which I expect will always register higher than the f=ma calcs and higher than the test results. As we move down the barrel, it's possible the 1640fps limit will grow so fast, that it will always run way ahead of the test values. So it will never be a factor.

I'm thinking that the 70F "Joke" formula is only valid at a barrel length of zero. Or at longer length, only if we assume no entropy production (i.e. inviscid flow?). Factoring entropy production allows the "Joke" formula to predict higher velocities, even with a 70F initial air source.

Note: I always wondered why my PCP guns heat up when filled from a SCUBA tank. Intuitively, I would have expected the gun to cool down from the isothermal expansion of air. But the gun heats up during filling.

I said, "I might be on to something" - or maybe not. Any thoughts?
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 26, 2016, 11:40:04 PM
The reservoir heats up because you are compressing (at least partially Adiabatically) the air that is already inside it.... while the tank you are filling from cools down from the air in it expanding (at least partically Adiabatically).... That's what I learned, anyway....

You may be onto something about the gas heating as it moves along the barrel.... I take it you don't like my "thought experiment".... *pout*.... I realize the temperature of the air is not a constant, but using that, at least in the beginning, in the above post made it (at least partially) understandable.... or at least I had hoped it made sense....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: match on March 26, 2016, 11:41:35 PM
The scuba tank cools and the air leaves it expanding - the air rifle's tank heats up as the air enters it and compresses.

The problem is this is NOT a net zero energy transfer - there are other losses and entropy to account for a total loss in energy during the transfer.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: match on March 26, 2016, 11:43:00 PM
Bob - I was editing as you were posting...
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 26, 2016, 11:44:30 PM
*LOL*

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 27, 2016, 12:06:56 AM
The scuba tank cools and the air leaves it expanding - the air rifle's tank heats up as the air enters it and compresses.

The problem is this is NOT a net zero energy transfer - there are other losses and entropy to account for a total loss in energy during the transfer.
The gun's tank is near empty. Not much air to compress. That cannot be much of a factor.

The air flowing through the fill hose is generating entropy. Enough to heat up the gun to a temperature that is much higher than the 70F SCUBA tank.

The air going into the gun's tank is expanding. But carrying lots of heat that it picked up in the process.

(SCUBA tank and gun tank) . Does the net loss end up as a net heat loss? Rather than a net heat intake as would be expected. That seems right to me.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 27, 2016, 12:20:31 AM
The air going into the SCUBA tank is flowing through a hose, but not expanding (merely slowing down when it enters the tank), and it is compressing the air already in the tank.... This is a continual process.... When you fill the tank 1/4 full, at 750 psi, the incoming air continues to squeeze that into a smaller space.... When you add another 25%, the first air is now at 1500 psi.... and hotter than before....

That's how I understand it, anyway.... If it was entropy picked up in the hose, a microbore hose would heat up a gun faster than a large diameter one, no?.... I'm betting if you open up the valve on the SCUBA tank wide open, the reverse is the case, when the gun fills faster, it gets hotter.... or rather the air has less time to cool through contact with the tube walls, and by conduction and radiation, the air surrounding it....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 27, 2016, 02:57:09 AM
I am glad you guys are willing to take on the math challenge because it is quite daunting. 
I took a shot tonight with a Teflon seal.  There was a technical difficulty and the air pressure never got high enough, but the performance was still reasonably close to what was predicted.

The projectile was long and heavy.  13.7 gns.  It needed a long stem so that the Teflon seal was deep enough into the barrel to seal properly. It is a 3-piece construction of a machined Teflon  U-cup style seal, with a 7075 aluminum head and stem, and a 7075 retention knob with a 6-32 thread  on the back end. The 3 piece construction was necessary for installing the Teflon seal.  The barrel was swabbed clean prior to firing.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/3-26-16-1688/1688-1_zps89jxqdqh.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/3-26-16-1688/1688-1_zps89jxqdqh.jpg.html)



I had a thermocouple on the breech block to monitor the fill temp.  The temperature of the breech block might have gone up a few degrees F, but that is all.
I had the projectile clamped in the breech mechanism, and started filling, and unfortunately, the retention knob slipped through the clam shell clamp at about 2500 psi.  I was disappointed at the early release. :(  BTW, By hand touch, I could not detect any temperature changes in the barrel or breech.
So here is the shot, 13.7 gn, .278 barrel, 47.5" long, 2500 psi, 55cc, 1688fps.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/3-26-16-1688/1688-2_zpsag364dfa.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/3-26-16-1688/1688-2_zpsag364dfa.jpg.html)
In the above picture, behind the chrony, you can see some plastic grocery bags sticking out of a cylindrical container. That is the bullet catcher, and it worked.
Here is the projectile after I retrieved it from the plastic bags. There were multiple layers of wad cutter circles of plastic bags on the front of the Projectile, but it remained fully in-tact.  There was no evidence of melting or fusing of the plastic bags to the aluminum front end of the projectile.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/3-26-16-1688/1688-3_zpslgnjqpa9.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/3-26-16-1688/1688-3_zpslgnjqpa9.jpg.html)

Here you can see the marks where the projectile pulled thru the retention clam shells and cut the test short.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/3-26-16-1688/1688-4_zpswaakzqe2.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/3-26-16-1688/1688-4_zpswaakzqe2.jpg.html)

Here is the projectile, after the shot, with the plastic bags peeled off. The Teflon looks perfect and the projectile is re-usable if I make a larger dia retention knob.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/3-26-16-1688/1688-5_zpslhxgvf0a.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/3-26-16-1688/1688-5_zpslhxgvf0a.jpg.html)

But even though the shot pressure was only 2500 psi, it is one more piece of data.
More refinements to the rig, and a few more HPA shots are needed before the nitrogen arrives.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 27, 2016, 12:31:51 PM
Great piece of data, Lloyd, I look forward to you trying again at higher pressure.... The fact that once again, you exceed the magic 1650 fps is interesting, because Maxwell's Demon (aka Steve_in_NC) has finally stopped using obscure language and spit it out that what you have accomplished is impossible....

http://www.network54.com/Forum/79537/message/1459063919/That%27s+a+vaguely+related+response. (http://www.network54.com/Forum/79537/message/1459063919/That%27s+a+vaguely+related+response.)

IMO, any scientist who digs in his heels behind a flawed theory, without even the curiousity, or professional courtesy, to investigate what might be happening.... but just outright rejects the facts.... isn't worth our time or effort.... It is unfortunate, as he could have so much to offer, should he not be so stubborn.... We are totally wasting our time trying to convince him.... Best we simply leave him behind, stuck at 1650 fps.... It really is a shame....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 27, 2016, 01:16:24 PM
Great piece of data, Lloyd, I look forward to you trying again at higher pressure.... The fact that once again, you exceed the magic 1650 fps is interesting, because Maxwell's Demon (aka Steve_in_NC) has finally stopped using obscure language and spit it out that what you have accomplished is impossible....

http://www.network54.com/Forum/79537/message/1459063919/That%27s+a+vaguely+related+response. (http://www.network54.com/Forum/79537/message/1459063919/That%27s+a+vaguely+related+response.)

IMO, any scientist who digs in his heels behind a flawed theory, without even the curiousity, or professional courtesy, to investigate what might be happening.... but just outright rejects the facts.... isn't worth our time or effort.... It is unfortunate, as he could have so much to offer, should he not be so stubborn.... We are totally wasting our time trying to convince him.... Best we simply leave him behind, stuck at 1650 fps.... It really is a shame....

Bob
It is unfortunate that our friend on the other forum chooses not to enter into this discussion in a constructive manner.   He is very intelligent and could certainly help explain what is happening, and his contributions would be appreciated by the entire airgun community.  Who knows, maybe he already has the explanation, but just chooses not to share it.   :-\   
A boss I once had used to say, "when your wagons are in a circle to protect your position, no forward progress can be made."  I am glad that our wagons are not in a circle.

Your explanation of the molecular speed being additive to the moving column of air in the barrel, seems most plausible to me.  Similar to cannon fire from a fighter jet.  The projectile speed is equal to the cannon MV plus the speed of the plane. Not only is that explanation plausible, but it is palatable, too.    ;)
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 27, 2016, 01:31:07 PM
In the words of the immortal Buzz Lightyear.... "To Infinity and Beyond !"

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Michael Loar on March 27, 2016, 02:00:34 PM
Lloyd and Bob
I agree with both of you in that it is indeed a shame the he (Steve) cannot or will not accept that theory is in fact just that and only serves as an example of where to start or design from not cold hard facts or a impassible boundary that is set in stone. The mere fact that the 1650 fps threshold has been broken with very well defined and proven data should in itself be sufficient to get him at the very least curious as to whether his math and calculations are incorrect or flawed in some respect.

The example of a fighter plane and its cannon fire is evidence and highly proven fact that indeed any projectile is not limited to a velocity of 1650 fps since if that were the case cannon fire out of a fighter jet moving at only 1650 fps with the jet at Mach 2 or above would never leave the barrel of the cannon or if it did the plane would be running into it own projectiles in flight. Then you have PB guns shooting at close to 4000 fps in this day and age so how are we stuck at 1650 fps as an impassible velocity.

Being no engineer or even much of a math guy other than simple measurements and basic formulas I still realize that nothing ever ventured is nothing gained and to say its impossible just drives those who want to know even harder to disprove that statement. It is a true shame that he cannot/will not join those that are only trying to improve and expand or hobby/sport to the fullest and most rewarding that it can be for all who care to enjoy and learn from other like minded individuals.

I myself know that without those of you here that put countless hours into the experiments and research that you do at considerable costs in money and time would be far less knowledgeable and have more struggles with my projects and not enjoy the fruits of my labor near as much as I do now all thanks to those of you who give so much of your time and money to help improve this for the rest of us.

I thank you all very much.

Now Lloyd I want to see you break Mach 2 with your new design projectile as I have all the faith it can be done. Its not a matter of IF but WHEN it happens.

Mike
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 27, 2016, 03:03:22 PM
I thought it might be helpful to show where we are for modelling what happens inside a PCP at the present time.... This is what I get using Lloyd's current (J4) version of his PCP Internal Ballistics Spreadsheet, set up to analyze his current test gun.... To recap, the barrel is .278" bore, 47.5" long, and fed with a 55 cc chamber.... The solid lines are the projected maximums, at the pressures stated, using an infinite reservoir, no bore drag, but including the mass of the air used to create the shot.... The dotted lines represent the best model I have of what he is accomplishing, using the 55 cc reservoir at 4000 psi, 1 lb. of bore drag, and 70% overall efficiency....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Lloyds%20Maximum_zpszgwg7ad2.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Lloyds%20Maximum_zpszgwg7ad2.jpg.html)

Both graphs are plotted vs. the weight of the projectile (in grains).... It predicts that at 4000 psi, we would need a projectile down around 4 gr. to hit Mach 2.... That is less than half the weight of the lightest tested so far.... Further increases in pressure will have some effect, while increases in reservoir size, at this point, have nearly no effect.... Changing to Nitrogen should produce a slight gain.... I think that reaching Mach 2 (2250 fps) is possible, with this test gun.... but it won't be easy, even with Nitrogen.... Helium, of course, would move us up towards Mach 3....  :o

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 27, 2016, 04:05:54 PM
Here is the diagram that the 1647 fps speed limit for air at 20*C is based on.... from  http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c4 (http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c4) .... 502 m/s = 1647 fps....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Velocity%20Distribution_zps1r9qixn2.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Velocity%20Distribution_zps1r9qixn2.jpg.html)

The V rms value of 1647 fps, as you can see, is not the velocity of all the molecules, it is the Root Mean Square average.... Many molecules are going faster, and many slower.... some are going over twice that speed.... If those are the ones colliding with the projectile, surely it could be accelerated well past 1647 fps.... As I said several years ago, when I saw that first shot at over 1700 fps, maybe it only takes a FEW, pushing on the pellet to create the speeds we are seeing.... That first 1705 fps shot was something like 3% efficient, based on the total volume of air released, IIRC....

It may be nothing more startling than the barrel FOCUSING the fast air molecules down the middle, while the stragglers get left behind along the edges of the flow.... The sum of all the velocities is under the 1647 fps RMS value.... but the fast molecules in the center still have enough push left to propel the pellet well over 2000 fps.... Other, more complicated, or elegant solutions may be the answer to what is taking place.... but having the velocity profile inside the barrel focusing the fast molecules down the center to accelerate the bullet may be all it takes to keep everyone happy.... Think of the barrel as Maxwell's Demon directing traffic if you like.... The detailed explanation of how and why can come later....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rgb1 on March 27, 2016, 09:24:29 PM
I tried seven years ago to gently show the troops on the YF that the proposed
1650 limit was nonsense because the thinking behind it was faulty. Made a
post showing several pressures and associated speeds, the highest was
1800+..........it was ignored. Oh well, maybe Lloyd finally has his attention.

                                                                                      Ron
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 28, 2016, 01:41:37 AM
Lloyd's test's were certainly the impetus for me looking at it more closely.

I think that Steve over on the yellow forum will come around. He is smart. I'm not always the best at explaining, so I'm taking several approaches. I'm hoping he gets that moment where:
(http://jeffnielsen.com/wp-content/uploads/2014/07/aha-moment.jpg)

On this forum, I have not detailed all of my recent thinking, since it's "preaching to the choir". But if your interested, follow this thread:
http://www.network54.com/Forum/79537/thread/1459019853/last-1459138839/Expand+Thread (http://www.network54.com/Forum/79537/thread/1459019853/last-1459138839/Expand+Thread)
Title: Spreadsheet addition
Post by: Scotchmo on March 28, 2016, 02:11:20 AM
If you are using an % efficiency in your spreadsheets, here is something you may want to add:

My spreadsheet accounts for the adiabatic expansion which is significant with small reservoirs. So there can be a significant temperature drop. I have a column showing that.

What about the % loss (1-%efficiency) or flow losses? We know that losses are mostly heat. So we could include it as entropy production.  My flow loss compensation does not work any better than your efficiency compensation, so just use % losses. Convert it to heat and add it back into the process at each step. Rather than get a temperature drop, you will likely see a net temperature rise.

Now make a new column with v(max) showing v(max) = 172 194 * sqrt(Q/(m+Z*Q)). Base Z on the new temperature at that point in the process.

The v(max) column will always be a larger value than your predicted velocity. So you never actually violate that formula.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 28, 2016, 07:47:36 AM
If you are using a % efficiency in your spreadsheets, here is something you may want to add:

My spreadsheet accounts for the adiabatic expansion which is significant with small reservoirs. So there can be a significant temperature drop. I have a column showing that.

What about the % loss (1-%efficiency) or flow losses? We know that losses are mostly heat. So we could include it as entropy production.  My flow loss compensation does not work any better than your efficiency compensation, so just use % losses. Convert it to heat and add it back into the process at each step. Rather than get a temperature drop, you will likely see a net temperature rise.

Now make a new column with v(max) showing v(max) = 172 * sqrt(Q/(m+Z*Q)). Base Z on the new temperature at that point in the process.

The v(max) column will always be a larger value than your predicted velocity. So you never actually violate that formula.
Scott,
Yes, I see that I have changes to make to my spreadsheet, beyond the VanDerWaals conversion that is in-process.

Thank you again for presenting this information to folks over on the yellow.   You have managed a difficult task very well, and presented some intriguing new thoughts about what is happening inside the airgun .  I had not considered much of what you discussed.
Thank you.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 28, 2016, 08:36:29 AM
Latest test shot data as of 28 March 2016

Here is a spreadsheet of the last 8 of the 59 high velocity shots that I have taken.  It includes 2 new shots that I took last night.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MaxVel%20Ver2/-3-27-16_zps7mwr3ra3.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MaxVel%20Ver2/-3-27-16_zps7mwr3ra3.jpg.html)

A couple of things about the spreadsheet: 
Shot number 52, 1745 fps at 4500psi, 7.5 gn, .22 cal, 23.3" barrel, is what I am calling the baseline shot.  It is the first shot that significantly exceeded the 1640fps velocity limit.  The column labeled "predicted velocity" is calculated using my spreadsheet with a 70% efficiency factor and a 1 pound pellet drag.
I think it is significant, that in 6 of the next 7 shots, the velocities were within an average of 1.3 percent of the predicted velocity.   The one slow shot was an anomaly because it failed at the clamping point and "self launched" with the propulsion air essentially going through a .155 dia orifice.

Here are the 7 latest significant shots:
1745 fps, .22 cal, 7.5 gn 4500psi, 23.3" barrel
1714 fps, .22 cal, 7.5 gn, 4500psi, 23.3" barrel
1802 fps, .278 cal, 15.3 gn, 3500psi, 47.5" barrel
2031 fps, .278 cal, 9.1 gn, 4500psi, 47.5" barrel
1688 fps, .278 cal, 13.7 gn, 2500psi, 47.5" barrel
1884 fps, .278 cal, 13.7 gn, 3700psi, 47.5" barrel
1938 fps, .278 cal, 10.3 gn, 4000psi, 47.5" barrel

In the .278 cal, the first 2 shots used an o-ring seal and the last 3 shots used Teflon seals in a clean, dry, bore. The Teflon seals weigh about 1.2 grains more than the o-ring seals and make it difficult to keep the weight of the projectile low.  Also of significance is the fact that shots are all so close to the predicted velocity, regardless of the type of seal.  One might surmise that the seal friction and resulting drag, along with any aspect of combustion of the Buna-n o-rings are rather insignificant. 

Next order of business before the nitrogen is utilized, is figuring out a way to make the projectile lighter weight.  The last projectile was only 10.3 gns, but it really needs to be closer to 8 grains.

Here are  pics of the last last 2 shots, 1884 fps and 1938 fps.

(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MaxVel%20Ver2/1884%20shot_zpsjtdkah4o.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MaxVel%20Ver2/1884%20shot_zpsjtdkah4o.jpg.html)

(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MaxVel%20Ver2/1938%20shot_zpsvbtj4mty.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MaxVel%20Ver2/1938%20shot_zpsvbtj4mty.jpg.html)



Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: MichaelM on March 28, 2016, 09:38:42 AM
I remember a few years ago watching some college kids launching ping pong balls through several pop cans using a setup that that placed the barrel in vacuum and then using relatively low pressure filling the pressure chamber with air till a thin layer of plastic ( like garbage bag thin) burst sending a ping pong ball with enough velocity to blow right through soda cans ....... theory being the vacuum pulled the projectile while the pressure pushed it to reach speeds......

at the sake of sounding ignorant(which I mostly AM when it comes to this type of maths) could something like this be happening to help with the velocities???? wouldn't the atmospheric pressure in the barrel be at a relative vacuum to the pressure chamber making for a lot more force being applied to the projectile both pulling and pushing????


sorry if thats been covered.... I will admit I glossed over a few pages in this thread as the maths was making my eyes go a bit crossed at a few points LOL!!
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: 39M on March 28, 2016, 09:43:10 AM
Could you not drill out the inside of the bolt to lighten it?
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: 39M on March 28, 2016, 09:50:53 AM
Don't have a formula or graph, but I'd guess that exceeding the threshold is accomplished by changing the environment through a higher pressure than which the threshold was originally theorized.
Just as we have a so called constant speed of gravity on earth, if the mass of the gravitational force were increased so would be the speed of gravity.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 28, 2016, 10:49:33 AM
I remember a few years ago watching some college kids launching ping pong balls through several pop cans using a setup that that placed the barrel in vacuum and then using relatively low pressure filling the pressure chamber with air till a thin layer of plastic ( like garbage bag thin) burst sending a ping pong ball with enough velocity to blow right through soda cans ....... theory being the vacuum pulled the projectile while the pressure pushed it to reach speeds......

at the sake of sounding ignorant(which I mostly AM when it comes to this type of maths) could something like this be happening to help with the velocities???? wouldn't the atmospheric pressure in the barrel be at a relative vacuum to the pressure chamber making for a lot more force being applied to the projectile both pulling and pushing????


sorry if thats been covered.... I will admit I glossed over a few pages in this thread as the maths was making my eyes go a bit crossed at a few points LOL!!
Hi Michael,
The vacuum on the ping pong ball keeps coming up but I never did the math on it to see what was going on.   ::)  If you pull a vacuum in front of the ping pong ball you really are just applying a pressure of about 14.5 psi (atmospheric pressure) behind it.  The PP ball weighs 2.7grams = 41.7 grains.  The caliber is 1.575.   If you use a 24" long tube/barrel you have the equivalent of a 766cc tank in front of the PP ball.
Doing the math with my spreadsheet, because the PP ball is so light compared to its caliber, at the end of the  24" barrel, it should be going about 460 fps.  You better be about 20 feet back from the table because that is a 313 mph serve!  :o
Basically, it is 1.575 cal, 41.7 gn, 766 cc dumptank at 14.5 psi, using a reasonable 60% system efficiency, gives you 460 fps.  Unfortunately, adding that extra 14.5 psi on top of 3,000 or 4,000 psi in a regular pcp, wouldn't be noticeable.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: match on March 28, 2016, 11:01:38 AM
I would go back to the Buna-n O-ring projectile and just make sure to clean the barrel well after each shot.

A very light lube would help in the cleaning - it should not have much effect on the actual velocity. 
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 28, 2016, 11:41:48 AM
After I get the nitrogen, I will be switching back to a size 007 o-ring, possibly Aflas in an 80 duro.

I also have to re-do the breech end of the barrel.  While deburring the entrance to the breech, I managed to get it oversized several thou for about a half inch.  The tube material was softer than I am used to.  That is why some of the projectiles were so long.  They needed to reach in past the oversized bore to get to the proper diameter for sealing.   
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 28, 2016, 12:42:49 PM
I have to take my hat off to Scott for suggesting that the missing 30% is changing to heat, and offsetting, or even reversing, the Adiabatic losses during the shot.... I agree that the spreadsheets could be revised to take into account this effect, predicting the temperature at each increment.... I would like to point out that not only does Z change according to temperature, but also it is not a linear function relative to pressure because of the VanDerWaals effect.... In fact, at 6000 psi, the air density is 20% less than predicted by Boyle's Law.... I have been looking at that the past couple of days, and when used in Steve's formula (the 172 constant is incorrect because of a missing PI/4 term in the numerator), it raises the predicted maximum velocity, and the higher the pressure, the more the effect....

The correct constant in the above equation is 194, but the value of "Q" must then be changed to include PI/4, with Q being the actual volume of the barrel (CI) times the pressure (PSIA).... In addition, as I mentioned, "Z" decreases as pressure increases, although we can ignore it below 3000 psi, as the error at the pressure is only about 4%, increasing to 13% at 4500 psi and 20% at 6000 psi.... I have a version of the equation where "Z" is calculated from the equation of an Excel Trendline fo a plot of Density vs Pressure....

While doing the detailed calculations in increments (ie spreadsheet integration) is the proper way, I think a quick estimate of the amount of heat generated by that 30% loss in energy (conversion to heat) is in order, and then using the specific heat of air at pressure, it should be possible to calculate the temperature rise.... I am NOT that familiar with Thermodynamics, but hope to get a rough idea of the magnitude of that effect later today....

Oh, and Lloyd, congratulations on two more high speed shots.... I didn't mean to lose your real-world accomplishments in the shuffle....  ::)

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Bill G on March 28, 2016, 01:30:09 PM
If at any point a person has decided that they are the smartest guy in the room, they would be well advised to find another room.  multiple smart minds are greatly better than one smart mind.   Uhhhhh, that's why we all started coming to forums....... remember?  I do. 

I think this has officially moved from trying to disprove that a limit exists to where is the limit?(on HPA of course)

Bill
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: MichaelM on March 28, 2016, 01:34:31 PM
I remember a few years ago watching some college kids launching ping pong balls through several pop cans using a setup that that placed the barrel in vacuum and then using relatively low pressure filling the pressure chamber with air till a thin layer of plastic ( like garbage bag thin) burst sending a ping pong ball with enough velocity to blow right through soda cans ....... theory being the vacuum pulled the projectile while the pressure pushed it to reach speeds......

at the sake of sounding ignorant(which I mostly AM when it comes to this type of maths) could something like this be happening to help with the velocities???? wouldn't the atmospheric pressure in the barrel be at a relative vacuum to the pressure chamber making for a lot more force being applied to the projectile both pulling and pushing????


sorry if thats been covered.... I will admit I glossed over a few pages in this thread as the maths was making my eyes go a bit crossed at a few points LOL!!
Hi Michael,
The vacuum on the ping pong ball keeps coming up but I never did the math on it to see what was going on.   ::)  If you pull a vacuum in front of the ping pong ball you really are just applying a pressure of about 14.5 psi (atmospheric pressure) behind it.  The PP ball weighs 2.7grams = 41.7 grains.  The caliber is 1.575.   If you use a 24" long tube/barrel you have the equivalent of a 766cc tank in front of the PP ball.
Doing the math with my spreadsheet, because the PP ball is so light compared to its caliber, at the end of the  24" barrel, it should be going about 460 fps.  You better be about 20 feet back from the table because that is a 313 mph serve!  :o
Basically, it is 1.575 cal, 41.7 gn, 766 cc dumptank at 14.5 psi, using a reasonable 60% system efficiency, gives you 460 fps.  Unfortunately, adding that extra 14.5 psi on top of 3,000 or 4,000 psi in a regular pcp, wouldn't be noticeable.
Lloyd

yea I have seen the ones where they basically just apply a vacuum to the tube and pop one side using just the atmo pressure of 14.5 psi... this is the video I am referring to.... where they add a converging
/diverging nozzle (venturie?) and a presurrized air chamber behind it and achieve supersonic speeds... *(&^ even if its not applicable it sure is impressive lol https://www.youtube.com/watch?v=YYNCGZCul1Q (https://www.youtube.com/watch?v=YYNCGZCul1Q)


dunno.. lol its obvious that extreme velocities are possible seems everyone is just trying to understand HOW it works lol... frankly my vote is magic....... :)
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 28, 2016, 01:58:34 PM
Don't have a formula or graph, but I'd guess that exceeding the threshold is accomplished by changing the environment through a higher pressure than which the threshold was originally theorized.
Just as we have a so called constant speed of gravity on earth, if the mass of the gravitational force were increased so would be the speed of gravity.

That was my first intuition, and it's very close. But this is what it is:

"...exceeding the threshold is accomplished by changing the environment through a higher pressure temperature than which the threshold was originally theorized."
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 28, 2016, 02:04:52 PM
If at any point a person has decided that they are the smartest guy in the room, they would be well advised to find another room.  multiple smart minds are greatly better than one smart mind.   Uhhhhh, that's why we all started coming to forums....... remember?  I do. 

I think this has officially moved from trying to disprove that a limit exists to where is the limit?(on HPA of course)

Bill
Smart is good, but being the smartest doesn't always get you there.

Be open minded and use impeccable logic. You either come up with the right answer or can admit that it is beyond your current knowledge base. Use logic, increase your knowledge base, and - AHA!
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 28, 2016, 02:10:21 PM
OK, here is the back of the napkin calculation for the temperature rise of the air in Lloyd's 2031 fps shot (but with infinite reservoir, and therefore constant pressure), assuming the 30% loss in efficiency all changes to heat.... I would appreciate it if someone will double check my method and calculations.... First, the shot criteria used in Lloyd's J4 Spreadsheet....

Pressure = 4000 psi, 9.1 gr. bullet, bore = 0.278", barrel length = 47.5", 1 lb. bore drag, 70% efficiency, air mass included, Isothermal expansion (because of dump shot and infinite reservoir).... Predicted velocity 2049 fps, energy = 84.85 FPE....

Change bore drag to 0, and efficiency to 100%, no other changes.... Predicted velocity 2459 fps, energy = 122.16 FPE.... Energy lost to heat = 122.16 - 84.85 = 37.31 FPE....

Using the calculator at Peacesoft for the properties of air at 4000 psi and 20*C.... http://www.peacesoftware.de/einigewerte/calc_luft.php5 (http://www.peacesoftware.de/einigewerte/calc_luft.php5)

Air density = 302.45 kg/m^3
Specific Heat Capacity = 1.343 kJ/kg.K
Multiplying those together gives 302.45 x 1.343 = 406.2 kJ/m^3.K .... ie it would take that much energy to raise the temperature of 1 m^3 of air at 4000 psi by 1 deg. K....

Barrel volume is 0.278^2 x PI/4 x 47.5 = 2.883 in^3 x 16.39 = 47.25 cc = 0.00004725 m^3
Multiply that by the energy per degree above, and we get 406.2 x 0.00004725 = 0.0192 kJ/*K, or 19.2 joules.... which is 14.2 FPE....
We have 37.31 FPE available, so dividing 37.31 / 14.2 = 2.63*K, which is 4.7*F.... The energy available in the 30% loss of efficiency would raise the temperature of the air in the barrel by less than 5*F.... It would appear that is nowhere near enough to account for any significant increase in the molecular velocity.... As I said, someone please double check my numbers....

It is interesting to note that if we calculate the theoretical maximum FPE for Lloyd's test gun at 4000 psi, neglecting the mass of the air, we get 961 FPE, as follows....

Bore area = 0.278^2 x PI/4 = 0.0607 in^2 x 4000 psi = 242.8 lbs x 47.5 / 12 ft = 961 FPE....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 28, 2016, 03:21:28 PM
.... The energy available in the 30% loss of efficiency would raise the temperature of the air in the barrel by less than 5*F.... It would appear that is nowhere near enough to account for any significant increase in the molecular velocity.... As I said, someone please double check my numbers....

It is interesting to note that if we calculate the theoretical maximum FPE for Lloyd's test gun at 4000 psi, neglecting the mass of the air, we get 961 FPE, as follows....

Bore area = 0.278^2 x PI/4 = 0.0607 in^2 x 4000 psi = 242.8 lbs x 47.5 / 12 ft = 961 FPE....

Bob
I made the same error at first. You used just the pellet. The air must also be included. So it's 30% of total energy.

The heat gain is 30% of 961fpe (0.37btu). And the highest concentration of that gain is directly behind the pellet.

The following picture is an attempt to visually show what is happening. The actual temperature rises will be different. But you get the picture:
(http://www.scotthull.us/photos/Misc/1640-01.jpg)
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 28, 2016, 04:21:23 PM
I wondered about that (why I mentioned the theoretical maximum).... but in fact a very large portion of that 961 FPE ends up being the KE of the air being blasted out the muzzle, right?.... Even if that was correct, we would have 30% of 961 FPE = 288 FPE / 14.2 FPE/*K = 20.3*K, which is less than 37*F increase.... The molecular velocity of air at 40.3*C is still only 1703 fps.... To reach 2000 fps, you need an air temperature of 160*C, way above the boiling point of water.... I still think that simple "focusing" of the faster molecules by the velocity gradient is the reason, or some/most of it.... Can we really explain more than a 140*C rise in temperature?....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 28, 2016, 05:27:39 PM
I wondered about that (why I mentioned the theoretical maximum).... but in fact a very large portion of that 961 FPE ends up being the KE of the air being blasted out the muzzle, right?.... Even if that was correct, we would have 30% of 961 FPE = 288 FPE / 14.2 FPE/*K = 20.3*K, which is less than 37*F increase.... The molecular velocity of air at 40.3*C is still only 1703 fps.... To reach 2000 fps, you need an air temperature of 160*C, way above the boiling point of water.... I still think that simple "focusing" of the faster molecules by the velocity gradient is the reason, or some/most of it.... Can we really explain more than a 140*C rise in temperature?....

Bob

Yes. We can't determine the exact peak temperature within the column of air without an exact model of the viscous shear. But we can easily speculate that it will be higher than the average temperature rise. And it will occur at the base of the pellet.

Imagine a 1 grain-mole (mole=chemical term for amount) cylinder of air that will travel down the barrel. It gains entropy in the first inch of travel down the barrel. It moves into the second inch of the barrel, gaining more entropy. It makes room for another grain-mole to enter the barrel and gain entropy. At this point in time, the first grain-mole to enter the barrel has gained twice as much as the second grain-mole. 2/3 of the heat gain is in the first grain-mole. The first grain-mole is right behind the pellet.

It’s not that simple as the air is accelerating, heating, and expanding faster than the air that comes later. The grain-mole cylinder of air immediately behind the pellet will be longer than the grain-mole of air just entering the barrel. I'm not sure yet how that will affect my numerical integration which models the process as small fixed length segments of barrel.

I think we have an integral within an integral.

I did not check your math, so I can’t say if the 37F rise is correct. But I say that the temperature rise of the air behind the pellet will be at least twice that of the average temperature rise.

Note: We will never be able to actually measure the peak temperature since it happens in the last microsecond before the pellet exits. And then it's gone.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 28, 2016, 05:29:12 PM
This is a very interesting puzzle.  I can see both possibilities:  heating the air to increase the molecular speed, and the focusing of the molecular movement toward the path of least resistance: the muzzle of the barrel. 
Scott, I see the hot leading edge of the air, basically in contact with the projectile.  The way heat energy manifests itself is very varied.  I normally think of something getting hot as a fairly slow and deliberate process, with solid evidence that an object got hot.  I don't tink of heat as being instantaneous in its happening and dispersing.  I watched a youtube experiment where they smacked two 1-1/2" ball bearings together.  One bearing in each hand, smacked together, and they came to a more or less dead stop.  The question was: Where did the kinetic energy go?"  The answer was: heat.   They smacked the balls together again but this time with a piece of paper between them.  afterwards, looking at the paper, it had a tiny hole at the collision point, with an almost invisible charred edge, and a burnt smell.  There was really no sensation of heat being produced in a conventional sense, but obviously all of that energy was converted to heat.

If there is heating of the air directly behind the pellet, maybe it is something similar: very quick, and then gone.  It requires a paradigm shift in my thinking if that is indeed the case.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 28, 2016, 05:42:13 PM
This is a very interesting puzzle.  I can see both possibilities:  heating the air to increase the molecular speed, and the focusing of the molecular movement toward the path of least resistance: the muzzle of the barrel. 
Scott, I see the hot leading edge of the air, basically in contact with the projectile.  The way heat energy manifests itself is very varied.  I normally think of something getting hot as a fairly slow and deliberate process, with solid evidence that an object got hot.  I don't tink of heat as being instantaneous in its happening and dispersing.  I watched a youtube experiment where they smacked two 1-1/2" ball bearings together.  One bearing in each hand, smacked together, and they came to a more or less dead stop.  The question was: Where did the kinetic energy go?"  The answer was: heat.   They smacked the balls together again but this time with a piece of paper between them.  afterwards, looking at the paper, it had a tiny hole at the collision point, with an almost invisible charred edge, and a burnt smell.  There was really no sensation of heat being produced in a conventional sense, but obviously all of that energy was converted to heat.

If there is heating of the air directly behind the pellet, maybe it is something similar: very quick, and then gone.  It requires a paradigm shift in my thinking if that is indeed the case.
Right on.

The heating is happening at the molecular level inside of the air. It is not flowing into the air. It is an instant heat increase. Some of that heat may flow back toward the start of the barrel, or into the barrel wall. But the shot cycle is fairly brief so not much time for that to happen. I would assume that virtually all of the heat stays in the air, exactly at the point where the entropy gain takes place.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 28, 2016, 05:55:27 PM
Scott, you made reference on the Yellow to the importance of integrating the addition of air to the system, instead of just using half the mass of the filled barrel.... To illustrate this, I used Steve's formula (modified to include the omitted PI/4 term, with the corrected constant), and compared it to the output of Lloyd's J4 Spreadsheet.... I used the criteria for Lloyd's 2031 fps shot (.278 cal, 9.1 gr. pellet, 4000 psi), and varied the barrel length.... For Lloyd's spreadsheet, that would provide a prediction of the MV if you progressively shortened the barrel (only)....  Here are the results....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Steve%20Bob%20and%20Lloyd%20vs%20Length_zpsmzlys12m.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Steve%20Bob%20and%20Lloyd%20vs%20Length_zpsmzlys12m.jpg.html)

Steve's equation, when corrected as above, predicts a maximum velocity of 1854 fps at zero projectile weight (instead of 1643).... You can see that without the integration being performed at intervals, my (Steve's) equation predicts too low a maximum velocity at longer barrel lengths, just as you suggested.... the proof being that Lloyd was able to exceed them.... In other words, you can't simply use half the total amount of air in the barrel to calculate the mass, and the error increases with barrel length.... in agreement with your statement that his equation may only be useful at zero barrel length.... Even so, when corrected, it would predict 1854 fps, not 1643, with zero projectile weight....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 28, 2016, 07:12:51 PM
I have some new theories of my own.

1) The 1640 1854fps 70F limit is correct for freely expanding air. efficiency = 100%

2) In a barrel, there are losses. efficiency < 100%

3) The entropy gain raises the limit to >1640 1854fps

4) When further entropy_gain = kinetice_energy_gain. efficiency = 50%

5) At 50% efficiency, the pellet is no longer accelerating.

6) 1640 1854fps/50% = 3280 3708fps

7) That happens at a barrel length of infinity.

Lloyd, If you attempt to prove that wrong, you've got your work cut out for you.  ;D
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 28, 2016, 07:47:03 PM
Gee, I think I heard that idea of a maximum of 3300 fps somewhere before.... *grin*.... both in my "thought experiments", and in the trend in the graphs in post #326....
Quote
Lloyd, If you attempt to prove that wrong, you've got your work cut out for you
and that's no joke.... sonic or otherwise....  ;D

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 28, 2016, 08:25:37 PM
Bob, Lloyd, et al,

My new theory is the result of a "thought experiment" that has been running through my head.

The missing piece of the experiment was entropy. No one seemed to be seriously considering it. The only way to ignore it is to let the air expand freely, without entropy production. Without the barrel, the 1640 1854fps works. If we are talking about airguns, you need a barrel. As a barrel gets longer and longer, the entropy production raises the limit, but also reduces the efficiency. The falling efficiency makes it that much harder to accelerate the pellet. Longer and longer barrels give diminishing returns. At some point it should stop accelerating. The efficiency keeps falling but will never quite reach a low of 50%. So you keep extending the barrel. Eventually you reach infinity and finally 50% efficiency.

I'm talking about overall efficiency that includes kinetic energy of the gas. Actually, the pellet mass can drop out for this thought experiment.

70% efficiency is still a ways away from 50%. How far are we willing to venture down an infinite path?

47.5" is far enough to satisfy my curiosity. Plenty of length to explore and keep us occupied.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 28, 2016, 09:54:33 PM
I can understand your argument about the 50% efficiency being a reasonable limit.... equal parts heat and kinetic energy.... Connecting the dots from there to doubling the velocity I'm having a little more trouble with.... Energy is proportional to velocity squared, half the energy (efficiency?) would be 0.707 of the velocity.... That might yield 1647 / 0.707 = 2330 fps.... and I'm not sure that can't be surpassed.... starting with air at 70*F, given enough pressure, reservoir, and barrel length, and a light enough bullet....

