Alternatives to foot pounds of energy (fpe)

An often discussed topic is what sort of caliber do I need to hunt coyotes. Or squirrels, or rabbits. There are tables that show a person's opinion but many of us disagree with at least portions of the table. Another way of comparing is to calculate the fpe of a gun and compare that. Like I have had good experience with 22 and 177 caliber pellet guns at about 18 fpe but not so good experience with lower energy in both calibers. Perfectly reasonable way to communicate.

But airguns have to deal with the fact that our power source is really high pressure air but it is at hugely lower pressures than powder burners. A rimfire can be over 24,000 psi, for instance with center fires often over 50,000 psi. To compensate more powerful airguns go up in diameter. That makes sense because the larger diameter provides more surface area for the lower pressure to push against.

But then how do you compare larger diameter potentially heavier airgun rounds to smaller diameter potentially lighter PB rounds that are moving at much higher velocity. FPE can be used but many feel it puts too much emphasis on velocity. The velocity is squared in the formula. Elmer Kieth is an old gun writer that liked large diameter handguns and felt they had much more effectiveness in hunting than the fpe would predict. He is just an example, others believe heavier slower moving projectiles can work effectively and more effectively than the fpe would indicate. John Taylor was an old african hunter and poacher who came up with the Talor Knock Out Factor. I believe Chuck Hawks came up with the killing power formula. These are alternatives to fpe which place less emphasis on velocity.

Knowing this the spreadsheet I use to look at shot curves calculates fpe for each shot but also the Taylor Knock Out Factor (TKO) and the Rifle Cartridge Killing Power (KPS). I do not think either are necessarily better than using fpe but they are alternate ways of looking at the rounds effectiveness. I calculated the following comparison:

22LR target round with 40 grain bullet going 1040 fps. Energy 96, TKO 1.31, KPS .431
35 grain 25 caliber going 950 fps. Energy 70, TKO 1.2, KPS .275
45 grain 30 caliber going 900 fps. Energy 81, TKO 1.7, KPS .41
50 grain 30 caliber going 900 fps. Energy 90, TKO 1.93, KPS .5
81 grain 35 caliber going 700 fps. Energy 88, TKO 2.8, KPS .8

As you can see, a 25 caliber airgun would have to be very powerful to challenge any of these factors for even a target round for a 22lr. But a 30 caliber gets close on energy, is higher on TKO and a little lower on KPS. Perhaps the biggest illustration of the difference in these values is for the 35 caliber. This is a pretty low velocity 35 and it is still lower in energy than a 22lr but significantly higher on both TKO and KPS. There are on line videos of the use of the Benjamin Bulldog in 35 caliber on deer and African plains game. Power was probably pretty close to this 35 caliber example. But it worked. I don't think most would body shoot any of that game with a 22 lr unless they had to. Just another way of illustrating why the other factors may make some sense.
 
There is another factor called the HITS (Hornady Index of Terminal Standards) number.

Here are the H.I.T.S. scores that Hornady recommends: Small Game, 500 or less; Medium Game, 501-900; Large Game, 901-1500; Dangerous Game, 1501 or more.

The formula is:
HITS = (W2 / 7000) * (V/D2) * 1/100

where
  • HITS = Hornady Index of Terminal Standards​
  • W = Weight of the bullet in grains.​
  • V = Impact velocity of the bullet in feet/sec.​
  • D = Diameter of the bullet in inches.​


Air:
8.4gr @ 900 fps = 2 @ 100yd
25.4gr @ 900 fps = 10 @ 100yd
33.95 @ 900 fps = 19 @ 100yd
43.5gr @ 900 fps = 35 @ 100yd

PB:
17gr .17 HMR = 26 @ 100yd
30gr .22 WMR = 36 @ 100yd
50gr .22 rem = 195 @ 100yd

https://chuckhawks.com/rifle_hits_table_syn.htm

-Matt
 
There is another factor called the HITS (Hornady Index of Terminal Standards) number.

Here are the H.I.T.S. scores that Hornady recommends: Small Game, 500 or less; Medium Game, 501-900; Large Game, 901-1500; Dangerous Game, 1501 or more.

The formula is:
HITS = (W2 / 7000) * (V/D2) * 1/100

where
  • HITS = Hornady Index of Terminal Standards​
  • W = Weight of the bullet in grains.​
  • V = Impact velocity of the bullet in feet/sec.​
  • D = Diameter of the bullet in inches.​


Air:
8.4gr @ 900 fps = 2 @ 100yd
25.4gr @ 900 fps = 10 @ 100yd
33.95 @ 900 fps = 19 @ 100yd
43.5gr @ 900 fps = 35 @ 100yd

PB:
17gr .17 HMR = 26 @ 100yd
30gr .22 WMR = 36 @ 100yd
50gr .22 rem = 195 @ 100yd

https://chuckhawks.com/rifle_hits_table_syn.htm

-Matt
That's interesting, I take it this doesn't take expansion into the equation, solely the power still available at 100yd
 
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That's interesting, I take it this doesn't take expansion into the equation, solely the power still available at 100yd

For that, I think you want to use the penetration formula, and once you determine enough penetration for whatever your target is, you increase diameter of the projectile to increase potential expansion, then revisit the penetration formula to ensure you still have good penetration.

I am unsure how accurate the pyramyd air method to calculate this is but here is the formula for 'projectile effectiveness'..the below formula uses muzzle velocity and estimates the projectile velocity upon impact, ill show both formulas in case you want to use your own impact velocity.

