# Muzzle Energy And Ballistics

**Jul 21, 2017**

There will always be an argument about which caliber is the best choice for self-defense. This is where the phrase "stopping power" is vaguely thrown around — two words that the FBI has labeled a myth.

But how does muzzle energy, the kinetic energy of a bullet when it leaves a firearm, factor into this? And how is this relevant and useful to the everyday civilian open or concealed carrier?

Well, as it turns out, muzzle energy is just a single iota of a sum total of variables that determine whether or not a lethal threat will be stopped in its tracks, and in handguns these variables have been studied since the late 1800s in relative stopping power equations.

The average-Joe gun owner can use this information to make key decisions about handguns and ammunition to balance caliber choice (9mm versus .45 ACP versus .40 S&W) against other related factors such as recoil, both perceived and actual, and the ability to place shots effectively.

**What Is Stopping Power?**

So, a common issue with stopping power is misidentifying what it actually is in terms of terminating deadly threats.

An accurate way of describing it is the sum force and factors needed to remove the lethal threat's ability to continue assaulting, or attempting to assault, the individual. There are varying definitions though.

Killing power, on the other hand, is the ability of a weapon to kill — pretty straightforward on that one. Thus, a .22 LR round has the same killing power as a .45 ACP bullet if shot through a major artery.

A threat can still initiate contact or fire more rounds under those circumstances until bleeding out, but stopping power, well, that's another story. But it's a term that is largely subjective.

The FBI has changed calibers a few times over the past three decades, most recently to the 9mm Luger, based on factors related to the term stopping power.

But, the ability for "stopping power" to be quantified has been studied in the field of ballistics, particularly terminal ballistics, which concerns the interaction between the bullet and its target.

Now, let's nerd out for a minute.

### Why Is Bullet Stopping Power Debated? Can It Be Measured?

There are formulas for handguns that have been used to quantify relative stopping power based on a series of variables like bullet weight, area, velocity, energy, type, composition and recoil.

Rewind 90 years.

Major Julian S. Hatcher, an officer in charge at the Small Arms Ammunition Department within the Frankford Arsenal, wrote a book titled Pistols and Revolvers and Their Use, and in it there was a formula for relative stopping power: RSP = E x A x y where E is kinetic energy at the muzzle, A is the cross-sectional area of the projectile measured in square inches and y is the shape factor, which ascribed extra value to square-nosed bullets and less value to round-nosed jacketed slugs.

This was in 1927, but Hatcher admitted that he assigned too much value to velocity, based on the idea that energy is a function of the square of velocity, according to Pistols, Revolvers and Ammunition by Michel Josserand and Jan Stevenson (we'll get to them in a moment).

So, Hatcher rewrote his formula in 1934 to: RSP = (M) x (V) x (A) x (Y) where M is mass, V is velocity, A is cross-sectional area or frontal surface and Y is the shape factor. The focus of this was transitioned to momentum, giving it a 1 to 1 ratio with velocity.

Josserand and Stevenson described the formula as a middle ground between American and British ideas of stopping power.

"This can be considered a prudent middle road, since the British have always put more stock in the mass of a bullet than in its velocity, and indeed have felt that for optimum effectiveness against human targets, the velocity should be kept as low as possible while still retaining acceptable range and trajectory," according to their book.

The cross-sectional area of the bullet is what people most often talk about and what the FBI weighed heavily after the 1986 Miami shooting that resulted in the death of their agents.

They searched for a larger caliber, which is the easiest way to increase stopping power. The weight and velocity of a bullet can theoretically stay the same, but if diameter is broadened then relative stopping power is quantifiably more effective.

The issue though, according to Josserand, with the Hatcher formula is bullet expansion — the modern hollow point, a lighter bullet with a higher velocity that is diminished in the formula.

"Yet it is precisely the low mass and high velocity which permit the bullet almost to double its diameter (hence quadruple its cross-sectional area) within the target," according to Josserand.

Josserand was a French physicist and mathematician who invented the Josserand Energy Delivery Index (JEDI, which is a nice acronym because it does use "the force" of a bullet).

As shown in the chart, he created a standardized formula for the energy transfer in various calibers.

Take that information as you will.

Well, that's all fine, but if you miss the target, all that math is useless.

### Bullet Penetration

Factoring penetration into the equation is another requirement, depending on the surface impacted (a bare human ribcage is different than a ribcage wrapped in ballistic nylon and kevlar). Matter, therefore, will have different rates of penetration on impact dependent only partially on the projectile.

Hatcher considered an equation for relative penetration as well: P = E / RA where E is the kinetic energy of the bullet on impact, A is the cross-sectional area of the projectile and R is the resistance of the target. The resulting value of P can be weighed against other calibers.

Depth of penetration will weigh into stopping power, and certainly affects law enforcement tests.

And all of this partially explains the issue of weighing and assigning meaning to the term "stopping power." It's a combination of subjective factors that are impacted by perception and obfuscated by differences in types and qualities of ammunition from different manufacturers.

It can't be a universal constant because situations change, targets change, calibers change, firearms change, ammunition changes and ultimately lethal encounters are rarely as neat and controlled as lawful shooters can hope for.

So, to answer the original question "is muzzle energy a useful metric for stopping power;" no. It's not. At least not by itself.

A better metric for stopping power is a well-placed placed shot. The capabilities of that shot, and all the factors that affect it, are where arguments for and against stopping power get lost in details.

Want to know more about your carry ammo? Bigfoot's got you covered!

Jake Smith (@notjakesmith) is a copywriter and photographer based in the Pacific Northwest who enjoys shooting pictures and ammunition outdoors. |