I'm not sure there is any way to prove this, one way of the other.... even on a theoretical basis.... For sure it is above my pay grade....  ::)

All we know for sure, is that 1647 fps isn't the limit.... nor is 2000 fps.... If we can get a light enough bullet, at 6000 psi, I think we will put Mach 2 behind us as well, with Lloyd's current setup.... Doubling the barrel length again might give us another 10%.... or not, depending on if/when we start losing efficiency as you are predicting.... Realistically, if we put Mach 2 behind us, I think it's time to quit.... at least for now....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 28, 2016, 10:21:27 PM
I am very confused. 
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 28, 2016, 10:28:53 PM
Just a short PS.... For the molecular velocity to reach 3280 fps requires a temperature of about 900*C.... Aluminum melts at 660*C.... the equivalent velocity of air molecules is 2940 fps....

I'm afraid I am too, Lloyd....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 29, 2016, 12:00:02 AM
I can understand your argument about the 50% efficiency being a reasonable limit.... equal parts heat and kinetic energy.... Connecting the dots from there to doubling the velocity I'm having a little more trouble with.... Energy is proportional to velocity squared, half the energy (efficiency?) would be 0.707 of the velocity.... That might yield 1647 / 0.707 = 2330 fps.... and I'm not sure that can't be surpassed.... starting with air at 70*F, given enough pressure, reservoir, and barrel length, and a light enough bullet....

I'm not sure there is any way to prove this, one way of the other.... even on a theoretical basis.... For sure it is above my pay grade....  ::)

All we know for sure, is that 1647 fps isn't the limit.... nor is 2000 fps.... If we can get a light enough bullet, at 6000 psi, I think we will put Mach 2 behind us as well, with Lloyd's current setup.... Doubling the barrel length again might give us another 10%.... or not, depending on if/when we start losing efficiency as you are predicting.... Realistically, if we put Mach 2 behind us, I think it's time to quit.... at least for now....

Bob
Bob,

You could be right about the actual velocity limit. We won't have enough energy remaining to even get close to the 3280fps molecule velocity.  The main point is that if you drive it to the point of 50% efficiency, you can't drive it any faster. And that speed will always be less than the molecule velocity, whatever it may be. 2330fps sounds almost too slow. I wanted a molecule velocity that was unreachable, but sounded plausible. ;)

It's just a starting point for discussion. You threw the first curve-ball.

Your 2330fps gives Lloyd a difficult, though maybe attainable goal. If we can't reach it while pushing hard enough to get 50% efficiency, I'll go with your improved version of the new theory.

I'll avoid "Mach", and stick with fps. Isn't the fps value of Mach changing directly with the molecule velocity?
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 29, 2016, 12:08:39 AM
I think it will be very difficult to reach 2330 at 70% efficiency.... at 50% I don't think we have a hope.... According to Lloyd's present J4 Spreadsheet, that would take 10,000 psi in an 8 ft. barrel, with a 3.5 gr. bullet in his existing gun.... The temperature of the air would have to be 310*C, if molecular velocity is really what matters....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 29, 2016, 12:13:55 AM
I think it will be very difficult to reach 2330 at 70% efficiency.... at 50% I don't think we have a hope.... According to Lloyd's present J4 Spreadsheet, that would take 10,000 psi in an 8 ft. barrel, with a 3.5 gr. bullet in his existing gun....

Bob
8 ft. is much less than infinity. I think it will still be around 60-70% efficient. Just guessing.

There is plenty of data still to be gained from a 4 ft. barrel.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 29, 2016, 01:33:00 AM
I agree, that was just one set of numbers that came out to get 2330 fps @ 50%.... If the efficiency is 60-70% (which I would expect) it would be a lot easier.... At 70%, it should take "only" 6000 psi with a 5 gr. bullet with the existing 47.5" barrel.... *LOL*....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: phoebeisis on March 29, 2016, 09:15:26 AM
2030 fps-pretty fast-congrats.Still following this-
Curious if you get a bit more with N2-?
I wonder what sort of FPS FPE a 270  (.277 of 130 grains or so) would do-?
The below is a cut from the yellow forum-this seems to be their(his take anyway) WHY of why you can't get over 1640 fps.
They seemed to have treated the air column as a solid rod-or a liquid column-not as tiny tiny particles with LOTS of empty space.




Nope. No matter how high the pressure, ~1640fps remains an absolute limit for cold air.   November 12 2008, 4:24 PM

This simply because as pressure rises, so does the mass of the air filling the bore behind the pellet. Since this air has to be accelerated along with the pellet, as pressure rises without limit, eventually all of the available energy goes to accelerate air and not lead.

The velocity at that limit is 1640fps.

To go any faster requires, not more pressure, but a propellant with a lower molecular density.

Steve


Bulldawg-Mike-in 362 below- I-charlie phoebeisis(our first greyhounds were phoebe isis)  was unclear-the above is a cut from the yellow forum-with STEVE's EXPLANATION-from Nov 12 2008-of what 1640 is the upper limit-I should have been more clear-
charlie
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Michael Loar on March 29, 2016, 12:10:28 PM
2030 fps-pretty fast-congrats.Still following this-
Curious if you get a bit more with N2-?
I wonder what sort of FPS FPE a 270  (.277 of 130 grains or so) would do-?
The below is a cut from the yellow forum-this seems to be their(his take anyway) WHY of why you can't get over 1640 fps.
They seemed to have treated the air column as a solid rod-or a liquid column-not as tiny tiny particles with LOTS of empty space.




Nope. No matter how high the pressure, ~1640fps remains an absolute limit for cold air.   November 12 2008, 4:24 PM

This simply because as pressure rises, so does the mass of the air filling the bore behind the pellet. Since this air has to be accelerated along with the pellet, as pressure rises without limit, eventually all of the available energy goes to accelerate air and not lead.

The velocity at that limit is 1640fps.

To go any faster requires, not more pressure, but a propellant with a lower molecular density.

Steve


Steve

Lloyd has already disproved that theory/fact with his 1745 fps shot in the .22 cal test gun and further disproved it with the 2030 fps shot in the .278 test gun as well.

I have all the faith he will break Mach 2 as well in the very near future.

Mike
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 29, 2016, 12:24:50 PM
Steve, you have pretty much found the point of this thread.... to disprove that theory that has been around for nearly a decade now.... which has now been done successfully, several times....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: I_like_Irons on March 29, 2016, 12:30:18 PM
How about measuring the pressure in the barrel at two points with respect to time?  The first point near the breach, and the second near the muzzle.

How does one do this?, you may be asking yourself while thinking it is a good idea.

The simple answer is to use strain gauges, Wheatstone bridges, a computer sound card with stereo microphone inputs, and Audacity sound analyzing software.  If you have a sound card that has four microphone inputs, then you can measure the pressure in four places.

In case you are not familiar with strain gauges, they work on the principle that when you stretch a wire it gets longer and skinnier and thus its resistance goes up.  Likewise if you compress the wire the resistance goes down.  The typical strain gauge is a flat serpentine wire laid onto a plastic backer.  The serpentine shape makes for more stretch in the wire for a given strain.   The gauges are glued to the item you want to measure the strain in. 

The Wheatstone bridge is a four resister device that amplifies the change in resistance in one of the resistors.  It consists of four "equal" resistors in a series loop.  The signal voltage is applied at two opposite nodes, while the voltage is read across the other two nodes.   Typically the strain gauge is one of the resistors while an "equal" value potentiometer (rheostat) is placed opposite.  The other two resistors are standard with a nominal value equal to the strain gauge at rest.

The bridge is balanced by adjusting the potentiometer so that the volt meter reads zero volts when the system is at rest.  If you are familiar with an analog multimeter you probably have balanced the bridge when you have used the ohm adjustment.

As far as the signal voltage, that is something which needs a bit more research, and may be dependent on the sound card, and perhaps the software.  But, the output signal will be fairly linear with respect to pressure since the strain and resistance response of the gauge will be linear as well.

I do know that Audacity has been used to make chronographs, and to measure time from one channel to the other along with frequency and amplitude.  Here, we would be interested in the amplitude with respect to time.  The other question I'm not too sure about is can Audacity deal with a direct current source and measure the voltage like a storage oscilloscope, or does it need an alternating source?  If the alternating source is required then it would have to be a pretty high frequency. 

The problem for the signal source, I think, would only be for calibration.  Here you have a static pressure for a period of time while you adjust the signals to get an equal and easy to read value.  The calibration procedure would go as follows:

Bridges are first balanced.  Then the muzzle is plugged (I suggest a "Champagne" cork).  The pressure inside the system is brought to the working pressure (4000 psi).  The output signals are adjusted to some equal value and reasonable value by adjusting the input voltages.  Note that the bridges will remain balanced regardless of the input voltage. 

Then the pressure is lowered  incrementally by some value like 500 psi, and notes made to the software output.  It should be linear, but, the software being designed for audio it may be logarithmic.  Too, there may be slight differences due to the sound card response.

The hardware (for a DC device) would be easy to make on a breadboard or a project board.  The things to get are strain gauges.  Make sure you get the type that only measure in one direction.  You will need two (or four) potentiometers that have an adjustment range the same as the nominal resistance of the gauges.  Two resistors for each bridge that have the same nominal value of the gauges. 

For the adjustable signal supply, you need to determine what your output voltages are likely to be.  Then you need to choose a battery, or battery bank/holder to get the desired input voltage.  A couple of voltage dividers with potentiometers might make for easily adjustable output signals.

Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 29, 2016, 12:45:19 PM
This idea could be used not only to confirm the accuracy of Lloyd's Spreadsheet (because it can predict the pressure drop vs. distance along the barrel).... but also to determine whether the expansion is Adiabatic, Isothermal, or in fact is increasing because of heating.... Calibration would be the key....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: I_like_Irons on March 29, 2016, 01:09:01 PM
More than just that.  The strain gauges may be sensitive enough to get at least a feel for the pressure ahead of the bullet.  Also of interest is the time it takes for the bullet to get from point A to B (to C and D).  That coupled with the muzzle velocity, one may surmise as to the true rate of acceleration in the barrel.

Another thing it could measure is the after exit cooling affect due to adiabatic expansion and the internal stress relief of the barrel itself.

Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 29, 2016, 01:36:37 PM
More than just that.  The strain gauges may be sensitive enough to get at least a feel for the pressure ahead of the bullet.  Also of interest is the time it takes for the bullet to get from point A to B (to C and D).  That coupled with the muzzle velocity, one may surmise as to the true rate of acceleration in the barrel.

Another thing it could measure is the after exit cooling affect due to adiabatic expansion and the internal stress relief of the barrel itself.


David,
Great ideas, all you need now is someone with the time and money and perseverance to implement them.   ;)
Lloyd
P.S.
Incrementally sawing the barrel off will will provide us with the acceleration information.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 29, 2016, 01:45:48 PM
I agree, that was just one set of numbers that came out to get 2330 fps @ 50%.... If the efficiency is 60-70% (which I would expect) it would be a lot easier.... At 70%, it should take "only" 6000 psi with a 5 gr. bullet with the existing 47.5" barrel.... *LOL*....

Bob
Bob,

As soon as Lloyd attains 2330fps, it blows your limit theory. It will likely happen in the 70% efficiency range (according to my theory). 70% efficiency is doable. 50% is not. 50% is the limit that can never be reached.

My theory says 16401854/0.5

Your theory says 16401854/(sqrt 0.5)

Here is something to think about:

At 100% efficiency, all of the energy gains result in a velocity increase.

At 50% efficiency, none of the energy gains result in a velocity increase.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 29, 2016, 02:40:42 PM
Actually, my theory says 3,300 is the absolute limit with 70*F air, based on the idea of a supersonic jet firing a cannon, as Lloyd's analogy goes.... In fact, there is an equation kicking around (also proposed by Steve, in connection with his "Sonic Horizon" theory.... that if modified to use 1650 fps I think predicts a limit of 3300.... I'll do up a post about that.... I was just saying that if your idea works, I would think that since the KE is proportional to the square of the velocity, and the limit you suggested was when KE = Entropy, perhaps 0.707 would be the appropriate divisor in that case.... I also stated I didn't think that was a high enough limit, because I thought it might be attainable.... and of course limits should never be reached, or they wouldn't be limits....

Incidently, a gun like a Disco is only about 58% efficient in stock form.... Lower efficiency is often not associated with high performance, but something else restricting/affecting what could be happening.... the most common thing being hammer bounce, of course.... Your idea could really only be applied to dump shots with wide open barrels, I would think....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 29, 2016, 03:28:23 PM
Actually, my theory says 3,300 is the absolute limit with 70*F air, based on the idea of a supersonic jet firing a cannon, as Lloyd's analogy goes.... In fact, there is an equation kicking around (also proposed by Steve, in connection with his "Sonic Horizon" theory.... that if modified to use 1650 fps I think predicts a limit of 3300.... I'll do up a post about that.... I was just saying that if your idea works, I would think that since the KE is proportional to the square of the velocity, and the limit you suggested was when KE = Entropy, perhaps 0.707 would be the appropriate divisor in that case.... I also stated I didn't think that was a high enough limit, because I thought it might be attainable.... and of course limits should never be reached, or they wouldn't be limits....

Incidently, a gun like a Disco is only about 58% efficient in stock form.... Lower efficiency is often not associated with high performance, but something else restricting/affecting what could be happening.... the most common thing being hammer bounce, of course.... Your idea could really only be applied to dump shots with wide open barrels, I would think....

Bob
1640fps vs 1650fps is just a minor temperature difference in air. They relate to my 3280fps and your 3300fps. So we are really talking the same thing here. That jet/cannon analogy is starting to make a lot of sense. A gas(jet) at 1640fps with 1640fps booster molecules (cannon) pushing the pellet.

It would be nice to show it with math. That's partly why I dwell on it.
--------------------------------------
Edit: substitute 1854 for 1640.

Thought experiment:

At 100% efficiency, all energy is converted to acceleration. 1854/(sqrt 1) = 1854

At 50% efficiency, no energy converted to acceleration. 1854/(sqrt 0) = ???

What about in between 100% and 50%?

What about at 70.71% efficiency? Is 50% of the energy converted to acceleration? 1854/(sqrt 0.5) = 2622fps

Looks about right, but I'm not sure if continuing gets us there either.

---------------------------------------

We could try to work backwards from 3708 as well.

1854/(sqrt ??) =3708

?? = 0.25, or 25% converted to acceleration? But, according to my pseudo-theory, it was supposed to be none or 0%. Is it still accelerating at 3708fps? That makes me question whether a velocity limit even exists.

I think we need to integrate the denominator. We can't simply use sqrt.

What if we integrate between barrel_length = 0 (100% efficiency), and barrel_length = infinity (50% efficiency)?

I struggled through calculus and differential equations. Numerical methods (my forte) fall short - literally.

I'm not really equipped to handle that problem mathematically. But I still like to think about it.

----------------------------------------

Lloyd can certainly test the 2330fps theory. Not sure about the rest.

----------------------------------------

As far as the 58% in the Disco:

In a actual physical system, efficiency will almost always be a little (or a lot) lower than theory.

It can also be higher if unaccounted for energy (heat) "leaked" into the system.

That's why well monitored tests are a necessity when testing limits of a theory. Lloyd runs a tight ship, with few "leaks" to worry about.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 29, 2016, 03:43:23 PM
Here is one of Steve's original posts about the "Sonic Horizon Theory".... He explains it in detail in that thread, no reason for me to rehash it....

http://www.network54.com/Forum/275684/message/1139726675/Friday+I+posted+a+sketch+showing+how+an+air-conserving+valve+can+save+1-3rd+of+the+air---- (http://www.network54.com/Forum/275684/message/1139726675/Friday+I+posted+a+sketch+showing+how+an+air-conserving+valve+can+save+1-3rd+of+the+air----)

I discussed this with Steve at length a few years ago, from the point of view that many PCPs can create shots well past what his theory predicted.... I presented evidence, but he remained unimpressed.... I asked him for the equation he used to plot the graph, and he gave me the following....

Position of Valve Ineffectiveness P = ( 1 - MV / ( 2 x SoS ) ) ^2

I am quite certain he showed me how he derived that, but I didn't record it, I just used it verbatim.... I then suggested that IF the equation made sense (to me) that we should use the molecular velocity of 1650 fps instead of the speed of sound.... I supplied him with this graph, comparing the two, using the different velocities....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Pellet%20Horizon%203_zpsyfltrzjh.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Pellet%20Horizon%203_zpsyfltrzjh.jpg.html)

He remained unimpressed, and we agreed to disagree.... A couple of days ago, I revisted my spreadsheet which I used to plot that graph, wondering what would happen if I carried it on to higher velocities.... To my surprise, it goes to zero at 3300 fps, like this....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Pellet%20Horizon%202_zpsqkdq4fbp.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Pellet%20Horizon%202_zpsqkdq4fbp.jpg.html)

The basic idea is that as molecules are released from the valve/chamber, (go back to the "packets of air" in my thought experiment) they push on the packet in front, and so on up the line, with eventually the front packet pushing on the bullet.... As the bullet goes faster and faster, eventually it will get to the muzzle before air being released from the valve can have any effect.... This happens in any dump shot, of course, eventually.... but the idea is that based on the velocity of the air entering the barrel there could be a limit.... Steve's equation, when modified to use the molecular velocity of 1650 fps, confirms the proposal in my "thought experiment" that limit may well be 3300 fps.... Note that at 2000 fps, only the air released when the pellet is in the first 15% of the barrel would be having any effect on the result.... This is consistent with the increasing insensitivity to reservoir volume (but not pressure) that we are seeing as the MV increases.... the size of the reservoir, once reasonable, means little at extreme velocities.... I think that is what the graph is saying.... At the limit, only the pressure would matter.... something to think about?....

Bob

Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 29, 2016, 11:27:04 PM
(http://www.scotthull.us/photos/Misc/1640-02.jpg)

For practical applications, the real problem is figuring out what happens between those two boundaries. Especially with a pellet along for the ride.

Edit: changed drawing. Replaced 172 with 194. Use D instead of Z. Constant ended up as 274.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 29, 2016, 11:48:22 PM
The constant is 194.... sqrt(450,436/12).... and Z may or may not be density/2....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 30, 2016, 01:18:38 AM
The constant is 194.... sqrt(450,436/12).... and Z may or may not be density/2....

Bob
Bob,

I looked a little closer at a derivation of the formula that someone posted on the yellow forum. It shows 172. I found the extra "piece of pie". No explanation of it.

194 sqrt(pi/4) = 172

I'm not sure at this point which to use.

I keep hearing that the number should net the rms of air. The rms calculator that I use for air confirms that 172 is the better number. 

I may look at it again later. As I would have cared more early on. I'll use 172 194 for now. It does not matter too much to me at this point, as that prediction appears to be the minimum velocity to expect for freely escaping air. It will climb as soon as the air enters the barrel. So it's never a limit for real airguns. 2x that number may be a limit. If we ever pass 3300fps, then 194 it is.

I changed the drawing to show the formula further decomposed. I got rid of Z and used density.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 30, 2016, 01:52:19 AM
If you follow through Herb1836's thread I posted above, he shows the deriviation of the constant.... The value of 172 is indeed different from 194 by the sqrt(Pi/4).... It is supposed to represent the collection of all the constants in the equation, and if the mass used is only the mass of the pellet, that would be correct.... However, when you add the mass of the gas in the denominator of the equation, you must use the volume of the barrel, multiplied by Z, the density factor, for which Steve used Density/2.... The problem is, that he forgot the PI/4 in the denominator of the equation.... The proper way to resolve this, is to change the constant to 194, and add the PI/4 back into BOTH the numerator and denominator of the equation in the barrel volume calculation.... Herb mentions this, and suggests that the proper value should be 2088 fps, but Steve blows him off by reminding him that it "can't be faster than the molecular velocity", and Herb basically gives up.... What Herb didn't realize, is that when he corrected the constant to 194, he forgot to put the PI/4 back in the numerator of the equation himself, when he got the 2088 result.... ie he corrected one error, and made another.... Had he done it properly, he would have got the answer I do, which is 1854 fps....

This is a combination of errors and comedy.... The original equation, by Steve, is incorrect, but worked out to a value that just happened to look like the molecular velocity.... Because of that, nobody has bothered to fix the error.... If you read through Herb's thread, and follow the derivation of the equation, and how he arrived at the constant, and then take the extra step to start from scratch, with the PI/4 term in BOTH places, where it should be.... you will arrive at the same answer I got, of 1854 fps.... The value of "Q" needs to have the PI/4 term in BOTH places.... Just because the equation Steve wrote happens to give a number that "looks right".... doesn't mean the equation is right....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 30, 2016, 02:23:22 AM
If you follow through Herb1836's thread I posted above, he shows the deriviation of the constant.... The value of 172 is indeed different from 194 by the sqrt(Pi/4).... It is supposed to represent the collection of all the constants in the equation, and if the mass used is only the mass of the pellet, that would be correct.... However, when you add the mass of the gas in the denominator of the equation, you must use the volume of the barrel, multiplied by Z, the density factor, for which Steve used Density/2.... The problem is, that he forgot the PI/4 in the denominator of the equation.... The proper way to resolve this, is to change the constant to 194, and add the PI/4 back into BOTH the numerator and denominator of the equation in the barrel volume calculation.... Herb mentions this, and suggests that the proper value should be 2088 fps, but Steve blows him off by reminding him that it "can't be faster than the molecular velocity", and Herb basically gives up.... What Herb didn't realize, is that when he corrected the constant to 194, he forgot to put the PI/4 back in the numerator of the equation himself, when he got the 2088 result.... ie he corrected one error, and made another.... Had he done it properly, he would have got the answer I do, which is 1854 fps....

This is a combination of errors and comedy.... The original equation, by Steve, is incorrect, but worked out to a value that just happened to look like the molecular velocity.... Because of that, nobody has bothered to fix the error.... If you read through Herb's thread, and follow the derivation of the equation, and how he arrived at the constant, and then take the extra step to start from scratch, with the PI/4 term in BOTH places, where it should be.... you will arrive at the same answer I got, of 1854 fps.... The value of "Q" needs to have the PI/4 term in BOTH places.... Just because the equation Steve wrote happens to give a number that "looks right".... doesn't mean the equation is right....

Bob
Sheesh!

I'll need to look at that all over again. I dropped out all of the pi, barrel_length, and mass terms. I probably should have used 194 then.

1854fps or 1650fps, they only represent a starting point. Lloyd broke 1854fps 3x.

1) At supersonic velocity, there will be significant entropy gain.
2) The air will heat up.
3) The temperature corrected density will decrease.
4) The lower mass will allow additional acceleration.
5) So, either one is not an upper limit!

I could be wrong about the infinity barrel length. But I think not, as long as the dump is infinite. It will keep accelerating.

Edit: I did take up the molecule velocity thing to explain why it was not a limit. I prefer the f=ma solution. I'll fix some posts.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: 39M on March 30, 2016, 11:10:35 AM
Turbocharging seems the next logical step.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 30, 2016, 12:11:02 PM
Scott, after sleeping on it overnight, I have decided to go through the whole equation, step by step, and lay it all out here, to make sure of everything.... You can only collect the constants if they apply to EVERY term in the equation.... The 172 was fine when there was only the pellet mass in the denominator, but when the air mass got added in everything got messed up.... I'll work on that after breakfast....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 30, 2016, 01:19:54 PM
Scott, after sleeping on it overnight, I have decided to go through the whole equation, step by step, and lay it all out here, to make sure of everything.... You can only collect the constants if they apply to EVERY term in the equation.... The 172 was fine when there was only the pellet mass in the denominator, but when the air mass got added in everything got messed up.... I'll work on that after breakfast....

Bob
Thanks Bob,

I knew I should do that but did not want to take it on with so many other things to look at.

It was sure comforting to think that the 1650fps rms molecular speed matched the f=ma speed limit.

If it doesn't, either:

1st choice) The formula had an error that coincidentally caused the match up.
2nd choice) We are missing something.
3rd choice) or, it was fudged to cause the match?

I'm going with 1st choice until I hear otherwise from you. And I'm going with f=ma, rather than the rms

I ended up factoring out the pellet completely for now, and the barrel dimensions. I guess that leaves a single string of air molecules. I still get 1854fps.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 30, 2016, 01:37:27 PM
The starting point for this idea is the equation for the energy that is produced in a shot, E = 1/2 mv^2.... If we go back to Lloyd's post about the theoretical maximum velocity (neglecting the weight of the air), we have the following equation, with it's derivation carefully explained.... Our eventual goal is to be able to input the weight (in grains), pressure (in psi), and all other dimensions in inches.... Getting there we will deal with those pesky constants.... From this thread http://www.gatewaytoairguns.org/GTA/index.php?topic=94054.0 (http://www.gatewaytoairguns.org/GTA/index.php?topic=94054.0) we have Lloyd's equation.... v = (F/m) x {sqrt ([2 x d x m]/F)}

This can be further simplilfied by squaring both sides, then rearranging, and taking the sqrt. again....

v^2 = (F/m)^2 x ([2 x d x m]/F) = F^2 / m^2 x 2 x d x m /F = 2 x F x d / m .... then take the square root of both sides and we have.... v = sqrt ( 2 x F x d / m) ....

That is EXACTLY the same equation as Herb1836 and Steve_in_NC are working with, once we add in all the constants to get the units correct....We need the force F in lbs. the distance d in feet, and the mass m in slugs (weight in lbs. / 32.174).... We also need to calculate the force F, which is the pressure in psi, times the bore area in in^2.... First, the force....

As explained by Lloyd, the force F accelerating the bullet (and the air) is the pressure P times the bore area A, which is A = cal.^2 x PI/4 .... The force F is therefore....

F = P x cal^2 x PI/4 with the caliber in inches, pressure in psi.... so our main equation now becomes....

v = sqrt ( 2 x P x cal^2 x PI/4 x d / m ) .... The distance the force is acting through, d (in feet) is the barrel length BLi (in inches), so we have d = BLi / 12 .... and our main equation now becomes....

v = sqrt ( 2 x P x cal^2 x PI/4 x BLi / 12 / m) .... We want to be able to input the pellet weight W in grains, and to convert that to the mass in slugs, we use m = W / 7000 / 32.174 = W / 225218, so now we have....

v = sqrt (2 x P x cal^2 x PI/4 x BLi / 12 / ( W / 225218 ) .... If we gather the constants at this point, we get Steve's equation....

v = sqrt { ( 2 x 225218 x PI / 4 / 12 ) x ( P x cal^2 x BLi / W ) } = sqrt {29481} x sqrt { P x cal^2 x BLi/ W } = 171.7 sqrt ( P x cal^2 x BLi / W )

This is a rearrangement of Lloyd's equation, and will give exactly the same results, which is really pretty KEWL, that two such bright guys got the same answer.... However, once we add the mass of the air, things change, and I will deal with that in my next post....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 30, 2016, 03:49:54 PM
Bob,

Looking forward to the rest of the story! And wondering what are the implications for 1650fps vs 1854fps.

FYI: grains is a mass, not really a weight(force). Technically, no reason to show the 7000/G calculation to convert to pounds(mass). You can go directly from grains to slugs.

In the mean time:

In trying to visualize the limits, I came up with this first pass at a velocity envelope for a 70F airgun at psig>0. The hatched area is the operating envelope.

(http://www.scotthull.us/photos/Misc/velocity-envelope-01.jpg)

Air would go from A to A' (assuming 0 friction - not possible, unless freely expanding)
Just pellet would go from B to A' (assuming a force from 0 mass air - not possible).
Just air would go from A to B' (assuming a 0 mass pellet).

A velocity curve for a pellet would go from B to B'. The curve for different setups can shift up or down but will still lie in the hatched region.  The curve for a very light pellet (magenta curve) would gravitate toward point A. The curve for a very heavy pellet (blue curve) would gravitate toward point A'. The more typical curve (green curve) would be in between. They all start at v(0) and end at v(max).

The curve could not fall outside of the hatched region without breaking some physical law.

I'm not sure if it is all that useful.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 30, 2016, 07:44:49 PM
Sorry, I had a appointment this morning and got interrupted just before I finished this post, so I saved it in Word and just finished it up now....

OK, so now it gets REALLY interesting.... let's include the mass of the air.... to do that, we will back up a bit, to the equation that had the mass m (in slugs) in it....

v = sqrt ( 2 x P x cal^2 x PI/4 x BLi / 12 / m )

We now want to add the mass of the air in the barrel Ma, to the mass of the pellet Mp, with everything in slugs.... We have m = Mp + Ma so the equation becomes....

v = sqrt ( 2 x  P x cal^2 x PI/4 x BLi / 12 / [ Mp + Ma ] )

The mass of the air Ma (in slugs) is the barrel volume Va (in in^3) times the density Da (in slugs/in^3), so Ma = Da x Va.... where Va (in^3) = cal^2 x PI/4 x BLi .... Hey, we have those same numbers in the numerator, so we can simplify the equation to the following....

v = sqrt ( 2 x P x Va / 12 / [Mp + Ma ] ) .... We want the pellet weight in grains, so we need the weight of the air in grains also.... Here is where it gets complicated (like it wasn't already?).... If we accept that air is an ideal gas, and use Boyle's Law, we can just calculate a value for Da at 1 psi, the way Steve did it, to get the density factor he called "Z".... He used half the air density at 1 psi, (which he calculated to be D = 0.0219 grains/in^3/PSIA).... so that he ended up with a weight in grains that could be simply added to the pellet weight W before converting to slugs.... The relationship to mass is as follows....

Ma = Da x Va where Da = Z x P so Ma = Z x P x Va.... If we substitute that for Ma in the equation above (Z to be in grains/in^3/PSIA), we get the following....

v = sqrt ( 2 x P x Va / 12 / [ Mp + Z x P x Va ] ) .... Checking the units, for Ma = Z x P x Va, we have Z in grains/in^3/PSIA x P (PSIA) x Va (in^3), the weight of air would be in grains, so we have to divide by 225218 to convert to slugs, just like for the pellet.... Hence, both the pellet weight W and the weight of air ( Z x P x Va) are divided by 225218, so we get the following....

v = sqrt ( 2 x P x Va / 12 / [W + Z x P x Va] / 225218 ) .... Now let's gather the constants....

v = sqrt { ( 2 x 225218 / 12 ) x P x Va / (W + Z x P x Va) } = sqrt { 37536 } x sqrt { P x Va / ( W + Z x P x Va ) } = v = 193.7 sqrt { P x Va / (W + Z x P x Va ) }

If we set the pellet weight W = 0, then we get the following....

v = 193.7 sqrt { P x Va / (0 + Z x P x Va) } = 193.7 sqrt { P x Va / Z x P x Va }.... the P's and Va's cancel out, so v = 193.7 sqrt ( 1 / Z )

The only variable left is the value of Z, and it drastically alters the maximum velocity.... Steve used half the air density he calculated, Z = D / 2, which gave Z a value of 0.01095 grains/in^3/PSIA.... That leads to the following calculation....

v = 193.7 sqrt ( 1 / 0.01095) = 193.7 sqrt (91.32) = 193.7 x 9.556 = 1851 fps.... We know that can't be right, because Lloyd already has achieved 2031 fps, with a pellet weighing 9.1 gr.... This calls the value of Z into doubt.... I'll look at that in the next post....

Bob



Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 30, 2016, 08:33:15 PM
OK, so if we assume that we have a problem with the air density factor, Z, let's see what we can determine.... Steve worked from the mass of air molecules and molar volume, and arrived at a value of 0.0219 grains/in^3/PSIA.... I'll try a different approach, to see if I can get the same value.... I will start from standard air density at 1 bar, at 20*C, which from this online calculator is 1.1894 kg/m^3.... http://www.peacesoftware.de/einigewerte/luft_e.html (http://www.peacesoftware.de/einigewerte/luft_e.html) .... I double checked this with another online air density calculator.... http://wahiduddin.net/calc/calc_da_rh.htm (http://wahiduddin.net/calc/calc_da_rh.htm) .... which gave a value of 1.188 kg/m^3 for dry air at sea level at 20*C.... The average of these is 1.1887, so I will use 1.189 kg/m^3....

From another online conversion calculator, the conversion factor for kg/m^3 to grains/in^3 is 0.252891, so that becomes 1.189 x 0.252891 = 0.30069 grains/in^3 air density at 1 bar.... However, 1 bar is 14.504 psi, and we want the value at 1 psi, so dividing 0.30069 / 14.504 = 0.02073 grains/in^3/PSIA.... That's pretty close to what Steve got, an error of only 5%.... He was using 25*C, and using that I get 1.168 x 0.25289 / 14.504 = 0.02037, a little further from Steve's number.... Therefore, I will use the value I calculated of 0.02073 grains/in^3/PSIA.... If we use Steve's estimate that Z = D / 2 (because only half the air column is being accelerated), then Z = 0.02073 / 2 = 0.01037.... Using this value in the equation for the maximum velocity with zero pellet mass, we have....

v = 193.7 sqrt ( 1 / Z ) = 193.7 sqrt ( 1 / 0.01037 ) = 193.7 sqrt ( 96.43 ) = 193.7 x 9.820 = 1902 fps.... This is still too low a value, particularly when you consider it is for a pellet weight of zero.... and has already been exceeded with a pellet weight of 9.1 and 10.3 grains at 4000 psi in a 47.5" barrel....

If the entire air mass is used, instead of half (not unreasonable, because it is all moving), so that Z = D = 0.0207, we get the following....

v= 193.7 sqrt ( 1 / Z ) = 193.7 sqrt ( 1 / 0.0207 ) = 193.7 sqrt ( 48.309) = 193.7 x 6.955 = 1346 fps.... an even lower value.... Scott suggested that working through using integration, an increment at a time, could make a difference, but the equation we are dealing with, at zero pellet weight, has no terms for caliber, pressure, or barrel length, so we can't do that using this equation.... I would suggest that pursuing this route may be a waste of time.... I would appreciate it if someone could check through my math and make sure I have not made a mistake somewhere.... It was a long process, and that is always a possibility....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Scotchmo on March 30, 2016, 09:30:09 PM
Bob,
Good work. I want to look at that more when I'm at my desk. I'm at the range this afternoon (working, not shooting). If you are correct, at BL=0, it's all pellet. So we start at 172? At BL=infinity, it's all air. So we use 194?

Z looks right.

Bob - are you sure that D/2 represents 1/2 of the air column? I thought it was the (1/2m) from 1/2mv^2. And density is not a constant during the shot cycle. Density changes with temperature. Entropy gain is significant for supersonic shear of air. You can't ignore it. And you can't average it over the entire air column. If you did, then Z=D/4. But most of it is right behind the pellet. I'm leaning toward Z=D/8 at the limit (50% efficiency).

If 1650fps is the least length maximum limit. The most length maximum is 2x1851fps, or 3702fps.

For a very light pellet, you can end up expending almost 8x the energy to go from 1651fps to 3702fps.

I could be wrong. I'm basing on my current theory. All data and formulas support it.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 30, 2016, 10:03:20 PM
The D/2 is the density factor.... and I have no way of working in a temperature change without data.... The 1/2mv^2 fraction is part of the constant, it is the first "2" that you see in the formula before the constants are collected.... The constant should be 194 all the time, I only included the 172 version to show how Steve got it, by omitting the PI/4 in the numerator.... that is why I put it in red, because it really does not belong in my calculations....

I plan on working with the ACTUAL air density which decreases relative to the pressure.... ie at 6000 psi the density is only 80% of what we are using in this simplified formula.... Since air density makes a big difference, that could be very important....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: rsterne on March 30, 2016, 11:34:18 PM
OK, let's back up again.... We will go back to where we still had separate terms for pressure P and the two masses, pellet Mp and air Ma....

v = sqrt ( 2 x P x Va / 12 / [Mp + Ma ] )

We will still use Ma = Da x Va.... but this time we won't accept Boyle's Law and it's simplified version of the relationship between pressure and density, but we will instead use the actual values for the air density at various pressures, as given by the Peacesoft calculator.... http://www.peacesoftware.de/einigewerte/luft_e.html (http://www.peacesoftware.de/einigewerte/luft_e.html)

I have gone through and compiled the actual air density, in kg/m^3, at all pressures from 15 - 10000 psi, in 1000 psi increments.... Here is that information, first in a table, and then as a graph....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Air%20Density_zpsdbuwszm8.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Air%20Density_zpsdbuwszm8.jpg.html)

In the table, the middle column is the actual density from the Peacesoft calculator.... while the right column is that predicted by Boyle's Law.... all at constant temperature....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Air%20Density%20vs%20Pressure_zps3f9ykfjn.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Air%20Density%20vs%20Pressure_zps3f9ykfjn.jpg.html)

You will note that below 2000 psi, Boyle's Law applied almost perfectly, but above that the actual density is less than Boyle's would give.... The actual density at 4,000 psi is 8% less than you would get if air was an Ideal Gas, at 6,000 psi 18% less, at 8,000 psi 28% less, and at 10,000 psi 36% less.... So let's see what the equation looks like using the actual air density Da....

v = sqrt { 2 x P x Va / 12 / [Mp + (Da x Va) ] }

At this point, the masses are still in slugs, so the units for air density Da are slugs/in^3 and for barrel volume Va are in^3.... Once again, let's let the pellet mass be zero, so we have....

v = sqrt { 2 x P x Va / 12 / [0 + (Da x Va) ] } = sqrt { 2 x P x Va / 12 / ( Da x Va ) } = sqrt { 2 x P x Va / 12 / Da / Va }, the Va's cancel, and we have

v = sqrt ( 2 x P / 12 / Da ) .... We need the air density Da in slugs/in^3, and pressure P is of course in psi.... To convert kg/m^3 to slugs/in^3 we must divide by 890575, so for the air density Da in kg/m^3 the eguation becomes....

v = sqrt { 2 x P / 12 / (Da / 890575) } = sqrt (2 x 890575 / 12 ) x sqrt ( P / Da ) = sqrt (148429 ) x sqrt ( P / Da) = v = 385.3 sqrt ( P / Da )

Let's check this to see how the results compare to our previous equation, and we'll do that at 1 bar (14.5 psi), where the air density is 1.189 kg/m^3 as follows....

v = 385.3 sqrt ( 14.5 / 1.189 ) = 385.3 sqrt ( 12.195 ) = 385.3 x 3.492 = 1346 fps.... Hey, using the full air density before, we got 1346 fps, I think it works ! ....

