Theoretical Maximum Velocity in a PCP

[Scotchmo]

...
Practical max pellet speed (including supersonic) can be calculated by changing m - mass of pellet.

I think there are pretty interesting conclusions can be made, but 1st - do you see any misses in logic above.

Practical max pellet speed (including supersonic) can be calculated by changing m - mass of pellet.

True, but it is a very complex calculation once you reach peak mass flux.

That happens when breech velocity of the air reaches mach 1. Any further increase for the pellet above that velocity, is the result of the air expanding inside the barrel.

[Euro2]

All above results are for internal ballistic only. I'm not touching external ballistic - flight outside of barrel.

Based on result that velocity of air in barrel is constant ~311 m/s slightly less than 344m/s (sonic) and does not depend on barrel length/bore. Velocity of pellet leaving barrel

v=311*sqrt(M/m)

so once m mass of pellet is less than 1.06 *M mass of air per discharge - pellet goes supersonic out of barrel. (1.106=344/311). 

[rsterne]

Euro2, I looked back through your math in your first post, and I see one small glitch in the calculations.... For the MRod, you calculated the mass of the air from....

Mass of discharged air per shot = (206*215*0.001225)/(206/62)=1.13gramm

while for the Texan you used....

Mass of discharged air per shot = (206*490*0.001225)/(206/14.8 )=8.88gramm

For the MRod, the number in bold (the air pressure) is in psi, while for the Texan it is in bar....  Since your answers are consistent, I assume the 62 in the first equation is just a typo, you actually used 4.27....

I still would like to understand your basic premise that the energy must be equally split between the bullet and the air.... Also, how do you account for the change in velocity along the air column caused by the air expanding, not moving as one solid mass?....

For a moment let's consider two objects touching each other, like two bullets in a barrel.... You apply a force on the back of the one which then pushes on the other, and the two accelerate together, travelling at the same velocity.... At the instant they leave the barrel, they both have the same velocity.... However, the only way they will have the same energy is if they have the same mass.... If one is 10 times the mass of the other, it will also have 10 times the energy, ie 10/11ths of the total.... Now replace the rear one with your air mass.... The only way the mass of air and the projectile can have the same energy as they exit the barrel is if they have the same mass, no?.... Is not your premise that the air and the bullet must have the same energy?.... If so, why?....

Bob

[Euro2]

Bob, thanks. I was typing formulas from piece of paper, and may have mistyped intermidiate results.

Equation is kinetic energy preservation in closed system. To be exact you can add energy of recoil But mass of pcp rifle is so much bigger than air&pellet - it has no measurable effect.
 

If you use PB gun wih stock loads the only thing that you can vary is bullet weight.

People who do reloading have advantages of varying type and  mass of powder. People who do reloading realised long time ago that optimal mass of powder is about 2/3 of the bullet.

Mass of powder burns and converts to mass of gas/fumes at pressure P that pushes bullet out.

PCP rifles are similar to reloading - theres usually way to control mass of air via transfer port & valve diameter and/or hammer spring/discharge duration. Speed of air expansion is pretty much constant.

I dont think that theres anything new in my logic. Except maybe experimental fact that speed of air is constant. It is just gives numerical measure of discharge and it can be correlated to barrel length/bore and  exit velocity.

Given all of that - plastic lightweight pellet will probably hit maximum velocity of mach 2 out of optimal lenth/bore PCP. You will need to have just enough pellet mass to hold it from destruction. But how far it will fly and how accurste it will be depends on external ballistics.

[rsterne]

I don't think you can apply the conservation of energy in that way, at least that's not the way I understand it.... You say that is in a experimental fact that the speed of expansion of the air is constant.... Could you please supply a source, and a value for that speed?.... Also, you may be interested in the experimental results in this thread....  http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.0

Bob

[Euro2]

I dont think that starting debates on elementary basics of general physics will be at the right place here:)

Thank you very much for constructive input and thoughtful discussion!

[lloyd-ss]

I dont think that starting debates on elementary basics of general physics will be at the right place here:)

Thank you very much for constructive input and thoughtful discussion!

Euro, it is difficult to avoid some of the debates but we are all still remaining to be friends.  I got busy on other projects and drifted away from the maximum velocity/ high velocity project, but will be starting back into it after the first of the year.  I am working on a new valve that is less "clunky" than the HV ones I have built so far, and will more closely resemble a valve that could be installed into an actual shoulderable air rifle.  I have some very unique lead projectiles that I will be using, which are coming from a GTA source.   I am very excited about them and am anxious to see what they will do at very HV.
Lloyd

[QVTom]

to be continued..... 

[Euro2]

Lloyd. That will be interesting even without shoulderable rifle. Maybe use plastic/acrylic instead of lead?

I'm under impression that something flat/fast and very accurate at 200 yards aka .17 hmr is impossible with air rifles.

