Why do heavier pellets tend to shoot at higher energy than lighter pellets?

[rsterne]

We made the assumption that the efficiency of both guns was 1.00 FPE/CI.... You are correct that the expansion ratio has something to do with the FPE, but that is not well quantified.... Artillery pieces are seldom more than 50 calibers long (the 16" guns on the Iowa class Battleships were 16"-50 cal, so 66.7' long)…. Our barrels are often 100 calibers long, sometimes more.... I have an "opinion" that once a barrel is about 100 cals. long after that we probably can't measure any gain in efficiency.... but when the barrel is short (eg. a pistol barrel might only be 25 calibers long), then the efficiency is affected.... It's probably some kind of logarithmic relationship, but it all falls apart at the limits.... BTW, I think for equal efficiency, the barrel length relationship would be (.22 / .177), not the ratio of bore areas.... Certainly, the FPE (and therefore the air used) is proportional to the bore VOLUME.... 

The maximum FPE produced is a function of force in lbs. (area times pressure) times barrel length in feet.... However, to max. out that, we have to keep the valve open until the pellet exits the muzzle, and have an infinite reservoir, to achieve constant pressure, so there really is no expansion ratio.... I know, this is all theoretical and not possible or practical, but we can only view some of this stuff from the limiting conditions.... I guess what I'm saying is that trying to pin down this stuff isn't much more than guessing.... but that certain relationships are valid and easy to understand.... One of those is that for any given pressure and barrel length, there is a maximum SD if you wish to reach a given velocity.... A lot of things get easier to compare between calibers when you look at the SD.... and I think the idea of air mass as a percentage of total required to produce a given velocity is one of them.... for a lot of reasons....

Bob

[VaporTrail]

Paul,
you've listed so many of the different facets of our incredibly varied hobby so well!
And have drawn the right conclusion from it all!
😄

ALL [these facets] waiting for you to experiment with them... [...]

This right here is fabled wormhole of AG shooting. [...]

This is the Dark Side for sure.

Thanks Matthias! Good to know that I'm slowly learning!

Then I try to follow Mr. Sterne and realize that the world is a very big place. And now subscriber is jumping in? I got lost trying to keep up with both of them. 

[Danny]

A lot of good detail.

In simple terms PCP's generally yield more power with heavier pellets, springers with lighter.  PCP's are more linear in the power to weight while springers follow more of a curve with the ideal weight being somewhere between the heaviest and lightest pellet.

But, of course, power is just one factor.  Accuracy and velocity are important too and it varies depending on the objective.

For target shooting for tight groups, for example, a heavier pellet might be better despite it being slower and more loopy.  For hunting you might give up some power and even a little accuracy for a pellet that shoots flatter and expends more energy in the target.

[avator]

Toss a small rock into a mudhole and watch the splash.... toss a big rock in and stand back...

[rjp]

...
Obviously, accelerating that air takes energy, and that energy is not available to accelerate the pellet or slug.... That 20 FPE PCP, shooting an 8 gr. pellet would be wasting a higher percentage of power on the air than the same PCP accelerating a 16 gr. pellet.... Therefore, the 16 gr. pellet will end up with more of the total energy available, and the gun will be more efficient shooting the heavier pellet....
.... The lost energy went to accelerating the air, which in this case weighed more than the lead bullet....

Bob

Bob,
Thank you for this excellent explanation. I had no idea the mass of air was that large as to be significant, but now that you point it out it makes perfect sense. I believe this is the physics ultimately explaining the phenomenon of heavier pellets having more kinetic energy in PCP airguns. Thanks!

I could not come up with any formula to support the "air is wasted by lighter pellets leaving the barrel too soon before they're done accelerating" hypothesis. I see now that it is because it was likely incorrect, or at least not the primary factor.

If we consider the combined mass of projectile and air as you say, then would the following be the way to formulate it:

m = mPellet + mAir
Assume the force, F, is the same for all shots since it is a function of the pressure alone.
The work done moving the pellet and air down the barrel is then W = Fd, where d is barrel length and is also constant, and it does not matter how much time it takes to perform this work.

Also, by definition the work is equal to the change in kinetic energy = (1/2)mv^2, where m is the combined mass above.
The point being that the total energy is roughly constant with each shot regardless of what we stick in the barrel (within reason).

So the total energy is the sum of the pellet energy plus the air energy
E = FPEpellet + FPEair, which means we can split it in proportion to the mass of each as you said.

Does this sound right to you?

[rsterne]

In theory, yes.... In practice it gets a whole lot more complex to calculate because the pressure during the shot is not a constant unless the valve is open until after the pellet leaves the muzzle and the reservoir is of infinite volume.... That is why for typical PCPs instead of starting with the theoretical maximum FPE (area x pressure x barrel length), I use a "lofty goal" of half that.... Even then, I have never achieved that when using a pellet/slug that has a velocity of 950 fps, my best results are only within about 10% of that goal.... ie I usually need about 10% more pressure or a 10% longer barrel length to achieve it.... Some guys manage to hit the goal, but nearly always they are using heavy slugs shooting well below 950 fps, and hence taking advantage of the extra efficiency that gives....

Also, I believe that different conditions exist in terms of the mass of air being accelerated whether the valve is open or closed.... Valve closed is easy, I think using 1/3 of the air mass inside the barrel at the instant the valve closes (ie the total air mass used) is a good estimate, because it is only expanding, like a spring.... When the valve is open, it's a different story.... An valid argument can be made that at any given time interval the air leaving the valve must accelerate ALL of the mass in front of it....

Let's say that the pellet is 25% of the way down the .25 cal 24" long barrel, and the valve is still open.... New air exiting the valve is pushing on the pellet, plus the mass of air filling that 25% of the barrel volume, at the pressure inside the barrel.... At 1500 psi and 70*F that is 31.3 gr./CI.... and the barrel volume is 1.178 CI, so the air mass already in the barrel is (31.3 x 1.178 / 4) = 9.2 gr.... If we are shooting a 25.4 gr. pellet, the total mass inside the barrel at that instant is 34.6 gr.... Doesn't the air coming out of the valve have to accelerate the entire 34.6 gr?.... I think so....

Lloyd's spreadsheet uses 1/2 the mass of air in the barrel because it comes close to empirical results.... Even in the "valve open" condition, using the entire mass may be too much, regardless of my reasoning above.... The bottom line is, we don't know how much of the air mass to include, but for sure it results in a significant reduction in the available FPE to the pellet.... and the heavier the pellet is, the more of the total FPE ends up in the pellet.... with the energy of the pellet and the air both reduced by frictional losses, of course....

Bob