How about at 2000 psi, where the air density is 164.4 kg/m^3....

v = 385.3 sqrt ( 2000 / 164.4 ) = 385.3 sqrt ( 12.165 ) = 385.3 x 3.488 = 1344 fps.... Still looking good over the (near) linear part of the pressure / density relationship.... What about 4000 psi?....

v = 385.3 sqrt ( 4000 / 302.4 ) = 385.3 sqrt (13.228 ) = 385.3 sqrt x 3.637 = 1401 fps.... The velocity is increasing as the density drops relative to the pressure rise, exactly what we were expecting.... Let's jump to 10,000 psi, where the air density is 524.3 kg/m^3....

v = 385.3 sqrt ( 10000 / 524.3 ) = 385.3 sqrt (19.073 ) = 385.3 x 4.367 = 1683 fps.... a huge increase.... However, we are still well below what we have already accomplished, so let's go back and use only half the air mass, instead of all of it.... This makes the equation....

v = sqrt { 2 x P / 12 / (Da / 890575 / 2) } = sqrt (2 x 890575 x 2 / 12 ) x sqrt ( P / Da ) = sqrt (296858 ) x sqrt ( P / Da) = v = 544.8 sqrt ( P / Da ) with Da in kg/m^3....

This will increase all the previous velocities by a factor of sqrt (2) = 1.414 times.... Here is a table of the calculated velocities up to 10,000 psi....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Air%20Density%20Max%20Velocity_zpsc66nowwo.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Air%20Density%20Max%20Velocity_zpsc66nowwo.jpg.html)

I had great hopes that we would finally have some maximum velocities that we haven't been able to reach, and looked unlikely in the foreseeable future.... Unfortunately, that is still not the case.... I do not know if having an actual pellet mass, and applying the equation to each interval as the pellet accelerates down the bore will do that or not.... However, since it still fails to predict a high enough velocity in the limiting case, where pellet mass is zero, I don't have much hope for it....

If anyone wishes to carry on from here, please do.... I would also appreciate it if someone will check my math to make sure I haven't made a mistake....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: lloyd-ss on March 31, 2016, 01:47:29 AM
I'll comment on all the math work that has been done in another post, but first I need to give an update with the newest Fastest Shot.
I had to shorten the barrel to 46" to remove an oversized portion of the breech. I had not machined it correctly originally, but this time it turned out good.  It allows the use of much shorter projectiles.  The one for this shot was .335" long and weighed 7.7 gns, including the o-ring,  both before and after the shot. I was able to retrieve the projectile from the tube of grocery bags.
Still not seeing any attenuation in the velocity, in fact, this shot was 102.6% of the prediction (using the 1745fps shot as the benchmark).

Shot specs,
.278 cal
46" long barrel
7.7 gns
4600 psi air (had  a slight overfill after adjusting the compressor)
55 cc dump chamber
Velocity  2162 fps
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/3-26-16-1688/2162FPS-shot%20photo_zpsxcv4joto.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/3-26-16-1688/2162FPS-shot%20photo_zpsxcv4joto.jpg.html)

Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Scotchmo on March 31, 2016, 02:31:09 AM
Lloyd - Wowee!

Bob,

You DO need to account for the entropy gain (heat gain in the propelling air), or you will be spinning your wheels. The inefficiency is absolutely needed.

Without it, the equation only shows the horizontal dashed line in the picture below:

(http://www.scotthull.us/photos/Misc/velocity-envelope-01.jpg)

The pic is a little confusing and would need a 3-D chart to correctly scale all the info (such as efficiency). And the barrel length would be some kind of  Logx scale as I need to show infinity.

If you include an equation with entropy gain, and run a line from your equation, you will have the upper boundary line shown (cyan line). The one that the very light pellet (maganta curve) mostly follows.

For now, I'm good with it as is. Until Lloyd breaks through the boundary.

Imagine taking an airgun and using as much as half the energy in the tank to heat the air before the shot. You just raised the velocity limit by raising the molecular kinetic energy, but you reduced the overall efficiency. That's what is happening DURING the shot. The process is substituting molecular kinetic energy for mass kinetic energy. It shows up as heat and disappears as soon as it leaves the muzzle. And we can't do anything about it.

At 1854fps, the molecule temperatures in the boundary layer might be in the 1000-1200K degree range. Now check the density of the air. A simple equation is never going to predict the actual velocity. It's too complicated. I think the best we can do for accurate modeling between the limits is to get data. And then do an empirical friction formula that takes into account any pertinent variables. Put it in our spreadsheets. It will be even better than a straight efficiency multiplier.
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Michael Loar on March 31, 2016, 03:53:45 AM
Lloyd
 WooHoo Getting closer to the magic number 2330 fps every shot. great work and its to late to turn back now.

Mike
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: lloyd-ss on March 31, 2016, 08:53:20 AM
Bob,
Thank you very much for presenting the derivation of the velocity and max velocity equations.  You have covered it quite well.  The one area that seems to be a struggle is the mass of the air, or actually, what assumption to make on how much of the mass of the air in the barrel is being accelerated.  I see several difficulties in that and I think that it varies with the barrel length, the length to diameter ratio, and the velocity (possibly just the MV) of the air or pellet.  I do not believe that just deciding to use some, somewhat arbitrary, portion of the air mass is realistic, even though that is what I do in my internal ballistics spreadsheet.  Here are a few reasons why.
We know that there is pressure drop within a pipe and that a pipe of some very long length will have almost no flow coming out the far end of the pipe.  There is friction in the barrel and friction in the air itself in a laminar flow situation, and it has the effect of (I believe) the air flowing thru more of a continually narrowing tapered barrel.  I think this is also dependent on velocity.  Slow heavy bullets are generally more efficient than light fast bullets, suggesting that there are more friction(?) losses with higher velocities. 
Could it be that at longer barrel lengths and higher velocities, the accumulation of additional air mass proceeds at a slower than expected rate, but also, at the same time, the force on the pellet is decreasing at a faster than expected rate?  It is not neat and tidy.  There is a continuum of pressures and velocities throughout the length of the and figuring that out is complex.  There could be some exponential function that determines the variable rate at which the mass of air is building up behind the pellet.  Quite complex.

Scott, I am still trying to get a handle on your entropy application in the calculations.  You seem to have it all going to heat that increases the temperature of the air and therefore the molecular velocity.  Is that correct?  But doesn't entropy also cover  non-recoverable, non-definable energy losses within the system?  Aren't some of those losses in a way  like the efficiency fudge factors that we are currently using.  Entropy losses are often empirically determined and isn't that in a way what we have been doing?  I agree that figuring the heat related energy losses (usage) helps to narrow down where the energy is going and will help to make the fudge factor  a smaller percentage number.  But there are still entropy  losses that will remain undefined, correct?  You have added a piece to the puzzle that I had not really thought hard about, but I can see that it is an important part.  Again, quite complex.

Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: rsterne on March 31, 2016, 12:17:25 PM
Lloyd, first of all a well deserved, and hearty CONGRATULATIONS ! on the latest 2162 fps shot.... Just think how far you have pushed the boundaries in such a short period of time.... truly remarkable.... It shows what can be done when you ignore those who say you can't do something.... *grin*....

I think I have gone as far as I can with using a simple model of the mass of the air that is being accelerated during the shot.... and unless somebody can find an error in my math, or methodology, I don't have a solution.... At 10,000 psi, by using the actual air density, and half the mass, I have pushed the velocity to 2379 fps.... but at 5000 psi the equation spits out 2039 fps with zero projectile weight, and you are already at 2162 fps with a 7.7 grain pellet at less pressure.... Scott, I don't have the math skills, or the understanding of airflow or thermodynamics to even know how to approach going down that path.... Lloyd, it is interesting you mention the length/diameter ratio of the barrel, and it makes sense that would be very important to the real-world results.... but in the equation the barrel volume doesn't care about that, the theoretical maximum FPE is proportional to the volume only, it doesn't matter if you have 1000 lbs. force over 1 foot, or 100 lbs. force over 10 feet, it's still 1000 FPE.... Right there, the departure between theory and reality lands with a THUD !!!

I am excited about one thing, however.... It appears that Lloyd's current spreadsheet, once corrected using the VanDerWaals air density, will work over a HUGE range of situations with only a simple efficiency "fudge" factor.... and being the practical guy I am, that is good enough for me.... If I want to find out what the maximum is for that set of conditions, I will just set the factor to 100% and know we can't get there from here.... I just won't know the details of why.... *LOL*.... Incidently, to get the latest shot to balance in Lloyd's J4 Spreadsheet, using Adiabatic expansion of the air, requires just shy of 74% efficiency....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Scotchmo on March 31, 2016, 01:11:18 PM
...

Scott, I am still trying to get a handle on your entropy application in the calculations.  You seem to have it all going to heat that increases the temperature of the air and therefore the molecular velocity.  Is that correct?  But doesn't entropy also cover  non-recoverable, non-definable energy losses within the system?  Aren't some of those losses in a way  like the efficiency fudge factors that we are currently using.  Entropy losses are often empirically determined and isn't that in a way what we have been doing?  I agree that figuring the heat related energy losses (usage) helps to narrow down where the energy is going and will help to make the fudge factor  a smaller percentage number.  But there are still entropy  losses that will remain undefined, correct?  You have added a piece to the puzzle that I had not really thought hard about, but I can see that it is an important part.  Again, quite complex.

Lloyd
"You seem to have it all going to heat that increases the temperature of the air and therefore the molecular velocity.  Is that correct?"
Yes. It goes to "molecular kinetic energy" - i.e. temperature increase. I mostly ignore the small pellet friction.

"But doesn't entropy also cover non-recoverable, non-definable energy losses within the system?"
No. I'm assuming there are none (or negligible) in your straight forward system.

"Entropy losses are often empirically determined and isn't that in a way what we have been doing?"
Yes. Fluid friction, Reynolds number, I think are mostly derived from empirical data. We are working outside of the range of most previously available data.

"But there are still entropy losses that will remain undefined, correct?"
Not really. We can pretend that they are insignificant until we get there.

I'll throw another theory out here.

Once we start producing heat, we have a work-to-heat engine. At the extreme (infinity) 50% of the original energy ends up as heat (entropy gain). 50% ends up as work (KE of pellet). Maybe like a backwards engine (heat-to-work) cycle. A Carnot cycle can easily do 50% efficiency. At a Carnot cycle efficiency of 50%, we need a temperature spread of 70F to 600F (295K to 589K). The hot side is 589K.

A Carnot cycle is very slow. Ours is instantaneous. The column of air will not have time to equalize in temperature. The 589K spreads out over the air column. High density, 70F(295K) at the inlet, to low density 1660F(1178K) behind the pellet.

Plug that into the equation:

v = 193.7 sqrt ( 1 / Z )

At 1178K, air density D = .0055gr/ci/psia.
Z = 1/D = 0.00275

v = 193.7 sqrt (1 / 0.00275) = 3694fps

I know it looks like circular reasoning.
But at least it's a complete circle.  ;)

The left graph in the picture represents the velocity limit equation that we have been trying to reconcile. But it ignores heat gain. The friction-less system is worthless as a predictor of the upper limit. It only gives you half the picture. And that picture is the lower half of the velocity envelope, which tells us very little:

(http://www.scotthull.us/photos/Misc/velocity-envelope-02.jpg)

We need the upper half. The right graph includes fluid friction and heat gain. It defines an upper limit that is more like what I would expect. But it follows Boyle's law, so it too will break down at pressures over 3000-4000psi. Until you use 6000psi nitrogen, we are probably OK.

Maybe the number we should be focusing on is the 50% efficiency. That is the limit. Once you drive it hard enough to generate 50% heat, it's balanced. Velocity will be maxed out. We don't really know what that velocity is. We'll just know when we are getting close. We need to test the theory:

At 50% inefficiency, velocity is maximum.
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: 39M on March 31, 2016, 02:40:26 PM
I probably missed this and it might have been mentioned somewhere in this thread.
But I have an idea, not sure if it qualifies as theory, that by changing the length and angle of the "funnel" behind the chamber, that you could tune it to match different barrel lengths.

A long less sharply angled "funnel" might provide less turbulence and be beneficial for a longer barrel. While a wider ratio, more sharply angled "funnel" would benefit a shorter barrel.

Might mean nothing, but just a thought.
Title: Re: Sonic Choke or Sonic Joke - 2031 FPS
Post by: Big Bore Bart on March 31, 2016, 03:33:35 PM
OK, so if we assume that we have a problem with the air density factor, Z,   (snip)   If we use Steve's estimate that Z = D / 2 (because only half the air column is being accelerated), then Z = 0.02073 / 2 = 0.01037.... Using this value in the equation for the maximum velocity with zero pellet mass, we have....

v = 193.7 sqrt ( 1 / Z ) = 193.7 sqrt ( 1 / 0.01037 ) = 193.7 sqrt ( 96.43 ) = 193.7 x 9.820 = 1902 fps.... This is still too low a value, particularly when you consider it is for a pellet weight of zero.... and has already been exceeded with a pellet weight of 9.1 and 10.3 grains at 4000 psi in a 47.5" barrel....

If the entire air mass is used, instead of half (not unreasonable, because it is all moving), so that Z = D = 0.0207, we get the following....

v= 193.7 sqrt ( 1 / Z ) = 193.7 sqrt ( 1 / 0.0207 ) = 193.7 sqrt ( 48.309) = 193.7 x 6.955 = 1346 fps  (snippedy snip)   I would appreciate it if someone could check through my math and make sure I have not made a mistake somewhere.... It was a long process, and that is always a possibility....

Bob

  Bob; you made me break out the calculator. ;D   
  My take is the barrel is a tube and therefore the boundary layer will cause a constriction.   I ran your equation with a divisor of 3 and got this...

       Z = 0.02073 /3=0.00691

    Plugging that in gives v = 193.7 sqrt ( 1 / Z ) = 193.7 sqrt ( 1 / 0.00691 ) = 193.7 sqrt ( 144.7178) = 193.7 x 12.0299 = 2330.186 fps....

   There is that magic number. ;D
 
   The boundary layer acts as an orifice, due to the friction of the air column at high velocity.  The core of the air column will be moving considerably faster than the outer portions.   IMHO the constriction can be as severe as 60%+. 

   Considering the fact that the pellet is accelerated to ~60% of it's final velocity in the first half of the barrel or less, the final acceleration must be being done by the air making it through the core.   This air could be those molecules that are moving faster than 1640fps.  Either way Steve is still wrong. ;D
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: rsterne on March 31, 2016, 06:03:51 PM
The problem is justifying using only 1/3rd of the air.... It could, in fact, be argued that we should be including all of the air in the barrel when we are using a dump shot, particularly if the reservoir is so large as to maintain a constant pressure.... Ultimately, the only proper way to do the calculation is by integrating the air mass used in increments as the bullet travels up the bore....

I think we are soooooooooo far past the idea of 1650 fps being the limit that we don't even need to think about justifying it any more.... I think that Scott's idea of the velocity gradient, with the air in the center moving much faster than the air on the outside (against the barrel wall).... added to my idea that one "packet" of air pushes on the next, with only the front one pushing on the bullet.... can explain velocities up to 3300 fps.... and I can pretty much state with confidence we won't get there with air.... While it would be nice to know exactly what is happening inside the barrel so we can model it accurately, I'm perfectly OK with just using an efficiency factor to balance the spreadsheets....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Scotchmo on March 31, 2016, 11:52:46 PM
The average air velocity right behind the pellet is higher than the air velocity entering the barrel. The mass flow rate is the same. Think about it!

On Lloyd's last test, the air enters at 1650fps (or 1854fps) and the first molecules to reach the muzzle were going 2162fps. What's the problem?
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: rsterne on April 01, 2016, 12:13:12 AM
That could very well be an accurate description of the situation, Scott.... The mass flow could be the same, but the pressure lower as the velocity increases (ala Bernoulli).... except the "narrowing" of the airstream towards the muzzle is caused by the slow molecules dragging along the barrel.... I don't suppose we will ever know for sure....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Scotchmo on April 01, 2016, 01:18:17 AM
That could very well be an accurate description of the situation, Scott.... The mass flow could be the same, but the pressure lower as the velocity increases (ala Bernoulli).... except the "narrowing" of the airstream towards the muzzle is caused by the slow molecules dragging along the barrel.... I don't suppose we will ever know for sure....

Bob

Flow rate is the same.
Pressure is the same.

Temperature is higher. Velocity is higher. That's the only difference.
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: match on April 01, 2016, 01:30:55 AM
...
I am excited about one thing, however.... It appears that Lloyd's current spreadsheet, once corrected using the VanDerWaals air density, will work over a HUGE range of situations with only a simple efficiency "fudge" factor.... and being the practical guy I am, that is good enough for me.... If I want to find out what the maximum is for that set of conditions, I will just set the factor to 100% and know we can't get there from here.... I just won't know the details of why.... *LOL*.... Incidently, to get the latest shot to balance in Lloyd's J4 Spreadsheet, using Adiabatic expansion of the air, requires just shy of 74% efficiency....

Bob

So using 70% in the spreadsheet would be "high end almost doable"  and 60% would be "readily doable"?
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: rsterne on April 01, 2016, 02:10:33 AM
PCPs typically run anywhere from 55-75% "fudge factor" efficiency using Lloyd's spreadsheet.... There is only one combination of valve dwell and efficiency that will yield both the muzzle velocity and FPE/CI (air use per shot) that the real gun you are trying to model produces.... Once you know that for your gun, you can change bullet weight, air pressure, barrel length, even caliber and get a pretty good idea of what the new configuration will do....

What we hope to do is to improve the modelling so that the range of efficiency values is narrower, by including a better understanding of the losses, and how the mass of the air affects the shot.... The latest improvement Lloyd is working on is to change from using Boyle's Law (for Ideal Gasses) to the actual relationship between air density and pressure (including the VanDerWaals corrections).... Boyle's works fine up to 2000 psi, it's pretty close at 3000, but by 4000 psi the density is about 8% high, and gets worse from there.... At 6000 psi, the error is 20%.... This is one of the reasons the efficiency changes, so making that correction to the model should reduce the range of the "fudge factor" to a narrow range.... IMO it isn't necessary to get that factor up to 100% (which would require a complete, perfect understanding of every loss in the system).... but if we can get the range narrow enough, it will make predicting PCP performance more and more accurate....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: lloyd-ss on April 01, 2016, 11:42:18 AM
Bob,  I worked on the VanderWaals correction and am very, very close.  Even with your formulas, it was more of a task than than anticipated.  But there is now additional information regarding mass and density embedded in the spreadsheet that will be available for additional modifications when the time comes.

I took 2 additional shots yesterday.  The barrel is now 46" long after I removed the bad portion in the breech and re-machined that entire end.  But it is good now, so the pellets can be a minimum length to keep the weight down.  So far the lightest pellet that uses the clam-shell clamping has been 7.1 grains.  I found what I think is a piece of G9 or G10 rod that has tensile and compression strengths in the 32ksi range at 60% the weight of aluminum, so I think the next projectiles will be made out of that.  The o-ring is .8 grains, so I "might" be able to get the weight down to about 5.5 grains.  The advances are becoming more difficult.

Here are the 2 shots from yesterday.
2164 and 2143 fps.
  Hope I'm not stuck in a rut!
One used the pinched waist aluminum pellet and o-ring design. 
7.1 gn, .278 cal, 46", 55cc, 4500 psi, 2164 FPS.  Interesting when you get to velocities this high that the percentage variations seem to tighten up.  The previous 7.7 gn 2162 fps shot was 102.6% of calculated, and this one with 7.1 gn at 2164 fps was still at 101.5% of calculated.  I would have expected a larger percentage spread, but thinking about it, I see why they are so close.

The second shot yesterday used a break-away pellet design.  The pellet had a long retention stem that was threaded via an adapter into the rear plug of the breech.  The pellet was 7575 aluminum, the same .278 cal, the stem was .090 dia, and I originally necked it down to .071 dia.  It didn't break at 4600 psi. Necked it down to .063.  Still no break.  Went down to .055, and this time it broke at 3800 psi.  I retreived the broken part that was fired, and it weighed 6.1 gn.  Velocity was 2143 fps.  I realized that not only was the 7075 stronger than I expected, but I forgot to deduct for the stem dia when figuring the stress on the stem.

Here is a pic of the breakaway setup.  The retention stem broke right inside the entrance to the barrel.
Lloyd

(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MaxVel%20Ver2/Breakaway-2143_zpsvbmfv1ps.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MaxVel%20Ver2/Breakaway-2143_zpsvbmfv1ps.jpg.html)


EDIT April 2, 2016 - Did the strength calc on the necked down breakaway portion of the 7075T6 aluminum rod and got a UTS of about 93ksi.  The UTS specs I have seen range from about 70 to 83ksi.  Maybe I can lighten the projectiles a little bit more without "high" risk of failure.

Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Scotchmo on April 01, 2016, 02:53:56 PM
Lloyd,

I'm away from my desk for a couple of days, so can't check it myself.

What was the overall efficiency of the last few (>2000fps shots)?

That info would be useful as a confirmation to something I'm working on. 

Entropy gain is related to efficiency and velocity.

I want to further develop my ideas on entropy gain vs maximum velocity. I need some confirmation that my "thought experiment" is still on track.
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: lloyd-ss on April 01, 2016, 03:41:20 PM
Lloyd,

I'm away from my desk for a couple of days, so can't check it myself.

What was the overall efficiency of the last few (>2000fps shots)?

That info would be useful as a confirmation to something I'm working on.

Entropy gain is related to efficiency and velocity.

I want to further develop my ideas on entropy gain vs maximum velocity. I need some confirmation that my "thought experiment" is still on track.
Scott,  All of my "predicted velocities" were based on the parameters from my first "real" high velocity shot.  That was the 7.5 gn .22 cal, 23.3" barre, 4500psi, 26cc.  That shot had an efficiency of 70% using 100% of the air mass progressively added to the mass of the projectile.     ALL of the hi vel shots since then ( one more 23.3" .22 cal, and all the rest .278 ~47" barrel) have also been at 70% eff.   

But interestingly, I just extrapolated the .22 cal 7.5gn shot to a 46" barrel and the predicted vel is 1952 fps.
Let me know if I can supply more info.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: rsterne on April 01, 2016, 07:12:17 PM
Scott, the .22 cal 7.5 gr @ 4500 psi, 26 cc, 23.3" barrel shot that was 2031 fps was 70% (Isothermal) or 71% (Adiabatic).... Here are the .278 cal, 55 cc shots so far.... showing the % efficiency (fudge factor) required to get the actual results....

2031 fps, 9.1 gr. @ 4000 psi, 47.5" barrel was 70%+ Iso, 71%+ Adb....
1802 fps, 13.7 gr @ 3500 psi, 47.5", was 70% Iso, 71%+ Adb....
1688 fps, 13.7 gr. @ 2500 psi, 47.5", was 67% Iso, 69% Adb....
1884 fps, 13.7 gr. @ 3700 psi, 47.5", was 71% Iso, 73% Adb....
1938 fps, 10.3 gr. @ 4000 psi, 47.5", was 67% Iso, 68% Adb....
2162 fps, 7.7 gr. @ 4600 psi, 46.0", was 73% Iso, 74% Adb....
2164 fps, 7.1 gr. @ 4500 psi, 46.0", was 72% Iso, 73% Adb....
2143 fps, 6.1 gr. @ 3800 psi, 46.0", was 71% Iso, 72& Adb....

There is a pretty clear tendency towards higher efficiency at higher pressure.... but I suspect that is because we are still using Boyle's Law, whereas the actual density is less at the beginning of the shot, and the pressure is less at the end of the shot, compared to what is used in the spreadsheet.... Once we incorporate VanDerWaals into the spreadsheet, those discrepancies will hopefully disappear....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Scotchmo on April 01, 2016, 09:04:43 PM
Bob,

Thanks.

I feel the same, that Boyle's is fine, until Lloyd gets a 6000psi cylinder.  :D

I appreciate the work you did Investigating the 1640fps and  1854fps formulas. That motivated me to start from scratch and go with a different approach. And it's looking like both those numbers can be right. But neither tells the maximum velocity. The molecular velocity, RMS= 1640fps is a leading indicator. We don't see it as muzzle velocity. It is the feedback loop. The mass velocity, 1854fps is a lagging driver. The difference ends up as fluid friction (entropy gain). That feeds-forward. Transferring irreversibly into the molecular velocity and raising the limit, but not raising the actual speed. The fact that 1640fps is an RMS velocity explains why there is still some fluid friction when air velocity is below 1640fps. I have got a long ways to go. But it's all starting make sense. I have one number, the max velocity at 50% efficiency, that I got through a cumbersome iteration. With RMS 1650fps as a starting point, I get 3902fps as the final molecular velocity. Air only, down an infinite tube.

I think the formula for the max velocity integral is about done. I'm going to try and come up with the solution first rather than resort to numerical methods. Don't hold your breath, my ability at calculus/differential equations was never that good.

I'm still dealing with just air. I'll incorporate a pellet mass later if I can.
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: lloyd-ss on April 01, 2016, 10:50:55 PM
One more piece of random "fail" data to add to the collection.
I guess the plastic rod that I thought was G10, wasn't. 
The projectile weighed 5.1 grains and pulled through the clam-shell clamps at about 1500 psi.  With the clamshell clamps in that position, there was probably about 75% of the bore area  clear.
Velocity was only 1777 fps.  Ha ha, seems funny to be saying "only" 1777 fps.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: rsterne on April 01, 2016, 11:45:54 PM
"only 1777 fps at 1500 psi"....  ::)  ;D

Bob
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: MichaelM on April 02, 2016, 12:51:04 AM
"only 1777 fps at 1500 psi"....  ::)  ;D

Bob

lol that was my thoughts exactly
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: rsterne on April 02, 2016, 12:52:21 PM
Efficiency on the latest shot (5.1 gr, 1500 psi, 1777 fps) is 63% Iso & 64% Adb.... Definite trend here for increased efficiency at increased pressure, makes me wonder if it's mostly the Density issue or something deeper.... After all, a stock .22 Disco (2000 psi down to 1100) runs only about 56% or so (Iso).... Of course it has relatively small ports as well....

I wonder, Lloyd, how much velocity you would lose with a conventional valve (possibly a spool valve?) so that you didn't have to load up the pellet structurally before the shot.... I guess the problem is the volume between the valve and the pellet, which really affects things?.... 1 cc of 4500 psi air weighs 5.5 grains, so if you had a pellet that weight, the air that needs to be accelerated would double it and cost a lot of velocity....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: lloyd-ss on April 02, 2016, 02:07:48 PM
................

I wonder, Lloyd, how much velocity you would lose with a conventional valve (possibly a spool valve?) so that you didn't have to load up the pellet structurally before the shot.... I guess the problem is the volume between the valve and the pellet, which really affects things?.... 1 cc of 4500 psi air weighs 5.5 grains, so if you had a pellet that weight, the air that needs to be accelerated would double it and cost a lot of velocity....

Bob

Bob,  Funny, I was sketching a different style of valve this morning to use for these tests.  The lightest I can make a .278 cal pellet that works with the current double clamshell clamp is about 5.5 grains,  which really isn't light enough.  I want to get all the bugs worked out using HPA before I get the nitrogen, and I feel like at this point I have something that works, but that does not work "well" or "easy". 
The valve I am thinking about would still dump directly into the rear of the pellet and might also be able to use conventional ammo.  It might be a bit clunky, but would eliminate some of the current problems.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: match on April 02, 2016, 02:33:22 PM
now you have zero time between release and pressure acting on the projectile.

using a valve of any kind will insert a non-trivial rise time for the pressure as seen by the projectile

this will be another variable to measure and manage (I assume you already do this in the current model)

so how does this rise time effect the overall true efficiency and the fudge factor efficiency?
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: rsterne on April 02, 2016, 03:43:52 PM
With a 46" barrel, I don't think the rise time will matter much, but any volume added to the mass of the pellet before it is subject to the full pressure won't help.... and perhaps they are the same thing.... Only trying it would give us that answer.... The velocity loss with the same pellet weight and air pressure would be directly attributable to the rise time, if the wasted volume is truly zero....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: lloyd-ss on April 02, 2016, 04:25:30 PM
now you have zero time between release and pressure acting on the projectile.

using a valve of any kind will insert a non-trivial rise time for the pressure as seen by the projectile

this will be another variable to measure and manage (I assume you already do this in the current model)

so how does this rise time effect the overall true efficiency and the fudge factor efficiency?
That might be true, but maybe not.  It will depend on the valve and the dead air space and the speed of the valve.  What I have in mind is a non-conventional valve as far as airguns are concerned.  But I do understand the concerns. I think empirical testing with the same weight projectiles will be the only way to determine what affect the valve has.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Scotchmo on April 02, 2016, 06:19:25 PM
One more piece of random "fail" data to add to the collection.
I guess the plastic rod that I thought was G10, wasn't. 
The projectile weighed 5.1 grains and pulled through the clam-shell clamps at about 1500 psi.  With the clamshell clamps in that position, there was probably about 75% of the bore area  clear.
Velocity was only 1777 fps.  Ha ha, seems funny to be saying "only" 1777 fps.
Lloyd

A reliable clam-shell pellet in the 7gr range seems like a good compromise for comprehensive data collection.

If you want to push the velocity envelope, the next phase might be a longer barrel (8') with a 100cc dump.

http://www.onlinemetals.com/merchant.cfm?pid=7760&step=4&showunits=inches&id=283&top_cat=0 (http://www.onlinemetals.com/merchant.cfm?pid=7760&step=4&showunits=inches&id=283&top_cat=0)

That could get you into the 2600fps range at 65% +/-. Just an estimate.

I don't want to be a back-seat driver. Sorry about that. FWIW - I'm just throwing out some ideas.
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: lloyd-ss on April 03, 2016, 09:13:46 AM
Scott,
I agree, the clamshell clamp has its limitations, plus, it is a pain to make the special pellets that are as light as possible, but strong enough so that they don't "self launch." How's that for a euphemism?  I think the minimum weight I can make is 5.5 grains, and I will try a couple of those to get some data.  But this current phase is just a warm up for the actual testing where the nitrogen is used and the barrel is incrementally cut back.  Making these complicated pellets is a pain, but I could have them cnc made for cheap if absolutely necessary.

The next pre-nitrogen phase, before going the brute force route of longer tube and more air, is the incorporation of a super fast, in-line dump valve with near-zero head space.  The valve, which is really a plug that is actually the tip of a piston,  is basically a cylindrical part, slightly  larger in dia than the barrel bore so that a force imbalance can be created, with a conical point that plugs the breech of the barrel.  The rear of the plug is  a straight piston that fits into a bore  and has about .25 of travel and less than 1cc of actuating air volume.  Charging this 1cc cylinder causes the conical point of the piston to plug the barrel, but still allows a full annular space around the plug to become the flow path of the reservoir, which is then filled with the HPA.  To fire, a mechanical poppet  that forms the exhaust for the 1cc cyl, instantaneously dumps the 1cc of air holding the plug in the barrel, then the pressure imbalance from the HPA shoots the plug/piston to the rear, and lets the HPA flow in a full annular entrance to the barrel.  It is a very simple design, common, especially in low pressure, low power applications.  I used a crude version of this design about 8 years ago (pre GTA days) when fiddling with some 1,000 FPE 50 cal stuff.  The devil is in the details though, and hopefully I can pull it off.  The goal, before I start using the nitrogen,  is to have a reliable, repeatable,  gun, that uses cheap (easy to make or off-the-shelf) projectiles, that delivers very high velocities.  Do you remember the old Mel Brooks movie, "Space Balls"?  In their space ship they didn't have the usual, boring, "warp factor" speeds, and I remember their fastest speed was called, "Ludicrous Speed."  That is the goal!!   ;D   Bob, you said it, "To infinity and beyond!"
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: lloyd-ss on April 03, 2016, 09:36:49 AM
This is really a continuation of reply #415. 
Here is a pic of an early (2008-2009 vintage) solenoid controlled dump valve set-up with .50 cal barrel.
The HPA reservoir is the big cylinder on the left and the actuating cylinder, operating at 125psi,  is the much smaller cylinder on the right. The piston in the small cylinder, when pressurized with the 125psi air,  has a rod that extends to the breech of the barrel and plugs it so that the HPA can be filled.  When the solenoid on the low pressure side is fired, the QEV allows an instantaneous dump of the low pressure and the HPA imbalance on the other side of the piston yanks the plug out of the barrel.  Wickedly fast and powerful. The design will be somewhat similar to this, but quite different. Electronics should not be necessary.
 
(http://i226.photobucket.com/albums/dd79/loyd500/general/2-dumpvalveproto_510barrel-a.jpg) (http://s226.photobucket.com/user/loyd500/media/general/2-dumpvalveproto_510barrel-a.jpg.html)
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: rsterne on April 03, 2016, 05:49:55 PM
You, Sir, are a master at coming up with KEWL ideas !!!!

Bob
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Scotchmo on April 03, 2016, 07:57:38 PM
I wrote a paper on the 1640fps "myth". Object was to better explain it to others:

http://www.scotthull.us/1640-myth.htm (http://www.scotthull.us/1640-myth.htm)

Any comments as to clarity of explanation would be appreciated. I did not want to get too technical.
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: rsterne on April 03, 2016, 10:18:19 PM
I think you have done a good job of explaining your theory.... but as I have said before, I am not at all versed in Thermodynamics, so not in a position to really comment.... I'm sure those who are will be willing to debate it with you, and hopefully add their own insight and ideas.... Who knows, it may well turn out to be the explanation.... The key, I would think, is whether temperatures high enough to sustain the velocities we are already reaching can be obtained.... when starting with air at 70*F....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Michael Loar on April 04, 2016, 03:27:48 AM
The average air velocity right behind the pellet is higher than the air velocity entering the barrel. The mass flow rate is the same. Think about it!

On Lloyd's last test, the air enters at 1650fps (or 1854fps) and the first molecules to reach the muzzle were going 2162fps. What's the problem?

I am not quite understanding the theory behind the statement that the air entering the barrel behind the pellet is either moving at 1650 fps or 1845 fps since it is at 4500 psi at the release of the pellet. I do not fully understand most of the math equations presented here so if that velocity is a result of the calculations done in this thread that has resulted in those being the velocities of the airs speed as it hits the pellet when released then disregard my question, but it seems to me that air at 4500 psi that is suddenly and fully released into the barrel behind the pellet would /should be moving at a much higher velocity if not close to the final velocity of the pellet at the muzzle.

I understand the acceleration of the smaller column of air in the center 1/3 to 1/2 of the diameter of the barrel as the walls of the barrel will tend to form a boundary layer of air that will slow down as it moves down the length of the barrel and thereby accelerating the center column of air faster as it nears the muzzle.

So is the 1650/1845 FPS of the initial release of the 4500 psi air part of the resulting calculations that have been worked out here or is it a fixed number from one of the laws of physics used in the calculations that states that is the maximum velocity the air can be moving. Please put it in laymen's terms as to how those numbers were derived to be stated and used as a basis for the extensive math shown through out this thread.

Thanks Mike
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: lloyd-ss on April 04, 2016, 09:21:40 AM
I wrote a paper on the 1640fps "myth". Object was to better explain it to others:

http://www.scotthull.us/1640-myth.htm (http://www.scotthull.us/1640-myth.htm)

Any comments as to clarity of explanation would be appreciated. I did not want to get too technical.
Scott,
Well presented paper.  Enough technical information without being overly so.  I definitely see merit in your argument, but I, like Bob, do not have enough of a thermodynamics background to add additional thoughts.
Lloyd
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: rsterne on April 04, 2016, 03:58:46 PM
Mike, the 1640 fps is the RMS (call it an average) velocity of the air molecules, bouncing around in random directions inside the reservoir before firing.... On firing, the molecules that would hit the base of the pellet and bounce back into the reservoir, now shove the pellet down the bore, and are replaced with more from the reservoir....

My idea is that the new ones exiting the reservoir, hit the ones in the barrel, which are already moving down the bore, accelerating them further, one packet of air pushing the one in front, and the front one pushing the pellet.... Add that to Scott's point about there being a velocity profile inside the barrel, with the molecules in the center moving faster than the average, and the ones on the side moving slower (from barrel friction), I don't think we are exceeding any laws of physics at all.... I can see it entirely possible for the RMS average of the molecular velocity to be 1640, but the ones in the center of the barrel are double that.... they are the ones in right hand, high-speed part of the Maxwell speed distribution curve.... some of which are moving more than twice the average speed.... The barrel merely "focuses" them to do useful work on the pellet....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Scotchmo on April 04, 2016, 04:06:30 PM
The average air velocity right behind the pellet is higher than the air velocity entering the barrel. The mass flow rate is the same. Think about it!

On Lloyd's last test, the air enters at 1650fps (or 1854fps) and the first molecules to reach the muzzle were going 2162fps. What's the problem?

I am not quite understanding the theory behind the statement that the air entering the barrel behind the pellet is either moving at 1650 fps or 1845 fps since it is at 4500 psi at the release of the pellet. I do not fully understand most of the math equations presented here so if that velocity is a result of the calculations done in this thread that has resulted in those being the velocities of the airs speed as it hits the pellet when released then disregard my question, but it seems to me that air at 4500 psi that is suddenly and fully released into the barrel behind the pellet would /should be moving at a much higher velocity if not close to the final velocity of the pellet at the muzzle.

I understand the acceleration of the smaller column of air in the center 1/3 to 1/2 of the diameter of the barrel as the walls of the barrel will tend to form a boundary layer of air that will slow down as it moves down the length of the barrel and thereby accelerating the center column of air faster as it nears the muzzle.

So is the 1650/1845 FPS of the initial release of the 4500 psi air part of the resulting calculations that have been worked out here or is it a fixed number from one of the laws of physics used in the calculations that states that is the maximum velocity the air can be moving. Please put it in laymen's terms as to how those numbers were derived to be stated and used as a basis for the extensive math shown through out this thread.

Thanks Mike
The air behind the pellet is less dense than the air entering the barrel. For any given mass flow rate, that means that the air behind the pellet is moving faster than the air entering the barrel.
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Scotchmo on April 04, 2016, 05:10:48 PM
Mike, the 1640 fps is the RMS (call it an average) velocity of the air molecules, bouncing around in random directions inside the reservoir before firing.... On firing, the molecules that would hit the base of the pellet and bounce back into the reservoir, now shove the pellet down the bore, and are replaced with more from the reservoir....

