Theoretical Maximum Velocity in a PCP

[Scotchmo]

...
Helium and 10ksi are each probably good choices for both energy and fps, but probably not for either practicality and/or efficiency.

The theoretical maximum velocity in a PCP helium-gun will be significantly higher than that of a PCP air-gun, regardless of how you fill the reservoir.

[rsterne]

Actually, the THEORETICAL maximum FPE is exactly the same, regardless of the gas chosen, because it is only a result of the force applied in lbs. (pressure times area) and the length of the barrel in feet.... What Helium does is allow more of that potential FPE to end up in the bullet, because less is wasted in accelerating the propellant gas....

When it comes to velocity, this is even more true, because you can use a lighter projectile before the mass of the gas becomes a serious factor.... and also the speed of sound in Helium is higher, increasing the efficiency at high velocities....

When it comes to the maximum theoretical FPE, however, they are the same....

Bob

[Scotchmo]

There is no THEORETICAL maximum FPE limit. Unless we are talking about a particular PCP gun, which is ultimately limited by the size/duration of the valve, and the amount of air that it can deliver. FPE is scalable, FPS is not. A bigger PCP system will always give more FPE, but not more FPS.

True, the FPE of the system is the same, regardless of gas density (helium vs air).

FPE(system) = FPE(gas) + FPE(projectile)

Everything else being equal, the FPE(projectile) is never exactly the same for Helium vs air. For ideal gases, the lighter gas gun will always have slightly more FPE in the projectile. As the mass(gas)/mass(projectile) ratio increases, the difference in projectile FPE increases.

So if you want the FPE(projectile) to be the same for both, the mass(gas)/mass(projectile) ratio must be the same. The air_gun will need a heavier projectile to keep FPE(projectile) the same as in the helium_gun.

[rsterne]

You are correct, of course, FPE is scalable, and depends on pressure and barrel volume.... It is also the thing that we can calculate.... whereas the velocity depends on the weight of the projectile.... For a given FPE, as the mass of the projectile approaches zero, then IN THEORY the velocity approaches infinity, but we all know that is a crock of doo-doo.... because of the mass of the propelling gas.... Ultimately we then enter a circular argument and end up back at Mach 5 for the gas and temperature in question as the ULTIMATE velocity limit at the pressure and temperature in question.... We also know that is NEVER going to happen in a PCP....

Lloyd started this thread trying to quantify what velocity could be calculated for a PCP of specified parameters.... bore, pressure and barrel length.... It then became a discussion about the theoretical maximum FPE for a PCP of specified parameters.... Where it went after that was something we know little about, and cannot quantify in any meaningful way, IMO.... I see no point in personally going there again, I would be just as lost as the last time.... Probably the best arguments about maximum velocity in PCPs are those presented by DomingoT, starting with Reply #281....

https://www.gatewaytoairguns.org/GTA/index.php?topic=94054.280

He is a Professor of Thermodynamics, and has written several papers on airguns published on ResearchGate.... While the concepts are very complex, he does make it somewhat easier to understand.... ALMOST to where I can get what he is talking about.... 

Bob

[Scotchmo]

.... whereas the velocity depends on the weight of the projectile....
... Mach 5 for the gas and temperature in question as the ULTIMATE velocity limit at the pressure and temperature in question....

I understand that velocity does depend on the "weight" (mass) of the projectile. And less projectile mass will give a higher velocity. But the velocity limit depends on the propelling gas. My research says that it is approximately MACH 2 (relative to the propelling gas being air at 70F), up to 10,000psi. I don't see it getting to MACH 5, even in theory, though I've only taken the calculations to 10ksi for air. Bulk modulus (k) is needed for the determination at higher pressures, and I can't find any k data for air above 10ksi.



PS - I did think the thread was about THEORETICAL maximum velocity, in general for a PCP, and not for a specific PCP - sorry if that's not the case.

[rsterne]

While I think that in practice we will never see Mach 2.... I have my own theory where I can "justify in my mind" the possibility of (1650 fps x 2) = 3300 fps for room temperature air.... When you consider that the speed of sound increases with pressure, our ideas agree at about 6000 psi....

BTW, I notice that the value for "k" peaks at about 5000 psi, any significance to that?.... I also note that the SoS at that pressure is close to the average molecular speed at 20*C of 1650 fps.... Just observations, is all....

However, I am not a thermodynamics expert.... and I certainly won't argue with a guy who lives and breathes it, and teaches it for a living.... 

Bob

[asdf1234]

BTW, I notice that the value for "k" peaks at about 5000 psi, any significance to that?....

Bob

It means we should start discussing max fps of hydraulic guns