Sonic Choke? Maybe not. 2162 FPS

[rsterne]

Yeah, 2 ft. is not an issue....

Bob

[Scotchmo]

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).

[rsterne]

Scott.... You need to read the thread that started this project.... 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

[Bill G]

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!    I need the exercise believe me.   

[lloyd-ss]

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.   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      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. 
Lloyd 

[lloyd-ss]

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.

[Scotchmo]

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.

[lloyd-ss]

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   

[lloyd-ss]

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

[Scotchmo]

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.

[Scotchmo]

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.

[rsterne]

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

[lloyd-ss]

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.

 

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.


Here is delta V against the actual velocities. 


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.)


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?


Any thoughts or comments would be appreciated.
Thanks,
Lloyd

[Scotchmo]

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.

[lloyd-ss]

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

[rsterne]

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

[rsterne]

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....



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



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....






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

[lloyd-ss]

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."  
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.   

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.


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

[rsterne]

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

[lloyd-ss]

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