VII. Reloading Information

F. Terminology

2. Energy, bullet; i.e. muzzle energy

by Scot E. Heath (scot@hpltby.fc.hp.com)

BULLET ENERGY CALCULATION:

The kinetic energy of a mass in motion is defined to be one half the mass of the body times the magnitude of it's velocity squared:


  KE =  .5 * M * V^2 

         or
                
  KE = .5 * Mass * Velocity * Velocity

For a 150 grain bullet traveling at 2390 feet per second:

  KE = .5 * 150 * 2390 * 2390 = 
    1,714,000,000 grain-feet-squared-per-second-squared

Looks a little funny, huh? My Winchester reloading manual lists this same situation as 1903 Foot-Lbs. The problem here are the units used. Bullet energies are quoted (in the USA) in Foot-Lbs. The problem is getting to Foot-Lbs. from these strange units. Lets start by translating the mass into something more familiar, slugs (just kidding about the familiar):


               1                                            1
  1 grain =  ----- lbs            -and-            1 lb = ------ slugs
             7000                                          32.2

therefore:

                  1
  1 grain = ------------- slugs
             7000 * 32.2

The pounds in the typical energy quote is a measure of force and force is equal to mass time acceleration. The units of acceleration are distance/time^2 or in our case, feet/second^2. If we look at a units only equation for KE we now see:


       slugs * feet * feet                    slugs * feet
  KE = -------------------     or   feet *  -----------------
        seconds * seconds                   seconds * seconds

The second part of the units only equation has the same units as pounds, that is, mass (slugs) times acceleration (feet/second^2), so we can write the units only equation as:


  KE = feet * pounds or foot-pounds

Now, let's look at our 150 grain (.000666 slug) bullet going 2390 feet/second:

        
  KE = .5 * .000666 * 2390 * 2390 = 1902 foot-lbs

That's more like it.