Relative Stopping Power (What is it, and why?)

—by M1911A1—

Way back in 1935, Major Julian S. Hatcher published his Textbook of Pistols and Revolvers. It was so well written and documented that it’s still the definitive work in its field. You can get Hatcher’s book through the inter-library-loan program, and reading it is worth your time. I specifically call your attention to Chapter Twelve, “Bullet Effect and Shock Power.”

Hatcher drew information from his own experience, and also from the gory, explicit tests conducted way back in 1904 by Colonel John T. Thompson (yes, “tommy-gun” Thompson) and Major Louis A. LaGarde. This material proved that more fight-stopping shock is delivered by bullets of large cross-sectional area (let’s call it “large bullet diameter”) than is delivered by small-diameter bullets, that bullets don’t reliably expand unless they arrive at high velocity (high “speed”), and that large, heavy, blunt, soft bullets do the most damage to people.

More recently (circa 1988), Martin L. Fackler, a US Army surgeon, published the results of a series of similar experiments, as well as what he thought about the wartime bullet wounds he had seen. Fackler’s published material closely agrees with both the Thompson-LaGarde tests and Hatcher’s observations. However, Fackler wrote about rifle-bullet performance, while Thompson, LaGarde, and Hatcher were looking only at pistol-bullet wounds.

And so shall we.

In pistols, barrel length limits bullet velocity (from now on, “speed”). You can get more speed from longer barrels, but getting a long-barreled pistol into action is very slow, and it’s difficult to use one in a tight place. You can also get more speed from a short barrel by using a larger powder charge, but the increased recoil may make your first shot painful, and your second shot both slow and inaccurate.

A very-low-recoil, 22-caliber rimfire bullet, shot from a short-barrelled pistol and travelling pretty slowly, can kill a person if it hits in the right place. Well, it’ll kill him sooner or later, anyway. But in self-defense, which is almost always a close-range proposition, death is not enough. The person attacking you must be immediately put out of action, before he can do any damage to you at all. An attacker can be “clinically dead,” that is, heart-, lung-, gut-, or even brain-shot, and still have the momentum, strength, and ability to kill or injure you while he bleeds or chokes to death.

To Hatcher, the small-diameter bullet was something like a needle, but the large-diameter bullet seemed like a sledgehammer. A person can receive a whole lot of needles poked into his body, even though each thrust is extremely painful, and still continue to attack you and do damage. But how many sledgehammer blows could someone take, and still come up swinging? A needle shoved into exactly the right place will eventually kill, but just one peripheral sledgehammer blow, maybe only to one shoulder or to one leg, will put a person out of action as soon as it’s delivered.

We want to transfer lots of energy to the target, since it’s energy that does the attack-stopping damage. Bullet (or sledgehammer) energy equals the moving object’s mass, times its velocity squared, divided by a foot-pounds constant. Let’s simplify things by calling mass “weight,” continuing to call velocity “speed,” and giving the resulting energy in foot-pounds. So to find a bullet’s energy, multiply a bullet’s weight in grains by the bullet’s speed in feet-per-second, and then multiply that answer by the bullet’s speed again, and finally we divide that answer by the foot-pounds constant of 450,435. Whew!

A small-diameter, lightweight pistol bullet that’s travelling very fast may be carrying the same amount of energy that a large-diameter, slow-moving pistol bullet could carry. However, a small, fast-moving bullet can easily go completely through its mark, carrying its energy out with it, maybe without even leaving much disturbance behind. But it’s that disturbance, caused by a transfer of energy, which damages the attacker and instantly ends the fight.

On the other hand, a big, slow-moving pistol bullet will usually stop within its target, because it doesn’t have the speed to push its way through all that flesh and bone. Therefore it transfers most, or even all, of it energy to whatever it hits.

Even if a small bullet stops within its target, it will deliver less energy than a large one does. It weighs less, and its speed was slow (or it would’ve gone right through), so there’s less energy to deliver in the first place. Like a needle, it’s too light, and it disturbs too little meat to be effective. But the large bullet, travelling at slow speed, delivers all of its considerable power within the target, just like a sledgehammer.

Hatcher took all of the information published by Thompson and LaGarde, added his own extensive experience, and derived a formula for predicting the ability of any pistol-and-cartridge combination to effectively damage an enemy and thereby stop a fight. He called it his scale of “Relative Stopping Power” (RSP). It’s interesting that his formula still works, even on cartridges which hadn’t been invented when he derived it.

Some people feel that Hatcher’s formula is mathematically incomplete, and that it suffers from certain flaws of reasoning. But even today it is the only method which predicts with reasonable accuracy what will happen when a bullet of a certain diameter and weight, going a specific speed, meets real flesh and bone. People whose business is predicting what self-defense pistol bullets will really do, all agree that the minimum RSP which will consistently put a human being out of action is a “score” of 50 on the Hatcher Scale.

The following chart shows a partial list of pistol cartridges and their RSPs, as calculated by Hatcher, and by others who used his method.

RSP Chart (partial list)
Cartridge ——————————————————- RSP
.22 LR High-Speed (rimfire)……………………………. 3.8
.25 ACP (.25 auto)……………………………………….3.7
.32 ACP (7.65mm) ……………………..……………… 10.0
.380 ACP (9mm Kurtz)  ……………………………….. 16.2
9mm Parabellum (Luger, FMJ) ……………………….. 29.4
.38 Special (+P)  ……………………………..………… 36.3
.357 Magnum (8.375″ barrel, 1,500fps) ………………67.0
.44 Special (soft bullet) ………………………………… 60.6
.44 Magnum………………………..………………….. 160.0
.45 ACP (RN, FMJ)…….……………………………….. 60.0
.45 “Long” Colt (soft bullet) ……………………………. 73.6

(Jeff Cooper stated that improved bullet design, including revised shape and better construction, resulted in better expansion, and could improve those figures by as much as 15%.)

Note that on this chart both the .38 Special and the 9mm Parabellum rate quite low. It suggests that although they are excellent killers, they are poor stoppers. Perhaps their bullets move so fast that they’re driven all the way through a man, and don’t cause enough disruption. It may also be partly true because the 9mm Parabellum sample used a full-metal-jacket bullet that didn’t expand at all.

The .357 Magnum seems to put its bullets out at speeds which reliably cause them to expand to a large enough size to make them stop within the target. Remember, though, that bullets from shorter barrels deliver less energy. The same is true of the .44 Magnum, rated highest on this partial scale. Consider, however, that many .357 Magnum loads deliver perceived recoil greater than that of the .223 rifle round, and that the .44 Magnum recoils more than does the .30-’06.

The defensive shooter’s problem, then, is to find a cartridge which will deliver enough RSP to instantly and reliably stop a fight, but which also presents controllable recoil, and which fits a gun that’s easy to learn to use effectively and is quick into action. Like all choices, the result will be a compromise.


A Side Issue:

If you want to become an effective self-defense pistol shooter, it is very important that you consistently practice your shooting skills. To do a good job of that, it is necessary that your practice ammunition both recoils and places its hits exactly the same as does your self-defense ammunition. An extreme counter-example is that you can’t practice to shoot a .44 Magnum well by shooting .44 Special ammunition through it. You won’t have prepared yourself for possibly-painful Magnum recoil, and your practice bullets won’t hit in the same place.


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