A systematic approach to pellet selection based on muzzle energy and momentum

[DOKF]

I’m just musing late at night, but does this make sense? 

There are two main types of air gun power plants exist based on primary and secondary pressurised gas sources.

Spring action guns (including gas rams) are secondary pressurised gas sources, while reservoir guns (PCP, CO2, and pumpers) are primary pressurised gas sources.  The distinction is that springers use a secondary pressure device to compress gas against the pellet-bore seal, while reservoir guns have high pressure gas momentarily in direct contact with the pellet seal.  In spring action guns the maximum pressure is determined by the pellet fit in the bore, while maximum pressure in reservoir guns is determined by the pressure capabilities of the reservoir tank and fittings.

In a springer, pulling the trigger releases a piston, which in turn rapidly compresses air until the burst seal created by the pellet fit is ruptured.  Any additional pressure generated by the piston then accelerates the pellet down the barrel.  In a reservoir gun, the trigger action releases a measured quantity of gas at a fixed pressure far greater than the burst pressure defined by the pellet fit.  Excess released pressure then accelerates the pellet down the barrel. 

The timing of the trigger action and pellet release is significant.  With a spring action gun, the air pressure is still increasing while the pellet is accelerating down the barrel, and peaks sometime before the pellet has exited the barrel.  Peak air pressure occurs just before the piston seal slams into the end stop with the predictable result.  If the pellet accelerates out of the barrel before the piston completes its stroke, then the pellet muzzle energy (KE) will be less than the spring’s useable potential energy (PE).  This may happen with lighter (faster) pellets.  If the piston completes its stroke and max pressure is reached well before the pellet exits, then some of the spring’s PE will be used by the pellet to overcome barrel friction, and the pellet muzzle energy will be lower than optimal.  This may happen with heavier (slower) pellets.

With a reservoir gun, maximum pressure is obtained virtually the moment the trigger is released, and the excess pressure smoothly guides the pellet along the full length of the barrel (no recoil).  The pellet’s muzzle KE is then similar to the pressurized reservoir’s useable potential energy less the energy lost to barrel friction.  With reservoir guns, the pellet muzzle energy is relatively independent of pellet mass.

The upshot of all this is that for muzzle energy there will be an optimal pellet mass for spring action guns, while reservoir gun muzzle energies will be less affected by pellet mass.

I chronographed my rifles (all “springers”) with a wide selection of pellets to determine the optimal mass energy characteristics.  From the plot for my gas ram 0.22 cal guns, one can see an energy envelope describing the maximum practical energy realized at each mass, diminishing to either side for light weight or heavy weight pellets.
 
The energy mass relationship shows pellets from both rifles having optimal muzzle energies for pellets between 14 and 20 grains.  However, being 14 ~ 20 gr still does not ensure a great pellet choice, and some pellet designs of a given weight perform better than others.  Factors such as bore fit and head design are also important to match pellet to gun for optimal performance; performance being a combination of projectile energy and on target accuracy. 

After the pellet leaves the muzzle, the rifle ceases to be an active influence on the projectile trajectory, leaving momentum and ballistic coefficient as the important factors affecting downfield performance.

From a simple perspective, the gun’s power plant has a capability to convert stored energy (“Potential Energy”, PE) of a compressed spring or reservoir of compressed gas into the energy required to accelerate a pellet down the barrel.  The pellet accelerates down the barrel absorbing as much energy as possible, and that energy is realized as momentum once the pellet exits the muzzle.
At the target, energy is required (by the target) to decelerate the pellet and absorb the retained momentum after losses in flight due to air drag (dependent on BC).  The momentum ~ mass relationship for 0.22 cal pellets implies a higher optimal mass of 25 ~ 30 gr for the same two gas piston rifles as above.

PCP muzzle energy (courtesy Bob Sterne) shows a relatively flat response to pellet mass from 10 to 30 grain.

The momentum plots also show the benefits of regulated pressure source.

non PAL (lower velocity) data shows an even flatter response for both KE and momentum suggesting that all practical energy has been transferred to the pellet before both pellet and air are exhausted from muzzle.

Higher muzzle momentum may be more important than muzzle velocity for down range results; better chance for retained velocity at target even if lower velocity at muzzle

The data strongly suggests an upper and lower limit for pellet mass in spring action guns, but to a lesser degree may suggest a lower limit for reservoir guns, and doesn’t really indicate an upper pellet mass limit for reservoir guns.  This appears to be in accordance with general wisdom.