My idea is that the new ones exiting the reservoir, hit the ones in the barrel, which are already moving down the bore, accelerating them further, one packet of air pushing the one in front, and the front one pushing the pellet.... Add that to Scott's point about there being a velocity profile inside the barrel, with the molecules in the center moving faster than the average, and the ones on the side moving slower (from barrel friction), I don't think we are exceeding any laws of physics at all.... I can see it entirely possible for the RMS average of the molecular velocity to be 1640, but the ones in the center of the barrel are double that.... they are the ones in right hand, high-speed part of the Maxwell speed distribution curve.... some of which are moving more than twice the average speed.... The barrel merely "focuses" them to do useful work on the pellet....

Bob
Something to remember about that statement in red:
The center column or cone has the higher mass flow rate, but the outer skin would have the higher molecular velocity.

The average (molecular_velocity + mass_velocity) of all regions in the barrel is the same.

We are looking at it as different molecules all having different molecular velocities that result in an RMS velocity. Instead, imagine them as vibrating molecules. Very high frequency vibration. At higher temps, the molecular velocity increases. They vibrate "faster" (higher amplitude). The molecules spread apart, reducing the density.

The RMS velocity is really a vibration which can take various forms:
(https://upload.wikimedia.org/wikipedia/commons/0/0e/Symmetrical_stretching.gif)(https://upload.wikimedia.org/wikipedia/commons/0/0c/Asymmetrical_stretching.gif)(https://upload.wikimedia.org/wikipedia/commons/6/60/Scissoring.gif)
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: rsterne on April 04, 2016, 06:59:43 PM
Now you're dealing with Physical Chemistry, and although not my Forte, I do understand a tiny bit about that.... The vibration modes you are showing are WITHIN the molecule, not how one molecule interacts with another.... IMO that is NOT what the RMS velocity is referring to at all, it refers to the velocity of the complete molecule, relative to the others, and the container, not one atom vibrating relative to another within the Nitrogen and Oxygen molecules.... Your diagrams, BTW, are for a molecule such as water (in fact they probably are water), with two Hydrogen and one Oxygen.... Water is a "bent" molecule, with the spare electrons on the Oxygen occupying the positions shown on your drawings, and does, in fact, vibrate as you show.... N2 and O2, being diatomic, only have two atoms, so all they can do is stretch and compress (imagine just one blue and one yellow in the first two diagrams), there is no interatomic force to make them vibrate like a tuning fork (like in the third diagram)....

Your statement about the center of the flow having the higher mass flow rate, but the edges a higher molecular velocity total confuse me.... Mass flow is molecules per second, so the only way that could happen would be for the air density to be higher in the middle of the barrel....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Bill G on April 04, 2016, 07:15:38 PM
Just got caught up with all the posts. I'm still out of town and do't have access to all of my toys. 

Lloyd, your valve concept is about exactly the same as the one That I have been working on.  The biggest difference is that the reservoir is under the the dump chamber.  The dump chamber if fed through a reg that will be externally adjustable in the future iteration of design.  from the reg it passes through a TP and then through a floating piston. The air then travels to the rear of the piston causing it to to push forward thus closing the access to the barrel.  There is a check valve in the bulkhead that the piston slides in.  You know how the rest works as to the evacuation.  What I am designing is very similar to our current poppet valve at the rear of the piston and bulkhead. The head of the poppet  will close the passage to through the piston when the stem is hit.  this will allow the air to evacuate causing the needed imbalance that causes the dump camber to empty.  when the piston shifts rearward it will maintain the seal of the piston port until the dump chamber is evacuated(nearly).  once the dump chamber psi is low enough the rear poppet and piston will separate allowing the cycle to be restarted.  Ideally the reservoir and dump valve as described will be separated by what I call the spar, which the TP is placed.  This spar will be what the barrel mounts to and will allow the barrel to slide forward to allow access to the chamber for loading.  the gap between the piston and the rear poppet will be equal to the certain distance required for maximum flow rate into the barrel.  it looks like the "waisted" volume to rear of the piston and dump chamber will be dependant on the I.D. of the dump chamber.  AS of now that is about .005 in^3 and I think that I may be able to decrease that. 

I had been working on this as a leap of faith and on what I had been getting from modeling using my calculator.  The fudge factor is exactly what I had been trying to explain away and make "automatic". Then Lloyd starts this thread, Bob and Scot start crushing the math.  Definitely at a perfect time for me.  I am hoping to be able to start fabricating more parts this winter when my sons aren't burning all my time with baseball.  New job isn't helping much either due to traveling for training.  Thanks a million fellas for all the hard work.  It has renewed the desire to move forward with this project since our calculations are so close to Lloyd's findings.  Bob and Scot are closer than me.  If I introduce the 70% efficiency factor I'm much closer,  within just a few FPS of what Bob and Scot have been getting .  I'd just like to be able to have that factor auto correct and it is just beyond my ability I suppose. 

Bob, the graph showing a divergence at 2000+ psi is very interesting.  I think that this showed up with Lloyd's early testing on the 3500 psi testing.  They all seemed to follow a power regression.  I had previously noted that they were above .99 on the R^2  but when the model was carried out to predict outcome at lower and higher psi's, the results were unrealistic.  But when modeled as a power regression the trends were very realistic. 

Great work gentlemen. 

Bill G           
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Scotchmo on April 04, 2016, 07:27:09 PM
Now you're dealing with Physical Chemistry, and although not my Forte, I do understand a tiny bit about that.... The vibration modes you are showing are WITHIN the molecule, not how one molecule interacts with another.... IMO that is NOT what the RMS velocity is referring to at all, it refers to the velocity of the complete molecule, relative to the others, and the container, not one atom vibrating relative to another within the Nitrogen and Oxygen molecules.... Your diagrams, BTW, are for a molecule such as water (in fact they probably are water), with two Hydrogen and one Oxygen.... Water is a "bent" molecule, with the spare electrons on the Oxygen occupying the positions shown on your drawings, and does, in fact, vibrate as you show.... N2 and O2, being diatomic, only have two atoms, so all they can do is stretch and compress (imagine just one blue and one yellow in the first two diagrams), there is no interatomic force to make them vibrate like a tuning fork (like in the third diagram)....

Your statement about the center of the flow having the higher mass flow rate, but the edges a higher molecular velocity total confuse me.... Mass flow is molecules per second, so the only way that could happen would be for the air density to be higher in the middle of the barrel....

Bob
You know more about chemistry than I do. Maybe I'm grasping at straws.

It still makes sense that (molecular_velocity + mass_velocity) of all regions in the barrel is the same.

Or, more precisely, (KEmolecular+KEmass) of all regions is the same.

And the motion that determines that KE can takes many forms. We have been focusing on the translation, but need to consider them all:

(http://www.honolulu.hawaii.edu/instruct/natsci/science/brill/sci122/Programs/p26/trans.gif)(http://www.honolulu.hawaii.edu/instruct/natsci/science/brill/sci122/Programs/p26/rotat.gif)(http://www.honolulu.hawaii.edu/instruct/natsci/science/brill/sci122/Programs/p26/vibrat.gif)

"...so the only way that could happen would be for the air density to be higher in the middle of the barrel.... "
Exactely!

Efficiency losses occur in the boundary layer. Raising the temperature in the boundary layer. Density goes lower on the edges. Now the density of the air in the middle of the barrel is higher than the average throughout that region of the barrel.

Edit: Calling the RMS a velocity is OK for total KE calculations, but it is not really a velocity. A translating velocity is a vector. RMS is not. RMS is a speed that has no direction. RMS is usually used to quantify the speed of something undergoing vibration.
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: rsterne on April 04, 2016, 10:05:21 PM
RE your second diagram.... the RMS molecular speed (you are correct, it is not a velocity, because it is random) is TRANSLATION....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Scotchmo on April 05, 2016, 12:47:26 AM
Bob,

You are saying that KEmolecular is from translation only. I'll go with that. That part is recoverable.

Gas molecules don't just translate.

The energy is divided between translation and any other degrees of freedom. (equipartition of energy?)

I think that is the same as the K=1.4 ratio for air.

The part of that is not recoverable goes to heat. The question is still whether it is enough heat.

Your original checks led you to believe that the temperature rise from the inefficiencies would be insufficient to account for the needed molecular speed.

I suspect that once it is integrated as an incremental increase along the barrel, it will be just enough.

The other possibility is that the molecular velocity has nothing to do with a speed limit. Until we exhaust all other possibilities, I'll have trouble letting that one go. In either case, a model that correctly includes temperature rise from fluid friction will give the most accurate model. Definitely better than a straight fudge factor.

Lloyd already proved that the 70F 1640fps molecular speed is not a limit. But the tests did not prove whether or not molecular velocity has any bearing on the speed limit.

A better model may help justify whether the molecular speed (at any temperature) is a limit to PCP velocity. I can't do the advanced math that is needed. I might be able to do a better numerical integration.  I'm just not sure I want to put that much work into it.

I'm slowly reworking my spreadsheet. I'm switching all inputs to SI units before doing the integration. The imperial units were getting too confusing. I'll still have the user input imperial when desired, but I'll convert any grains, inches, psi, fps, degreeF, lbf, etc. to kg, meters, kpa, m/s, degreeK, newtons, etc., before doing any integration.

I am learning (and relearning) a lot from this whole exercise.
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Michael Loar on April 05, 2016, 03:22:19 AM
Ok Bob and Scott got a better grasp on the molecular FPS thing except for the fact that the 4500 psi air in the dump chamber is stagnate until the release of the pellet is it not so is it the fact that the heat contained it that 4500 psi air is causing the molecules to stay moving inside the dump chamber at a much reduced speed until the pellets release and basically then all heck breaks loose and the race is on to see who makes it to barrels end first.

Bob  I understand your packet of air theory with each one pushing harder on the one ahead of it since the ones still accelerating out of the dump chamber would still have more energy to release than the ones already ahead of the ones leaving the chamber and it acts as a continuation of momentum from the back to the front so that the more molecules compressed into the barrel the harder they push on the ones in front of them hence increasing the ones at the very fronts speed until it is all released at the barrel end.

I also know from racing and building race engines that the venturi effect inside an intake manifold from the air speed outside of the carb or throttle body to where it passes thru the restriction at the throttle plates serves to increase its velocity quite significantly and helps prevent the boundary layer of air/fuel molecules to collect along the walls of the intake manifold and lean the mixture out from lack of the full air fuel charge making it into the cylinders. That is why the inner surface of most street cars intakes work better with a slightly rough surface to prevent that accumulation of that boundary layer from forming and causing the air/fuel molecules to collect on the walls of the intake much like the dimples on a golf ball increase it flight distance due to decreased drag.. Now a full on race engine like top fuel dragsters and Nascar engines that are designed to run at peak rpm only all the time and only see low rpm situations when at the starting line or in the pits benefit much more from a highly polished intake walls since the air/fuel molecules are moving at the highest possible velocities all the time and don't have time to form a boundary layer of air/fuel on the intake walls that amount to any significant amount that would decrease power and torque output. I am talking the difference of 2000 rpm to 4500 rpm on the street and 8000 rpm to 10,000 rpm on the race track being a constant engine speed or to put it a better perspective. A Nascar engine at 8000 rpm has a piston speed of 5000 FPS and a top fuel dragster at 10,000 rpm has a piston speed of 6000 FPS with the pistons stopping and starting back to that speed at every revolution at top dead center and bottom dead center or twice for every single revolution of the engine. Where as a street driven car that will last 100,000 plus miles as they do today has a average piston speed of 2000 to 3000 FPS at interstate speed of say 2000 to 2500 rpms and 70 MPH.

Mike
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: rsterne on April 05, 2016, 01:56:59 PM
Scott, if you work strictly with the idea that RMS molecular speed is needed that will exceed the pellet velocity, then for Lloyd's 2162 fps shot you need over 230*C just to match the pellet velocity.... As Steve keeps pointing out, Adiabatic expansion should cause a net cooling effect on the air, so you need to not only generate enough heat to completely overcome that, but to raise the temperature to over 500*K.... It is highly unfortunate that he continues to slide in comments about how you can't get to where we are today, or why your theory is wrong, without putting any actual effort into explaining it.... Perhaps as Lloyd says, he already knows the answer but is not willing to share his insight to explain the facts which overturned his long held position.... If so, that would indeed be a great shame.... I am hoping he is as much in the dark as the rest of us, and simply doesn't want to admit it....

I'm still convinced that the original thought I had many years ago, that since the RMS value is much less than the speed of a portion of the molecules (as shown by Maxwell's speed distribution).... there are enough "fast ones" to drive the pellet well past 1650 fps.... as I first saw on the CAF way back when.... Your idea of the velocity profile, where the outer molecules are slowed by friction with the barrel, while the inner ones are moving much faster than 1650, is I think sufficient explanation of what amounts to a focusing of the high velocity molecules down the center, providing plenty of push on the pellet to explain Lloyd's results, without violating the RMS average at the ambient average temperature in the barrel, whatever that is....

You can drive a solid object to hypersonic speeds, and the molecules in it are still vibrating independent of the forward velocity.... A liquid is the same thing, but the molecules are more loosely bound, but still vibrating.... A gas is yet the same thing again, but the molecules are not bound to each other, but colliding, providing "pressure".... Why should it be possible to accelerate one to extreme velocity but not the other?.... Perhaps the whole concept of molecular speed having anything to do with it is what is flawed....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Scotchmo on April 05, 2016, 03:29:02 PM
Bob,

Looking at is as some of the RMS molecules being faster than others and allowing/causing the higher velocities - That parallels what I'm saying. The only difference is that I see those faster molecules as being concentrated behind the pellet.

I know that the temperature needed to keep the molecular speed above the projectile speed (2150fps) seems very high. But I'm not ready to say that those high temps can't happen for a millisecond right behind the pellet.

I decided that I need to start over on my spreadsheet. Integrating by barrel length increment was convenient at first, but is now messing things up. I now want to do it by air mass increment. Track each milligram of air as it enters the barrel and works it's way to the muzzle. That will let me to heat it, expand it, without also having to deal with a change in quantity.

"Why should it be possible to accelerate one to extreme velocity but not the other?.... Perhaps the whole concept of molecular speed having anything to do with it is what is flawed...."

There is a difference between accelerating a solid and accelerating a gas. The solid stays the same length. The gas shrinks in volume as you accelerate it. Is it shrinking fast enough to cancel out any added force trying to accelerate it?

I have suspicions too - the whole concept of molecular speed as a limit may be flawed.  If the spreadsheet model can't keep the molecular velocity ahead of the pellet velocity, I'll being going with my suspicions.
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: rsterne on April 05, 2016, 05:53:06 PM
My posting may dry up somewhat, I will be away until April 11....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Michael Loar on April 06, 2016, 03:45:57 AM
As far as a solid staying the same length that may hold true if that solid is only traveling in one direction but in the case of an engine with pistons and rods and a crankshaft that's most definitely untrue as the rods and crankshaft flex and bend and contort all over the place at the sudden stops and starts at top dead center and bottom dead center when running. The rods in a street car at 2000 rpm are being compressed and expanded by up to .050" every time the piston change directions as well as the crankshaft journals being twisted in the reverse direction of rotation every time a cylinder fires.

I was given the opportunity to see the inside of a small block Chevy motor running at 3000 rpm with a strobe light and camera inside the block and the crankshaft and rods looked like wet noodles being twisted and bent is all directions as it rotated and is why there are a harmonic balancer on the front of the crank and a balanced or unbalanced flywheel at the rear to help absorb all those vibrations and impulses from the cylinders firing and applying extreme forces to the rods and crankshaft not to mention the camshaft is doing the same thing under the valve trains loads. Without those counter measures to help absorb and balance the rotation cranks and rod would break in very short order.

Mike       
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Scotchmo on April 06, 2016, 08:51:57 PM
I asked a somewhat rhetorical question in my last post:

"There is a difference between accelerating a solid and accelerating a gas. The solid stays the same length. The gas shrinks in volume as you accelerate it. Is it shrinking fast enough to cancel out any added force trying to accelerate it?"

First inclination might be to agree with an answer of "yes". But the 2000fps shots indicate "no". Because the dump gun creates a constant pressure process, or nearly so, the gas does not compress. So Bob is right in that respect. But there is even more - It actually grows in length as heat from friction raises the temperature while pressure stays the same. It undergoes a constant pressure (or nearly so) expansion.

We may be dealing with a mass of air that is significantly less than we think it is.
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: rsterne on April 06, 2016, 08:57:58 PM
While it is possible that you may be right, the fact that the spreadsheet works over a complete shot string, predicting the correct number of shots based on the volume (and therefore mass) of air per shot.... I rather doubt it suddenly is overpredicting the mass on a dump shot.... but there is really no way to prove that because the entire reservoir is dumping....

Bob
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: Scotchmo on April 06, 2016, 09:48:31 PM
While it is possible that you may be right, the fact that the spreadsheet works over a complete shot string, predicting the correct number of shots based on the volume (and therefore mass) of air per shot.... I rather doubt it suddenly is overpredicting the mass on a dump shot.... but there is really no way to prove that because the entire reservoir is dumping....

Bob
I can't prove it's happening, other than it can't NOT happen without breaking some laws of thermodynamics. :)

1) There are losses. Besides a litle bit of pellet friction, air friction is the only other.
2) The losses raise the temperature of the gas.
3) At a constant pressure, that higher temperature gas MUST expand.

If someone says, no friction, no heat gain, no expansion - I say not possible.

If we are below supersonic, the friction and expansion may be negligible. In which case the model is good as is, and air usage is about what we predict. - we can ignore heat gain. When the apparent efficiency drops enough, we need to account for it when looking at air use efficiency. And it may not be quite as bad as our spreadsheet shows, because we are attributing the net energy to more air than we should.

I'm postulating, so I'm willing to change when more info/ideas are are included.
Title: Re: Sonic Choke or Sonic Joke - 2162 FPS
Post by: MicErs on April 06, 2016, 10:13:27 PM
While it is possible that you may be right, the fact that the spreadsheet works over a complete shot string, predicting the correct number of shots based on the volume (and therefore mass) of air per shot.... I rather doubt it suddenly is overpredicting the mass on a dump shot.... but there is really no way to prove that because the entire reservoir is dumping....

Bob
Bob


One could do the statistics by taking thirty samples or so.... Yes one shot is a total dump of teh reservoir but you can still sample 30 shots.  So yeah... While I agree with you I disagree that "there is really no way to prove that".
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: dan_house on April 08, 2016, 04:52:38 PM
Wow, just wow.... You guys ROCK! Great Job Lloyd! Kudos to Scott and Bob for their analysis and support for Lloyd.

It amazes how much work got done when the three of you worked together, debated, argued yet always acted civilly... Quite the contrast to other places.... And this whole discussion, the objectives and the results, have made me realize a number of things. First, it is possible to gather smart folks and let them work toward a common goal, second, the current airgun setups are flawed in any number of ways (but had to be given the state of technology when they are/were designed, customer base and efforts to ensure reliability), third out of this research and experimental test will come the next/new generation of air gun mechanisms. 

While reading the entirety of this thread (and the references to the yellow and other forums) I had the thought(s) rolling around in my head about how to transliterate Lloyd's setup into something I could shoulder and take to the range. It may take some time, but I wont be surprised to see upgrades and improvements that is rooted in this research and experiments.

Again, you all deserve a huge round of applause
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 08, 2016, 06:20:47 PM
Temperature effect of a fast fill rate on a PCP gun's reservoir.

There has been some concern with these high velocity shots about heat transfer within the system and it possibly leading to inflated velocity numbers.  The concern is, I think, that filling the reservoir at a fast rate will heat the air to a point where the molecular velocity (?) is higher than would be seen in a normal PCP.  Darn, where are all the thermodynamics experts when you need them? There is nobody on this forum who professes to having aced there thermo courses, so we'll have to do the best we can.

I am sure that anybody who fills from a tank knows that a guns reservoir will heat up if it is filled very fast.  Then, after a short period of time, the heat dissipates and the reservoir pressure drops a little.  Scott and others mentioned this and Scott suggested that I fill the Max Vel gun's reservoir quickly, record the pressure, then let it cool down for a few hours an see how much the pressure dropped.  The idea is that the more the pressure dropped during the cooling phase, the more the air was "super heated" during the fill, and thus the more extra power could have been extracted from the superheated air IMMEDIATELY after the fast fill.  Something along those lines, and Scott can clarify what I have mis-stated.

So I ran an experiment last night and did a photo-documentation of it, viewable as a slide show in photobucket
http://s226.photobucket.com/user/loyd500/slideshow/MaxVel%20Test%20Gun/Max%20Velocity%20Gun%20Temperature%20Test (http://s226.photobucket.com/user/loyd500/slideshow/MaxVel%20Test%20Gun/Max%20Velocity%20Gun%20Temperature%20Test)
The slide show isn't as slick as I would have liked, but there are photos at various time intervals to show the pressure and thermal changes.

Basically, I filled the sealed breech block of the Version 2 Max Vel gun in about 20 seconds and then monitored the temperature and pressure as it cooled. Total monitoring period was 7 hours and 50 minutes.
Here is the intro page for the Photobucket slideshow and it explains the important points:

Max Velocity PCP Version 2.
Breech block fill temperature test.


55 cc, 1 lb 10 oz aluminum block.
55 cc chamber.

Fill started with block at 79.3*F (room temp).
Block was filled in 20 seconds to 3530 psi.
Temp immediately rose 3.7*F.
After 1 hour, block had returned to room
temp and pressure had dropped 30 psi.
After 2 hours pressure had dropped 40 psi total.

After 7 hrs 50 mins, room temp had dropped
7.2*F and pressure had dropped  only 100psi total.



Conclusion-
This fast fill rate had, at the most, only a  trivial effect on the velocity.
This shows that there was very little heating of the air that could have contributed to a velocity increase in the high velocity shots.  The fill was done at a very fast rate, but the overall affect was that the system only lost 100 psi (out of 3,.530 psi) due to the thermal losses.  If the air were excessively heated during the fill to the point that significant velocity gains could be made, the pressure loss would have to have been on the order of 1000 psi, not 100.
Therefore, the fill rate had nothing to do with the high velocities.

Anyone, please add your thoughts.
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 08, 2016, 06:33:24 PM
Wow, just wow.... You guys ROCK! Great Job Lloyd! Kudos to Scott and Bob for their analysis and support for Lloyd.

It amazes how much work got done when the three of you worked together, debated, argued yet always acted civilly... Quite the contrast to other places.... And this whole discussion, the objectives and the results, have made me realize a number of things. First, it is possible to gather smart folks and let them work toward a common goal, second, the current airgun setups are flawed in any number of ways (but had to be given the state of technology when they are/were designed, customer base and efforts to ensure reliability), third out of this research and experimental test will come the next/new generation of air gun mechanisms. 

While reading the entirety of this thread (and the references to the yellow and other forums) I had the thought(s) rolling around in my head about how to transliterate Lloyd's setup into something I could shoulder and take to the range. It may take some time, but I wont be surprised to see upgrades and improvements that is rooted in this research and experiments.

Again, you all deserve a huge round of applause

Dan,
Thanks from all of us for the kind words.  It really makes it so much more fun and productive when we all work together.  The synergy is pretty phenomenal.  You look at something like Bob's SSG hammer thread and the group effort is pretty unbelievable.
So Dan, a shoulderable version of a HV airgun? 8)  We'd have to throw the pellets away, though, LOL.   ;)
Airgunning at the next level! ;D
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 08, 2016, 07:32:16 PM
Lloyd, I'm very glad that I am on a short holiday and had limited time to respond to what you are referring to in the last couple of days.... I was delighted that you took the time to document the limited amount of heating that occurred in the shot reservoir and how quickly it disippated.... After reading the proposal that Joule-Thompson heating could raise the temperature by 250*F through the heat absorbed from the environment while the air passed through the fill hose for 20 seconds.... and then the completely contrary denial that the reservoir could cool because air was an insulator and had poor heat conductivity.... which are two completely contradictory versions, chosen to support the authors position of the moment.... I was about to make a fool of myself.... It is soooooooooooo much better to dazzle with data then baffle with BS....

It is a pleasure to see a true professional at work, Sir.... and it is an honour to know you....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Michael Loar on April 08, 2016, 09:08:10 PM
Lloyd
I am so glad to see you perform this test since while I agree the air when filling a PCP gun is heated if done so fast, but I myself never felt it was enough to be of any consequence or have a significant effect on pressure. The fact that it only lost 100 psi after cool down of an excessive time frame IMO and did not even gain 10*F is very informative and proof in my belief that it had no true value or effect on the velocity of your numerous test shots.

I think we can safely say it is time to put the theory of heated air molecules contributing to the velocity of any shot up this point to rest for good and for any further test shots as well.

Mike.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 08, 2016, 11:39:04 PM
I'm on my iPhone for the time being so posting is more difficult but will still do.

Thanks for all the work Lloyd. Keep in mind that different fill hoses/tanks/valves/etc. will have different amounts of isothermal gains or entropy gains. But after your test, I doubt they could be near enough to make much difference in your test velocities.

I have been thinking about the original rms theory. And what basis for it. That line of thinking also gave me some other ideas. I'm going to avoid the math, as merely understanding of the process is sufficient for now.

First, the basis. If I were asked, without knowing how an airgun  is configured, what is the maximum speed of the air, I would have said Mach 1. People knew soon enough that was not a limit for pre-charged guns. So another theory of molecular velocity came about. That might be worse than the first theory, but since it was harder to reach that 1640fps velocity, it was harder to refute with real evidence.  For 70F air, Mach 1 is 1128fps. That is the max air velocity from a tank into a straight pipe, regardless of pressure. That max flow happens when the flow becomes choked. With no pellet or very light pellet, I think the choke occurs when pipe length reaches around 50 diameters. That assumes typical friction coefficients. That choke establishes the max flow rate of the system, which occurs at Mach 1 inlet velocity.

Let's forget the 1640fps molecular velocity theory, as that one is a stretch. Let's see why the Mach 1, 1128fps muzzle velocity limit does not hold up in an airgun. The 1640fps theory falls away for the same reason. So, how does the muzzle velocity exceed that 1128fps inlet velocity?

Once the air passes the choke point, it appears to be undergoing a constant pressure expansion. Even as the mass flux (mass flow rate) falls off a little, the exit velocity increases. So the 1128fps inlet velocity limit holds up. But what about the muzzle velocity?

Some have argued that there is a temperature drop in the pipe. And there well may be a drop in "static" temperature. Me, with a basic mechanical engineering background, I prefer to use what I consider to be the real/measured/perceived/total temperatures and pressures. Someone designing ram jet engines might call that the "stagnation" temperature or "stagnation" pressure.  And they will deal with each type of pressures and temperatures  as needed. For my type of work, I don't need to.

The static temperature might be what you would measure if you could pluck a single molecule out of the air stream, and measure the temperature. The stagnation temperature would be what you might measure if you stuck a sensor/probe into the air stream.

Back to the flow. With a slight simplification. Assume the inlet air flow reaches Mach 1, and maintains that inlet flow once the pellet passes the choke point. After that, air friction comes into play and some energy goes to heating the air. That energy is forever lost from the possibility of doing work inside the system. That's called entropy. The extra heat expands the air while maintaing "real" pressure. Volumetric density falls. The expanding air adds more velocity. Mass flux is constant while velocity increase when moving downstream from the choke point. The process becomes less and less efficient as it proceeds down the pipe.

Our airguns have adiabatic, friction flow, in a pipe. Closest to our airguns would be "fanno" flow in pipes or ducts.

All this work has given me some other ideas for experimental, supersonic air guns.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Bryan Heimann on April 09, 2016, 12:27:09 AM
Have ya'll thought of advancements in the form of the projectiles?  Maybe something many times smaller than the bore, in an ultralight sabot?
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 09, 2016, 03:57:29 AM
Wow, just wow.... You guys ROCK! Great Job Lloyd! Kudos to Scott and Bob for their analysis and support for Lloyd.
...
Dan,
I feel like part of Lloyd's support crew, but he's the driver. What I get out of it, is it answers questions for me definitively. I'm making some future plans to play with this new found info. I started designing my "Entropy Gun". A .375 caliber 2kfps monster. But before actually building something like that, I might design an "entropy generator" that can slip into an existing PCP. I won't need the extra long barrel. One shot to prime it, and then it's good for 2000fps for quite a few more shots. With light pellets of course. I think it could work.

My "flux capacitor" didn't pan out however. ;D
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 09, 2016, 08:52:43 AM
Wow, just wow.... You guys ROCK! Great Job Lloyd! Kudos to Scott and Bob for their analysis and support for Lloyd.
...
Dan,
I feel like part of Lloyd's support crew, but he's the driver. What I get out of it, is it answers questions for me definitively. I'm making some future plans to play with this new found info. I started designing my "Entropy Gun". A .375 caliber 2kfps monster. But before actually building something like that, I might design an "entropy generator" that can slip into an existing PCP. I won't need the extra long barrel. One shot to prime it, and then it's good for 2000fps for quite a few more shots. With light pellets of course. I think it could work.

My "flux capacitor" didn't pan out however. ;D

Scott, 
I like the sound of your plans.   ;D    I remember that crazy Monty Python TV comedy series from years ago, and one of the lines they always used was, "And now, for something completely different."   That's what you have to do to make leaps in progress.  I am scratching my head a little at what you are describing, so I know it is going to be good.  But I also know that it is hard work and takes a long time with a lot of dead ends.  :P
Lloyd
P.S. And I definitely appreciate the support and enthusiasm of you and everyone else here.    ;)
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 09, 2016, 10:08:22 AM
High velocity shots from another source....

http://www.network54.com/Forum/79537/message/1460082362/UNI+doesn%27t+know+there+is+a+%26quot%3Bspeed+limit%26quot%3B (http://www.network54.com/Forum/79537/message/1460082362/UNI+doesn%27t+know+there+is+a+%26quot%3Bspeed+limit%26quot%3B)

Nearly 1900 fps with a 2.75 gr. Delrin ball at only 3000 psi.... I think you can now stamp a big CONFIRMED INDEPENDANTLY on Lloyd's data....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 09, 2016, 11:43:51 AM
High velocity shots from another source....

http://www.network54.com/Forum/79537/message/1460082362/UNI+doesn%27t+know+there+is+a+%26quot%3Bspeed+limit%26quot%3B (http://www.network54.com/Forum/79537/message/1460082362/UNI+doesn%27t+know+there+is+a+%26quot%3Bspeed+limit%26quot%3B)

Nearly 1900 fps with a 2.57 gr. Delrin ball at only 3000 psi.... I think you can now stamp a big CONFIRMED INDEPENDANTLY on Lloyd's data....

Bob
Bob,
Slowly whittling away at it, but it certainly isn't going down without a fight.  ;)
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 09, 2016, 11:50:22 AM
New 2035 fps  shot with extensive documentation.

EDIT ===========
April 10, 2016.  IMPORTANT NOTE ABOUT VIEWING THIS VIDEO ON YOUR PHONE
-
All of the documentation in this video is in the form of annotation text boxes inserted into the video via the YouTube editor.  Unfortunately, the YouTube annotations do not show up on most mobile devices.  It is a YouTube problem.  So, if you want to see all the documentation, you have to watch this on your computer.
Lloyd
 ==================== 


Here is the latest high velocity shot, 2035 fps.  This shot was taken with particular attention given to thorough documentation  that will answer some previous questions and concerns.
Lloyd

http://www.youtube.com/watch?feature=player_embedded&v=qUq4OQqZ2bw# (http://www.youtube.com/watch?feature=player_embedded&v=qUq4OQqZ2bw#)

Title: The "sonic choke" exists.
Post by: Scotchmo on April 09, 2016, 02:27:07 PM
There is "sonic choke" in fanno flow.

It limits mass flux to Mach 1 at the inlet, but does not limit velocity in the tube downstream of the choke point.

Realize that and everything is good.

Edit: fixed the title. exits exists
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: madeInLV on April 09, 2016, 03:50:39 PM
This was interesting, but now it's EXCITING!!!!


Loyd,
loads of useful data-thank you.
As for your next valve set up-a picture tells a thousand words:) A graphic representation of the internals would help a lot. I think i get your idea, but some parts are confusing. Here is  a link to a "Pif-Paf" valve.
forum.guns.ru/forummessage/30/78330.html
It's a pilot activated plunger valve. Pilot valve being very small for easy opening. There is one pressure in the entire system-simplifies the setup i think.

Word of advice (from experience): area imbalance on the plunger/piston causes force imbalance as you described. Ideally you want the acceleration of the plunger/piston=acceleration of the projectile, since at one point the pressure will be acting on both the  projectile and the piston/plunger pushing them in the opposing directions.
It is very doable with heavy bullets but might be a challenge for light pellets.
Thus the valve must be made in such a way that pressure imbalance during the pilot " pressure drop" is enough to generate needed acceleration of the piston/plunger.

That might allready be thecase in your design, I'm just sharing my 0.02$ to possibly save time in the future.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 09, 2016, 05:31:04 PM
Very well documented, Lloyd... whittling away, indeed....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Motorhead on April 09, 2016, 05:38:11 PM
Lloyd,
have a Q

Being we know O-rings deform under pressure as there shape shifts against there retention groove, it is a safe assumption the same is happening to the o-ring on your pellet ?

What I'm alluding too is the VERY high frictional losses that likely are happening as the ring is being forced to seal against the pressure, it is "Putting on the brakes" as it is pushed down length of the bore.

Could you Not make a pellet from Peek or similar material having a skirt or waist that creates the seal required for a single trip down the barrel that would mitigate these frictional losses I assuming are present ?
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 09, 2016, 07:15:15 PM
I think the problem, Scott, is that the pellet has to have huge structural strength because the "skirt" is clamped by the release mechanism to allow the full pressure to build on the O-ring prior to firing.... Lloyd has tried some plastics and none has survived past about 1500 psi, IIRC....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 09, 2016, 09:55:21 PM
Lloyd,
have a Q

Being we know O-rings deform under pressure as there shape shifts against there retention groove, it is a safe assumption the same is happening to the o-ring on your pellet ?

What I'm alluding too is the VERY high frictional losses that likely are happening as the ring is being forced to seal against the pressure, it is "Putting on the brakes" as it is pushed down length of the bore.

Could you Not make a pellet from Peek or similar material having a skirt or waist that creates the seal required for a single trip down the barrel that would mitigate these frictional losses I assuming are present ?
Scott,
I agree about the deficiencies of o-rings.  I made a Teflon U-cup seal in posts 321 and 332 and it performed well, but making it was a chore.  I think with the o-rings, the amount of crush  they have in the gland depth has as much to do with their performance as anything else.  At 4500 psi they need enough crush to seal, but not enough to cause high friction losses like you are talking about.  Its a balancing act to meet both requirements.
The current plan is to eliminate the current clamp-and-release mechanism so that the projectile will no longer be a structural element.  Then, a more conventional style of pellet or bullet can be used.  That will open up the possibilities for the types of projectiles, and their weight.
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 09, 2016, 10:24:48 PM
This was interesting, but now it's EXCITING!!!!


Loyd,
loads of useful data-thank you.
As for your next valve set up-a picture tells a thousand words:) A graphic representation of the internals would help a lot. I think i get your idea, but some parts are confusing. Here is  a link to a "Pif-Paf" valve.
forum.guns.ru/forummessage/30/78330.html
It's a pilot activated plunger valve. Pilot valve being very small for easy opening. There is one pressure in the entire system-simplifies the setup i think.

Word of advice (from experience): area imbalance on the plunger/piston causes force imbalance as you described. Ideally you want the acceleration of the plunger/piston=acceleration of the projectile, since at one point the pressure will be acting on both the  projectile and the piston/plunger pushing them in the opposing directions.
It is very doable with heavy bullets but might be a challenge for light pellets.
Thus the valve must be made in such a way that pressure imbalance during the pilot " pressure drop" is enough to generate needed acceleration of the piston/plunger.

That might allready be thecase in your design, I'm just sharing my 0.02$ to possibly save time in the future.
LV,
The concept of the pif-paf valve (I have never heard it called that) is similar to what I am trying to do for the version 3 gun.  Very simple in concept, but many details to work out to get it to function well.  Your concern regarding the acceleration of the valve vs the acceleration of the pellet has to do with the mass of the valve being too large to open quickly enough when light weight pellets are used, correct?  I can see how that would be a problem, but here is a possible way to overcome that, that I am hoping will work.

The valve piston, instead of being a straight sided rod, will have a step in it such that the front end (toward the pellet) will be larger than the back end.  The diameters are sized so that the annulus of the front end of the valve (the area outside of the sealing diameter of the barrel) will be approximately 80% of the area of the rear end of the piston.  The pressure imbalance will provide enough force to seal the valve, but when the pilot air is released the pressurizer imbalance is heavily biased to blow the valve open immediately.  The step in the valve piston means that it needs a second set of o-rings with an atmospheric bleed for the step so that the piston doesn't build up pressure in the stepped area when it is moving.  If the full high pressure air is bled back into the rear piston area, it will close the valve automatically, but it will not (usually) be able to close the valve until the bullet has left the muzzle and the barrel pressure drops enough allow the force of the rear piston to close the valve.

The idea of using the full reservoir pressure to operate the valve piston is nice, because it eliminates the need for a regulator.  It also keeps the valve piston forces in proportion to the reservoir pressure for more consistent operation.

I will post a sketch shortly.
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: phoebeisis on April 10, 2016, 11:22:00 AM
Good stuff-pretty fast
and your temperature drop agrees with your pressure drop .007-.008  drop    3.7/520 and 30/3500-
might be worth 15-20 fps  at most-probably less

Like MOTORHEAD SUGGESTS- the O-ring is a speed killer
Might be possible to  have the O-Ring  JUST  in the chamber- while it is being held
not  attached to the projectile-but set in a machined groove in chamber

The 2000 fps  foil ball   pellet made over 2000 fps-with no  effort made to get a good seal



Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 10, 2016, 06:25:56 PM
Charles,
If the build of the Version 3 Hi Velocity gun is successful, it will accommodate conventional projectiles and eliminate the need for o-rings.  My hopes are to just make the custom  built projectile and o-ring friction problems go away.
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: phoebeisis on April 10, 2016, 09:15:48 PM
Lloyd
Thanks for the quick response
Version 3 sounds like a good plan.
Your machined projectiles were/are a lot of work
Thanks
Charlie
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 10, 2016, 11:45:01 PM
Here is a rough schematic of Max Vel Version 3.  This is similar to the pif-paf valve that LV showed, but with a central difference.
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/Version%203/AGL-MaxVel-Ver3_zpsyw49v8cz.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/Version%203/AGL-MaxVel-Ver3_zpsyw49v8cz.jpg.html)

Balancing, or more correctly, un-balancing the ports and piston areas is the trick to getting this to operate properly.  There are design similarities to some paintball markers, but in general, the circuitry used in paintball markers deals with a few hundred psi and cannot be made robust enough to work with 3 or 4 thousand psi.  The tubular valve with the fixed solid center core (patented), shown in the schematic,  makes this valve more controllable by greatly reducing the reaction forces that the HPA applies to the valve.