Where

  • pV = projectile velocity
  • tD = target distance
  • bC = ballistic co-efficient
  • pW = projectile weight
  • pD = projectile diameter
  • pE = projectile effectiveness aka wound depth

pE = pV/EXP(tD/(8000*bC))*pW/(53014*pD)^2)



Or with your own impact velocity:

Where
  • tV = terminal velocity
  • pW = projectile weight
  • pD = projectile diameter
tV*pW/(53014*pD^2)

Plugging in the above, for a 33.95gr .25 cal projectile arriving at 821 fps terminal velocity or 51 terminal FPE, I get a 'wound depth' of 8.4 inches.

-Matt
 
Last edited:
What is EXP? Is that just expansion abbreviated?

Also with this formula I got .207139

1911*17/(53014*.172^2)

@Stubbers

It's a mathematical term "Exponential function" that excel and other spreadsheets recognize. , must not leave it out if your impact velocity is not known.

I get 20.7" using your above data, suggesting basically 21" of penetration through flesh, I am unsure how your 2 orders of magnitude off but its close!

1726777398917.png

-Matt
 
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The cool thing about making your own ballistic program

This shows flight time, how many mils of drift you get for every mph of wind at your target distance, wound depth, and many others based on selection of what you want to view. If JimD shares his spreadsheet or formula, I wouldn't mind adding more data into my personal ballistic calculator (currently only setup to handle GA/pellets, nothing fancy)

1726777854767.png
(100 yard target with 3 o'clock winds and shot direction 12 o'clock)

And some other nifty calculations I happen to run, stability factor (sg), projectile average rpm, and ideal twist rate. (data shown is for jsb 33.95 going 860 fps)

1726777802880.png


-Matt
 
Not to diminish the value of all the number crunching (and I'm sure there's some in there), but I'm convinced that this issue is over thought. Air guns are not very powerful. Use the one that you shoot the best, and put the pellet where it needs to go.

Hard disagree, don't need people out there thinking they can shoot Yotes with a .177/.22 with that kind of statement...crunching numbers and understanding terminal ballistics is crucial in proper hunting.

Some airguns are very powerful, some are not. Lets not go bashing people who like to paint a fuller picture with 'number crunching' than they can without. You probably crunch some numbers, right? FPS, FPE? Use a ballistic program to calculate your drop/poa? Well then...

-Matt
 
Hard disagree, don't need people out there thinking they can shoot Yotes with a .177/.22 with that kind of statement...crunching numbers and understanding terminal ballistics is crucial in proper hunting.

Some airguns are very powerful, some are not. Lets not go bashing people who like to paint a fuller picture with 'number crunching' than they can without. You probably crunch some numbers, right? FPS, FPE? Use a ballistic program to calculate your drop/poa? Well then...

-Matt
Actually, I don't. I don't mean to bash anyone, and I sincerely apologize, without limitation, to all those considered bashed.
 
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Actually, I don't. I don't mean to bash anyone, and I sincerely apologize, without limitation, to all those considered bashed.
I have never crunched FPE numbers in my life. Archery, big game rifle, big game handgun, small game or airguns. It’s just common sense. But if someone didn’t spend a lifetime killing stuff with everything that shoots a projectile, they may find comfort in numbers I guess. But I’ll take accuracy/consistency plus the right projectile over relying on a certain FPE every time. A non big bore airgun is seriously lame compared to a powder burner. FPE puts things in perspective when guys compare their amazing killing machine PCP to this dumb little thing.

IMG_6367.jpeg
 
It's a mathematical term "Exponential function" that excel and other spreadsheets recognize. , must not leave it out if your impact velocity is not known.

I get 20.7" using your above data, suggesting basically 21" of penetration through flesh, I am unsure how your 2 orders of magnitude off but its close!

View attachment 497524
-Matt
I see why now. And your screenshot formula at the end.You also times that by two whereas in the first one it ended with to the power of two.
 
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The cool thing about making your own ballistic program

This shows flight time, how many mils of drift you get for every mph of wind at your target distance, wound depth, and many others based on selection of what you want to view. If JimD shares his spreadsheet or formula, I wouldn't mind adding more data into my personal ballistic calculator (currently only setup to handle GA/pellets, nothing fancy)

View attachment 497529 (100 yard target with 3 o'clock winds and shot direction 12 o'clock)

And some other nifty calculations I happen to run, stability factor (sg), projectile average rpm, and ideal twist rate. (data shown is for jsb 33.95 going 860 fps)

View attachment 497528

-Matt
That's pretty sweet! If my math teachers had told me thay I could use math for calculating things like shooting and how to shoot. I would've paid WAYYYY more attention
 
I see why now. And your screenshot formula at the end.You also times that by two whereas in the first one it ended with to the power of two.

^2 = ² when you write a formula in excel which is how I showed the above formula, which means to square the quantity or multiply it by itself. Same thing as power of two.


-Matt
 
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I got thay part, but in the screen shot you took it shower ^2)2).

Where as in the original formula you showed it ended in ^2

In the screen shot the second 2 = the rounded decimal place with the use of the round function in excel. ^2,2)

Here it is again, without that ",2"...showing the number unrounded to the 2nd decimal..matches your original just 2 orders of magnitude difference.

1726841629384.png


-Matt
 
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