Do we look at velocity or energy? I am looking at the specs for .357 sig and 10 mm auto on wikipedia.

The Hatcher Formula The Hatcher Formula is an attempt to mathematically evaluate the approximate effectiveness of pistol ammunition at incapacitating a person. Developed by Gen. Julian Hatcher in the 1930's, it uses the bullet momentum, frontal area, velocity, and a 'form factor.' The formula is: RSP = M * A * F Where RSP = Relative Stopping Power Index, M = Momentum of the bullet in foot pounds, A = Area of the bullet in square inches, F = Form factor derived from his observations with some additions for later bullet types. http://www.abaris.net/info/ballistics/hatcher-table.htm

The following article sort of rambles on and is pretty long, but it will raise some questions in your mind that you'll want to consider as you further ponder your original question. http://www.gunthorp.com/Terminal%20Ballistics%20as%20viewed%20in%20a%20morgue.htm This article was previously posted in another thread on this Forum.

The truth is that no handgun round has reliable stopping power, without a CNS hit. Rifles are a bit different, as Roy Weatherby learned shooting hundreds of head of cattle in carefully controlled experiments. Velocity was the deciding factor, but in order for the velocity to become the deciding, it had to exceed 2650-2700 FPS in order to generate hydrostatic shock. Those of us old enough to remember the Russian-Afghanistan war, remember the Afghans complaining to the U.N. that the Russians were using "poison" bullets. That was when the Soviet Union switched from the large, heavy 7.62X39 in the AK-47 to the light, fast 5.45X39 in the AK74. The increase in lethality of the smaller, higher velocity round was very dramatic. In reality, momentum is a meaningless figure, since it gives equal weighting to mass and velocity, rather than factoring in the square of the velocity. (energy). Even energy has little effect compared to velocity.

I like Taylor Knock Out or TKO TKO = Bullet Mass (gr) x Expanded Bullet Diameter (in) x Terminal Velocity (fps) / 7000 or momentum x expanded diameter Taylor first described this measure of stopping power in his classic work "African Rifles and Cartridges." Taylor referred to number generated by the equation as the "Knock Out Value" or "Strike Energy." Common practice today is to refer to this value as the "Taylor KO factor" or simply "Taylor KO." The TKO has no physical meaning and is strictly used as a figure of merit for comparing cartridges. Its main advantage is the ability to attempt to represent complex terminal ballistics as a number; specifically momentum x expanded diameter. This can be utilized to assign different wounding capabilities to projectiles. It does have good general correlation. For example, the TKO of a .22Mag is about 2, a .38Spcl about 6, a .357 about 10, the 10mm, .44Spcl and .45acp all about 13, a .44Mag 17 and a .454Casull at least 30. Clearly the TKOs are, at least loosely, tracking stopping power. You can't really say that about energy because a .22Mag produces more energy than a .380acp AND a .38Spcl. Momentum works a little better but still has problems: .22Mags and .380acps have about the same momentum and some .38Spcl+Ps have more momentum than .357Mags.

I suspect not, just that momentum is not an entirely meaningful estimate of stopping power (it's also not meaningless, just imperfect).

It's not that the 5.45x39s were more lethal than the 7.2x39, it's that the foot soldiers can carry far more rounds and the guns can put more bullets in the air. Same logic why the US switched away from the 30-06 in WWII to the .223 -- no one can reasonably argue that a .223 is more lethal than a 30-06, but the combined ammo carrying capacity and rounds-in-the-air seem to be. As to the physics, momentum is imperfect but it's certainly not meaningless. And "even energy has little effect compared to velocity" ignores the math. Energy is just velocity squared x mass, so for any given bullet energy and mass are interchangeable. As are momentum and velocity. Velocity is no more inherently useful than energy or momentum; all are just mathematical representations of the physics. If a bullet has sufficient velocity for penetration and expansion, then its not at all clear that more velocity is of any benefit. The same cannot be argued bout increasing weight (momentum and energy) and diameter (TKO). If you take the velocity argument to it's logical extreme, a 1 gr .17 bullet going 10,000 fps would be the ultimate round. Unfortunately that would produce a trivial wound channel, delivering only 0.2 ft-lbs of energy, and would be easily stopped by even light clothing.

Newton wasn't wrong, but attempting to apply his laws thandguns is. According to newton's third, if the hanfgun has adequate momentun to "knock a man down", it would also knock the shooter down.

Look up Roy Weatherby's tests. (You know- Weatherby rifles??) Increasing momentum has no effect. Increasing frontal area will have a very small effect. Increasing velocity has an enormous effect if that velocity is beyoong 2650 FPS. And the 5.45X39 is enormously more efective, bullet for bullet than the 7.62X39. It's not putting more bullets in the air, it's increasing the velocity that makes the difference. Google "Hydrostatic shock" sometime.