Fun with Math and Guns…Part Whatever

In between paying attention in class, working to earn a living in this wonderful economy brought to us by a constitutional law professor’s flawed understanding of Keynesian economics and trying to get a few hours of sleep in, I’ve been spending a little time thinking about my firearms wish list. As most things based on desire as opposed to need, items on the list ebb and flow with the regularity of the tides.

Currently, there are 24 guns on the list from .22s all the way up to .45-70s. Only five of those are really, really must haves. I’d put a .50 BMG rifle on the list, but there is no way (even in fantasy land) for me to ever justify the price of poker for one of those beasts. Ditto for full auto playthings that cost more in ammo for one day at the range than most of the other guns on the list. If I ever do become even modestly wealthy, an MG42 would be lots of fun. Until then, I’ll stick to guns that don’t need a controlling interest in an ammo manufacturing company to shoot regularly.

Anyweapon, as part of this exercise in self delusion, I’ve been trying to really examine the relative benefits of each addition to the list including caliber, capacity, purpose, etc. You know…so that I can explain to The Queen why I really NEED to spend $1800 on a Sharp’s .45-70 because you never know when you need to hit a bucket (or a mounted Indian) from 1500 yards away.

Incidentally, I recently read an article written by someone who was asked to go out with a bunch of scientists to recreate Billy Dixon’s amazing shot (http://powderburns.tripod.com/sharps.hmtl). Apparently, one foolish egg head bet that the Sharp’s .50-90 was incapable of making the shot. He lost the bet soundly. Based on the numbers reported, the Sharp’s was/is capable of making shots out past 3500 yards. I’d really like to see a U.S. Marine sniper lug one of those to the sandbox and take the sniper kill distance record back from the Canadians. That would be epic to see modern Barrett and MacMillan rifles bested by 140 year old technology. It would be even better to set up the shot Road Runner style. Paint a huge “X” on the ground with a hookah next to it and a little note written in Pashtu pasted to the hookah that says “smoke me”. The bullet would arrive while our intrepid terrorist tokes away on the hookah and you would hear the cartoon “hammer/anvil” sound when he drops.

So, anyway, I don’t know how many digressions that is, but we have strayed just a bit from my intended point. Bad writer. No donut. Emmmm….donut. [slobber, drool] Sorry. This is supposed to be about fun with numbers and guns. What I’m trying to talk about here is kinetic energy.

A bullet sitting in the chamber has a finite amount of potential energy stored in the mass of the bullet and the measure of gunpowder behind it. Once the primer is struck by the firing pin, that potential energy is converted into kinetic energy. Most people tend to focus on the amount of kinetic energy at the muzzle end of the barrel (creatively enough called muzzle energy) since kinetic energy begins to decrease the moment the projectile leaves the barrel due to a variety of factors including drag; however, the calculation is the same whether you are figuring muzzle energy, terminal energy or energy anywhere in between.

The calculation for energy is one half the mass of the bullet times its velocity squared. Since this is America, we still calculate the mass of the bullet in pounds which necessitates a little more mathemagical juggling since bullet weights are normally advertised in grains. There are 7000 grains in a pound. Since mass is the weight of the bullet divided by the force of gravity (which is about 32 feet per second more or less). The final energy calculation looks something like this:

Energy = (bullet weight in grains) x (velocity) x (velocity)

                2 x 7000 x 32 ft./sec./sec.

So, for example, a 230 grain bullet (a typical .45 ACP bullet weight) travelling at 1000 feet per second has an energy of 513.13 ft. lbs. 513 ft. lbs. of energy is a respectable number for a pistol round. I don’t know about you, but I certainly wouldn’t want to get shot by one.

Most fanboys and haters deeply invested in the caliber wars want to focus on magazine capacity (how many rounds of 9mm can you hold steady at arms length?), muzzle velocity (that .44 is awesome cooking along at warp 5) or bullet diameter (a .45 will never shrink to 9mm!). Others chant the mantra of bullet placement, bullet placement…. Well, duh. If you don’t hit something vital, you’re not going to do much more than poke a hole in your target.

Let’s throw the Holy Hand Grenade into the caliber wars here for a second and look at some muzzle energy figures for comparison. I must confess that the following figures come from elsewhere, but I cannot for the life of me remember where I found them as I would like to give them credit where credit is due. The information comes from what can only be described as a backyard experiment, albeit a thorough one, done with some folks with time, money, ammo and a Thompson Center Contender on their hands. The bought a bunch of barrels for the TC in common handgun calibers. Each barrel started out at 18 inches in length. They would shoot a string of 6 shots for each type of ammo and barrel length combination through a chronograph and record the results. They would then cut off an inch of length from the barrel, lather, rinse, repeat. The muzzle velocity figures would then be averaged and used to calculate an average muzzle energy for a given load and barrel combination. The test was by no means exhaustive of every single load offered for a given caliber as that would have involved even more expense that the considerable amount these people already expended in their efforts, but it was fairly representative nonetheless.

*****11/13/11 Update - I finally tracked down the link and bookmarked it. It's from Bullets By The Inch.*********

Without further adieu, here is a quick and dirty comparison of some common pistol calibers from the study’s results:

                              Low                                                       High

9mm                     295 ft.lbs. (147 gr./951 ft./sec.)             442 ft.lbs. (115 gr./ 1316 ft./sec.)

.38 Special           250 (110/1013)                                       315 (135/1027)

.357 Magnum      403 (110/1286)                                       633 (125/1511)

.40 S&W      355 (165/985)                                        545 (135/1350)

.45 ACP               338 (230/814)                                         504 (185/1109)

For apples to apples comparison, all the above velocity figures come from the 4 inch barrel. The low is the “worst” performing round for that category in terms of muzzle energy. The high represents the “best” muzzle energy figure. The bullet weight and muzzle velocity are the figures in parentheses above.

I can hear you already. “Yes, Shepherd. But what does it all mean?” Well, let’s start with the obvious. In a self defense context, you’re not going to stop a threat unless you can get a bullet to penetrate a vital area. Setting aside certain variables like bullet design that can affect penetration, the bottom line is that more energy means more penetration. The ideal configuration to maximize kinetic energy would be a fast, heavy bullet (can anyone say .50BMG? I thought you could). However, speed can make up for a lighter bullet. If you need proof of that, do the math on a 72 grain 5.56mm round moving along at 2850 feet per second (1305 ft.lbs.). I wouldn’t want to get shot by one of those either.

What’s the best round? It depends. Mainly on you and your preferences. A .38 will get the job done within certain limitations. So will a 9mm, so will a .40 and a .45. The fact is that a pistol round will be outperformed by a rifle round every time.