Energy is there - 200-300lb/ft is pretty normal for big bores, but most of that energy is coming from projectile mass flying at relatively low velocity. Big bore + big transfer port gives pretty big mass of air at pretty low velocity.

I think that putting .17 barrel on texan will not spill 20g .17hmr bullet at mach 2, unless your barrel length is measured in yards:)

[rsterne]

I think that putting .17 barrel on texan will not spill 20g .17hmr bullet at mach 2, unless your barrel length is measured in yards:)

That is a pretty realistic statement.... In addition, as the velocity goes up, the efficiency goes down, because the mass of air being accelerated increases faster than the weight of the projectile.... Pretty soon you are using huge amounts of air for very small gains in velocity.... Add to that the huge increase in drag in the Transonic region between Mach 0.8 and 1.2 and the bullet slows down very quickly are launch, loosing all that extra energy fast, and ending up with additional wind drift to boot.... In PRACTICAL terms, airguns work the best in the mid 900 fps range for just sooooooooooo many reasons....

However, exploring the limits is fun and educational, which is why we do it.... 

Bob

[Buldawg76]

Glad to see this experiment still in progress. I am just following for the most part as I am lost in the math but the theory and discussion of all the possibilities are very informative and riveting to say the least.

Mike

[Euro2]

I have question. Is that true that none of side injected (aka transfer port is 90 deg to barrel) PCPs are not capable of super sonic  projectile velocities? I know that inline injection i.e. AirForce/Huben are capable of supersonic.

My thinking is that 90 deg air injection creates way too much turbulence and there's no sonic choke, so air flow never crosses sonic. Inline injection models have natural air choke that is capable to produce super sonic air flow.

Am I way off?

[Motorhead]

Well,
Any of my higher power 90* port PCP's when launching Felt cleaning pellets certainly do .... CRACK !!!
As too launching light lead, alloy or plastic pellets that fast  ... why care

[Euro2]

Well subject is "Theoretical Maximum Velocity in a PCP" so I think anything counts:)

Can you please chronograph cleaning pellet next time you fire it? Is it almost sonic or way supersonic?

[Motorhead]

OK ... here ya go 
Felts weigh .4 grains

RAW TM-1000 in .177 cal w/16" barrel 1333 fps.
War WarP in .177 w/12" barrel 1365 fps

Elevation 1488 feet , humidity @ 82% , Temp 52*f 
Distance to front screen @ 1 foot

[Euro2]

Wow calculated power is 4lbfts based on .4g weight. I just speculate that  velocity in barrel was  almost sonic, muzzle worked as choke and pushed pellet a bit supersonic at exit?


Is that limit for side injection? Can somebody fire plastic from some big bore  to see if it will go any faster?

[Motorhead]

Actually the reverse .... In guns represented BOTH have extremely short dwell cycles.
In all likelihood FELT is fastest within the barrel first few inches and looses speed as it travel down the barrel slower further passing by choke and then MAJORLY slowing down every inch traveled pass muzzle !!! 

[rsterne]

Euro.... there is a thread here you may find interesting, although it runs many pages in length.... The post that may answer your question is Reply #490 on this page....

http://www.gatewaytoairguns.org/GTA/index.php?topic=102604.480

Using a .25 cal Discovery which I built and modified, and a 6mm airsoft bb covered in tinfoil (to increase the diameter to fit the bore better), which weighed 2.2 gr.... I achieved 1752 fps.... Anyone with a .25 cal PCP capable of 100 FPE or more should be able to duplicate these results.... Not only is that supersonic (in fact over Mach 1.5), it is faster than the 1650 fps molecular velocity of air at room temperature, which was previously proposed as the maximum possible speed for a PCP on air.... Other shots in that thread were well over 2000 fps, but mine was done with a side-ported barrel, where the airflow turned 180* before reaching the "pellet".... My barrel, BTW, is NOT choked....

Bob

[Gippeto]

Think he might be referring to the barrel choking the flow...or the choke acting as a converging nozzle....

[rsterne]

Lloyd was unable to confirm any of the theoretical effects of "sonic choking".... As I understand it, all that does is create a mass flow limit.... True CD nozzles (converging-diverging) are quite complex in design, I somehow doubt we could be achieving such sophistication by accident, in many varied designs.... but I suppose anything is possible.... I'm just pleased to have been a small part of disproving the 1650 fps "speed limit" for PCPs on air at room temperature....

This thread is not based on any particular design, but on the general concept that there is a theoretical maximum velocity (and energy) for any PCP.... The energy is actually very easy to compute, it is barrel volume (in CI) times pressure (in PSI) / 12.... However, you can never reach that FPE in any given projectile, because the mass of the air propelling it is part of the mass that needs to be used to calculate the FPE.... and it would also require infinite reservoir volume, no friction, and several other factors.... In reality, 50% of the theoretical maximum is pretty good going for even the best PCPs.... and I have not seen that achieved with a pellet weight that ends up with a muzzle velocity of 950 fps (ie half the FPE).... Close, but no cigar....

Bob