Here is how the valve works:
The red piston (tubular valve) is the main moving part.  It is basically a double acting piston, that can shuttle between an open and a closed position.  The tapered front end of the valve can seal the breech of the barrel when it is forced tightly into it.  The front end of the valve is surrounded by the working volume of the HPA reservoir.  The rear of the valve also has the force of the HPA against it via a small bleed hole from the HPA reservoir.  There is a small knock-open valve (pilot valve) that provides a quick exhausting of the rear piston chamber. 
In the closed position, the force of the HPA on the rear annulus area of the piston (the end that is away from the pellet), is somewhat greater than the force on the outside margin of the tapered valve face.  This force imbalance keeps the valve closed.  The amount of force imbalance is based on the force necessary to keep the valve from leaking.

The blue center core can be removed when the gun is under pressure, thus it could actually be used as a bolt, allowing loading from the rear.

To fire the valve, the small knock open valve is hit, and it drains the rear piston chamber instantaneously.  The knock open valve drains the rear piston chamber much faster than it can be refilled through the tiny bleed hole from the front HPA reservoir.  The exhausting of the air from the rear piston chamber drops the closing force so that the opening force on the front margin of the valve  forces the valve rearward and cracks the valve open at the barrel breech. As soon as the valve is cracked, the pressure imbalance doubles and the valve slams open and fires the pellet.  Lag time is virtually nil. 

To end the cycle, once the tiny knock open valve closes, it allows the pressure to build back up in the rear piston chamber.  This increased force on the rear of the piston tries to close the valve, but the pressure imbalance from the front of the valve remains too great until the projectile leaves the muzzle.  Once the projectile leaves the muzzle, the pressure in the barrel drops enough such that the valve will close.   
This particular variation of the valve is well suited to a function as dump valve and will provide high velocities.  Getting it to CLOSE fast enough is the problem.  Easy to open..... difficult to close.  This is not a problem for the high vel gun, but in applications where air efficiency is required,  controlling the closing strictly by passive means is difficult.  Active circuits can solve the problem, but their incorporation is not easy.

Just as a side note, if you study the schematic, the center of the 3 visible o-rings might seem superfluous.  However, it serves to reduce friction and galling between the sliding parts, and also is needed to control the bleed re-fill rate to the rear piston.
 
The actual design is farther along than the schematic shows, and building will start very soon.  I have made several styles of this valve over the years but am keeping my fingers crossed for this new application.
Lloyd

   
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 11, 2016, 12:27:44 AM
Lloyd,

That last video was very thorough. I won't post it on the yellow as there is no urgency. They should spend some time chewing on what they have recently heard/seen. I will revisit it over there in the future. At some point, for a demo movie, you should cut to a clock, after the fill, and then cut back several hours later to show the temp gauge had fallen back to room temp. That would eliminate one other point of contention for the skeptics.

For the next version that has an actual valve, have you thought about round projectiles for testing. Delrin balls, ABS .177 BBs, airsoft balls, etc. An actual valve and a projectile that could be purchased would simplify when doing multiple shots.

On another note - the spreadsheets:
After some research on fanno flow, I found there is a known limit at the inlet. It is not a velocity limit perse, but it would limit the mass flux of the system. The limits of the inlet into a straight pipe is Mach 1. Or 1128fps for 70F air. Knowing this we can adjust the conditions in the barrel behind the pellet to more closely match reality.

If we ignore all friction and fudge factors, once the velocity down the barrel reaches 1128fps, pellet is at a choke point. Mass flux cannot go higher. So the inlet is maxed out. In order for velocity to continue increasing, for the next increment, we start to expand the air behind the pellet to maintain the same force. The temp will need to rise in that increment to account for the expanding air. And that continues all the way out. Mass flux is choked, and in each subsequent increment, velocity continues to increase, density decreases, and temperature increases. I think this will accounted for a big chunk of the inefficiencies from friction without having to actually use any friction coefficients.

And I think I can do this without having to start from scratch.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Michael Loar on April 11, 2016, 01:29:58 AM
Lloyd
I like the design of the knock open valve in your drawing and it appears to be a very simple operating system in concept but as you said the subtle differences in pressures on either side of the tubular valves will be the key to its proper operation and rapid release of the HPA chambers full pressure in an instant to truly act as a full dump valve.

It will be some very subtle fine tuning to get it working as needed but I know you will get it working better than expected and further impress us all with your achievements here in proving that there is "maybe" a limit to how fast a projectile can be accelerated with HPA or it may be all depended on just how much pressure and for how long it acts on the projectile that is truly the only limit in the velocity threshold.

I am curious to see if commercially available ammo when used in the max version 3 valve can withstand the velocities as well as forces placed on it by the full dump system without damage or disintegration from the hyper velocities it will be subjected to that is far above the norm for its intended use.

Keep up the great work and as Bob has said "To infinity and beyond" 

Mike
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 11, 2016, 08:29:54 AM
Mike,
I am not sure how the pellets will hold up, or if I will need to stick with cast bullets.  My guess is that if I am going to eventually incorporate any accuracy testing into this set-up that I need to stick with bullets.  The fastest I have ever shot a pellet was a .25 cal H&N match wadcutter 21.6 gn, 1354 fps, using a 24" LW barrel.  I still have that barrel.  That was shot using a valve similar to the one in the schematic above.
Lloyd

Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: phoebeisis on April 11, 2016, 02:04:24 PM
Lloyd
Wow-cool setup.
If you use a common caliber-
firearm or pellet-it will certainly save lots of work-
lotta choice in firearm projectiles

Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 11, 2016, 03:17:48 PM
Lloyd
Wow-cool setup.
If you use a common caliber-
firearm or pellet-it will certainly save lots of work-
lotta choice in firearm projectiles


Charles,
Agreed on the calibers.  Particularly pistol calibers where there might be a better selection of lighter weight bullets and molds.
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 11, 2016, 03:49:47 PM
I think I just made some big breakthroughs on the spreadsheet. I was able to keep the integration by barrel increment, but I switched all calcs to metric, so as to make it easier to keep things straight. For familiarity, I still allow some of the inputs in imperial units, and I have a separate output sheet that displays the familiar imperial units. I was up late last night working on it, and back up early this morning. My mind too busy, I could not sleep.

I'm using the "OpenOffice Calc" spreadsheet. Spreadsheets sure have a lot more capability than when I once used them. I learned about it's logic functions and conditionals last night. It's almost like a complete programing language (I did about 15 years of duty heavy LISP programming). And this morning I discovered an iteration tool in the spreadsheet that simplified the whole process of what I was trying to do. It took care of the recursion errors, without having to reorganize the spreadsheet. I was contemplating a very deep multi-layer spreadsheet when I stumbled on that capability.

My solution to the simulation model was to assume a fanno flow model with the addition of a pellet mass at the front of the air stream. Sounds simple enough.

Bottom line - it is matching Lloyd's data very closely, with no additional friction coefficients or fudge factors at this point. I may add a small friction or fudge factor later. It won't take much. The predicted velocities are running just a little ahead of Lloyd's tests. And that makes sense because I'm not including any pre choke-point friction. Up until Mach 1 at the inlet, the only resistance is force needed to accelerate the mass of air and pellet. I can also display the temperature behind the pellet at any point in it's travel down the barrel.

There is a "Sonic Choke". It limits the mass flux to Mach 1 at the inlet. Carry that mass flux through the whole simulation model and voila!

It still needs refinement and further checking, but it appears to be a much closer simulation than any of my previous versions. I'm jazzed!

I also shoot FT competition and our small club hosts some big matches. We are hosting a big piston FT match this coming weekend. And I still have lots of preparation to do. So I won't be able to work on the spreadsheet as much as I'd like for a awhile.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 11, 2016, 04:42:21 PM
Scott,
Hot dog !  You pumped or something!!  That sounds really good.  Is that similar to what Bill G was talking about a while ago about maximum mass flow through an orifice, or something different?  So there is a limit to the maximum mass of air that can flow into the breech of the barrel, and that occurs at Mach 1?

The spreadsheet programs are so darn powerful and I think most of us only touch the tip of the iceburg as far as there capability goes.  I don't think I have used the iteration tool.  What is that?
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 11, 2016, 07:10:47 PM
Scott,
Hot dog !  You pumped or something!!  That sounds really good.  Is that similar to what Bill G was talking about a while ago about maximum mass flow through an orifice, or something different?  So there is a limit to the maximum mass of air that can flow into the breech of the barrel, and that occurs at Mach 1?

The spreadsheet programs are so darn powerful and I think most of us only touch the tip of the iceburg as far as there capability goes.  I don't think I have used the iteration tool.  What is that?
Lloyd
Lloyd,

That may have been what Bill G was referring to. In the case of fanno flow, the orifice is the full diameter pipe/duct inlet, continuing with a constant diameter down stream.

We are now in the realm of computational fluid dynamics (CFD).

The combination of spreadsheet, numerical integration, and automatic iteration (thank you OpenOffice!). It's a powerful tool.

During my research, I noticed that AutoDesk has a CFD simulation program out now. Years ago, I used to write engineering applications for AutoCAD. In the late 1990's, AutoDesk bought out one of my main competitors and started to offer applications similar to mine. The merger mostly killed that part of my business. I kept at it for a few years, but found it increasingly difficult to compete directly with them. I continued to do some engineering work but, got out of engineering for hire about 13 years ago. All work that I do now is for my own enjoyment and knowledge.

Here is a good read on fanno flow. Skip the math parts (save that for later):

http://www.pua.edu.eg/PUASite/uploads/file/Engineering/Fall%202012/ME254/lec%2010.pdf (http://www.pua.edu.eg/PUASite/uploads/file/Engineering/Fall%202012/ME254/lec%2010.pdf)

Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Michael Loar on April 11, 2016, 08:18:03 PM
Mike,
I am not sure how the pellets will hold up, or if I will need to stick with cast bullets.  My guess is that if I am going to eventually incorporate any accuracy testing into this set-up that I need to stick with bullets.  The fastest I have ever shot a pellet was a .25 cal H&N match wadcutter 21.6 gn, 1354 fps, using a 24" LW barrel.  I still have that barrel.  That was shot using a valve similar to the one in the schematic above.
Lloyd

Lloyd
Yea I am concerned about common pellets holding up to the hyper velocities as well but would be interested to see if indeed they do or not just as a curiosity stand point. It will likely require real bullets for the tests with the new valve setup if not still custom made projectiles also.

How did that H&N wadcutter hold up at the 1354 fps and was it shot into a trap or backstop that caused deformation or into a soft trap to try to save its integrity. just curious is all.

Mike
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 11, 2016, 09:39:04 PM
I'm not the expert at charts (not like Bob). But I decided to try and produce a couple using the spreadsheet:

(http://www.scotthull.us/photos/Misc/1745fps-00.jpg)

(http://www.scotthull.us/photos/Misc/2162fps-00.jpg)

Here is the amazing thing: I have no fudge factors, not even any pellet friction. The only resistance in system, is the pellet and air mass. And the energy needed to push back the "Sonic threshhold". I assumed adiabatic expansion. Once I put in a little pellet friction, and maybe a little heat loss, we should be right on.

If you look at the graphs, you'll see the blue velocity curve, and a red temperature curve. The temperature actually falls a little at first and then climbs fast as it pushes through the "threshold".

The long barrel is predicted to perform well at lower pressures. Nearly 2000fps should be possible even at 3000psi, when using the long barrel, and .278, 7.5gr pellet. The "choke point" just pushes a little farther out.

The initial velocity spikes quickly. The starting velocity is the average speed over the first increment. I'm currently using 1mm increments. I can easily reduce the increment to get a smoother take off, but it cuts the barrel length proportionally, unless I add a lot more rows. And then it becomes cumbersome to scroll.

I can't stop playing with simulations. OK - I've got to start prepping for the match.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 11, 2016, 10:32:05 PM
So what I want to know, is if the air inside the firing chamber is 413*F, as Steve says.... how is it possible that the pressure doesn't drop more than 100 psi after 8 hours?.... Anybody?....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 11, 2016, 11:31:16 PM
So what I want to know, is if the air inside the firing chamber is 413*F, as Steve says.... how is it possible that the pressure doesn't drop more than 100 psi after 8 hours?.... Anybody?....

Bob
Bob,

It's not possible. But it does not matter.

The leader of the 1640 movement appears to be SteveNC. He won't entertain the type of question you asked because it does not support his theory. He would rather assume faulty experiments in every case. I'm starting to think he cares more about having others perceive him to be right, rather than seeking the truth. I'm done over there for now. It's entertaining and fun to play, but I'll hang out with the adults for now. Though I'll still be on the yellow/green field target forum.

They are spinning their wheels if they keep chasing that 1640rms theory. I don't know what it applies to, but it is not airguns. The limit is Mach 1 (1128fps), and it applies to the mass flux of the inlet. What happens after the inlet is variable.

If I'm going to be convinced otherwise, I need to be provided with more than I've been offered. And believe me, If I am wrong, I'll admit it and adjust my thinking. All I'm getting over there is remarks suggesting:
the firing air was a "hot potato"
semantic arguments
The chrony is inaccurate
the lights are bad
the chrony moves
etc.

Maybe Lloyd should use a PaperChrony.  ;D

I'm ready to be here and let them stay in the "dark ages". They are having fun. I'll let them be.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 11, 2016, 11:49:09 PM
Scott, I see you are chasing the Sonic Choke idea, and I wish you luck with that.... Please note, however, that Mach 1 in 4000 psi air is NOT 1128 fps, but 451.1 m/s (1480 fps).... Here is the calculator....  http://www.wolframalpha.com/widgets/view.jsp?id=b63c87b0a41016ad29313f0d7393cee8 (http://www.wolframalpha.com/widgets/view.jsp?id=b63c87b0a41016ad29313f0d7393cee8)

type "air at 4000 psi" in the box and hit "submit".... If you want a higher temperature, you can enter both.... eg. "air at 4000 psi and 200 C" will give you 516.5 m/s (1695 fps)....

I agree, what they are doing on the Yellow now is playing with being Trolls.... better to leave them behind and try and figure out a new theory that fits the facts, rather than stick your head in the sand....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 12, 2016, 12:11:35 AM
So what I want to know, is if the air inside the firing chamber is 413*F, as Steve says.... how is it possible that the pressure doesn't drop more than 100 psi after 8 hours?.... Anybody?....

Bob
Bob,

It's not possible. But it does not matter.

The leader of the 1640 movement appears to be SteveNC. He won't entertain the type of question you asked because it does not support his theory. He would rather assume faulty experiments in every case. I'm starting to think he cares more about having others perceive him to be right, rather than seeking the truth. .................................................
.................(sections omitted by Lloyd)..................................................
the firing air was a "hot potato"
semantic arguments
The chrony is inaccurate
the lights are bad
the chrony moves
etc.

Maybe Lloyd should use a PaperChrony.  ;D

I'm ready to be here and let them stay in the "dark ages". They are having fun. I'll let them be.

Scott,
I think you summed it up pretty well.  Its the old NIH philosophy... Not Invented Here.....
They are just being silly and having fun making up straw arguments against real evidence. 
I no longer wish to actively share any of my work with them.  It is disappointing, but they are a not worth my time. Let them believe what they wish.
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 12, 2016, 02:33:34 AM
Scott, I see you are chasing the Sonic Choke idea, and I wish you luck with that.... Please note, however, that Mach 1 in 4000 psi air is NOT 1128 fps, but 451.1 m/s (1480 fps).... Here is the calculator....  http://www.wolframalpha.com/widgets/view.jsp?id=b63c87b0a41016ad29313f0d7393cee8 (http://www.wolframalpha.com/widgets/view.jsp?id=b63c87b0a41016ad29313f0d7393cee8)

type "air at 4000 psi" in the box and hit "submit".... If you want a higher temperature, you can enter both.... eg. "air at 4000 psi and 200 C" will give you 516.5 m/s (1695 fps)....

I agree, what they are doing on the Yellow now is playing with being Trolls.... better to leave them behind and try and figure out a new theory that fits the facts, rather than stick your head in the sand....

Bob

Bob,

Thank you for that info. The higher the value of the speed of Mach 1, the higher the mass flux. So it will end up with less temperature gain, and higher velocity. I currently start with 70F air., and adjust Mach 1 for temperature. I'll need to look at your info more. If needed, I will definitely use a pressure compensated Mach speed after I figure it out. Regardless of what the speed of Mach 1 is, it is not a fixed obstacle and will change during the process. A higher speed for the Mach 1 "sonic choke" simply means that the choke happens farther downstream before it is encountered.

I re-ran it it with a fixed c=452m/s (1480fps). Not really how it will be, but this is it:

(http://www.scotthull.us/photos/Misc/2162fps-01.jpg)

The simulation starts to raise the temperature but never goes very high.

I'll quit using the 1128fps reference and stick with the Mach 1.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: phoebeisis on April 12, 2016, 09:36:55 AM
Scotmo/scott
Is that STEVE NC the same as this  STEVE-  the one who made this  post-yellow forum- Nov 12  2008-with the EXPLANATION of WHY it is IMPOSSIBLE to go over 1640 fps

I'm reposting the yellow forum 1640fps explanation
-  Steve yellow forum Nov 12 2008- of why anything over `1640fps  IS IMPOSSIBLE

anyway the below is their WHY  of why anything over 1640 is impossible
Steve seems to think the WHOLE column of air behind the pellet has to be accelerated along with the pellet-as if it was a solid rod-or a liquid like water
Sorry I was unclear back in  #361 when I first posted this cut from YELLOW FORUM NOV 2008 -this is Steve yellow forum nov 2008


Nope. No matter how high the pressure, ~1640fps remains an absolute limit for cold air.   November 12 2008, 4:24 PM

This simply because as pressure rises, so does the mass of the air filling the bore behind the pellet. Since this air has to be accelerated along with the pellet, as pressure rises without limit, eventually all of the available energy goes to accelerate air and not lead.

The velocity at that limit is 1640fps.

To go any faster requires, not more pressure, but a propellant with a lower molecular density.

Steve


Charlie-phoebeisis-once again-
Steve- NOV 2008 seems to insist that the  barrel air column must  be accelerated as much as the pellet-
like it was a solid rod-or a water column-
Steve is clearly wrong-to go faster requires LIGHTER molecules-not because they are less dense-but because they are FASTER-
NASA used H2 in their super guns not because it was LESS DENSE- but because at the same TEMP-they are faster than heavier molecules-higher peak speeds higher average speeds-
I would bet that the N2 and the H2O might be slightly more concentrated at the leading edge of the column-actually I wouldn't bet-since it is a pure guess-but it a one molecule thick disc  of air was released into an empty  barrel-no pellet in front-no air in front -H2O N2  would win the race over O2 CO2 etc
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 12, 2016, 01:35:23 PM
Yes, Charles, this is pretty much the whole point of the thread.... to prove that it is possible to exceed not only the Speed of Sound, but also the 1640 fps RMS Molecular Speed of air at room temperature.... after all, RMS means Root Mean Square, which is essentially an average speed, and as shown by the Maxwell Speed Distribution diagram, many molecules are going much faster, some more than twice as fast.... Looked at from a couple of ways, it has been suggested that twice the RMS Speed may in fact be the limit, based on the speed of the molecules at the temperature present during the shot.... Yes, Steve_in_NC is the primary proponent of the theory that 1640 fps cannot be exceeded.... and rather than put any effort into suggesting a mechanism that could explain the high velocity shots done by Lloyd AND OTHERS, he is picking and choosing ideas to present that support his case, even though those same numbers create roadblocks for his ideas.... The latest was to propose that the air inside the shot chamber was heated to 413*F on filling, while ignoring the fact that when left to cool for nearly 8 hours the pressure only dropped 100 psi, not the 1000+ psi that would occur had the temperature been that high.... The fact that the pressure didn't drop by over 1000 psi is proof positive that the temperature after filling was not elevated anywhere near that high.... In fact, the temperature of the air at the end of the fill can be calculated from the pressure drop as follows....

Starting pressure 3530 psi.... ending pressure 3430 psi.... ending temperature 72.1*F (531.8*R).... Starting pressure = (3530/3430) x 531.8 = 547.3*R = 87.6*F....

Had the temperature inside after filling been 413*F (873*R), the pressure after cooling would have been (532/873) x 3530 = 2150 psi....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 12, 2016, 02:07:54 PM
Scott, how are you calculating the maximum mass flow rate?.... During a discussion in another thread we multiplied the air density at the pressure (kg/m^3) used by the orifice area (m^2) times the speed of sound at that pressure (m/s) to get the maximum mass flow rate (in kg/s).... This was then derated about 5-10% to allow for losses.... You can use the calculator I linked to above for the speed of sound and air density.... http://www.wolframalpha.com/widgets/view.jsp?id=b63c87b0a41016ad29313f0d7393cee8/ (http://www.wolframalpha.com/widgets/view.jsp?id=b63c87b0a41016ad29313f0d7393cee8/)

For example, at 4000 psi and 20*C, we get Mach 1 of 451.1 m/s and a density of 302.7 kg/m^3.... for an orifice of 1 cm, we get....

451.1 x 302.7 x 1 x  PI/4 / 100 / 100 = 10.72 kg/sec.... which is 10.72 grams/mSec.... or 165.4 grains/mSec.... less a derating factor of course.... 150 gr/mSec seems about right....

The only way to increase the mass flow at that temperature is to increase the inlet pressure, it is completely independent of outlet pressure.... In addition one of the conditions for choked flow is a pressure drop of 47% across the choke.... Here is the discussion, if you haven't gone through it yet.... Jim_Hbar's Post #69 is particularly revealing.... http://www.gatewaytoairguns.org/GTA/index.php?topic=66737.60 (http://www.gatewaytoairguns.org/GTA/index.php?topic=66737.60)

How does that compare to what you are doing?....

Bob

Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 12, 2016, 02:52:32 PM
Scott, how are you calculating the maximum mass flow rate?.... During a discussion in another thread we multiplied the air density at the pressure (kg/m^3) used by the orifice area (m^2) times the speed of sound at that pressure (m/s) to get the maximum mass flow rate (in kg/s).... This was then derated about 5-10% to allow for losses.... You can use the calculator I linked to above for the speed of sound and air density.... http://www.wolframalpha.com/widgets/view.jsp?id=b63c87b0a41016ad29313f0d7393cee8/ (http://www.wolframalpha.com/widgets/view.jsp?id=b63c87b0a41016ad29313f0d7393cee8/)

For example, at 4000 psi and 20*C, we get Mach 1 of 451.1 m/s and a density of 302.7 kg/m^3.... for an orifice of 1 cm, we get....

451.1 x 302.7 x 1 x  PI/4 / 100 / 100 = 10.72 kg/sec.... which is 10.72 grams/mSec.... or 165.4 grains/mSec.... less a derating factor of course.... 150 gr/mSec seems about right....

The only way to increase the mass flow at that temperature is to increase the inlet pressure, it is completely independent of outlet pressure.... In addition one of the conditions for choked flow is a pressure drop of 47% across the choke.... Here is the discussion, if you haven't gone through it yet.... Jim_Hbar's Post #69 is particularly revealing.... http://www.gatewaytoairguns.org/GTA/index.php?topic=66737.60 (http://www.gatewaytoairguns.org/GTA/index.php?topic=66737.60)

How does that compare to what you are doing?....

Bob


Bob,
I'm calculating the mass flux that same way.  The problem is in determining what Mach 1 for all conditions and every point in time at the inlet.

I'm not pushing "sonic choke" as a limit on pellet speed. But as a means to estimate how much friction to apply.

The mass flux at the inlet is limited by pressure. Pressure is not a limit. It is just a another variable.
The mass flux at the inlet is limited by Mach1. Mach1 is not a limit. It is just another variable. Where to go from there?
 
I have not yet figured out how to get an exact Mach 1 velocity yet. But I'm closer. Except for that last test graph I posted for you, I have never entered the value of Mach1 into my program.  The program determines and uses it to as a point where and how much friction to apply. Some interesting things though:

It appears that the same variables that are needed to calculate the Mach1 speed, are the same variables that control the compress-ability (expand-ability). One of those variables being the specific heat ratio Cp/Cv. And that changes with pressure (high pressure). I never really considered those changes to Cp/Cv in pipe flow work since I only dealt with low pressures up till now. I have always used 1.4, but more research shows that to be way off for 1000-6000psi air. It gets up into the 1.7 range. When I use the correct value of Cp/Cv, the Mach1 speed gets closer to what that WolframAlpha program predicts (though still not enough). But that change also changes the expand-ability of the gas in the program, which I have also been taking into account. They almost cancel out. I change Cp/Cv, increasing expand-ability, and Mach1 value changes as well. The main affect of the change is to push the point where I start applying friction farther down the tube. only minor changes in the result. If I were to pick a fixed Mach1 value (that is not the right way to do it), and change Cp/Cv, there are bigger changes in the results. If I set Cp/Cv, and vary Mach1, there are also bigger changes in the results. When changed in concert, the maximum velocity down a long barrel does not change much.

All of the spreadsheet models are using f=ma. Mine included. That part is easy enough. But we also consider the expand-ability (compress-ability) of air. Cp/Cv. And then we need to consider friction factors as that is an opposing force. That gets complicated. We can use a fudge factor or efficiency coefficient. I'm just trying to get a more precise model.

For this latest spreadsheet model, I don't start using any friction until the inlet hits Mach1. So my model is not valid for predicting subsonic projectiles. In my model, friction appears to spike from zero at velocities over Mach1, The base friction is ignored and I still get accurate results at supersonic velocities. Eventually, I want to include all friction. This exercise gives me better insight into how that can be accomplished.

Mach1 determines the maximum mass flux. Mass flux does not determine the expansion velocity downstream. Increasing pressure increases value of Mach1. We can increase the mass flux with higher pressures. We can increase the downstream velocity with longer barrels. That only real limit is that imposed by the resulting fluid friction. And I know that is the most difficult part to figure out. At this point, it looks like there will always be a way to increase the velocity a little more.

The Mach1 "choke" is just a design parameter, not a constraint.

Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 12, 2016, 05:10:02 PM
Here is a little more about what I'm trying for in a better simulation. I avoided any math as I'm just trying to convey the concept.

------------------------------
Vehicle A (current model):

The PSI x area is the throttle. No limit. More throttle, more pressure = more speed.

Mach1 is used as feedback to apply the automatic brakes (friction). Only two settings. Zero, or all.

Jerky ride as the brakes finally pulse on and off while the speed is increased.

------------------------------

A little research shows that viscosity is a function of molecular speed. Friction is a function of viscosity. It makes me want try a slightly different approach to friction.

------------------------------
Vehicle B (my next vehicle):

The PSI x area is the throttle. No limit. More throttle, more pressure = more speed.

RMS is used as feedback to apply the automatic brakes (friction). Variable brake settings. Zero up to sqrt2 x RMS.

The ride is smooth as the brakes are gradually applied while the speed is increased.

-----------------------------------

I'm not even sure I can implement this in a spreadsheet. But if so, I think it will get a me a better simulation. An abstract image of the concept. Hatched area is the braking force:

(http://www.scotthull.us/photos/Misc/MACH1vsRMS.jpg)

If these shortcuts to friction don't work out, I'll take a couple steps back on the evolution of my model, and figure out the actual friction. Once we start getting down close to 50% efficiency, modeling the friction accurately becomes very important. There is a lot of good info out there. But not sure if anything covers 4000psi and 2000fps:

http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/Viscosity.pdf (http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/Viscosity.pdf)
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 12, 2016, 05:12:57 PM
Scott, what I have done is to put the density and speed of sound, from the online calculators, into a spreadsheet, using pressures up to 6000 psi, and then used Excel to generate a trendline for each.... This equation is then used to calculate the density and Mach 1 from the pressure for ANY pressure <= 6000 psi.... It is what Lloyd is using for his new spreadsheet with the VanDerWaals corrections.... In the spreadsheet I have the trendline equations for air, Helium, and Nitrogen, and I will send you a copy of the same one I sent to Lloyd.... All the data is at 20*C.... Lloyd hasn't added a column for maximum Mass Flow yet, but once you have the Density and Mach 1 for each Pressure increment it's just one more column.... If there are no restrictions, the orifice ends up being the bore diameter....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 12, 2016, 06:13:10 PM
Scott, what I have done is to put the density and speed of sound, from the online calculators, into a spreadsheet, using pressures up to 6000 psi, and then used Excel to generate a trendline for each.... This equation is then used to calculate the density and Mach 1 from the pressure for ANY pressure <= 6000 psi.... It is what Lloyd is using for his new spreadsheet with the VanDerWaals corrections.... In the spreadsheet I have the trendline equations for air, Helium, and Nitrogen, and I will send you a copy of the same one I sent to Lloyd.... All the data is at 20*C.... Lloyd hasn't added a column for maximum Mass Flow yet, but once you have the Density and Mach 1 for each Pressure increment it's just one more column.... If there are no restrictions, the orifice ends up being the bore diameter....

Bob

Yes. I would appreciate that equation. I could not get it figured out so I was going to make a lookup table to retrieve values. Last night I used that WolframAlpha to get every Cp/Cv from 100 psi up to 6000psi in 100psi increments, and plotted it but had not yet worked it into the spreadsheet. The equation will make it much easier.

Thank you,
scott hull at scott hull . us

PS: remember that when you add the limit for mass flux, the air will keep expanding and accelerating the pellet. You could model it as a pressure drop behind the pellet. That's what us M.E.s normally do but we are usually more concerned about flow rate. I modeled the airgun with a temperature increase. OK - now I have to think about that. Yeah - there will be heat from the entropy gain. Now we are back to how much. Any that is not available for work. So I'll use all of it. Too much ends up back as work anyway.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: phoebeisis on April 13, 2016, 11:04:29 AM
Scott
Thanks for the quick reply.
So Steve or SteveNC did some calculations back in 2008-they indicated -to him-that 1640 fps was maximum velocity with air room temperature-that about it-
now data says he is wrong-
he doesn't agree

Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 15, 2016, 02:16:28 PM
Interesting little tid-bit here for you.... Prompted by a calculation done by Steve about how rapidly a .25 cal Delrin ball travelling supersonic slows down (he claimed 5% each foot), I decided to work through a couple of examples to see what the actual muzzle velocity might be, when corrected for the distance to the Chrony.... First I used a .25 cal Delrin ball weighing 2.75 gr. as used by NickN in his UNI to achieve 1882 fps on 3000 psi, with the Chrony 3-4 ft. from the muzzle.... Then I did Lloyd's 2162 fps shot on 4600 psi with a 7.7 gr. aluminum pellet, same Chrony distance.... I assumed ICAO atmospheric conditions, and adjusted the MV to obtain the recorded velocity at 3.5 ft. (average) from the muzzle.... For the sphere, I used the Cd for a roundball travelling at the observed velocity, taken from the GS profile, which is 1.009.... and without having a drag profile for Lloyd's pellet, I assumed the same Cd, because I have found that our pellets typically have about the same drag as a roundball when supersonic....

2.75 gr. Delrin sphere, .250 cal.... SD = 0.0063.... MV = 2116 fps
7.7 gr. Aluminum pellet, .278 cal.... SD = 0.0142.... MV = 2277 fps (over Mach 2)

Acccording to my calculations, Lloyd's shot had already slowed over 100 fps by the time the velocity was measured, and Nick's well over 200 fps.... The curious thing is that Steve should bring this up, because is makes his arguments for a 1640 fps limit even harder to justify.... Incidently, several years ago, on the Yellow, one of the non-believers in the limit used similar calculations on the Quackenbush and Dean high velocity shots using Delrin bullets to question the 1640 limit.... They recorded 1474 fps, with the Chrony's about 10 feet or more from the muzzle, and when he calculated the MV, it was over 1700 fps....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Bill G on April 16, 2016, 12:39:12 AM
Yes!  Mass flux.  that is a great way to see it.  through the orifice it is limited to mach1 but the expansion has no limit (?)....keep the orifice as exactly that and the amount or air at any psi will be greater than through a port, of any length, that is equal to the bore diameter.  >< (this shape)  reservoir at the left and bore at the right.  Compared to what we typically use in valve and transfer porting, I imagine there are serious gains.  that being said and with some reflection on thought,  to use full bore orifice is still going to be superior I think.  The inlet side being converging would seem to promote sonic flow early and in concert with next to no dead volume, result in superior velocity.  Now the benefit here would be to apply this idea to the calibers that are large enough to cause poppet material to become compromised.  With this orifice idea,  the mass flow could be high enough to allow a smaller diameter yet attain the high mass flow.  Helps make for an easier opening valve and a lot lighter hammer and spring to achieve a high order of energy.  The balance valve would reduce that even more.     

 You guys have left me in the dust and contributing by me has come to an end.  I hear school bells and I'm in the seat early when I can make it to class. LOL 

Good call on leaving all the "smartest guy in the room by himself"  Let us dumb guys lead the way to discovering the whys and hows by way of not being "the smartest guy in the room".  I've said it before.   If you find your self being the smartest guy in the room, you probably need to find another room.  Why?  because your not going to learn anything in the current room.


Great work guys!
Bill
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 16, 2016, 12:59:35 AM
Bill, using a restriction (ie CD nozzle between the reservoir and barrel less than bore-size) WILL reduce the velocity and energy of the pellet, because the mass flow is limited by the orifice area, and upstream pressure.... While you might be able to increase the downstream air velocity past Mach 1, the mass of air pushing the pellet, and hence the pressure, will be less....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: I_like_Irons on April 16, 2016, 02:34:54 PM
Yes, the pressure will be a lot less which reduces expansion with a convergent/divergent port.  In an ideal convergent/divergent rocket nozzle, for instance, you want the  exiting high velocity gas to be at atmospheric when it leaves the nozzle opening.  In this ideal case there is no room for expansion afterwards.  You get thrust from the acceleration of the air mass to that velocity. 


On another note, I've been working on trying to find an inexpensive ADC (analog to digital converter) to instrument a barrel.  I still think it would be instructive, to know what the air pressure is doing at various points in the barrel.  The problem I'm having is finding a fast enough ADC with sufficient channels without a whole lot of extra stuff, and is affordable. 

On the analog side of the system with strain gauges and signal conditioning, I have a good handle on those design principles.  It is with the ADC and type of input to the computer (serial, or parallel)  that I'm having trouble.  Software will depend on how data is delivered to the computer, which is yet another hurdle. 
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 16, 2016, 06:47:11 PM
Great way of summing up the divergent portion of the nozzle, David.... I hadn't thought of that before, but since velocity increases and pressure (and density) drops to keep the mass flow constant, for maximum efficiency in a rocket nozzle, the pressure at the outlet should be ambient (hence generating the greatest velocity, and hence thrust....  Any excess pressure at the exit is wasted energy because the gas can still expand.... Not really applicable to a PCP, but makes perfect sense.... and is in complete agreement with the fact that the lower the residual muzzle pressure the more efficient (and quieter) the shot....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 17, 2016, 11:08:04 PM
Here is a little more confirmation that 1650 fps is not the limit.... The rifle is my .25 cal Discovery, with a 24" TJ's barrel, running tethered at 2900 psi.... The gun is tuned to shoot 50.6 gr. cast bullets in a 3 shot string at 960, 966, and 956 fps (104 FPE) starting from that pressure, and was not retuned for this test.... I did, however, shoot a couple of JSB pellets over the Chrony to confirm the performance.... The 34.2 gr. Heavy shot at 1152 fps (101 FPE), and the 25.4 gr. King reached 1254 fps (89 FPE).... Here is the setup I use, and have used for the last 7 years, to Chrony all my guns.... The muzzle is 2 feet from the first sensor and 3 feet from the second, and this setup is rock solid and reliable from under 500 fps to over 550 FPE, the velocity readings are steady, reliable, and consistent with what I get outside.... The lighting kit is a factory Chrony setup, running two long 40W incandescent bulbs.... Without a pellet in the gun, it NEVER registers anything, so muzzle blast is having no effect.... The Chrony is on an angle to be parallel to the path of the pellet, because my target is on the floor, 20' away.... When shooting, the butt of the gun is slightly higher than in the photo, and I am shooting right through the center of the triangle formed by the rods and diffusers....

(http://i378.photobucket.com/albums/oo221/rsterne/Discovery/Chrony%20Setup_zpspvyexetg.jpg) (http://s378.photobucket.com/user/rsterne/media/Discovery/Chrony%20Setup_zpspvyexetg.jpg.html)

This gun holds air perfectly, and when I took it down off the rack, where it has been stored for over a month, the gauge still said 2900 psi.... Likewise, the Great White tank it was tethered to, was filled at the same time, about a month ago, and both were at room temperature, 68*F.... I hooked it up to the regulated tether, ran the shots with the JSBs to confirm it was performing normally, and then proceeded with the testing.... The first test was a pellet made from a 1/4" piece of Delrin rod that was 3/8" long, rounded at the front, and counterdrilled at the back to resemble a cylindrical skirted pellet.... It weighed 6.9 gr, and crossed the Chrony at 1595 fps.... I then changed over to something much lighter, based on a 6mm Airsoft BB, as shown in the photos below....

(http://i378.photobucket.com/albums/oo221/rsterne/Discovery/.25%20cal%20Hyperball_zpsepgp9ctl.jpg) (http://s378.photobucket.com/user/rsterne/media/Discovery/.25%20cal%20Hyperball_zpsepgp9ctl.jpg.html)

The BB, which weighed 1.8 gr., was too small for the .25 cal barrel, and rolled out the muzzle, although a quick test firing (muzzle raised, lowered just before firing) produced a velocity of 1740 fps.... I assume the Airsoft BB was already rolling down the barrel, so didn't get the benefit of the entire 24" for acceleration.... In order to make the BB stay in place until fired, and fit the bore a bit better, I wrapped it in tinfoil, as shown in the photo above.... The piece of tinfoil was a bit over 1" square, folded over the front and twisted 1/2 turn at the back while stretching it as tight as possible.... I then cut the back of the foil off with scissors, to produce the pellet shown.... As you can see in the photo below, it weighs 2.2 gr....

