Date: 24/3/2019 14:18
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# Airgun formulas and other neat stuff, how to calculate foot-pounds and velocity

Airgun formulas and other neat stuff
How to calculate foot-pounds and velocity

By Tom Gaylord
What is muzzle energy?

Muzzle energy is simply the energy of a projectile measured at the moment it exits the muzzle of a gun, which is when it is going fastest. With firearms, it's often very difficult to hold the muzzle of the gun next to the start screen of a chronograph. The gases from the blast could blow the screen apart! So, firearms testers are used to backing away from the start screen by about 15 feet. They then apply a formula to their recorded velocity figure to correct for this distance, and they call that number the muzzle velocity, which gives them the muzzle energy from the formula we learned at the start.
Except for big bore shooters, airgunners usually don't have this problem. They can shoot right at the start screen and call the number the chronograph gives them the muzzle velocity. In truth, even that number is a little off, but no one needs to worry about the difference.

The formula for energy

Try our Airgun Energy Calculator!
Don't want to read the whole article?
Just use the calculator below and skip the math altogether!
For pellet weight: grain and  velocity: ft/sec  foot-pounds  or joules

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Want to know how it works?
Multiply the product of the weight of the pellet (in grains) times the square of the velocity and divide that number by 450240. That last number is a constant created by multiplying two times the acceleration of gravity by 7,000 - the number of grains in a pound. The number I am using for the acceleration of gravity is 32.16 f.p.s. That number is obsolete, but the number that replaces it, 32.174 feet per second (f.p.s.) below the 50th latitude, does not change the energy calculation significantly.
Here's how the formula works. Suppose we shoot an 8-grain pellet at 800 (f.p.s.). The energy would be 8 times the square of the number 800, which is 640,000. So, it's 8 times 640,000 - which is 5,120,000. Now, divide that number by the constant 450240 and you get 11.371712. There may be even more digits out to the right of the decimal point, but that's where my small calculator stops, so that's my answer. I'm going to round off the number to two decimal places anyway, so I write it down as 11.37 foot-pounds.
The problem above looks like this when written in mathematical notation:

What do I care what muzzle energy is?

You may not care, and it's OK! However in many cases when you read an airgun specification you may see only muzzle energy indicated or only muzzle velocity. While for some people it's irrelevant to some people it matters. For instance some country laws may prohibit ownership or import of air rifles above certain muzzle energy. Remember to multiply all the numbers above the line before dividing the answer by the number below the line.
671 - the magic number

A velocity of 671 f.p.s. for any projectile gives the same energy number in foot-pounds as the weight of the projectile in grains. For example, an 8-grain pellet traveling 671 f.p.s. generates 8 foot-pounds. A 20-grain projectile going 671 f.p.s. generates 20 foot-pounds and a million-grain (142.86 lbs.) projectile going 671 f.p.s. generates a million foot-pounds. A 3,000-lb. automobile going 671 f.p.s. generates 21 million foot-pounds, which is why we should be glad not too many cars ever go that fast.

The magic number is helpful when you have projectiles going near that velocity. For example, many big bore airguns shoot about that fast, so all you need in order to determine their energy is look at the weight of the projectile they shoot in grains. If someone tells you that his big bore .50-caliber rifle shoots a 180-grain lead ball at 700 f.p.s. and gets 500 foot-pounds of energy at the muzzle, you can now determine in your head that he is wrong. You may not be able to calculate the correct number in your head, but it's going to be a lot closer to 180 foot-pounds than to 500 foot-pounds.

If you know the energy, how do you find the velocity?

Airgun energy foot-pounds and  pellet weight: grain  ft/sec
The quick way to find the answer is to work a reciprocal of the energy formula; but, if you're like me, you need to be reminded how that's done.

Take the energy times the constant 450240 and divide by the weight of the pellet in grains. The square root of that number is your velocity.

Let's find the velocity of an 8-grain pellet that generates 11.37 foot-pounds of energy. That would be 11.37 times 450240, and divide that number by 8. Then hit the square-root key on your calculator. My calculator comes up with 799.93974, which is pretty close to 800. Remember, we rounded off the energy number, which accounts for the small difference between our answer and the number 800.

Summary

You can shoot airguns a lot without ever getting into the numbers like these, but since a lot of advertising is based on numbers, you now have a way of decoding what they are saying.