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  An intro to physics for shooters.

ShootingThere is always a great deal of chatter among hunters, as well as shooters primarily interested in defense, about "energy" and "momentum" and how they relate to "knock down power", etc. I find, however, that the terms used are often misunderstood. Having been involved in so many of these discussions I thought I'd offer some definitions and examples of what these terms mean with regard to terminal ballistics, that is, what happens when a bullet hits a critter or other target.

Before I even get started I want to recommend an excellent book every serious shooter ought to have. "Understanding Firearm Ballistics" by Robert A. Rinker should be required reading for anyone who wants to really know how internal, external and terminal ballistics works. The book offers relatively simple explanations of the nuts and bolts of ballistics and also includes the formulas to go deeper into it if you want to. I don't know of any better reference for those of us who want to really understand ballistics.

The first thing we need to do is define a few of the terms that get used so often. I'll have a list of my references at the end of this article. Forgive me for using "English" units instead of metric units but I'm just used to them!

Mass - Mass is the amount of matter that makes up an object. The unit used for this is the "slug". It isn't the same thing as weight. If an object is in space it has almost no weight but still has the same mass as on earth. An object's mass can be calculated by dividing its weight in pounds by the acceleration due to gravity, which is 32.12 ft/sec/sec. Since we used "grains" to measure bullet weight we also have to convert grains to pounds before dividing by gravity. There are 7000 grains in a pound. For example: a 150 grain bullet would weigh 150/7000 = 0.02143 pounds. Its mass would be 0.2143/32.12 = 0.000667 slugs.

Velocity - Velocity is simply how fast our object is going. In shooting we usually measure velocity in feet per second (ft/sec).

Momentum - This is the "push" you get from a bullet leaving the gun and also hitting its target. Momentum is calculated by multiplying an object's mass by its velocity. When people are talking about an "equal and opposite reaction" in shooting this is what they mean. The bullet and propellant gases go one way and the rifle goes the other way. The unit used is the slug-foot/sec. A 150 grain bullet going 2900 ft/sec has a momentum of 1.935 slug-ft/sec.

Energy - Energy is the ability to do work. In shooting we are talking about "kinetic energy", that is, the energy of a moving object. The unit we use for energy is the "foot-pound". To calculate an object's kinetic energy you have to know its mass and its velocity. The formula for kinetic energy: KE = 1/2 x mass x velocity x velocity. A commonly used method to calculate energy of a bullet is; bullet weight x velocity x velocity / 450380. The constant of 450380 takes care of the conversion from grains to slugs. Our 150 grain bullet going 2900 ft/sec has an energy of 2801 foot-pounds.

So, what's all this stuff mean to us shooters? Let's look at what momentum and energy actually do for us, and to the targets. Keep in mind that there are a lot of variables that will muddy the water here.

As mentioned above, momentum is the "push" the moving bullet gives to both the rifle and the target. When the bullet leaves the muzzle the "equal and opposite reaction" is pushing the gun back against us. That's recoil. When we calculate recoil we also have to take into account the weight and velocity of the powder gases. The velocity of the gas is usually estimated as 1.5 times the velocity of the bullet. If we take that 150 grain bullet at 2900 ft/sec, along with a 50 grain powder charge exiting the muzzle at around 4350 ft/sec, and fire it in an 8 pound rifle we'll have the rifle coming back at us at about 12 ft/sec. But, if we are holding the rifle correctly, you also have to include our mass in the calculation. A 180 pound man firing that rifle would be given a backward velocity of about 0.5 ft/sec. Now for some of those variables. Our muscles aren't rock hard (as much as we'd like to believe they are!) so they soak up part of that recoil. So do any recoils pads. The stock material and design can make a difference too. The point to take away here is that the recoil isn't going to knock us into the next county, even if it does smart some.

Now, how does the momentum affect the target? In every single case the bullet will hit the target with less momentum than the gun hits the shooter. Remember that part of the gun's recoil comes from the propellant gases and those don't make it to the target. If you're shooting a steel plate like a metallic silhouette ram, which weighs around 50 pounds, you can give the plate a velocity of 1.24 ft/sec. That's enough momentum to tip it over, if the base isn't too wide. Since the bullet doesn't go through the plate it transfers all of its momentum to the plate. You might even get a little extra push if the bullet spatters back toward the shooter.

If you are shooting a 150 pound deer (or bad guy), and the bullet doesn't go all the way through, you'll again transfer all of the momentum to the target. In this case the velocity you'll give the deer is a little over 0.4 ft/sec. If the bullet passes through the target the momentum would be even less. We've all heard stories of deer being knocked down, flipped over, etc. when struck by a bullet but those incidents are the result of the reaction the animal made to being struck, not the momentum itself. It's like a person reacting to a bee sting. The momentum of the sting doesn't cause all those contortions and gymnastics, the person's reaction to the sting does. The big variable here is whether the bullet stays in the critter or passes all the way through. The take away, however, is that there really isn't any such thing as "knock down power" except maybe on very small critters.

How about this energy thing? As mentioned above, energy is the ability to do work. In the case of a moving bullet the energy gets used up on several ways. Initially some of the available energy is used up by pushing through the air on the way to the target. More is used creating heat and noise. On impact energy is used by making a hole in the target and deforming the bullet. The big variables to remember here are the bullet's construction and the target's construction. When you start comparing loads using their energy levels you need to make sure that you're comparing apples to apples. Let me offer a couple of examples to illustrate my point.

If I take identical 150 grain .30 caliber spire point bullets and load one in a .30-30 and the other in a .30-06 I'm going to get somewhat different results when the bullet hits the target. The .30-30 will start the bullet off at around 2200 ft/sec and at 100 yards will have an energy of 1300 foot-pounds. The .30-06 will start the same bullet at 2900 ft/sec and at 100 yards will have an energy of 2317 foot-pounds. With that extra energy the .30-06 will do more tissue damage and also deform the bullet more.

What if we took two bullets of the same weight but very different construction and loaded them so that they would strike the target with exactly the same energy? Let's say that I load a very frangible bullet, like a Barnes "Varmint Grenade" in one case and a monolithic bullet, like a Barnes TSX, in another. In this case the frangible bullet would come apart on impact, creating a shallow wound. The monolithic bullet would stay together and keep penetrating the target. If we're talking about a small critter this doesn't make much difference but if we are talking about a deer-sized critter it could easily mean the difference between a lost animal and venison steaks on the grill.

The point to all this is that neither momentum nor energy are magic numbers. Momentum won't knock big game over and energy alone won't cause humane kills. When you start making comparisons of cartridges you also must keep in mind the bullet construction. Also keep in mind that there are a number of other variables that will affect the terminal performance of the loads. The biggest variable of all while hunting (and defensive shooting) is shot placement, and that takes practice with the gun, not the calculator.

References:
"Understanding Firearm Ballistics" by Robert A Rinker
"Applied Physics" by Paul E. Tippens
"Principles of Physics" by Frederick Bueche

Posted by Pumpkinslinger on Friday, September 16, 2011 (21:08:43) (1330 reads) [ Administration ]
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