(http://i378.photobucket.com/albums/oo221/rsterne/Discovery/.25%20cal%20HB%20Weight_zpssqn3esd1.jpg) (http://s378.photobucket.com/user/rsterne/media/Discovery/.25%20cal%20HB%20Weight_zpssqn3esd1.jpg.html)

The pellet was loaded normally, with the twisted part of the foil at the back, and slid into firing position with the bolt.... I fired a total of 10 of these pellets, and the velocities varied from 1722 to 1752 fps except for one shot at 1706 fps, where I noticed the tinfoil following the pellet to the target (I assume it dislodged in the barrel).... I made up each pellet between shots, so the gun had a couple of minutes to stabilze in temperature, although all that was happening between shots was for the regulator to top up the gun about 200 psi after each shot.... There was NO observable change in temperature of any part of the system during the tests.... The average over the 10 shots was 1734 fps (14.7 FPE).... I had two shots at 1750 fps, and one at 1752 fps, as shown in the photo below....

(http://i378.photobucket.com/albums/oo221/rsterne/Discovery/.25%20cal%20Hyperball%20at%201752_zpsqtaarxil.jpg) (http://s378.photobucket.com/user/rsterne/media/Discovery/.25%20cal%20Hyperball%20at%201752_zpsqtaarxil.jpg.html)

All 10 shots hit my target backstop, 20' away, producing a group size of about 3".... As you can imagine these shots were extremely loud, since the high velocity meant the pellet was exiting while the valve was still open, even though the gun was not retuned.... The calculated residual muzzle pressure was nearly 2500 psi.... I cannot stress enough that there were NO changes made to the gun, it was shot as tuned to deliver 104 FPE with 50.6 gr. cast bullets.... It didn't have any special firing chamber or valve, the barrel was only 24" long, and the pellet was a lousy fit, shimmed up with tin foil....

I would suggest that anyone having a .25 cal PCP that is capable of hitting 100 FPE should be able to duplicate this experiment and prove to yourself that the long-proposed 1650 fps velocity limit for PCP running room temperature air is a flawed theory.... I have no doubt that a smoothbore barrel of the proper diameter for airsoft BBs, that was 36" long or more, and running higher pressures, could achieve much higher velocities, up to 2000 fps or more....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Michael Loar on April 18, 2016, 02:52:49 AM
Bob
You got my seal of approval on a very well presented and accurate test structure to insure the are no hiccups that could skew the results IMO.

That's some impressive FPE out of a airsoft BB covered in tin foil as well.

Mike
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: MichaelM on April 18, 2016, 03:40:27 AM
there has been and idea buzzing around and around in my poor noggin....  Been  thinking about convergent/divergent nozzles and talk of laminar flow and i think they had a date night and some poor child was born from it....

ANYWAYS I dont have the smarts to figure out the maths and models ...its more of a picture in my head.. and its also probably completely dumb...

from what I understand a converging/diverging nozzle is basically eating up the energy to accelerate the flow of gas.... ideally the gas leaving it is at atmospheric pressure turning its energy into high velocity movement.....

Now Laminar flow down a tube describes how the gas would be denser and slower on the outside layers while faster and less dense down the middle in dumb speak.... forming its OWN restrictions in the barrel

the picture I have in my head is this laminar flow of gas forming a continuously evolving convergent/divergent nozzle as it travels down the barrel and helping form a stream that is constantly accelerating its self as its converting its stored energy into supersonic and even hypersonic velocities????



to kinda even further back this up as silly as it seems..... you ever see the parlor trick of blowing up a really long cylindrical plastic bag with a puff of air from your lungs??? if its a REALLY long bag ( I have done it with 15 and 20 foot bags...) that little puff starts out slow but by the time it reaches the end of the bag its traveling quiet fast  and if your not holding onto the bag it can take it from your hands and have a nice POP as the pressure wave an fast moving air hits the end... (as an aside I understand the inflation of the bag is due to the bernoulli effect drawing in air... I am thinking more about the pressure was created from that first hard puff of air and watching it accelerate down the tube...)

 
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: madeInLV on April 19, 2016, 05:49:27 PM
Loyd,

The exhausting of the air from the rear piston chamber drops the closing force so that the opening force on the front margin of the valve  forces the valve rearward and cracks the valve open at the barrel breech. As soon as the valve is cracked, the pressure imbalance doubles and the valve slams open and fires the pellet.  Lag time is virtually nil.

Please reread my earlyer post about the acceleration of the projectile and the plunger. According to your description the pilot stage creates an imbalance which merely "cracks" the valve open creating further pressure imbalance. "Time lag is virtually nil" True. I CASE OF A HEAVY PROJECTILE THIS IS THE CASE. In case of a LIGHT projectile the smallest (slow moving valve) crack will push the pellet way down the barrel before the main valve has reached full steam. TESTED EXPERIMENTALLY.

Imbalance needs to be designed such that the pilot stage is enough to accelerate the valve sufficient for ACCEPTIBLE speeds. As you can see this is a dead end-the lighter the projectile the larger the imbalance needs to be. Start by figuring out what the weight of the pellet will be.

"Easy to open..... difficult to close
" Man ....you have no idea:)

Also, you mentioned that paintball marker have similar valves. Would you mind pointing me in that direction? Or is there a name for it that i can google?
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: madeInLV on April 19, 2016, 06:19:11 PM
Scott, Bob,

thank you for the passion for the subject and the unquenched desire to get to the bottom of this. I recognize fellow engineers when i see them:)

Loads of usefull information and thought provoking analysis.
I once was doing exactly that until i realized my BS in ME was not enough. My conclusion was that i understood the energy transfer during the firing cycle well enough and sort of understood the key variables that are at play and realized what i can actually influence within the framework of a reasonably sized PCP gun. Shortly put-least Resistance (in line valve, no choke points), no dead space (proved to be false for real valves), max pressure (limited to 4500psi for now) Limited to about 325m/s due to the transsonic region and the associated inefficiencies.

From what I see, you are trying to find a closed loop algebraic equation that will give you a "digital PCP" so to speak. IMHO it is not possible. At best we can come up with general equations that fit Loyd's empirical data and shows general trends.

I hope I'm wrong though.

Have you looked at the "Theory of High Speed Guns" Seigel, 1965 (NASA) that i posted a ling to in my very first post? I believe it addressed everything you are talking about here. 

BTW Scott, where did you find the info of gamma (Cp/Cv) being close to 1.7 for air at high pressures?

Also, as Loyd is working on the next valve model (the pif-paf aka pilot-plunger) at some point it will become obvious that we are dealing with a converging nozzle here as well as an annular transfer port (the area between the plunger valve and the cone/valve seat that increases while the plunger moves rearward) Both of these areas will need optimization. So....are any of you good at CFD?:):):)
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 20, 2016, 12:15:43 AM
Alex.... There is a chart in the very first post a thread in this Gate.... http://www.gatewaytoairguns.org/GTA/index.php?topic=105696.0 (http://www.gatewaytoairguns.org/GTA/index.php?topic=105696.0) .... that shows a chart of gamma vs. pressure at various temperatures.... If you look at the one for 70*F, a value of 1.7 would be the one to use from 2000-6000 psi.... bang on at 3000 psi and within about 0.05 (3%) over that range....

PS, I am definitely NOT an Engineer, I want my solutions simple, if at all possible.... *grin*.... I do wish I had paid more attention in Math and Physics while getting my BSc (Chem), though....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 20, 2016, 11:10:35 PM
Bob,
Nice work on getting the high velocity out of your high powered .25 Disco.   Even though the math explains it, it is still surprising how much lighter the projectile has to be to get only incremental increases in velocity.
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 20, 2016, 11:23:44 PM
Loyd,
.................................................
Imbalance needs to be designed such that the pilot stage is enough to accelerate the valve sufficient for ACCEPTIBLE speeds. As you can see this is a dead end-the lighter the projectile the larger the imbalance needs to be. Start by figuring out what the weight of the pellet will be.

"Easy to open..... difficult to close
" Man ....you have no idea:)

Also, you mentioned that paintball marker have similar valves. Would you mind pointing me in that direction? Or is there a name for it that i can google?

LV,
"Easy to open..... difficult to close" Man ....you have no idea:)

Believe me, I DO know how difficult it is, LOL!

For the paint ball marker info, look at the animations on this site (markers and regulators, too).  Some of the best that I have found.  Even though they might not provide exactly the information you are looking for, they will definitely stimulate the thought processes. Some very sophisticated equipment.

http://www.zdspb.com/tech/misc/animations.html (http://www.zdspb.com/tech/misc/animations.html)

Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 21, 2016, 12:14:28 AM
I have been working on my internal ballistics spreadsheet to see if the predictions can be made more accurate.  It is quite a daunting task.  The VanDerWaals corrections are in place and now the mass flow/mass flux limits are underway.  I am having trouble figuring what the air velocity at the breech end of the barrel is.  If I understand correctly, the mass flow limit is reached when the velocity of the air entering the barrel is at the speed of sound for the pressure of the air entering the barrel.  But the speed of the air entering the breech of the barrel is not necesarily the same as the speed of the projectile in the barrel. Correct?

Look at this example as part of what is puzzling me.
This is one of the fastest shots I have taken so far.  .278 cal, 7.7 gn, 4500 psi, 55cc air, MV = 2162fps.
If you look at what I will call the maximum INPUT FPE (machines have input BTUs and OUTPUT BTUs, and never are they over 100%.
So, even though it is impossible, lets say the INPUT fpe equals :  bore area x psi x barrel length(feet). 
Max INPUT FPE = .0607sqin x 4500psi x 3.833 feet = 1047 FPE
The final air mass in the barrel (based on the expanding 55ccs of original air) is 127.4 grains. (a full barrel of 4500 psi air would be 234gns).  If you back figure the velocity from the air mass + the pellet mass,  Velocity in FPS=sgrt [( 1047fpe x 450240)/(127.4gn + 7.7gn)] = 1880 FPS. But the actual FPS was 2162.  So, the actual velocity is much higher than calculated, even though the 1047 fpe is also too high.  One explanation is that a much smaller mass of air is being accelerated in the barrel behind the pellet.  Baffling.  There is a lot of thermal activity (Scott's entropy?)  or something happening that is not easily identified or quantified.

No response necessary, I am just rambling.
Thanks,
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 21, 2016, 02:12:40 AM
I would agree that the logical explanation is that the mass of air being accelerated behind the pellet must be less for the pellet to reach the velocity it does.... Perhaps the velocity profile of the air moving down the bore, as Scott often draws, and as typically shown for laminar flow, where the air against the barrel is basically stationary and each layer slides over the next until the air in the center is moving at twice the average velocity, is the key?.... The volume of a parabola is half the volume of a cylinder of the same size.... sooooooooooooo....

Using Lloyd's 2162 fps shot as the inputs to his new L4 spreadsheet, and using 0.5 of the air mass in the calculations, requires dropping the efficiency number down to 48% to bring the MV to 2162 fps.... When you do that, the air mass used for the shot drops from 127.4 gn to 64.7 gn, and the maximum velocity ends up being 2580 fps.... That is certainly far enough above the 2162 MV measured to allow for losses, I would think....

I did find one reference about the KE in a fluid moving through a tube here.... http://hyperphysics.phy-astr.gsu.edu/hbase/pfric2.html (http://hyperphysics.phy-astr.gsu.edu/hbase/pfric2.html) .... complete with a formula for calculating it.... I haven't worked through it at all, but the variables are the maximum flow velocity (which is likely the pellet velocity) and the density of the fluid.... both of which we have for each time increment.... The result being the avg. KE per unit of volume.... Anything there we can use?....

Bob
Title: Re: Sonic Choke
Post by: Scotchmo on April 21, 2016, 04:03:24 AM
This pic is from an earlier post. Ignore the equation and 1640fps.  Im on my iPhone and cannot create a new pic right now:

(http://www.scotthull.us/photos/Misc/1640-01.jpg)

At 50% efficiency, the 100's of lost FPE do not just vanish. It turns to heat. A portion of that heat continues to provide work. The heat accumulates in each "parabola" of air and expands it as progresses down the barrel. Providing some work, and some entropy gain (inefficiency).

Portions of the air are not as dense as you might think they are. And it may be even less dense when the temps are not allowed to stabilize before a shot.

We still need a baseline after letting the filled chamber rest several hours after fill disconnect, before taking the shot. There is a good chance that it will be much lower than 2162fps.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 21, 2016, 09:50:29 AM
Yes, I agree with what you guys are saying.  It is fairly easy to visualize in general terms, but quantifying it is difficult.  I haven't done anything with the heat changes in the spreadsheet other than the exponent in the expansion ratios, but I realize that the thermal part is quite important.

Scott, the shot with the chamber first setting loaded and idle for several hours is upcoming.  And the nitrogen, too.  I have prep to do for the Funshoot in the meantime.

Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: match on April 21, 2016, 10:45:14 AM
I think a slightly different point of view may be useful.

Think back to Bob's thought experiment with the packets flowing down the barrel:

 - these packets are really pre-compressed springs which expand while moving down the barrel.

The speed of the center of mass of the packets slows down as the packet expands and moves down the barrel but the speed of the forward "edge" increases.

These packets can also overlap, the molecules can mix with the adjacent packets, so a packet "behind" does not force a forward packet to move like a solid ball so we lose a bit of the combined forward velocity of the leading edge at the pellet.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 21, 2016, 12:34:08 PM
From Steve on the Yellow.... The new limit is 2515 fps....  http://www.network54.com/Forum/79537/message/1461247651/So+--+Just+how+fast+can+a+jet+of+air+REALLY+go-++1640fps+-+or+2515fps- (http://www.network54.com/Forum/79537/message/1461247651/So+--+Just+how+fast+can+a+jet+of+air+REALLY+go-++1640fps+-+or+2515fps-)

We shall see.... I think that is fast enough we likely can't test it anyway....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 21, 2016, 03:08:57 PM
Scott, I can't see how letting the chamber rest "for hours" can possibly make any significant difference.... The fact that the pressure did NOT drop more than 100 psi after nearly 8 hours, instead of well over 1000 psi, is proof positive that the air available for the shot after a couple of minutes is NOT at a high temperature.... Pressure and absolute temperature are highly correlated for a fixed volume and mass (ie density)....

John, I like your analysis, comparing the packets to decompressing springs moving down the barrel and intermixing, because of course there are no "finite" barriers between them.... that was just a way to visualize the process.... If the reservoir is infinite volume (relative to the barrel volume), the pressure should stay relatively constant, of course, not really allowing the "springs" to decompress, although they could still intermix as they travel down the barrel to some extent.... At some point, as the front packet and pellet reach a high enough velocity (driven by the ones behind), that further air released at the breech can have no further effect, and I think that point occurs at twice the molecular speed, ie about 3300 fps....

While I cannot rule out temperature effects, neither can I quantify them, because they are in two directions, cooling through Adiabatic expansion (with a gamma of about 1.7 ? ), and possible heating through friction, compressibility, or other unknown effects.... I still think we can have a successful model based just on F = mA.... Did anyone look at the equation at the Hyperphysics link I posted at the bottom of the previous page?.... This is for the KE of a fluid flowing in a tube....

(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Air%20in%20Tube_zpsxqyskufl.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Air%20in%20Tube_zpsxqyskufl.jpg.html)

At any given time increment, we know the Vm (maximum velocity at the center of the barrel = pellet velocity), the density (rho), and the barrel volume V.... It may even be possible to apply the equation at the moment the pellet exits.... For Lloyd's 2162 fps shot, where the pressure at the muzzle, from his L4 calculator (which uses the VanDerWaals corrections, and sonic Flow limiting), is 2213 psi, the air mass in the barrel is 0.0005746 slugs, the barrel volume is 2.792 CI, and the density is therefore 0.0002058 slugs/CI, and the MV is 2162 fps, so the equation would yield....

KE = ( V / 2 ) x rho x (Vm^2 / 3) = ( 2.792 / 2 ) x 0.0002058 x ( 2162^2 / 3 ) = 1.396 x 0.0002058 x 1,558,081 = 447.4 FPE

The KE of the pellet is 80.0 FPE, so the total energy is 447.4 + 80.0 = 527.4 FPE, which is 49.3% of the Input energy (1070 FPE).... Seems entirely reasonable to me....

Regarding Lloyd's L4 spreadsheet, if I use 100% of the air mass, and an efficiency of 76.4%.... the flow chokes when the pellet is 12.9" from the breech.... If I use 50% of the air mass and 47.6% efficiency, the flow only chokes at 44.3", right near the muzzle.... but I get exactly the same results for the KE of the air and the total KE of the shot.... However, the "maximum fps" number increases from 1880 fps to 2580 fps, because less of the air mass is being accelerated.... It would appear that the latter choice makes more sense....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 21, 2016, 04:12:09 PM
Now for the next step....  can we turn that equation around, and predict the maximum velocity Vm from the volume (2.792 CI) , density (0.0002058 slugs/CI), and KE (1070 FPE) ?.... If we were just accelerating the air, and no pellet....

( Vm^2 / 3 ) = ( KE / V ) x (2 / rho)

Vm^2 = 2 x 3 x KE / V / rho

Vm = sqrt ( 6 x KE / V / rho ) = sqrt ( 6 x 1070 / 2.792 / 0.0002058 ) = sqrt ( 6420 / 0.0005745 ) = sqrt ( 11,174,934 ) = 3343 fps ....

hmmmmmmmmm that looks intriguing, doesn't it.... or maybe just a coincidence?.... If we look at the equation, it is really KE = 1/2 MV^2, but the mass M is being derived from the density (rho) times volume (V), which is then divided by 3 to correct for the losses caused by fluid flow in a tube, and the velocity used (Vm) is the maximum velocity at the center of the flow (in our case, the pellet velocity).... So let's see how we could include the pellet mass.... rewriting the equation yet again....

Vm^2 = 2 x KE / ( V x rho / 3).... where the denominator is the mass of the air used to calculate the KE, actually only 1/3 of the total air mass....  So let's add to that the pellet mass M (0.0000342 slugs)....

Vm^2 = 2 x KE / { ( V x rho / 3 ) + M }

Vm = sqrt [ 2 x KE / { ( V x rho / 3 ) + M } ] = sqrt [ 2 x 1070 / { ( 2.792 x 0.0002058 / 3 ) + 0.0000342 } ] = sqrt [ 2140 / {0.0001915 + 0.0000342} = sqrt [ 2140 / 0.0002257 ] = sqrt [ 9,481,613 ] = 3079 fps....

If I use only 1/3rd of the air mass in the barrel in Lloyd's L4 calculator, I have to reduce the overall efficiency to just 37.1% to make it balance.... however, when I do that, it spits out 3079 fps as the maximum theoretical velocity.... exactly the same answer.... Maybe I'm onto something here?.... or maybe not....

Please note, I had the "Input FPE" wrong at 1047, it is actually 1070, (I had used 4500 psi instead of 4600) and I went back and corrected this post using that....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 21, 2016, 06:33:12 PM
--------
Another way to look at it:

Start with the concept of a plug of air. The plug is bore area x a small fixed segment length.

FPE is energy that accumulates by applying power over a length of time. The power (not velocity or FPE) of the system is limited by pressure and bore diameter. At a Mach 1 inlet velocity, we have reached max power  (not max FPE, not max velocity).
Once Mach 1 at the inlet it achieved, momentum density becomes fixed. For every "plug" anywhere in the system, the mass x velocity is constant. To increase velocity, mass in that plug must decrease.

Mach 1 is 1128fps for air at 70F.

At 3307fps, the density of the air in the plug behind the pellet will be 1128/3307 or 34% of the density at the inlet. It will have expanded at about a 3:1 ratio. What air temperature will it take to accomplish that with an equal pressure throughout the system?

At some point, the power needed to progressively increase the temperature of every plug as they move down the barrel will consume all the power the inlet can provide. Acceleration ceases. Max velocity has been reached.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 21, 2016, 07:17:32 PM
In case anyone cares, Steve has revised 2515 fps downwards to 2259 fps because of a misplaced parenthesis.... I'm betting that can be broken, so we may be back to square one.... or would that be square two?.... I wonder what he would get using a gamma of ~ 1.7, which is applicable at 2000-6000 psi (within ~ 3%), instead of 1.4.... or would you need some intermediate value because the pressure at the muzzle is greatly reduced?....

Quote
Mach 1 is 1128fps for air at 70F.
not at high pressure, it's not.... 1547 fps @ 20*C @ 4500 psi....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 21, 2016, 08:31:27 PM
You are right Bob. Mach in air is a variable.

For a chamber pressure of 4500psi:
At 3307fps, the density of the air in the plug behind the pellet will be 1547/3307 or 47% of the density at the inlet. It will have expanded at about a 2:1 ratio. What air temperature will it take to accomplish that with an equal pressure throughout the system?

That's more like Lloyd's test system (with very large dump). I'll see if it looks doable when I get back home this weekend.

Since Mach is a variable, based on temp and pressure, I'm not sure if there is a set muzzle velocity limit for 70F air. The limit may change with pressure as well.

2259fps? Time for a 100cc dump and an 8 foot barrel. ;)
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 21, 2016, 10:23:36 PM
In case anyone cares, Steve has revised 2515 fps downwards to 2259 fps because of a misplaced parenthesis.... I'm betting that can be broken, so we may be back to square one.... or would that be square two?.... I wonder what he would get using a gamma of ~ 1.7, which is applicable at 2000-6000 psi...

I jumped in on the yellow, hopefully before a new myth springs up. I gave them the Wolfram Alpha link for high pressure specific heat ratios. Higher gammas soak up more energy, so it results in lower velocity. 1968fps. So it's already been broken.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 22, 2016, 01:27:35 AM
Scott, I still don't understand the temperature thing.... I have enough to do to warp my brain around the idea that only 1/3rd of the air mass should be used to calculate the KE of the air moving down the barrel, when using the velocity of the center of the stream.... I could grasp the idea of 1/2, because the volume of a parabola is half the volume of the same size cylinder of air.... I guess the rest of the reduction in mass has to do with using the velocity of the center of the stream, rather than the average velocity....

From what I have read, the idea of a parabolic shape to the velocity profile only applies for laminar flow, when the flow is turbulent the shape of the velocity profile is shortened.... That should make the mass used a larger percentage of the total mass, which would reduce the velocity, so maybe using the parabola, and the equation I showed above, is a good way to calculate the maximum velocity for a given combination of barrel volume and air density, based on the maximum KE value arrived at from bore area x pressure x barrel length, which does seem to be a valid maximum for the "input FPE".... However, a change in any of those parameters, and of course pellet weight, will change the maximum velocity.... Still, it may be a valuable way to create a maximum velocity for any given PCP setup....

For an absolute maximum velocity with room temperature air, I'll stick with my WAG of 3300 fps....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 22, 2016, 03:45:31 AM
3300fps could be right. I'm not ready to put number on it. :D

Laminar is easier to visualize with "parabola" shaped gradients of velocity or temperature. But at the pressures and velocities we have, it is a turbulent boundary layer. Probably very high Reynolds numbers, which I should look into more and actually try and come up with a reasonable friction coefficient.

So the other way to visualize it is as plugs of air. Each one homogeneous throughout it's short length. But after reaching Mach 1 at inlet, different temperature and density than the adjacent plugs. That's how I set up the numerical integration in my spreadsheet.

Whether you model it as moving only 1/2-1/3 of the air down the middle, or as progressively less dense segments, either method will get close to the same result. The momentum of each segment is the same. The difference between the two methods will be in how fast the dump chamber depletes during pellet acceleration. In reality, you can't really have full density farther along the barrel. If that were the case, pellet velocity would be limited to Mach 1 of chamber air. That's not the case, so the air farthest along the barrel has to "thin out" as the pellet outruns the inlet velocity.

What part of the temperature thing that is not understood? It all balances out fairly well. The wasted FPE is from air friction. Friction causes a temperature rise. The temperature rise causes the decrease in air density.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: phoebeisis on April 22, 2016, 10:20:41 AM
 In does an increase in gamma mean
    More work energy available?
or Less work energy available?
Thanks
Charlie
PS at 300k via eyeball looks like 2-3% of air molecules are 1000m/s or more-if the pellet is light enough-low friction enough-no reason you can't hit 1000m/s-
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Bryan Heimann on April 22, 2016, 12:11:53 PM
I have to ask, how close are ya'll to launching a "real" projectile at over 2,000 fps, with accuracy?  It is cool ya'll have taken it this far, but that is what I want to see!
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 22, 2016, 12:42:45 PM
I also haven't checked the Reynold's numbers, Scott, but I suspect Turbulent flow would dominate as well.... The shapes I have seen for the velocity profile would suggest that the mass compared to a cylinder is larger than the 1/2 you get with a parabola, which would logically mean that the mass for the KE formula could easily be about 1/2 instead of 1/3.... a number that just seems more "comfortable" to me.... (see, I told you I'm not an Engineer, I seek the simple explanations).... You are 100% correct, the "plugs" of air must be less dense (lower pressure) towards the muzzle, after all, you need a pressure gradient to cause flow to happen.... I suspect that the mass inside each plug is relatively constant (and once the velocity at the breech reaches Mach 1, starts decreasing slowly as the reservoir pressure drops), but that it expands somewhat as it moves along the barrel, lowering pressure and increasing velocity, while conserving momentum....

Charles, when you are talking about extracting energy from compressed air, the higher the gamma the more cooling you will see as the air expands, which results in lower pressure because of the lower temperature.... This calculator will quickly show you....  http://www.tribology-abc.com/abc/thermodynamics.htm (http://www.tribology-abc.com/abc/thermodynamics.htm) .... If you change Cp or Cv you will see the effect on the energy released and the temperature.... gamma is Cp/Cv, of course.... If you are talking Adiabatic compression, like occurs in a Springer, the situation is reversed, the higher the gamma the more energy, because the temperature increases more....

Bryan, if by "real projectile" you mean something heavy enough to have reasonable FPE, I don't think that will ever happen with air.... To achieve such high velocities requires extremely light projectiles, which means that the mass of the gas driving it becomes dominant in drawing energy from the expanding air.... In Lloyd's 2162 fps shot, the pellet weighed 7.7 gn. but the air in the barrel when the pellet exited weighed 127.4 gn.... Changing to Helium, which is only 1/7th as dense, changes things in a hurry, and modern PCPs can be pushed into the 1500 fps range relatively easily with "real projectiles".... so 2000 fps would not be out of the realm of possibility.... However, you are then faced with the situation of the drastic increase in drag in the Transonic and Supersonic zones slowing the bullet down again once outside the barrel..... The Supersonic drag is 3-5 times as high as the Subsonic drag.... You have to drive bullets over 2500 fps to get the wind drift down to what can be achieved at 900 fps with the same bullet.... While this is exciting, and interesting, from a Scientific point of view, it realistically isn't practical....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 22, 2016, 01:03:57 PM
..................................................
On another note, I've been working on trying to find an inexpensive ADC (analog to digital converter) to instrument a barrel.  I still think it would be instructive, to know what the air pressure is doing at various points in the barrel.  The problem I'm having is finding a fast enough ADC with sufficient channels without a whole lot of extra stuff, and is affordable. 

On the analog side of the system with strain gauges and signal conditioning, I have a good handle on those design principles.  It is with the ADC and type of input to the computer (serial, or parallel)  that I'm having trouble.  Software will depend on how data is delivered to the computer, which is yet another hurdle. 

          Sorry folks, sidetracking the thread a tiny bit. Lloyd

David,
I have fiddled a little with strain gages in the past and used a Parallax Stamp microprocessor to process the data.  I don't know if that microprocessor has the speed to do what you want, but the basic set-up ought to be similar.

Here is the basic circuit to convert the low level analog output from the strain gage to a digital signal.  It has an instrument amp to boost the output voltage, then a A/D convertor (I think mine was a 12 bit, but you'd probably need a 16 bit to get the speed), then the digital output was processed by the Stamp and its programming, and finally, output to a laptop via RS232 serial.  The connections are usually USB now.  The instrument amp and A/D convertor are a few bucks each.  The microprocessor (Stamp, Propeller, Pic, Arduino, etc), maybe $75+, which includes the builtin I/O and power supply, etc.  I liked the Stamp because the programming was so easy.  Just another version of Basic.  In fact, in the end, I didn't need the 2 adjustment pots on pins 1 and 3 of the A/D convertor because I could make those compensations in the programming.
(http://i226.photobucket.com/albums/dd79/loyd500/Pressure%20transducer/xducer_schematic_zpsael1fsxi.jpg) (http://s226.photobucket.com/user/loyd500/media/Pressure%20transducer/xducer_schematic_zpsael1fsxi.jpg.html)


Here is the strain gage, which is actually a pressure transducer that I made.  You'd need a strain gage with a pretty high frequency to accurately detect the strain in the barrel. (Sorry for the fuzzy picture.  I forgot to have the camera in macro mode when I took the pic years ago.)
(http://i226.photobucket.com/albums/dd79/loyd500/Pressure%20transducer/P1010067a_zpslaxxfufp.jpg) (http://s226.photobucket.com/user/loyd500/media/Pressure%20transducer/P1010067a_zpslaxxfufp.jpg.html)


And here is the circuit board with some other I/O, a multi-channel solenoid driver, RS232 connection, additional regulated power supplies, and output to a 3 line LCD display.  It looks more complicated than it is.  I know very little about electronics, but these hobbyist microprocessors have a pretty good support community to lend help with projects.
(http://i226.photobucket.com/albums/dd79/loyd500/Pressure%20transducer/CircuitBoard-A_zpsbz9loaak.jpg) (http://s226.photobucket.com/user/loyd500/media/Pressure%20transducer/CircuitBoard-A_zpsbz9loaak.jpg.html)
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: match on April 22, 2016, 01:32:48 PM
Bob -

I am not sure momentum is strictly conserved in the macro "packet" sense.

The air packet absorbs energy cooling as it moves forward and expands - That is the molecules slow down in translational modes but speed up in vibrational/rotational modes.

In Helium you get the strange effect of while expanding the molecules speed up in translational modes (and temp increases) because there are NO rotational/vibrational modes available to absorb the energy due to He being a single atom.

This may also be another reason He works so well to increase fpe at the muzzle.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 22, 2016, 03:49:46 PM
John, there you go, making it complicated again.... *LOL*.... I need it simple....

Scott, you remember the equation Steve had that we discussed way back about post #310 and page 16, and discussed the constant being 194, not 172, because of the omission of a PI/4 term in the denominator?.... With that corrected, the maximum velocity (with zero pellet mass) worked out to 1854 fps, using 1/2 the mass of air in the barrel (Steve got 1644).... If we use only 1/3rd of the air mass, as per the equation above, that increases to 2257 fps, assuming air is an ideal gas.... Once we apply the VanDerWaals corrections, which effectively mean that the pressure is higher for a given density, once the pressures are above about 2000 psi, the equation is no longer independent of pressure.... Here is a chart comparing Steve's original equation (with the 172 constant, and as an Ideal Gas), my version, using VanDerWaals, (with the 194 constant) using 1/2 the mass and 1/3 the mass of air in the barrel.... compared to the output of Lloyd's L4 spreadsheet (in red).... for the 2025 fps shot @ 4000 psi with a 47.5" barrel....

(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Steve%20Bob%20and%20Lloyd%20vs%20Length_zps55rhwo5j.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Steve%20Bob%20and%20Lloyd%20vs%20Length_zps55rhwo5j.jpg.html)

You can see that only the version using 1/3 of the mass of air in the barrel predicts maximum velocities higher than Lloyd achieved in that shot.... So if there is any validity to that equation, something on the order of that ratio of mass is necessary for it to predict high enough numbers.... Note I am not suggesting this is the answer, just what will not work, based on existing results.... I wonder if there is any relationship between Steve's latest number of 2259 fps and the 2257 fps I obtained using his previous formula, corrected to include the PI/4 omission, and using only 1/3 of the mass of air in the barrel.... or if that is just another coincidence.... With air not acting as an Ideal Gas at over 2000 psi, it doesn't matter anyway, I guess.... because the maximum is higher than that at high pressures....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: match on April 22, 2016, 04:24:19 PM
aren't diatomic molecules fun!
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: phoebeisis on April 22, 2016, 05:12:56 PM
Bob
Got it-
- so in PCP   lower gamma gases have relatively  more  energy stored in not translation motion- 
so the  the temperatures-speeds- don't drop as much when it starts expanding  and doing work-
Thanks-I had been puzzling over that-
Charlie

Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: match on April 22, 2016, 06:10:09 PM
there are also micro state changes in the electron shells and quantum effects which store and release energy in diatomic gasses but I digress.... :)
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: I_like_Irons on April 22, 2016, 10:54:02 PM
LLoyd,

I've reached the point of (tentatively) selecting an appropriate ADC (analog/digital converter).  It is the LTC2351-12.  I think it is fast enough, has simultaneous multi-channel capabilities, and its12 bit resolution should be adequate for this.  I am now at the point of selecting the strain gauges and appropriate op-amps. Choices, and choices, and still more choices.  :-\ I'm still  quite fuzzy about software and programming, however.   But, as with any worthwhile endeavor, it is a significant learning experience. 


Now back to the thread:

A thought has occurred to me about how to treat the column of gas.  Like Tim McMurray stated in another thread, it is like a compressed spring. 

I am wont to think the column of gas like a very long coil spring that is fed into the barrel at up to Mach 1 for the pressure and temperature of the gas.  The pellet, initially, has enough resistance to keep the spring at "full" compression.  The mass of the spring itself prevents it from being fed faster than that rate.

However, when the pellet has reached that speed, the front part of the spring (also traveling at that rate) is now free to expand, and release stored energy. But, the coils behind the Mach 1 limit cannot yet expand.  Those coils that wind up in front of this Mach 1 "wave" get progressively more numerous and thus add more energy to the system.  They get in front due to the expansion of the coils in front of them.

The upper limit will be when the friction and compressed air force in front of the pellet (in a very long barrel) equal the expanding air behind the pellet.  There will be a barrel length  (for a given pellet mass and initial pressure) that will allow a maximum velocity of the pellet inside of it, while a longer barrel will not allow this velocity to occur, as there will be too much air in front of it. The optimum barrel will release just enough air to the atmosphere.

Now if one were to make a vented barrel whose vents would close just as the pellet reached them . . . . 
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 22, 2016, 11:05:16 PM
David, I like your analogy of the compressed air spring.... The second part, about the limit coming when the air in front of the pellet compresses to the point of balancing the force behind would take an incredibly long barrel.... and could be completely eliminated by applying a vacuum in front of the pellet.... Therefore, such a gun in space, should have no limit, right?.... Somehow I think that the compressed air behind the pellet will eventually lose it's ability to continue to accelerate the pellet.... I still think that will occur at twice the molecular velocity for air at the temperature involved.... ie at room temp about 3300 fps.... but it really is just a hunch, I can't prove it.... The three things that point me in that direction are my "thought experiment" with packets of air, the fact that the maximum velocity of flow in a tube is twice the average velocity, and Steve's equation for the "point of valve ineffectiveness", but using the molecular velocity instead of the speed of sound.... That equation goes to zero effect at 3300 fps for room temperature air....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 22, 2016, 11:53:24 PM
Further to my post # 517, if we apply the idea of using 1/3 of the air mass to the equation in post # 386, we get the following results for pellet mass equals zero....

V = sqrt { 2 x P / 12 / (D / 890575 / 3) } = sqrt (2 x 890575 x 3 / 12 ) x sqrt ( P / D ) = sqrt (445288 ) x sqrt ( P / D) = V = 667.3 sqrt ( P / D ) with P in psi, D in kg/m^3, and V in fps.... Here are the results for pressures up to 10,000 psi....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Air%20Density3%20Max%20Velocity_zpsldcmtpup.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Air%20Density3%20Max%20Velocity_zpsldcmtpup.jpg.html)

These results for zero pellet mass are interesting, because they show how much air diverges from an Ideal Gas at very high pressures.... the pressure (force) increasing faster than the density (mass).... Remember, the prediction for maximum velocity using the same equation (and 1/3 of the mass), but assuming air was an Ideal Gas, resulted in a velocity of 2257 fps, regardless of pressure.... If nothing else, I think the above numbers may be high enough that they will prove difficult to reach....

It occurred to me that I should be consistent in the units, and provide a Metric and Imperial version of the above equation.... In Imperial units, using Pressure P in psi and Density D in lb./in^3, and calculating the maximum Velocity V in fps, for zero pellet mass, and using 1/3 of the air mass, we have the following....

V = sqrt { 2 x P / 12 / (D / 32.174 / 3) } = sqrt ( 2 x 3 x 32.174 / 12 ) x sqrt ( P / D ) = sqrt ( 16.087) x sqrt ( P / D ) = V = 4.011 sqrt ( P / D )

In Metric units, using pressure P in bar (1 bar = 100,000 N/m^2), Density D in kg/m^3, and calculating the Velocity V in m/s, for zero pellet mass, we have the following....

V = sqrt { 2 x P x 100000 / (D / 3) } = sqrt ( 2 x 3 x 100000 ) x sqrt ( P / D ) = sqrt ( 600000 ) x sqrt ( P / D ) = V = 774.6 sqrt ( P / D )

All three equations give the same results, of course....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: I_like_Irons on April 23, 2016, 12:20:18 AM
Therefore, such a gun in space, should have no limit, right?.... Somehow I think that the compressed air behind the pellet will eventually lose it's ability to continue to accelerate the pellet....

When the pressure x area equals friction, that will be the limit in a vacuum.  If frictionless, then the limit will likely have to do with relativity.  ;)  Although, the acceleration after some point will be quite small well before the relativity limit.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 23, 2016, 01:43:55 AM
Therefore, such a gun in space, should have no limit, right?.... Somehow I think that the compressed air behind the pellet will eventually lose it's ability to continue to accelerate the pellet....

When the pressure x area equals friction, that will be the limit...
That's the simple view, and I like it.

