Theoretical Maximum Velocity in a PCP

[rsterne]

HI Lloyd.... Well you know I had to run your numbers through your spreadsheet (I'm sure you already have).... Using zero TP volume, 23.3" barrel, 2150 psi, dump shot, 1 lb. drag, 5 lb. starting friction, air volume included (of course).... here is what I got for the required efficiency....

10.3 gr @ 1180 fps = 68%
13.6 gr. @ 1065 = 68%
42.7 gr. @ 708 fps = 75%

The 75% is on the high side, but it was with a very heavy bullet which helps, but the others are not at all unusual.... If I change only the TP volume, and add 0.02CI (typical), the velocities drop to....

10.3 gr = 1142 fps
13.6 gr = 1039 fps
42.7 gr = 693 fps

It looks like eliminating the TP volume is worth 2-3% in velocity (4-6% in FPE).... significant, but not earth shattering.... Man I love your spreadsheet !!! .... Talk about an invaluable resource !!!

Bob

[lloyd-ss]

I think the significant part of this is getting those velocities and the corresponding muzzle energies of 31.9, 34.3, and 47.5 FPE from a 5cc reservoir at 2150 psi.   With those shots you have a reservoir volume range of  from 0.16cc/FPE to .11cc/FPE.
Lloyd

[rsterne]

I understand, this is very much pumper territory, not the usual setup for PCPs.... The residual muzzle pressure is about 557 psi in each case, with a dump shot.... Since the valve volume is about 35% of the barrel volume, you are in a good range to get reasonable efficiency with a dump shot.... Your test setup is much more efficient than you would get with most pumpers, of course.... You are using a total of 46 CI of air for each shot, but I realize some of that (26%) is being wasted (blown out the barrel after Elvis has left the building)....

During early testing, with a dump shot, my .25 cal Pumper Carbine was getting 25 FPE (670 fps) with a 25 gr. pellet at 1500 psi from a 20" barrel, with a 5.5 cc valve.... which was 34% of the barrel volume, a reasonable comparison.... That works out to about 57% efficiency using your spreadsheet, not bad for the low pressure and conventional construction.... Residual muzzle pressure would have been about 382 psi.... and wasted air about 25%.... Later versions used more pressure and a longer barrel, but a larger reservoir and were no longer a dump shot.... they were basically a PCP with an onboard pump....

Bob

[Airsnipe]

I'm still trying to precess all the math and insight in this thread.

But I had a thought of a possible idea that might help maintain pressures a little longer in a dump valve design. What if the dump chamber was also a spring loaded piston chamber that, at full desired pressure the piston was at full stroke and when the dump/shot took place the piston would move to shrink the volume the the chamber. The spring pressure collapsing the chamber should help maintain the pressures for longer, would it not? The energy in the spring should add to the overall energy of the shot correct?

Then you use the motion of the moving piston to drive a semi-auto mechanism. 

[lloyd-ss]

Air Snipe,
This thread is going to take a bit of a twist in the next week or so, which might make it more interesting.

The idea of using a spring loaded chamber in a dump valve application is good in theory, but in application is rather difficult.  If the piston were 3/4" dia with a fill pressure of 2000 psi, the load on the spring is 884 pounds.  It is very difficult to find a spring that is compact enough that will handle that kind of load.  Still, if it could be done, you'd be getting the energy from the compressed air AND from the compressed spring. For a single shot.  Could be good.
Lloyd

[rsterne]

The Webley Paradigm used that system, and was IIRC a single stroke Pneumatic.... I think it used a stack of Bellevilles against the piston to maintain the pressure in the air chamber during the shot.... Sort of combines a Springer and a Pumper.... The big problem in using the system with large volumes of air is the mass of the piston and the forces required.... This idea has been discussed in this gate (which we call the Geek Gate, for obvious reasons) previously....

Looking forward to where you are taking us, Lloyd.... should be interesting....