In springer powered guns the compressed air pellet interaction is characteristic of “inelastic collisions” in that KE is not conserved.  Energy losses to barrel drag, pressure leaks are significant relative to spring PE.  Excess pressure is “wasted” on lighter pellets, and optimal energy transfer is not realized before the pellet exits the muzzle.  The remaining pressure exhausts ineffectively after faster pellets have exited.

Pressure reservoir guns approximate “elastic collisions” in that KE is apparently conserved, which is probably a factor of the compressed gas PE being much greater relative to the KE energy losses of pellets in the barrel.

Beeman, Werner, and others suggested a general upper and lower limit for pellet mass in 0.177 and 0.22 cal spring action guns, but those numbers may need to be qualified with the newer magnum class rifles.

I use this method as a first screen to determine optimal pellets for my guns.  Once optimized for KE and momentum, I can then work on accuracy knowing that the pellets will have optimal momentum on target.

I use higher muzzle energy and muzzle velocity pellets for short range targets, and use higher muzzle momentum and heavier pellets with optimal BC for longer range targets.

[rsterne]

The upshot of all this is that for muzzle energy there will be an optimal pellet mass for spring action guns, while reservoir gun muzzle energies will be less affected by pellet mass.

Sorry, that is incorrect.... In fact, most PCPs show significantly more FPE with heavier pellets.... Your graphs confirm that.... I agree that springers tend to have an "optimum" pellet weight where the FPE plateaus, being less when the pellets are lighter or heavier.... With PCPs, generally heavier pellets have more FPE, this relationship usually only breaks down if you push the weights past what you find for pellets and get into bullets.... Even then, all is takes is a tweak of the hammer spring preload to increase the dwell and the FPE peak rapidly moves to a higher weight.... This is a simple matter of dwell, with heavier pellets being able to better use longer dwell....

I have been using the idea of finding the optimum weight range where FPE peaks/plateaus for years as the primary "first cut" for springers, it is a good method....

Bob

[DOKF]

The upshot of all this is that for muzzle energy there will be an optimal pellet mass for spring action guns, while reservoir gun muzzle energies will be less affected by pellet mass.

Sorry, that is incorrect.... In fact, most PCPs show significantly more FPE with heavier pellets.... Your graphs confirm that.... I agree that springers tend to have an "optimum" pellet weight where the FPE plateaus, being less when the pellets are lighter or heavier.... With PCPs, generally heavier pellets have more FPE, this relationship usually only breaks down if you push the weights past what you find for pellets and get into bullets.... Even then, all is takes is a tweak of the hammer spring preload to increase the dwell and the FPE peak rapidly moves to a higher weight.... This is a simple matter of dwell, with heavier pellets being able to better use longer dwell....

I have been using the idea of finding the optimum weight range where FPE peaks/plateaus for years as the primary "first cut" for springers, it is a good method....

Bob

Bob,

Yes, I should have said that springers are more sensitive to pellet mass than PCP guns.  My bad for speculating outside the box.

Is there a practical upper limit to the increased energy with pellet mass for PCP?  I guess it would depend on reservoir volume and pressure limitations?

Kim

[Bullit]

Bob will tell you that the reservoir to chamber input is the limiting factor, as it's still the "input" to power the pellet...no matter the powerplant.  The PCP does offer more "manageable", impetuous for the heavier pellet, of course.  There's guys that are building some pretty radical PCP stuff out there now.  Big bore stuff is cool and I like reading about their works.    Kinda like racing.  How fast do you wanna go?

[DOKF]

Bob will tell you that the reservoir to chamber input is the limiting factor, as it's still the "input" to power the pellet...no matter the powerplant.  The PCP does offer more "manageable", impetuous for the heavier pellet, of course.  There's guys that are building some pretty radical PCP stuff out there now.  Big bore stuff is cool and I like reading about their works.    Kinda like racing.  How fast do you wanna go?

Can you connect a PCP gun directly to a large air tank?  Like an N₂ bottle? or like a nail gun connected to an air tank with HP hoses?

Wouldn't work for hunting; but then you can't really drive a rail dragster downtown.

[Bullit]

Shortly.  Yes.  The input won't increase, but it will be more consistent for many more shots.

[rsterne]

The limiting factors on a PCP are ultimately the pressure and the barrel length.... More of either will allow you to use a heavier (higher Sectional Density) bullet.... There are many other factors that can limit the performance, such as port size, hammer strike, and the volume available for the valve to draw from (the reservoir or plenum) which if too small (or too restricted on the inlet) causes a drop in the pressure during the shot cycle.... You can get a feel for how those limits work in this thread....

http://www.gatewaytoairguns.org/GTA/index.php?topic=57828.0

Bob