It would be nice if there were a single equation to tell us that limit. I'm not so sure that there is.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 23, 2016, 01:45:27 AM
there are also micro state changes in the electron shells and quantum effects which store and release energy in diatomic gasses but I digress.... :)
I think I'll skip that part. For now at least.  :)
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: phoebeisis on April 23, 2016, 08:33:33 AM
 
How hard would it be to test how quickly the muzzle blast/pressure change-no pellet- is detectable?
Might tell you how fast the fastest detectable  energy wave is going




Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Bill G on April 23, 2016, 08:57:47 AM
Sorry, but could someone define Cp and Cv?.  I seem to have missed this.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 23, 2016, 12:54:33 PM
They are the Specific Heat Constants for a gas.... Cp is at constant pressure and Cv is at constant volume.... The constant gamma, (k =Cp/Cv) is most used as the exponent in the Adiabatic expansion process.... Beyond that, I have little understanding of them.... other than the oft-quoted value of k = 1.4 for air varies with pressure and temperature.... There is another gas constant, R = Cp-Cv, which I know nothing about....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 23, 2016, 12:56:12 PM
Charles, I think as soon as you try and measure the velocity of the muzzle gas, with no pellet in place, you will alter the reading....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: phoebeisis on April 23, 2016, 02:18:17 PM
Bob
Thanks
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 24, 2016, 02:16:29 PM
Further to my post # 517, if we apply the idea of using 1/3 of the air mass to the equation in post # 386, we get the following results for pellet mass equals zero....

v = sqrt { 2 x P / 12 / (Da / 890575 / 3) } = sqrt (2 x 890575 x 3 / 12 ) x sqrt ( P / Da ) = sqrt (445288 ) x sqrt ( P / Da) = v = 667.3 sqrt ( P / Da ) with P in psi, Da in kg/m^3, and v in fps.... Here are the results for pressures up to 10,000 psi....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Air%20Density3%20Max%20Velocity_zpsldcmtpup.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Air%20Density3%20Max%20Velocity_zpsldcmtpup.jpg.html)

These results for zero pellet mass are interesting, because they show how much air diverges from an Ideal Gas at very high pressures.... the pressure (force) increasing faster than the density (mass).... Remember, the prediction for maximum velocity using the same equation (and 1/3 of the mass), but assuming air was an Ideal Gas, resulted in a velocity of 2257 fps, regardless of pressure.... If nothing else, I think the above numbers may be high enough that they will prove difficult to reach....

Bob
How about some higher numbers:

After a recent discussion on the yellow about de Laval nozzles and how the associated equations might apply to airgun, I decided to look at the Fanno flow equations a little more closely. When compared to the de Laval, the Fanno model looks a lot more like an airgun with a dump chamber. I'm looking for something that we might be able to use. There is no easy way to include pellet mass, but maybe it will give a maximum possible velocity of the air.

Here is the wiki link to some of the equations:
https://en.wikipedia.org/wiki/Fanno_flow (https://en.wikipedia.org/wiki/Fanno_flow)

(http://www.scotthull.us/photos/Misc/fanno-00.jpg)

I used the velocity ratio equation V/V*, substituting SOS for V*, and used the k (gamma) values for air at different pressures. I used some very high Mach numbers in order to maximize the velocity ratios:

(http://www.scotthull.us/photos/Misc/fanno-S1.jpg)

The unrealistic, very high mach numbers (>M10) indicate where the air had already been fully expanded, as velocity had mostly maxed out already.

Maybe these are the max velocities for air at 70F? They may just be a theoretical limit rather than what can actually be achieved.

Edit: for the equation used, as k approaches 1, max possible velocity approaches infinity.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 24, 2016, 03:58:37 PM
If you look over the Siegel equations, you will find that the maximum velocity is Mach 5.... This applies even to light gas guns, providing you are working at the correct temperature....

I think if you look at the equation again, when k = 1, the value becomes M, does it not?....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 24, 2016, 10:11:15 PM
If you look over the Siegel equations, you will find that the maximum velocity is Mach 5.... This applies even to light gas guns, providing you are working at the correct temperature....

I think if you look at the equation again, when k = 1, the value becomes M, does it not?....

Bob
The equation is not giving a Mach number, it gives a velocity ratio. When k approaches 1, the ratio becomes 1x. At M1, the ratio is always 1/1, for any value of k.

If I change k to 1, the air can expand indefinitely and continue to accelerate itself. At normal k values, the downstream Mach velocity falls faster than the Mach number grows. It runs out of "gas" after M10:
(http://www.scotthull.us/photos/Misc/fanno-02.jpg)

Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 24, 2016, 10:38:44 PM
OK, but using the equation, with k = 1, I get the following....

V/V* = M x { 1 / sqrt  [ ( 2 / k + 1 ) x ( 1 + [ ( k-1 ) / 2 ] x M^2 ) ] } = M x { 1 / sqrt [ ( 2 / 2 ) x ( 1 + [ 0 / 2 ] x M^2 ) ] } = M x { 1 / sqrt [ ( 1 ) x ( 1 ) ] }  = M x { sqrt 1 } = M ....

If you say the trend is to infinity, please show what I did wrong?....

BTW, here is the reference to Siegel's equation showing Mach 5 as the maximum for air (gamma = 1.4).... http://dspace.dsto.defence.gov.au/dspace/bitstream/1947/4048/1/DSTO-TR-1092%20PR.pdf (http://dspace.dsto.defence.gov.au/dspace/bitstream/1947/4048/1/DSTO-TR-1092%20PR.pdf) .... the equation appears on page 12.... As gamma increases, the maximum Mach number decreases....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 24, 2016, 11:45:24 PM
I think I get it.... V/V* equals Mach if gamma = 1 (which is the proof I did above).... However, gamma can never drop to 1 unless you are adding energy to the system (Isothermal = 1).... and Mach can never exceed the value given by the Siegel equation, based on the gamma from column C in your table (k = 1.4 at STP).... With air, the lowest gamma is 1.4 (see below), which in Siegel's equation gives you a maximum of Mach 5....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/specific%20heat%20ratio_zpsb7wxxwov.png) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/specific%20heat%20ratio_zpsb7wxxwov.png.html)

In fact, if we want the output of Siegel's equation in Mach, it becomes even simpler.... 

Vmax = 2/(k-1) .... which yields Mach 5 when gamma = 1.4 (STP).... and at the maximum gamma in your table (@ 5000 psi, k = 1.745) it gives....

Vmax =  2 / ( k-1 ) = 2 / ( 1.745 - 1 ) = 2 / 0.745 = Mach 2.68 (at 5000 psi and 70*F)

Using Mach 2.68 as the limit in your equation gives....

V/V* = 2.68 x ( 1 / sqrt ( 2 / 2.745 ) x ( 1 + ( 0.745 / 2 ) x 2.68^2 ) ) = 2.68 x ( 1 / sqrt ( (0.729) x ( 1 + (0.373 x 7.18) ) ) = 2.68 x ( 1 / sqrt (0.729 x 3.68) ) = 2.68 x 1 / 1.64 = 1.63

which for V* = 1615 fps yields 2632 fps.... It would seem that if you first apply Siegel's equation (which is based on gamma, which is in turn based on pressure) to calculate the maximum Mach number, and then use that Mach number in your Fanno Flow equation, the result should be the absolute maximum velocity for that pressure, at 70*F....

Until we come up with a better idea.... *LOL*....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 25, 2016, 12:22:17 AM
Bob,
That's it.

If the equation for maximum Mach# given by Siegel is correct, you could use that with the Fanno flow equation and get the max velocity.

At 5000psi, 70F:

With no limit on Mach#, we get a 3100fps velocity limit.

With the Siegel Mach limit of M2.68, we get a 2632fps velocity limit.

Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 25, 2016, 12:44:00 AM
OK, I'm not saying if the method is sound or not, but just for discussion and visualization purposes, here are the results.... I used the raw data you sent me for the values of gamma, for every 500 psi increment, to calculate Siegel's maximum Mach number.... and then from that, using your Fanno Flow equation I calculated the maximum V/V* ratio (ie maximum Mach number) for Fanno Flow.... assuming Siegel is correct....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Fanno%20Siegel%20Maximum_zpsxkf2411y.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Fanno%20Siegel%20Maximum_zpsxkf2411y.jpg.html)

I then used the raw data I have for the Speed of Sound in air, at the same pressure increments, to convert the Fanno Mach numbers into the velocity in fps....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Fanno%20FPS%20Maximum_zpsfbwzeb0u.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Fanno%20FPS%20Maximum_zpsfbwzeb0u.jpg.html)

It might be interesting to extend these curves out to 10,000 psi, just out of curiosity, but I don't have the gamma values for that.... I note that the maximum velocity at 2000 psi is not all that fast, at just over 2200 fps.... I don't know if that is a problem or not.... but that's the results I got, anyway....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 25, 2016, 01:23:59 AM
Bob,
That last graph is the velocity allowed by the Siegel Mach limits.

The max Fanno velocity is higher at each pressure. The M100 column from my chart is high enough to flat line the velocity for each pressure.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 25, 2016, 02:17:53 AM
No, the last graph is the Fanno Flow equation, but with the Mach number input to the Fanno equation limited by the output of the Siegel equation.... The blue line on the upper graph is the Siegel equation by itself.... I have not graphed the Fanno Flow data by itself, as I don't see how Mach 100 makes sense, you said yourself they are unrealistic.... However, your results from your M100 column could certainly be graphed.... Here is a chart I have prepared showing the three current ideas which vary with pressure....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Fanno%20Siegel%20and%20Mass_zps8uu6mdun.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Fanno%20Siegel%20and%20Mass_zps8uu6mdun.jpg.html)

I didn't use the trendline equations, so as not to introduce any small errors, I went back to the original data that Scott sent me for Gamma, and the data I got from the Peacesoft and Wolfram Calculators for the Speed of Sound and Air Density, for every 500 psi up to 6000.... The Fanno Flow is using Scott's equation, using Mach 100 (to max. the velocity), and the Fanno / Siegel data is using the output of the Siegel equation as the limiting Mach, which is then used in the Fanno Flow equation.... The Pressure / Mass curve is plotted by using the equation developed by Steve_in_NC for maximum velocity based on pressure and density, but is corrected to use the actual Density values at each Pressure (because air is not an Ideal Gas over 2000 psi), and using 1/3 of the mass to incorporate the KE of flow in a tube, which has that factor in it, as explained in my post # 517....

I have no idea if any of these theories are valid, but presenting them all in one chart may be useful.... All these curves are plotted using zero pellet mass.... The Fanno and Siegel equations are based on Gamma while the other is based on Density.... both of which vary with Pressure....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 25, 2016, 04:00:22 PM
No, the last graph is the Fanno Flow equation, but with the Mach number input to the Fanno equation limited by the output of the Siegel equation.... The blue line on the upper graph is the Siegel equation by itself.... I have not graphed the Fanno Flow data by itself, as I don't see how Mach 100 makes sense, you said yourself they are unrealistic.... However, your results from your M100 column could certainly be graphed.... Here is a chart I have prepared showing the three current ideas which vary with pressure....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Fanno%20Siegel%20and%20Mass_zps8uu6mdun.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Fanno%20Siegel%20and%20Mass_zps8uu6mdun.jpg.html)

I didn't use the trendline equations, so as not to introduce any small errors, I went back to the original data that Scott sent me for Gamma, and the data I got from the Peacesoft and Wolfram Calculators for the Speed of Sound and Air Density, for every 500 psi up to 6000.... The Fanno Flow is using Scott's equation, using Mach 100 (to max. the velocity), and the Fanno / Siegel data is using the output of the Siegel equation as the limiting Mach, which is then used in the Fanno Flow equation.... The Pressure / Mass curve is plotted by using the equation developed by Steve_in_NC for maximum velocity based on pressure and density, but is corrected to use the actual Density values at each Pressure (because air is not an Ideal Gas over 2000 psi), and using 1/3 of the mass to incorporate the KE of flow in a tube, which has that factor in it, as explained in my post # 517....

I have no idea if any of these theories are valid, but presenting them all in one chart may be useful.... All these curves are plotted using zero pellet mass.... The Fanno and Siegel equations are based on Gamma while the other is based on Density.... both of which vary with Pressure....

Bob
Bob,

Here is another take. The Siegel speed of sound is referring to the initial chamber value (Wolfram Alpha value). So would not be combined with the Fanno equation. At least that's my take on what is being said here:

http://yarchive.net/mil/maximum_muzzle_velocity.html (http://yarchive.net/mil/maximum_muzzle_velocity.html)

"The *initial* value of c, before the projectile and gases have started to
move, is the correct value to use in this analysis.

This is a classic mistake people make in analysis of unsteady flows (such
as internal ballistics).  Since the maximum velocity, as Carey pointed
out, is

     u = 2c/(gamma - 1)

some people are tempted to say that the maximum projectile velocity is
Mach 5, since u/c = 2/(gamma -1) = 5 for gamma = 1.4.  However, c here
refers to the initial sound speed of the propellant gases, before any
expansion has occurred.  It is more properly labeled "c0."  Once the
projectile begins to accelerate, the gases expand and cool, and the
projectile velocity with respect to the gas immediately behind it (Mach
number) could be much greater than 5.  The projectile's Mach number with
respect to the air is another matter entirely."
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 25, 2016, 04:55:04 PM
You need to work with the speed of sound in the propellant gas at the beginning of the cycle, which for 5000 psi air is 1615 fps.... Five times that is 8075 fps, but that isn't the output of the Siegel equation, because k = 1.736 at that pressure, so Siegel's equation yields 1615 x 2 / (1.736-1) = 4389 fps.... Siegel's equation does NOT give the Mach number relative to the expanding and cooling gas behind it, but to the starting point.... Most light gas guns (which were the reason Siegel developed his equation) do NOT start with air at high pressure, they start, in fact with Helium at 1 atmosphere (although it may be heated).... If you start with air at 1 atmosphere, k = 1.4, and the maximum Mach relative to that starting air is Mach 5.... With Helium, where k = 1.67, it is Mach 3, but of course the SoS in Helium is higher to start with....

If you note, I am using the SoS for the starting gas, just as Siegel's equation is intended to be used.... I have never seen any experimental results quoted that exceeded Siegel's equation, so I think it is a valid starting point for the maximum Mach number used for Fanno Flow.... Neither of us can prove it, it's just another possibility.... I still don't see how you can develop Mach 100, as you suggest....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 25, 2016, 05:34:40 PM
You need to work with the speed of sound in the propellant gas at the beginning of the cycle, which for 5000 psi air is 1615 fps.... Five times that is 8075 fps, but that isn't the output of the Siegel equation, because k = 1.736 at that pressure, so Siegel's equation yields 1615 x 2 / (1.736-1) = 4389 fps.... Siegel's equation does NOT give the Mach number relative to the expanding and cooling gas behind it, but to the starting point.... Most light gas guns (which were the reason Siegel developed his equation) do NOT start with air at high pressure, they start, in fact with Helium at 1 atmosphere (although it may be heated).... If you start with air at 1 atmosphere, k = 1.4, and the maximum Mach relative to that starting air is Mach 5.... With Helium, where k = 1.67, it is Mach 3, but of course the SoS in Helium is higher to start with....

If you note, I am using the SoS for the starting gas, just as Siegel's equation is intended to be used.... I have never seen any experimental results quoted that exceeded Siegel's equation, so I think it is a valid starting point for the maximum Mach number used for Fanno Flow.... Neither of us can prove it, it's just another possibility.... I still don't see how you can develop Mach 100, as you suggest....

Bob
Hypersonic wind tunnels. Downstream Mach >5. Usually M5 to M15.

There is one that does M27, but only runs for 1 second. They call that piston powered wind tunnel "Gun Tunnel". It is similar to Siegels gas guns, but is used for studying hypersonic flow rather than launching projectiles.

I'm not suggesting M100 is pratical. I just wanted a near infinite value that would surely be the max. The velocity is near maxed out way before that. Even at M10, the velocity is near flatline. Just like an infinite dump chamber is not possible, but using a very large value gets us close to the maximum possible.

If you don't like M100, use M10. M10 has been achieved. Either way, it ends up with about the same results.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 25, 2016, 08:54:23 PM
Just goes to prove that, in my case, a little knowledge is a dangerous thing.... I don't even know what I don't know....

Incidently, Photobucket is having net-wide problems ATM, none of my photos/charts seem to be available.... Hope they can fix it !!!

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 26, 2016, 07:15:26 PM
In case you don't know the history of the discussion of the "Sonic Horizon" (which dates back to about 2005), here is a link to the discussion I had with Steve_in_NC about it on the Green Forum in 2012....

http://www.network54.com/Forum/275684/message/1352000609/Not+a+Crosman.... (http://www.network54.com/Forum/275684/message/1352000609/Not+a+Crosman....)

At the bottom of the page is a menu of the entire thread.... Lloyd had some very interesting input which of itself deserves study, as it gives huge insight into his Internal PCP Ballistics spreadsheet....

The basic concept is that when the valve closes, that pressure drop takes a finite time to reach the pellet, which is already travelling up the bore.... The idea is that at some point, whether the valve is open or closed can no longer have any effect on the pellet before it exits the barrel, because the pellet is so far away from the valve, and travelling so fast, that information cannot reach the pellet before it leaves the muzzle.... Steve postulated that drop in pressure (a pressure, or sound wave) was propagated at the Speed of Sound, which he stated was independent of pressure, but varied with temperature.... Because he believes that the expansion in the barrel is Adiabatic, causing a cooling of the air in the barrel, and hence a lowering of the SoS, he originally used a figure of only 1000 fps for the velocity of the wave travelling from the valve to the pellet, to produce this chart....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/valveineffect_zpsow04p5s5.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/valveineffect_zpsow04p5s5.jpg.html)

In 2012 I had quite detailed data which I felt contradicted Steve's theory, and proposed that instead of using the SoS, that we use the RMS velocity of air at 20*C instead, which is about 1650 fps.... The chart showing that, and also Steve's results, (but using the SoS at 20*C without derating for cooling) is shown below.... I should add that a constant acceleration for the pellet is assumed (ie constant pressure), so the pellet position x as a function of time T is given by.... x = aT^2 / 2 .... where the acceleration a is of course a function of the pressure x bore area (force) and the mass of the pellet.... Steve did not give the steps in the derivation of his equation for the Sonic Horizon, but he did give me the equation, which is.... x = ( 1 - MV / 2S )^2 .... where MV is the Muzzle velocity and S is the Speed of Sound.... and x is the pellet position, expressed in the chart as a percentage of barrel length, with zero being the breech and 100% being the muzzle....


(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Pellet%20Horizon%203_zpsyfltrzjh.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Pellet%20Horizon%203_zpsyfltrzjh.jpg.html)

A short while ago, in post # 371 of this thread, I extended that graph for the RMS velocities out to where the valve becomes completely ineffective (at least in theory), and that chart follows.... although labelled differently, it is still based on the same concept....Note that the maximum velocity predicted is 3300 fps....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Pellet%20Horizon%202_zpsqkdq4fbp.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Pellet%20Horizon%202_zpsqkdq4fbp.jpg.html)

This morning I awoke thinking about this idea in a new light.... I searched the Green for the thread linked in the first paragraph and reviewed it to refresh my mind, and found one particularly revealing statement of Steve's, in the title of a post.... "the speed of sound is independent of pressure".... While that is true for small changes in pressure, it is NOT true once the pressures build to any significant degree.... I was not aware of that in 2012, so did not dispute his statement at the time.... Here is how the SoS varies with pressure.... this information available from the Wolfram online calculator....
http://www.wolframalpha.com/widgets/view.jsp?id=b63c87b0a41016ad29313f0d7393cee8 (http://www.wolframalpha.com/widgets/view.jsp?id=b63c87b0a41016ad29313f0d7393cee8) .... type in "air at xxxx psi" to see the result....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/SpeedofSound20C_zpsa0791bdb.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/SpeedofSound20C_zpsa0791bdb.jpg.html)

Since we are looking at the case where pellet acceleration is constant, that means that the pressure is constant, which means that the reservoir is orders of magnitude larger than the barrel volume.... That should further mean that there is virtually no Adiabatic expansion to drop the temperature during the shot, until the pellet exits the barrel.... That means we can assign a different value for the SoS in Steve's equation for the Sonic Horizon, based on the pressure.... Here is what happens to the Sonic Horizon (assuming it, in fact, exists), at different pressures....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Valve%20Ineffectiveness%20vs%20Pressure_zpsdzxjdchs.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Valve%20Ineffectiveness%20vs%20Pressure_zpsdzxjdchs.jpg.html)

Note that each line goes to zero at Mach 2 for the pressure involved.... If we take that as the maximum velocity possible, because no air added after that MV is reached can have any effect on the pellet, we get one more chart....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Valve%20Effect%20on%20Max%20Velocity_zpslpbdnt6u.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Valve%20Effect%20on%20Max%20Velocity_zpslpbdnt6u.jpg.html)

Is this the bottom line for the maximum velocity?.... I seriously doubt that.... Other factors may exist that create lower limits for the velocity, and the RMS velocity of 1650 fps, times two to produce the 3300 fps limit suggested above, may superimpose that limit over this one.... That would mean that the limit increases with pressure up to about 5000 psi, and then plateaus.... The same could apply where even lower limits are suggested by alternate theories, if those theories are correct, they would also be superimposed on more lenient ones.... Of course the point of any limit is that it should be impossible to reach and can only be approached.... so, if anyone provides good experimental evidence they are close to any limit, it immediately makes that limit suspect....

Am I a solid believer in the "Sonic Horizon" theory, once modified to take into account the increased Speed of Sound at high pressures?.... No, but I can see the detailed reasoning that went into the idea originally.... and I respect greatly the intellect of the guy who proposed it (Steve_in_NC).... Yes, I have come up with arguments to counter it, such as "packets" of air, each being inserted sequentially into the barrel, etc.etc.... but there remains that lingering, gut feeling, that at some point, and at some velocity, nothing you do at the breech can effect the pellet before it exits.... IF the equation is valid, it simply becomes a matter of what number you plug in for "S".... be that 1127 fps, 1650 fps, or the SoS at the pressure inside the barrel.... Maybe some day, we will figure it all out.... in the meantime, this is just one more theory to ponder....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 27, 2016, 01:35:34 AM
I keep going back to the Fanno flow equations.

I was finally able to factor out the Mach. That leaves the speed of sound(SOS) and gamma(k), for the inlet as the the only variables. Resulting in a single equation to predict max possible velocity based on inlet conditions:

Vmax = SOS x sqrt((2/(k-1))+1)

That's my equation for the maximum possible velocity in a PCP. I'm going with that for now.

(http://www.scotthull.us/photos/Misc/fanno-vmax.jpg)
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 27, 2016, 10:15:16 PM
CO222 on the Yellow is going to (easily) join the 2000+ club, IMO.... providing he gets the 9mm projectile weight down to the 8 gr. proposed for the test....
http://www.network54.com/Forum/79537/message/1461804297/Maximum+airgun+velocity+-+building+the+new+hypergun (http://www.network54.com/Forum/79537/message/1461804297/Maximum+airgun+velocity+-+building+the+new+hypergun)
Based on Lloyd's previous shot data, my prediction is 2300+ at the Chorny, assuming it is about the same distance away as Lloyd's.... Two versions of Lloyd's spreadsheet give 2312 and 2308 based on Lloyd's 1745 fps .22 cal shot, and 2362 and 2354 based on his 2162 fps .278 cal shot.... Steve_in_NC is predicting (revised to) 2206 at the muzzle and 2163 at the Chrony, based on resetting one of his formulas for his 2259 fps maximum possible recently proposed.... It will be extremely interesting if the shot breaks that new 2259 maximum.... which I think entirely likely, at least at the muzzle....

Incidently, using my version of Steve's equation, adjusted for 1/3 of the air mass, with an 8 gr. bullet @ 4350 psi, 0.354" barrel that is 59" long (Va = 5.81 in^3) yields a maximum velocity of 2389 fps.... The air density I used is the average from Peacesoft & Wolfram @ 4350 psi = 323 kg/m^2 = 81.7 gn/in^3....

v = sqrt ( 2 x P x Va / 12 / [W + D x Va / 3 ] / 225218 ) = sqrt ( 2 x 225218 / 12 ) x sqrt ( P x Va / [ W + D x Va / 3] ) = 193.7 sqrt ( 4350 x 5.81 / [ 8 + 81.7 x 5.81 / 3 ] ) = 193.7 sqrt ( 25274 / 166.2 ) = 2389 fps

The actual velocity should be less because the reservoir is only about 1.8X the barrel volume, which will cause a pressure loss during the shot.... which is allowed for in Lloyd's spreadsheet calculations....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 28, 2016, 12:29:28 AM
CO222 on the Yellow is going to (easily) join the 2000+ club, IMO.... providing he gets the 9mm projectile weight down to the 8 gr. proposed for the test....
http://www.network54.com/Forum/79537/message/1461804297/Maximum+airgun+velocity+-+building+the+new+hypergun (http://www.network54.com/Forum/79537/message/1461804297/Maximum+airgun+velocity+-+building+the+new+hypergun)
Based on Lloyd's previous shot data, my prediction is 2300+ at the Chorny, assuming it is about the same distance away as Lloyd's.... Two versions of Lloyd's spreadsheet give 2312 and 2308 based on Lloyd's 1745 fps .22 cal shot, and 2362 and 2354 based on his 2162 fps .278 cal shot.... Steve_in_NC is predicting (revised to) 2206 at the muzzle and 2163 at the Chrony, based on resetting one of his formulas for his 2259 fps maximum possible recently proposed.... It will be extremely interesting if the shot breaks that new 2259 maximum.... which I think entirely likely, at least at the muzzle....

Incidently, using my version of Steve's equation, adjusted for 1/3 of the air mass, with an 8 gr. bullet @ 4350 psi, 0.354" barrel that is 59" long (Va = 5.81 in^3) yields a maximum velocity of 2389 fps.... The air density I used is the average from Peacesoft & Wolfram @ 4350 psi = 323 kg/m^2 = 81.7 gn/in^3....

v = sqrt ( 2 x P x Va / 12 / [W + D x Va / 3 ] / 225218 ) = sqrt ( 2 x 225218 / 12 ) x sqrt ( P x Va / [ W + D x Va / 3] ) = 193.7 sqrt ( 4350 x 5.81 / [ 8 + 81.7 x 5.81 / 3 ] ) = 193.7 sqrt ( 25274 / 166.2 ) = 2389 fps

The actual velocity should be less because the reservoir is only about 1.8X the barrel volume, which will cause a pressure loss during the shot.... which is allowed for in Lloyd's spreadsheet calculations....

Bob

My current spreadsheet predicts 2395fps, but on average, it predicts a little high for Lloyd's tests, each time, so I'll say 2350fps.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 28, 2016, 11:59:58 PM
Very interesting.  I've been away for less than a week (gardening and building) and so much has happened in this thread.  Sorry, but I am having trouble keeping up with the theory, so I will just stay out of the way for that part. 

I do have another test in process right now.  A couple of weeks ago Scott asked me to verify the temp and pressure change in the breech block before and after the shot.  I set a shot up this evening, again with the .278 cal 46" barrel, 55cc dump chamber.  This time with a 6.3 gn projectile.
The test started at 9:04 PM eastern time tonight and is being documented with photos.  The block started out at 73.3F.  Fill took about 3 minutes and the maximum block temp reached 77.1F (3.8 degree rise) with a fill of 4000 psi.  After exactly 90 minutes, the temp had dropped by 3.6 degrees F,  to 73.5F, and the pressure had dropped by  50 psi to 3950 psi.  So again, no changes of any significance in pressure or temperature.

In a short while I will take a shot with the fully "cooled" block.  Predicted velocity will again be in the 2130fps range.  However, something could go wrong, such as the o-ring trying to extrude past the end of the projectile and partially locking the movement.  Anyway, we will see shortly.  I will record the before shot temps of the barrel and block, and then check them again 30 minutes after the shot to see if anything changes.
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 29, 2016, 12:50:27 AM
Here are the results from tonight's shot, start to finish.
.278 cal, 6.3 gn, 46" barrel, 55 cc dump chamber.
9:04 PM, ready to begin, 73.3F block, 0 psi.
9:07 start and fill,  77.1F block, 4000 psi.
11:21, temp and pressure stable, ready to take the shot:    72.2F block, 71.9F barrel muzzle, 3940 psi.
11:23, take the shot, 71.9F block, 71.2F barrel muzzle,  2063 fps.
11:41, temperatures again stabilized, 71.8F block, 71.5F barrel muzzle.
Lloyd

edit- The temperature in the shop varies a few degrees, so I would consider  the resolution on the temperature readings to be maybe +/- one degree F.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 29, 2016, 01:19:44 AM
CO222 on the Yellow is going to (easily) join the 2000+ club, IMO.... providing he gets the 9mm projectile weight down to the 8 gr. proposed for the test....
http://www.network54.com/Forum/79537/message/1461804297/Maximum+airgun+velocity+-+building+the+new+hypergun (http://www.network54.com/Forum/79537/message/1461804297/Maximum+airgun+velocity+-+building+the+new+hypergun)
Based on Lloyd's previous shot data, my prediction is 2300+ at the Chorny, assuming it is about the same distance away as Lloyd's.... Two versions of Lloyd's spreadsheet give 2312 and 2308 based on Lloyd's 1745 fps .22 cal shot, and 2362 and 2354 based on his 2162 fps .278 cal shot.... Steve_in_NC is predicting (revised to) 2206 at the muzzle and 2163 at the Chrony, based on resetting one of his formulas for his 2259 fps maximum possible recently proposed.... It will be extremely interesting if the shot breaks that new 2259 maximum.... which I think entirely likely, at least at the muzzle....

Incidently, using my version of Steve's equation, adjusted for 1/3 of the air mass, with an 8 gr. bullet @ 4350 psi, 0.354" barrel that is 59" long (Va = 5.81 in^3) yields a maximum velocity of 2389 fps.... The air density I used is the average from Peacesoft & Wolfram @ 4350 psi = 323 kg/m^2 = 81.7 gn/in^3....

v = sqrt ( 2 x P x Va / 12 / [W + D x Va / 3 ] / 225218 ) = sqrt ( 2 x 225218 / 12 ) x sqrt ( P x Va / [ W + D x Va / 3] ) = 193.7 sqrt ( 4350 x 5.81 / [ 8 + 81.7 x 5.81 / 3 ] ) = 193.7 sqrt ( 25274 / 166.2 ) = 2389 fps

The actual velocity should be less because the reservoir is only about 1.8X the barrel volume, which will cause a pressure loss during the shot.... which is allowed for in Lloyd's spreadsheet calculations....

Bob

Human nature is funny, isn't it? 
My best to CO222 in his endeavors.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 29, 2016, 02:19:40 AM
I also wish CO222 the best in his endeavours, and hope he presents detailed data on his results, whatever they may be....

I proposed the above post #545 in the hopes it might heal some of what has recently taken place, by offering a large olive branch.... I certainly won't be trying to come up with any further explanations where everybody could be right.... at least until we are given credit for the work we have done and our contributions recognized and not simply dismissed or ridiculed....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 29, 2016, 02:23:29 AM
Lloyd, I missed your prior posts about tonight's test.... Congratulations on completely putting to rest all the nonsense about heating, and pulling off yet another shot at well over 2000 fps....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 29, 2016, 09:26:52 AM
Lloyd, I missed your prior posts about tonight's test.... Congratulations on completely putting to rest all the nonsense about heating, and pulling off yet another shot at well over 2000 fps....

Bob
Thank you Bob!  You are gentleman!
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 29, 2016, 12:54:02 PM
It was too late last night to run Lloyd's latest shot through his spreadsheet, but I have now.... Using his J4 version (Boyle's) and the baseline from the .22 cal 1745 fps shot, which used a 70% efficiency factor, predicted a velocity for the latest shot of 2128 fps.... This is for .278 cal, 46" barrel, 55 cc chamber, 6.3 gr. pellet, and 3940 psi.... The velocity of 2063 fps works out to 66% efficiency.... The 2162 fps shot balanced at 73% in the same calculator....

Using Lloyd's new L4 version, which incorporates both the VanDerWaals pressure/density corrections, and the maximum mass flow rate possible for the SoS at the reservoir pressure, both done incrementally, requires slightly higher efficiency numbers to balance, which to me indicates it is closer to reality.... The .22 cal 1745 fps shot balances at 73%, the .278 cal 2162 fps shot balances at 76%, and the latest 2065 fps shot balances at 69%.... All three shots balance at 3% higher efficiency with the new L4 version, compared to the previous J4 spreadsheet.... Changing the pressure to 4500 psi predicts a velocity of 2110 fps with the 6.3 gr. pellet in a temperature stabilized environment in the current test setup....

Incidently, using this latest L4 version, balanced at 69% as per Lloyd's most recent test, predicts a velocity of 2241 fps for the 8 gr., 9mm test at 300 bar proposed by CO222 on the Yellow.... Of course that assumes his gun is exactly the same efficiency as Lloyd's.... It should be noted that all velocities quoted are at the Chrony, which is 3-4 feet from the muzzle.... Actual muzzle velocities will be higher, meaning that Lloyd's spreadsheet models are actually closer to reality than the percentages listed....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 29, 2016, 05:27:33 PM
Just a little aside here, about Ballistics Coefficients and their effect on the velocity of these high-speed shots when measured 1 yard from the muzzle.... If we use the latest "velocity limit" of 2259 fps, and use a BC equal to the SD of a 9mm pellet that weighs 8 gr. (ie an SD and hence BC of 0.009), we get the following velocities at 1 yard, using several different drag models.... NTP conditions are assumed, calculations from ChairGun....

G1 (bullet) = 2169 fps
GA (pellet) = 2169 fps
GS (sphere) = 2109 fps
GC (cylinder) = 2023 fps

Using a BC that equals the SD likely greatly overestimates the BC of a pellet, particularly when using the G1 or GA models, and particularly at Supersonic speeds.... I have done measurements on many pellets at over Mach 1, and the Cd is generally over 1.0, which corresponds better to the drag for a sphere.... I would therefore suggest that any velocity measured with a Chrony at 1 yard from the muzzle of over 2100 fps would put any suggestion of an absolute limit of 2259 fps in serious doubt....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 29, 2016, 06:17:28 PM
There seems to be a high degree of subjectivity in determining how much velocity is lost in those first few feet.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on April 30, 2016, 12:11:12 AM
I was over on the yellow forum for a while. I proposed the reduction of the Fanno velocity ratio as a maximum for PCP velocity. Steve proposes the de Laval velocity equation as the maximum, and that's OK as we will see if 2258fps gets broken.

The problem is he keeps trying to resurrect the V(max) = 172 * sqrt(Q/(m+Z*Q)) equation as a predictor of maximum velocity. By simply changing the fudge-factor Z. I'm now of the opinion, that equation will never be able to predict the supersonic maximum of air. Once 1640fps was broken, that equation became irrelevant to maximum velocity. It does work good for subsonic conditions.

The equation:
V(max) = 172 * sqrt(Q/(m+Z*Q))

As the pellet mass goes to zero:
V(max) = 172 * sqrt(Q/(0+Z*Q))

And then Q's cancel out:
V(max) = 172 * sqrt(Q/(Z*Q))

For just max air velocity:
V(max) = 172 * sqrt(1/Z)

2258fps=172 * sqrt (1/.0058)

Steve chose .0058 as a new fudge-factor "Z" in order to "force" the equation to "predict" a V(max) of 2258fps. Steve does not not see the fallacy in doing that. It also messes up the equation when trying to use it to predict subsonic velocities. .011 is the better fudge factor, but that "predicts" a max velocity of only 1640fps. As soon as he realizes that particular equation cannot accurately "predict" any supersonic velocities, the better off they will be over there.

I think we'll need a 60"-96"+ barrel to go for 2300fps. Bigger caliber, lighter pellets?
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 30, 2016, 01:10:32 AM
The equation is irrelevant anyway, because the constant is incorrect.... as originally pointed out by Herb1836 in this thread.... http://www.network54.com/Forum/79537/message/1236441062/But+Q+is+out+of+whack... (http://www.network54.com/Forum/79537/message/1236441062/But+Q+is+out+of+whack...)

I addressed all of that in posts # 380, 382 & 383.... In addition, the "Z" factor ignores the fact that pressure and density no longer track in simple proportion once the pressures exceed 2000 psi, because air does not act as an Ideal Gas.... I addressed that by introducing the ACTUAL density and pressures in post # 386.... When I discovered that the KE of a moving column of air is based on only 1/3 of the product of the mass and velocity of the center of the stream, I updated it again in posts # 504, 505, 517 and 523.... The equation can be used in two different ways, with the pellet mass in place, or simplified with the only variables being Pressure and Density.... The constants depend on the units chosen, of course....

The de Laval equations are also based on an Ideal Gas.... so may or may not be irrelevant for PCPs....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Michael Loar on April 30, 2016, 07:37:49 AM
I will just say this very short and direct statement in that those of us who have been following this thread from its beginning until now know who the true unbiased and totally objective people are and what has been accomplished for the sole purpose of finding the truth and limits if there is actually one to be found.

There will always be those that believe theirs is the only way and to mock it or rebel against it is either hierarchy or lunacy since it just cannot be any other way but theirs. If that were the case our technology would have been stagnated centuries ago and we would still be in the dark ages.

Since we all know for a fact that is not the case then how can one person knowingly in good conscious and faith be so ignorant as to continue to keep his head buried in the sand in an attempt to force the discovered facts to be seen as impossible or inaccurate due to faulty or skewed testing of which has been as far above scrutiny or inconsistencies as humanely possible.

It is truly a sad day in this country when such thinking takes place and only tries to divide us instead of unite us for the common good not unlike the direction this country is headed as well.

 "To infinity and beyond "

Mike   
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 30, 2016, 10:02:34 AM
Mike, some good thoughts there.
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 30, 2016, 10:41:53 AM
Version 3, and barrel length of Version 2.
Progress on Version 3 is moving slowly as preparing for the Funshoot in a week and a half is taking priority. But I will be bringing Version 2 there.
Just thinking out loud, but it would not be too difficult to swap out the .278 bore barrel for a nominal .334 smooth bore barrel with a length up to 71". Still 4500 psi and 55 cc dump.  There is a slim chance of getting the projectile to less than 8 grains. Personally, I think it is worth doing, and it could be done quickly and at little expense.  Any thoughts?
Thanks, Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: MichaelM on April 30, 2016, 12:11:53 PM
I know there would be slimmer chance of getting the projectile down to the weights your looking for.. but it seems to me the larger bore diameter would allow for better efficiency and more force acting on the base of the projectile.... ALSO seem to me that it would be a heck of a lot easier to machine a larger projectile then a small one lol...  maybe even opening up some possibilities of a less draggy sealing method like maybe a reversed "parachute: type of seal like whats used on springer pistons???   though thta sounds like a pain in the butt to machine lol..... either way maybe something like a sleeved aluminum projectile with delrin to help cut back on weight...
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on April 30, 2016, 12:36:19 PM
Michael, Yes, with the larger dia, it might be easier to stretch a Teflon seal over the aluminum center part, and cut both the weight and friction. 
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on April 30, 2016, 01:04:56 PM
You know you're going to do it, Lloyd!.... and good on ya' for that....

buldawg.... Amen to that !