Bob

[lloyd-ss]

Bob,
Yes, planning on looking at some things from a different direction. Let's say maybe a little more pragmatic and little less esoteric    ??  After all these months off I have forgotten a bit, so I can start fresh.
Lloyd

[rsterne]

pragmatic?.... esoteric?....

where did I put my dickshunery?.... 

Bob

[lloyd-ss]

pragmatic?.... esoteric?....

where did I put my dickshunery?.... 

Bob

Ha, ha.  My wife makes me learn new words every so often.  Says it will slow down the progress of my dementia. 

[rsterne]

HUH?.... WHA?....

My wife looked up them thar fancy words on the internet for me.... (really, she did!).... I'm too busy to get dementia.... DEMENTED, though, I admit to freely.... *LOL*....

Bob

[Airsnipe]

Air Snipe,
This thread is going to take a bit of a twist in the next week or so, which might make it more interesting.

The idea of using a spring loaded chamber in a dump valve application is good in theory, but in application is rather difficult.  If the piston were 3/4" dia with a fill pressure of 2000 psi, the load on the spring is 884 pounds.  It is very difficult to find a spring that is compact enough that will handle that kind of load.  Still, if it could be done, you'd be getting the energy from the compressed air AND from the compressed spring. For a single shot.  Could be good.
Lloyd

Lloyd, you could reduce the piston dia and increase the stroke length. The problem I see is the piston would have to come to an abrupt stop and would put shock into the gun. Would not be near as bad as a springer but I would think, would be noticeable.

[rsterne]

The problem I see is the piston would have to come to an abrupt stop and would put shock into the gun

That was our conclusion in previous discussions.... not only putting shock into the gun, but destroying the piston from the high forces and deceleration involved....

Bob

[lloyd-ss]

This really is an intriguing idea, but making it work is another story.  I had wondered if the main air tube on a PCP had a free floating divider piston in the middle and one side of the cylinder was precharged to a certain amount, like a spring would do.  Call that the spring side.  Then if you filled the active side and it compressed the spring side, like adding a booster spring.  I think I did the math and in the end, for all the effort, the amount of usable air was the same.  Oh well.

[rsterne]

I think the concept is that the pressure during the shot should stay higher instead of dropping off the way it would without the booster spring.... If you pressurized the booster side to 2000 psi, and then the active side to 1999 psi, the piston would not move (assuming equal diameters).... If you went to 3000 psi, the booster side pressure would have to match, so the volume of the booster side would reduce from full reservoir volume to 2/3rd of that.... while the active reservoir would be the other 1/3.... On firing, the pressure would start at 3000 psi, fall gradually to 2000 psi, and if the pellet was still in the barrel, then the air would continue to expand just as if the valve had closed at 2000 psi.... To put some numbers on it, let's assume the swept reservoir volume is 30cc, full to 2000 psi.... If we pressurize the active side, to 3000 psi, we have 10cc of air available for the shot at 3000 psi.... The air in the booster side is now 20 cc at 3000 psi.... Let's say the barrel volume is 20cc.... At the instant the valve opens, the pressure is ~3000 psi.... By the time the pellet has moved 1/4 of the way down the barrel (5 cc) the total volume is 35 cc, so the pressure is (30/35) x 3000 = 2571 psi.... At half way down the barrel (10 cc), the total volume is now 40 cc, so the pressure is 2250 psi.... At 3/4 travel (15 cc), the pressure would be 2000 psi, and after that expansion would be taking place because the piston has stopped.... At the muzzle (20cc), the total volume is 50 cc, but 30 cc is still at 2000 psi (the booster side).... so we have 10cc of 3000 psi air now occupying the 20cc of barrel, and the residual muzzle pressure is 1500 psi....

