Sonic Choke? Maybe not. 2162 FPS

[rsterne]

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

[lloyd-ss]

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




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.

[Scotchmo]

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.

[lloyd-ss]

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

[rsterne]

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

[Scotchmo]

Bob,

Thanks.

I feel the same, that Boyle's is fine, until Lloyd gets a 6000psi cylinder. 

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.

[lloyd-ss]

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

[rsterne]

"only 1777 fps at 1500 psi"....   

Bob

[MichaelM]

"only 1777 fps at 1500 psi"....   

Bob

lol that was my thoughts exactly

[rsterne]

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

[lloyd-ss]

................

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

[match]

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?

[rsterne]

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

[lloyd-ss]

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

[Scotchmo]

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

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.

[lloyd-ss]

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!!      Bob, you said it, "To infinity and beyond!"
Lloyd

[lloyd-ss]

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.
 

[rsterne]

You, Sir, are a master at coming up with KEWL ideas !!!!

Bob

[Scotchmo]

I wrote a paper on the 1640fps "myth". Object was to better explain it to others:

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.

[rsterne]

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