## Shotshell Ballistics

Dr. Gauss,

As I was accidentally shot while pheasant hunting, I would like to know how to calculate the energy, in foot-pounds, for a #4 lead pellet with a stated muzzle velocity of 1350 ft/sec at a distance of 30 yards. I had access to the same shells and the average weight of each pellet was 3.4 grains. I am still carrying all 10 that hit me, including one in my left lung. I know that I was/am lucky to have recovered but my natural curiosity leads me to this point. I am 72 years young and have studied physics in college but over 45 years ago and am stuck. The recent NRA journal uses a formula but it is magic. Like where did he get the denominator of 450,400? As you know, the NRA does not respond to emails from individuals. If it is not asking too much, I would like the conversion of grains, ft/sec to foot-pounds, with all of the units involved. I believe that 2KE=mv.v is the proper approach but…….. Thank you,

Emile
Troy, NH

Dear Emile,

It’s good that you are curious enough to want to know the details of the pellet energy calculation. Thankfully this one is not too tough.

You have the formula right; it is KE = 0.5 x M x V squared, where M is the mass of the pellet and V is the velocity of the pellet at the distance of interest, 30 yards in this case. The only really tricky part is in the conversion of the mass (or weight) of the pellet from grains to slugs (remember those nasty things from your days in physics class?).

Let’s start with the pellet velocity, V. I checked my ballistics tables for the parameters you stated (No. 4 lead pellet, 1350 ft/sec muzzle velocity), and came up with a pellet velocity of 852 ft/sec at 30 yards.

Now the tricky part. You gave the weight (M) of the pellets as 3.4 grains. For the above equation to give the energy in foot-pounds when V is expressed in ft/sec, you must convert the mass M from grains to pounds, and then from pounds to slugs. Now, one pound equals 7000 grains, and one slug equals 32.174 pounds. Combining all these constant factors, we multiply 2 x 7000 x 32.174 and get 450,436 as the number in the denominator. In the numerator, we have 3.4 x 852 x 852 = 2,468,074. Dividing this by the denominator gives our answer for the pellet energy at 30 yards: 5.48 ft-lb.

Sorry to hear about your hunting injury. Here’s wishing you a healthy New Year.

Happy shooting,

Warren Johnson (“Dr. Gauss”)