If we compare this to a 10 cc dump valve at 3000 psi, same 20 cc barrel volume, we get the following.... At opening ~ 3000 psi.... at 1/4 travel the pressure is (10/15) x 3000 = 2000 psi.... At 1/2 travel, the pressure is (10/20) x 3000 = 1500 psi.... at 3/4 travel, it is (10/25) x 3000 = 1200 psi.... and at the muzzle it is (10/30) x 3000 = 1000 psi.... In both cases, the total amount of air used was 10 cc at 3000 psi (207 bar) = 2070 cc = 126 CI.... However, the pressure profile using the booster chamber at 2000 psi is greater from breech to muzzle, so we would expect a higher velocity from the same amount of air, and hence greater efficiency.... The extra energy is coming from the work done to compress the 30 cc of air at 2000 psi to 20 cc at 3000 psi....

Unfortuntely, using this example, we have a piston being drive at high velocity coming to a crashing halt while there is a huge force behind it.... Let's look at that.... If we have a cylinder of 1/2" diameter, it would take 9.3" of length to store 30 cc of air (plus the length of the piston itself, so at least a 10" reservoir).... The average pellet takes about 1.5 mSec to travel 3/4 of the way down the barrel, at which point the piston hits the end of its travel.... It's average velocity for the trip is (9.3 / 12 / 0.0015) = 517 fps, and it's terminal velocity will definitely be higher than that.... I'm not sure what the piston would weigh, but whatever it is, it's going to hit the end of the reservoir and come to an abrupt halt from over 600 fps.... At that instant, in addition to its own momentum, it still has a force of 393 lbs. pushing it.... Lloyd, you can do the math if you wish, all I can say is OUCH!....

Bob

[lloyd-ss]

Bob,
Just want to let you know that visualizing those piston volumes changing size and pressure as the event unfolds, makes my head hurt.  Rocker 1, I see what you mean, now, ha, ha.

If the piston didn't have to come to a halt, or say that it was damped, or that the air could not drain completely from it, so that it was more  like  a spring, maybe then the movement of the piston would be less violent.

[Airsnipe]

If the valve closed before the pellet left the muzzle, the pressure left would act as a dampener and slow the piston down. But of course that is not a dump valve.

You could have a piston between two equal force sides connected to a shot side piston. But this would need enough space for the whole system to over travel under momentum and would probably oscillate until reaching equilibrium. Might sound cool.

     ()-------[------()       ]

[rsterne]

If you have a timed valve, just use the entire volume available for the reservoir, I don't think you can do better than that for power and efficiency.... After all, the pressure on both sides of the piston is the same, so why not gain the volume occupied by the piston?....

Bob

[I_like_Irons]

I have one more idea to throw out there to perhaps achieve higher velocities:  The Gerlich tapered gun barrel. 

A-square made a special .416 caliber rifle (powder burning) with a very light bullet (for caliber) to achieve at least 5280 ft/s (one mile per second).  They drew their design from Gerlich's tank gun barrel which has a taper from breech to muzzle.   So too did the .416 Gerlich as A-square named the cartridge.
 
I wonder if a tapered bore and collapsible projectile wouldn't tend to separate the slower from the faster molecules leaving the slower ones behind and pushing the faster ones to the base of the bullet.   You would want the collapsible bullet to keep friction down.

Intuitively, I see the air column being extruded longer as the bore reduces.  The slower molecules may want to be left behind, while the faster ones move ahead.

[rsterne]

I have no idea if that idea will work with expanding air.... The gasses in a PB are under such pressure and temperature they act completely differently.... not to mention they are already hypersonic, and hyperspeed from the temperature.... I guess the only way to find out would be to try it....

Bob

[K.O.]

hmm air spring chamber that sound like the Quigley wonder if it could be   sized up... or just  a np piston that reduces size of chamber as shots are taken...

http://www.americanairgunhunter.com/quigley.html

Me I have been in love with the Idea of a taper bore for a while... .25 paper patched to 30 cal in a taper bore... probably only need 6"-8" of rifle at the muzzle..?

.25 jsb monster with .30  head and tail...