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on May 01, 2016, 02:21:06 PM
My Grandfather once told me that if you cannot say something nice about someone, it is better to say nothing at all.... My Dad added that sometimes it is better to keep your mouth shut and be thought a fool, than open it and prove that fact.... I will endeavour in future to reflect on their advice, tempered by the caveat that I will always try and defend the truth....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on May 01, 2016, 07:14:08 PM
Yet another possibility exists for a way to calculate the maximum velocity of an airgun.... Let's start with the equation for the KE of a moving column of air in a tube.... from the Hyperphysics website.... http://hyperphysics.phy-astr.gsu.edu/hbase/pfric2.html (http://hyperphysics.phy-astr.gsu.edu/hbase/pfric2.html)

(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Air%20in%20Tube_zpsxqyskufl.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Air%20in%20Tube_zpsxqyskufl.jpg.html)

We have another, very basic equation, for the maximum Kinetic Energy (ft.lb) that can be developed by a PCP, which is the force F (lb) times the distance (ft), as follows.... The force F, is the pressure P (psi) times the bore area A (in^2), and the bore area is the caliber (in) squared times PI/4.... The distance (ft) is the barrel length L (in) divided by 12 (in/ft).... so the absolute maximum KE for a given pressure and barrel can be found from the equation....

KE = P x (cal^2 x PI/4) x (L / 12) .... Note Lloyd and I use this in his maximum velocity thread.... http://www.gatewaytoairguns.org/GTA/index.php?topic=94054.0 (http://www.gatewaytoairguns.org/GTA/index.php?topic=94054.0)

It should be noted that the barrel volume V (in^3) is the bore area A (in^2) times the barrel length L (in), so substituting V in the equation above, we get....

KE = P x V / 12 .... the units are (lb/in^2) x (in^3) / (in/ft).... which reduces to ft.lb, exactly as it should....

If we rearrange the first equation to solve for the maximum velocity in the middle of the air column Vm (fps), we get....

(D/2) x ( Vm^2 / 3 ) = KE / V .... where D (which I use instead of rho) is the air Density (slug/in^3), and then....

Vm^2 = KE x 2 x 3 / V / D .... take the square root of both sides, and we have....

Vm = sqrt ( 6 x KE / V / D ) .... However, from the equation for the maximum KE above, we can substitute ( P x V / 12 ) for the KE, which gives us....

Vm = sqrt ( 6 x ( P x V / 12 ) / V / D ) .... The volume V cancels out, leaving us with....

Vm = sqrt ( P / D / 2 ) .... the units are (lb/in^2) / (slug/in^3) / (in/ft).... with the unit for slugs being (lb.sec^2/ft).... so we end up with ft/sec, exactly the way it should be.... 

Air density D is usually quoted (in the Imperial system) in lb/in^3, and to convert to slugs, we must divide by 32.174, so the equation then becomes....

Vm - sqrt ( P / ( D / 32.174) / 2 ) = sqrt. ( 16.087 x P / D ) = Vm = 4.011 sqrt ( P / D ) .... with Pressure P in psi and Density D in lb/in^3....

This is exactly the same equation I came up with in posts # 517 & 523 by a completely different method.... If nothing else, that proves I am consistent....  ;D .... Here is a graph of the predictions using this formula.... Note this is for zero pellet mass and constant pressure, it represents the maximum velocity of the center of the air stream in the barrel.... At least in theory, the pellet should not be able to exceed that velocity unless there are some unknown temperature effects taking place....

(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Theoretical%20Maximum%20Velocity%2020C_zps2v21id7e.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Theoretical%20Maximum%20Velocity%2020C_zps2v21id7e.jpg.html)

It is worth noting that for an Ideal Gas, where the Density is directly proportional to the Pressure, the predicted velocity would be a constant.... Using NTP conditions (20*C, 14.7 psi and 1.204 kg/m^3 = 0.0000435 lb/in^3) that value would be 2332 fps.... However, air is not an Ideal Gas, with the pressure increasing significantly faster than the density at over 2000 psi.... This means that the gas itself is less dense, and therefore easier to push along the barrel, compared to the pressure pushing it.... resulting in an increase in the maximum velocity at high pressures.... Please note that the above is only one theory among many, and is only valid until somebody exceeds these numbers, at which point it must be discarded....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on May 02, 2016, 09:08:50 PM
Bob, I am having a problem with one substitution you are making in the above post. 

in this section, quoted from your post,==========
Vm^2 = KE x 2 x 3 / V / D .... take the square root of both sides, and we have....

Vm = sqrt ( 6 x KE / V / D ) .... However, from the equation for the maximum KE above, we can substitute ( P x V / 12 ) for the KE, which gives us....

Vm = sqrt ( 6 x ( P x V / 12 ) / V / D ) .... The volume V cancels out, leaving us with....
===============
Referencing the 3 lines above, in the first  line, the KE is "average KE".   In the first part of the second line, the KE is "average KE."  But in the second part of the line, the KE that you want to substitute for the average KE, is actually the maximum KE, which is different.  Am I missing something?

Thanks,
Lloyd



Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on May 02, 2016, 11:32:28 PM
Lloyd, as I understand it, the term "Average KE" from the Hyperphysics post means the average kinetic energy of the column of air per unit of length (volume).... The air in the center of the column is moving twice as fast as the air at the outside edge, so the KE of the center of the stream would be four times as great.... So in a "packet" of air of, say, 1" long, the average KE of that packet would be given by the equation, and that is where the 1/3 factor comes from (and they show the derivation of that).... I simply chose the unit of length (volume) to equal the length (volume) of the barrel, so they cancel out....

The maximum KE for any give PCP is the Force times Distance, which distills down to ( P x V / 12 ) in FPE.... If we substitute that for the KE in the original (Hyperphysics) equation we can calculate the maximum velocity Vm of the airstream.... ie the velocity in the center of the moving column of air....

Sound OK now?....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on May 03, 2016, 01:16:37 AM
As I understand it, the term "Average KE" from the Hyperphysics post means the average kinetic energy of the column of air per unit of length (volume).... The air in the center of the column is moving twice as fast as the air at the outside edge, so the KE of the center of the stream would be four times as great.... So in a "packet" of air of, say, 1" long, the average KE of that packet would be given by the equation, and that is where the 1/3 factor comes from (and they show the derivation of that).... I simply chose the unit of length (volume) to equal the length (volume) of the barrel, so they cancel out....

The maximum KE for any give PCP is the Force times Distance, which distills down to ( P x V / 12 ) in FPE.... If we substitute that for the KE in the original (Hyperphysics) equation we can calculate the maximum velocity Vm of the airstream.... ie the velocity in the center of the moving column of air....

Sound OK now?....

Bob
Should be OK for subsonic.

Some things that I found in my research and believe to be true:

The mass flux is at a maximum once the inlet reaches Mach 1.

Go any further downstream, and there is a reduction in average air density. So that packet of air that was originally 1" long may grow to longer than 1".

Or you could say that, for supersonic velocities, the mass of air in a 1" section of barrel is less near the muzzle, than it is close to the breech.

For Fanno flow, the density ratio is the inverse of the velocity ratio. That makes sense, because it would result in a constant momentum density (momentum per unit volume).

I think the density at maximum velocity will be:

Density_muzzle = Density_inlet/sqrt((2/(k-1))+1)
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on May 03, 2016, 01:49:22 AM
Scott, I'm strictly working with F=ma here, not trying to incorporate any temperature change.... I know you are working with Fanno Flow, but I don't understand it, so I'm just plodding along the best I know how.... The assumption above is that the pressure and density are constant throughout the barrel.... I know that is not realistic, but it should produce the maximum velocity with zero pellet mass.... This model, of course, does not work incrementally, it looks at the barrel full of air as one chunk, all moving at the same (average) velocity (center faster, of course).... but since it is based on the maximum KE that the gun can produce, I feel it at least bears investigating.... Like any other theory, it's only valid until it's broken....  ;D

It is entirely probable that the mass flow limit at the inlet is the actual governing factor, and Lloyd has worked that into his new L4 spreadsheet, using the correct SoS for the incremental reservoir pressure, along with the VanDerWaals correction for density.... In Lloyd's new spreadsheet, the velocity curve is highlighted where the flow chokes, and it's a pretty interesting visualization.... However, in the models of his actual shots, the choking is not very severe, so it's effect on the results is rather small.... His new spreadsheet only has about 3% greater losses than the previous one, using Boyle's Law and no choking.... ie if you increase the efficiency factor by 3% the model again matches the experimental results.... I think that is because the VanDerWaals density effect works in the opposite direction to choking.... by increasing the velocity calculation, while choking decreases it....

One comment I will make is that if the density of a set length "packet" of air decreases, ie it's mass is less, then so is the pressure.... The ratio will be according to VanDerWaals corrections.... If indeed the density is inversely proportional to the velocity, then eventually the pressure loss will decrease the available acceleration.... Of course if that only occurs near the muzzle, it won't matter much.... but most of the velocity gain occurs early, so the effect on the pressure available to produce acceleration could be significant.... If you apply your equation incrementally, you may find you have a lot less pressure available for your F=ma acceleration calculations....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on May 03, 2016, 03:06:48 AM
...
One comment I will make is that if the density of a set length "packet" of air decreases, ie it's mass is less, then so is the pressure.... The ratio will be according to VanDerWaals corrections.... If indeed the density is inversely proportional to the velocity, then eventually the pressure loss will decrease the available acceleration.... Of course if that only occurs near the muzzle, it won't matter much.... but most of the velocity gain occurs early, so the effect on the pressure available to produce acceleration could be significant.... If you apply your equation incrementally, you may find you have a lot less pressure available for your F=ma acceleration calculations....

Bob

True. Apparent pressure will fall. The Fanno pressure ratio is the same as the density ratio.

The falling pressure means that it will take a longer barrel to reach the higher velocities allowed by Fanno flow. But, at the same time, the total air mass being accelerated will be lower.

From Wikipedia:
(https://upload.wikimedia.org/math/5/c/f/5cf3f44ea6a3bfb9c8abcc8734b4f985.png)

pressure ratio, density ratio, temperature ratio, velocity ratio, stagnation pressure ratio.

Those equations are ratios. They don't predict conditions for different barrel lengths. Just for different Mach numbers. We are interested in M=1.

The difference will end up being, that your supersonic inlet will predict a higher velocity with shorter barrels. But the max velocity attainable will be higher with the Fanno model, even though the Fanno inlet will be limited to sonic.

Those Fanno equations would be for an ideal gas. So they are only approximations for our case which is not ideal.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Michael Loar on May 03, 2016, 04:10:03 AM
My Grandfather once told me that if you cannot say something nice about someone, it is better to say nothing at all.... My Dad added that sometimes it is better to keep your mouth shut and be thought a fool, than open it and prove that fact.... I will endeavour in future to reflect on their advice, tempered by the caveat that I will always try and defend the truth....

Bob

Bob
I believe our grandparents and parent were cut from some of the same molds as I have heard the same phrases all my life as well and try to live as close to them as possible. It is truly difficult to do so at times when you know that the facts are glaringly evident and well proven yet to defend them only serves to fuel the fire, not that it is bad to fuel a fire.

If feeding the fire does make unwilling minds see the flames even if only briefly then it has served its purpose and that is to some extent I believe the case here.  The facts are compiled and presented here so that to deny it has been accomplished only serves to make the joker even more of a fool.

In an age where universal deceit is considered normal, telling the truth is considered an act of rebellion.

Mike
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on May 03, 2016, 11:56:04 AM
"The progress of science is that of a focused rebellion in the search for truth"....

rsterne, 2016
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Michael Loar on May 04, 2016, 08:13:07 AM
Bob
Agreed 100%

Mike
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on May 04, 2016, 04:39:39 PM
You know you're going to do it, Lloyd!.... and good on ya' for that....

buldawg.... Amen to that !

Bob

I got the 6' lengths of 1/2" O.D. x .083 wall DOM tubing today.  They do indeed check out at .334 I.D.  Since this is strictly a lab set-up for the Version 3 valve, it can use Teflon or Delrin for very light weight projectiles, or possibly lead slugs, too.  The Version 3 valve does not use the projectile as a structural element, so that means that it will be much easier to make lots of shots. After the version 3 valve is proven to be effective (fingers crossed  :P ) a .30 cal TJ's/Bob's airgun barrel can be used to see how lead projectiles will do at high velocities. John Cripe is preparing some swaged lightweight lead bullets for testing.  His concern is that the twist rate might be too high for the hi vel, light weight bullets.  We might be in uncharted territory, but I would be surprised if someone else hasn't already been there. 
The version 3 valve is designed for a max 6000 psi, so Scott, the high pressure nitrogen is in the not-too-distant future.   
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on May 04, 2016, 06:33:03 PM
Good news on the Version 3 progress, Lloyd.... A Delrin cylinder of that caliber and 3/8" long would only weigh 12 gn.... less if you use a center drill to create a hollow skirted base....

The TJ's barrel is only a 26" twist, which will certainly help.... I don't think there is a slower twist .30 cal barrel available anywhere....

PS, I answered your question about the KE above.... hopefully to your satisfaction....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on May 04, 2016, 07:09:02 PM
Bob,
Yes, I saw the response Bob, and thank you for the explanation, but I forgot to reply.  I hear what you are saying and I think I am ok with it, but still not 100% sure. I just need to think about it some more.

Part of it has to do with my interpretation of the KE avg equation. If you rearrange that equation to make it
KE avg = 1/2 x density x volume x Vel max squared x 1/3
Basically, that equation is the old standard KE = mass x velocity squared, but also multiplied  1/2 and 1/3.  I see the 1/2 as the multiplier for the average, and 1/3 as the multiplier for the volume of a cone, which is the higher velocity center portion of the moving mass of air.
That means that the average KE of the moving column of air is 1/6 th of the maximum velocity portion.
Does that get us back to the old formula of :  Output energy = Input energy - system losses?  Probably not, because that would mean the 5/6 of the energy is not delivered to the projectile.

I hope that in the end we might be able to come up with an empirically "augmented" equation to predict the output of a PCP.  All of the various methods of calculation that take into account pressure and density and velocity and temperature get us closer and closer, but in the end, I am sure that some sort of fudge factor(s), the "empirical" part of the equation, will still be needed to correct for those unknowns.    I applaud the efforts of everyone to track down all the actual calculations for the internal ballistics, because, I am certainly not up to the task, LOL.  I will continue to build and test and hopefully provide useful empirical data to be used in conjunction with all of the physical formulas.

This is quite a process!
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on May 04, 2016, 09:19:38 PM
Well, KE = 1/2 Mv^2, and in this case M is the air volume in the barrel times the air density in the barrel.... The only factor in addition to that equation is the 1/3, and that takes into account the velocity profile across the moving column of air where the center is moving the fastest (about twice the average) and the outside hardly at all.... Since the velocity used in the formula is the velocity at the center of the stream (ie the maximum velocity), but the KE is the total (averaged across the stream).... and the total cannot exceed the input KE.... I think it makes perfect sense....

Don't forget that the "average KE" of the moving column of air is the integral of all the layers added together, divided by the volume.... If you use 1" increments, each 1" packet of air will have a total KE equal to that of all the layers, across the diameter (area) of the tube, times the 1" of length.... That's what makes it the "average KE", but for that 1" packet of air, it is also the total KE (of that packet).... If you follow through the integration on the Hyperphysics website, that factor of 1/3 is the result of the integration, relative to what the KE of the packet of air would be if it were all moving at the same velocity of the center of the stream (the maximum velocity).... You state that the KE is 1/6th that of the center portion, but in fact it is only 1/3, right?....

All of the KE is delivered to the air (in the case where the projectile mass is zero).... but more of it shows up in the center of the stream....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on May 04, 2016, 10:11:32 PM
Let's look at this another way.... Let's assume that all the air in the barrel moves as a solid rod, all at the same velocity, with no friction with the barrel.... The accelerating force acts on the end of this "rod" of air....

We know that the KE of that air, once accelerated to velocity V (fps) is 1/2 MV^2.... We can calculate the mass by multiplying the volume by the density, and we need the result in slugs.... Let's use 2000 psi air, which has a density of 164.4 kg/m^3, which is 0.0001846 slugs/in^3 (from an online calculator).... Let's use a barrel with an area of 1 in^2 and a length of 100 in.... It has a volume of 100 in^3, so the mass of that rod of 2000 psi air is 0.01846 slugs....

Now let's look at the maximum possible KE such a gun can produce.... We know that is equal to the force F (lbs.) times the distance (ft.).... We have 2000 psi pushing on 1 in^2, so that is a force of 2000 lbs.... The barrel is 100", which is 8.333 ft, so the maximum possible KE the gun can produce is 2000 x 8.333 = 16,666 FPE.... Let's combine the two equations and solve for the Velocity V....

KE = F x D = 2000 x 8.333 = 16,666 FPE

KE = 1/2 MV^2 = 0.01846/2 x V^2 = 0.00923 x V^2 = 16,666

V^2 = 16,666 / 0.00923 = 1,805,634

V = sqrt 1,805,634 = 1344 fps

This seems like a very low number to me, but I welcome anyone (and particularly Lloyd) to doublecheck my math.... Since in a "real" barrel, the center of the airstream moves much faster, it makes the value calculated from my formula of 2327 fps a lot more believable....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on May 04, 2016, 10:34:52 PM
=====I was typing this as Bob was making another response, so the posts might seem out of sequence.  Lloyd
========================
Bob, Yes, 1/3, not 1/6th.  Ok, I see what you are saying and the explanation sounds good. I'll go with it. 

I'd like to take a slightly different approach to this (at least I think its different), at a fairly elementary level.
Going back to the original Hi Vel shot of 1745 fps, 7.5 gn , 26 cc, 4500 psi, 23.3" barrel, dump shot.
This shot yielded 50.7 FPE and was 70% efficient, meaning that 70% 0f the energy that was in the air entering the barrel was actually transferred tot he projectile.  If the shot had been 100% efficient, the velocity would have been 2090 fps and 72.9 FPE.  Therefore, the difference in energy between the actual shot and the theoretical shot, was 22.2 FPE.  That 22.2 FPE was lost, so where did it go?  It had to be converted to something, and heat is the only possibility, correct?

If the energy was converted to heat in the air in the barrel, final air mass is .0069 lbs, specific heat of air at that final average pressure is about .32 BTU/lb deg F.  So, the temperature change in the air would have been:

delta T (deg F) of the air in barrel = (22.2 x .0013 BTU/fpe) / (.32 BTU/lb air x .0069 lbs) = 13 deg F temperature rise of the air.

If all the energy were converted to heat in the barrel (.73 lbs) the calculation is this:

delta T (deg F) of the barrel itself = (22.2 x .0013 ) / ( .115 BTU/ lb steel x .73 lbs ) = 0.34 deg F temperature rise of the barrel.

Seems logical that all the energy loss is in heat.  But maybe that is already a given.
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: wilsonj1018 on May 05, 2016, 12:10:21 AM
hey Lloyd , could you do me a favor and contact my buddy David Goldstein, he has been trying to reach you and isnt getting replies or returned calls.its concerning his gun that he still doesnt have back yet.
thanks
Josh
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on May 05, 2016, 12:16:55 AM
hey Lloyd , could you do me a favor and contact my buddy David Goldstein, he has been trying to reach you and isnt getting replies or returned calls.its concerning his gun that he still doesnt have back yet.
thanks
Josh
Josh,
Yes, I will try and contact him again.  I emailed him on April 7th and May 2nd with data and information and have not heard back from him.
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: wilsonj1018 on May 05, 2016, 12:18:37 AM
thanks
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on May 05, 2016, 12:50:59 AM
Lloyd, the 70% efficiency isn't 70% of the energy in the air ending up in the projectile, as I see it.... It means that the FPE is 70% of what COULD be in the projectile if ALL the input FPE ended up in the projectile AND the air in the barrel, right?.... but it's done incrementally, not all at once, so a lot of the acceleration of the projectile occurs while there is little air mass being accelerated.... It's pretty complex, which is why doing the calculations by intervals, like your spreadsheet, is the only proper way to do it....

I agree, that missing 30% (22.2 FPE) ends up as heat.... but there is also less KE in the air as well, as it is only reaching 1745 fps instead of 2090 as well.... so that missing KE must be going somewhere (heat) as well.... I think the total energy ending up in heat is the input KE minus the final KE in the pellet and air mass.... Since the starting pressure is 4500 psi, and some of the losses occur early, when the air is likely conducting heat to the barrel better.... it is likely REALLY complicated....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on May 05, 2016, 01:08:15 AM
=====I was typing this as Bob was making another response, so the posts might seem out of sequence.  Lloyd
========================
Bob, Yes, 1/3, not 1/6th.  Ok, I see what you are saying and the explanation sounds good. I'll go with it. 

I'd like to take a slightly different approach to this (at least I think its different), at a fairly elementary level.
Going back to the original Hi Vel shot of 1745 fps, 7.5 gn , 26 cc, 4500 psi, 23.3" barrel, dump shot.
This shot yielded 50.7 FPE and was 70% efficient, meaning that 70% 0f the energy that was in the air entering the barrel was actually transferred tot he projectile.  If the shot had been 100% efficient, the velocity would have been 2090 fps and 72.9 FPE.  Therefore, the difference in energy between the actual shot and the theoretical shot, was 22.2 FPE.  That 22.2 FPE was lost, so where did it go?  It had to be converted to something, and heat is the only possibility, correct?

If the energy was converted to heat in the air in the barrel, final air mass is .0069 lbs, specific heat of air at that final average pressure is about .32 BTU/lb deg F.  So, the temperature change in the air would have been:

delta T (deg F) of the air in barrel = (22.2 x .0013 BTU/fpe) / (.32 BTU/lb air x .0069 lbs) = 13 deg F temperature rise of the air.

If all the energy were converted to heat in the barrel (.73 lbs) the calculation is this:

delta T (deg F) of the barrel itself = (22.2 x .0013 ) / ( .115 BTU/ lb steel x .73 lbs ) = 0.34 deg F temperature rise of the barrel.

Seems logical that all the energy loss is in heat.  But maybe that is already a given.
Lloyd

Yes, all losses go to heat gain.

The heat gain is not evenly distributed. Most of the heat gain is in the air that travels the farthest. That would be the air right behind the pellet.

Knowing the air is heated some, and if we simplify and assume pressure to be constant, density will be reduced. So you are accelerating and heating less air than you think. Since the mass and therefore the KE of the air is less than you think, the losses are therefore higher than you think.

That may balance out with the fact that you are not inputting as much energy into the system as you think you are. So the losses are not as great as you think. Confused? I am a little.

You can probably assume a solid rod of air up until inlet reaches Mach 1. With a zero pellet mass, that happens instantly.

------------------------------------

Imagine it like this:
Once you reach supersonic, you are pushing a "solid" rod of air into the barrel at a fixed velocity of Mach 1. There is no more acceleration at the inlet. Once it enters the barrel, all additional acceleration comes from the expansion of the "air rod" inside the barrel, at the front of the "rod".
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on May 05, 2016, 01:19:24 AM
I think a better assumption might be that density is constant and the pressure is increased.... but it could easily be a balance between the two, less density AND more pressure as the temperature increases.... Regardless, the net effect is that the air, being hotter, accelerates faster (easier).... Interesting that this effect is exactly the opposite of Adiabatic cooling, which some like to assume is happening.... I read in an online college paper not long ago (can't remember the source) that the expansion in an airgun inside the barrel is essentially Isothermal, possibly because of these effects cancelling each other?.... Once the air exits the muzzle I have NO doubt that Abiabatic expansion takes place.... This explains the "shoot over the thermometer and see the drop" effect, and also the "cloud of condensing water vapour at the muzzle" reported as well.... Inside the barrel, I'll bet Isothermal may be a pretty close model, especially while the valve is open....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on May 05, 2016, 03:15:16 AM
I think a better assumption might be that density is constant and the pressure is increased.... but it could easily be a balance between the two, less density AND more pressure as the temperature increases.... Regardless, the net effect is that the air, being hotter, accelerates faster (easier).... Interesting that this effect is exactly the opposite of Adiabatic cooling, which some like to assume is happening.... I read in an online college paper not long ago (can't remember the source) that the expansion in an airgun inside the barrel is essentially Isothermal, possibly because of these effects cancelling each other?.... Once the air exits the muzzle I have NO doubt that Abiabatic expansion takes place.... This explains the "shoot over the thermometer and see the drop" effect, and also the "cloud of condensing water vapour at the muzzle" reported as well.... Inside the barrel, I'll bet Isothermal may be a pretty close model, especially while the valve is open....

Bob
"I think a better assumption might be that density is constant and the pressure is increased..."
Maybe.

"I'll bet Isothermal may be a pretty close model..."
Isothermal is constant temperature, but implies heat flow in from an outside source. Usually a slow process. But in Fanno flow, the heat is generated internally.

Constant temperature could be a way to model it. As long as all heat came from energy within the system.

Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: phoebeisis on May 05, 2016, 08:42:02 AM
Bob
I cut out your post-below
But that approach-which you aren't suggesting be used of course
Is more or less what Yellow Forum Steve used to get the MAXIMUM VELOCITY 1640FPS
The treat barrel  air like a rod or like "water"-with some slight differences-this is what he did-
insisted the air-all the air was matching the pellets velocity-and suggesting that ALL the  barrel
air molecules  were being accelerated-in the "speeding up sense" not the changing direction sense
to me the momentum is transferred in a wave like motion-a "bunch" of tiny independent "waves"-some are moving at close to the peak speed shown in a air molecule distribution graph
Not wanting a fight here-
and I know you aren't suggesting adopting your arch enemies approach-old approach-
he has found another "lotta math to obscure what he is saying  approach" so he has more "up to date numbers-
yes joking about the arch enemy-
I feel for him-hard to give up an idea that you pushed for so long-
but his adherents seem forgiving ,so...

Let's look at this another way.... Let's assume that all the air in the barrel moves as a solid rod, all at the same velocity, with no friction with the barrel.... The accelerating force acts on the end of this "rod" of air....

We know that the KE of that air, once accelerated to velocity V (fps) is 1/2 MV^2.... We can calculate the mass by multiplying the volume by the density, and we need the result in slugs.... Let's use 2000 psi air, which has a density of 164.4 kg/m^3, which is 0.0001846 slugs/in^3 (from an online calculator).... Let's use a barrel with an area of 1 in^2 and a length of 100 in.... It has a volume of 100 in^3, so the mass of that rod of 2000 psi air is 0.01846 slugs....

Now let's look at the maximum possible KE such a gun can produce.... We know that is equal to the force F (lbs.) times the distance (ft.).... We have 2000 psi pushing on 1 in^2, so that is a force of 2000 lbs.... The barrel is 100", which is 8.333 ft, so the maximum possible KE the gun can produce is 2000 x 8.333 = 16,666 FPE.... Let's combine the two equations and solve for the Velocity V....

KE = F x D = 2000 x 8.333 = 16,666 FPE

KE = 1/2 MV^2 = 0.01846/2 x V^2 = 0.00923 x V^2 = 16,666

V^2 = 16,666 / 0.00923 = 1,805,634

V = sqrt 1,805,634 = 1344 fps

This seems like a very low number to me, but I welcome anyone (and particularly Lloyd) to doublecheck my math.... Since in a "real" barrel, the center of the airstream moves much faster, it makes the value calculated from my formula of 2327 fps a lot more believable....
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rgb1 on May 05, 2016, 09:13:26 AM
Guys, the reference to   http://hyperphysics.phy-astr.gsu.edu/hbase/pfric2.html (http://hyperphysics.phy-astr.gsu.edu/hbase/pfric2.html)   is incorrect.
Hagen-Poisseuille is the solution to very low Reynolds number (laminar) flow. After going
through an old college text (Boundary Layer Theory, Schlichting) I can offer the following info.
For pipe flow, the transition Rn lies somewhere between 2e3 and 4e4. In Lloyds setup, that
is greatly exceeded in less than 1 inch of barrel travel and the turbulent boundary layer
profile (u/U vs radius) will stabilize in ~ 30 diameters (about 8 inches), changing very
little beyond that point.
Sorry for the late reply.

                                                                                                         Ron
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on May 05, 2016, 01:00:46 PM
HI Charles.... You are absolutely correct, I am not suggesting that the 1344 fps number is any kind of a limit.... I was merely using the "rod" model to point out that IF you do that, the mass of the air quickly puts a limit on the velocity to something at or below that number up to 2000 psi (and then increasing above that as the pressure/density ratio increases).... This is a COMPLETELY different reasoning than using the speed of the air molecules as a limit (be that 1650 which has already been disproved, or the new 2259 fps).... Pretty much comparing apples to oranges.... The argument was presented to show (dare I say prove) that the air in the barrel is NOT moving as a single unit, or that math would apply (creating a ridiculously low "limit").... and that something more along the lines of using the 1/3 factor in the Hyperphysics equation would be more realistic.... BTW, I am still waiting for somebody to check the math on the "rod" model to make sure I got it right....

Ron, I do realize, of course, that the model used in the Hyperphysics article referenced is that for Laminar Flow.... However, it also represents (as I understand it) the lowest fraction than could reasonably be used in the equation (and therefore the highest central velocity).... If the flow is Turbulent (which I believe to be the case, as you do) then the velocity profile of the air in the tube (barrel) is shortened (truncated, or flattened) and no longer a parabola.... As such, the fraction of mass used would be close to 1/2 than 1/3, which of course produces an even lower velocity for the center of the airflow.... because the "Input FPE" is still limited by the pressure, bore area, and barrel length..... In fact, using a factor of 1/2, it is so low, on the order of 1900 fps at 2000 psi (and just over 2000 fps at 4000 psi), that it cannot apply, making the whole process a non-starter, as we have already seen velocities that exceed that....

I don't think we have a very good understanding of what is occurring inside a barrel in high pressure, high density, high speed conditions.... Yes, I am grasping at straws trying to come up with suggestions about what might be occurring.... IF the flow was laminar (which I understand would produce the highest central velocity), then the 1/3 factor would apply, and the velocities could, in theory reach the values in the graph in my post # 567.... As I understand it, if the flow is Turbulent (and it should be), then an even lower limit would apply, with the bottom limit being if you treat the air as a "rod", which we know is a non-starter (~1344 fps for an Ideal Gas)....

Scott, I perhaps used the term Isothermal incorrectly, but I meant it in the truest sense.... ie constant temperature.... I agree that the mechanism, if that is occurring, is that the energy losses which are occurring, do so in the form of heat, and cancel (and possibly reverse) and Adiabatic cooling which could in theory take place inside the barrel.... at least while the valve is open....

Please let's not loose sight of the fact that all of these theories are just that.... THEORY.... They are only valid proposals until they are proven or disproven by experiment.... I have stated that several times, a quite different attitude that I have seen elsewhere.... One other thing I would like to comment on.... the reference to an "arch-rival".... I would suggest that you read Post #545, which was a different way of looking at the Sonic Horizon Theory, incorporating the increased Speed of Sound at high pressures.... a proposal that just might let "everyone" be correct.... I don't think I need to comment further on my motivations or actions.... I just want the truth, and reality, to prevail.... I also feel for him, BTW....  :(

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on May 05, 2016, 02:17:54 PM
Bob,
Your post # 591 was a great summary to help me see where you were going with this.  I was floundering a little trying to follow your discussion, but now it makes sense.  The discussion from everyone else is extremely helpful too.

But, trying to get things ready for the Fun Shoot now, and it is raining outside, so perfect shop work time.
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on May 05, 2016, 05:01:59 PM
Just a quick summary of some of my ideas at the present time.... The graph below shows some of the possibilities for things that may limit the velocity at 20*C, and also shows the existing test shots to date....

(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Maximum%20Velocity%20Theories_zps9jcwaibm.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Maximum%20Velocity%20Theories_zps9jcwaibm.jpg.html)

The purple line is the 1647 fps RMS speed of air molecules at 20*C, originally proposed as the "speed limit" for PCPs....
The black dots are shots taken by Lloyd, Nick, and myself as of May 5, 2016 that exceeded that velocity....
The blue line is from the idea that the KE is calculated using 1/3 of the total mass of air in the barrel, as per the Laminar Flow Model from Hyperphysics which I used....
The red line uses the Sonic Horizon equation with the RMS velocity in place of the Speed of Sound, which places the limit at 2 x 1647 = 3294 fps....
The green line uses the Sonic Horizon equation with the Speed of Sound being the value at various pressures, so the limit is Mach 2 at that pressure....
The dotted black line uses the Sonic Horizon equation with the Mach 2 (green line) or RMS x 2 (red line), whichever is less....
Note I omitted a recent suggestion that the limit is 2259 fps from the DeLaval equations, because it doesn't take into account that air is not an Ideal Gas....
I have not graphed Scott's ideas because I don't fully understand them, other than that they are not at a steady temperature of 20*C....

This is just a snapshot of some of the current ideas.... They are all THEORY only, and as such only valid until experimental evidence proves or disproves them....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on May 05, 2016, 05:38:43 PM
Bob,

Here is max Fanno velocity (as best I can determine) vs pressure for pressures up to 10000psi:

PSI    SOS fps@70F     k        V max fps
500        1142.0   1.461   2638.7
1000   1169.9   1.526   2563.8
1500   1204.1   1.585   2531.0
2000   1247.0   1.637   2537.2
2500   1297.6   1.677   2580.2
3000   1354.6   1.707   2650.7
3500   1416.3   1.727   2743.1
4000     1481.0   1.739   2851.1
4500   1547.6   1.744   2972.0
5000   1615.1   1.745   3100.3
5500   1682.7   1.742   3234.8
6000   1749.7   1.737   3371.7
7000   1881.9   1.716   3665.2
8000   2008.2   1.700   3944.0
9000   2129.2   1.683   4220.1
10000   2244.4   1.666   4490.5

It looks close to the Mach 2 curve.

At the higher pressures, air is well inside the super-critical region.
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on May 05, 2016, 06:45:12 PM
Yeah, that is very close to the Mach 2 curve....According to the Wolfram Widget, air becomes a Supercritical Fluid at about 550 psi at 20*C....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: MichaelM on May 28, 2016, 01:42:10 PM
I should post the video of Lloyds super gun blowing my sky screens off at the fun shoot :)
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Privateer on May 28, 2016, 01:47:03 PM
I should post the video of Lloyds super gun blowing my sky screens off at the fun shoot :)

Yes you should! LOL!!
Does that chrony still work by the way?
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on May 28, 2016, 11:14:38 PM
I should post the video of Lloyds super gun blowing my sky screens off at the fun shoot :)
Michael,
Your poor chrony, and it was a very early version, too.  I think it had a heart attack.  Can you clean the video up so that it is "suitable for all audiences"?
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: MichaelM on May 29, 2016, 12:19:19 AM
I should post the video of Lloyds super gun blowing my sky screens off at the fun shoot :)
Michael,
Your poor chrony, and it was a very early version, too.  I think it had a heart attack.  Can you clean the video up so that it is "suitable for all audiences"?
Lloyd

lol I think it did too.... still never seen a chrony sit there and just spin numbers like it did after the second shot..... and yea I was planning on probably editing it down pretty short just because we where all being goofy and laughing so much... either that or setting it to the Benny Hill theme music.... that might be even better :)
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Michael Loar on May 29, 2016, 08:26:40 AM
I hate that I could not make the fun shoot but would love to see the " super " gun blowing the sun screens off the chrony and the ensuing exhilaration of all involved at the time.

You know what they say " No pictures means it did not happen " LOL.

Mike
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: MJP on February 24, 2017, 02:52:42 AM
Bob wanted this in here, along with the info.
Gun is AF style inline valve with 12mm porting to stem and 9.5mm stem port.
Barrel 540mm 357 16:1
250bar helium
Sabot around 1gram I'll weight that if I find one from my shop.
500cc tank
Ambient temp around 20C

(http://i5.aijaa.com/m/00610/14339932.jpg) (http://aijaa.com/o5VaTn)

Marko
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: lloyd-ss on February 24, 2017, 10:07:52 AM
Marko, 
Excellent work!  I had to get the calculator out to see just how fast that is in fps:  2,787fps !!!
And you are thinking about 15 grains for the projectile?  The inline valve and the helium really make a big difference when going after maximum velocities.
Very good!
Lloyd
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: MJP on February 24, 2017, 02:16:59 PM
Thanks Lloyd, it does work wonders on helium. I'll update the weight of the projectile if and when I find the bag where they are, it's somewhere around but quick search around my workshop turned out everything else that I have missed but the sabots.
Come spring and we will continue testing with new and interesting stuff.

Marko
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on February 24, 2017, 07:14:41 PM
Ahhhhhh.... the Helium explains a LOT, short barrel though at 21.3"!.... I'll look forward to the weight of the sabot, this will be an invaluable data point for perfecting Lloyd's spreadsheet, IMO....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: CapArms on February 21, 2024, 08:59:02 PM
Has anybody done CFD analysis of shock wave formation or choked flow conditions at modern airgun pressures?
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: rsterne on February 21, 2024, 10:55:32 PM
If you have such information, please feel free to share it....

Bob
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on March 04, 2024, 08:07:36 PM
Has anybody done CFD analysis of shock wave formation or choked flow conditions at modern airgun pressures?

Choked flow is a “standing shock wave” at the port that restricts flow from going above sonic. What are you trying to find out from a CFD analysis?
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: CapArms on March 11, 2024, 11:26:48 AM
Has anybody done CFD analysis of shock wave formation or choked flow conditions at modern airgun pressures?

Choked flow is a “standing shock wave” at the port that restricts flow from going above sonic. What are you trying to find out from a CFD analysis?

   I was figuring that iterative CFD analysis and redesign would enable one to eliminate Choked Flow and standing Shockwaves.  Often these phenomena are so counter intuitive and complex that Computational Fluid Dynamics are the only way to "see" what is happening inside the flow passageways. 
Title: Re: Sonic Choke? Maybe not. 2162 FPS
Post by: Scotchmo on March 16, 2024, 05:46:07 AM
Has anybody done CFD analysis of shock wave formation or choked flow conditions at modern airgun pressures?

Choked flow is a “standing shock wave” at the port that restricts flow from going above sonic. What are you trying to find out from a CFD analysis?

   I was figuring that iterative CFD analysis and redesign would enable one to eliminate Choked Flow and standing Shockwaves.  Often these phenomena are so counter intuitive and complex that Computational Fluid Dynamics are the only way to "see" what is happening inside the flow passageways. 

For a given pressure, maximum flux occurs at Mach 1. Choked flow simply means that we are at that maximum throughput. Besides removing any constrictions, there is nothing to redesign. There’s no way around it.