Projectiles, Kinetic/Muzzle Energy and Stopping Power

When bad guys are shot in Hollywood movies, they fly backward from the force of the shot and are immediately disabled. You can see an example in this clip from Dirty Harry at about 45 seconds in:

That’s not really what happens. Here’s a video that shows various animals shot by hunters. Some of them drop immediately, while others run away.

The video is about “impact shots”. Presumably that means they’re good hits. So if a 200-pound animal doesn’t automatically go right down after being hit with a good shot from a hunting rifle, what does that mean when a homeowner shoots a 200-pound man invading her home with a pistol, or the demonized AR-15?

Many people think of the AR-15 as a powerful rifle. But the AR-15 is actually less powerful than most hunting rifles used for animals like deer. For starters think about what a gun does – it pushes a projectile – a bullet of a certain mass or weight – at a high rate of speed (velocity) at its target. Guns and ammunition vary in the mass (usually measured in grains) and velocity of the projectile (usually measured in feet per second or meters per second).

Think of other projectiles we’re used to seeing in sports, such as baseballs, golf balls, and hockey pucks.

A baseball weighs a little over 5 ounces, or about 145 grams. A 100 mph fastball travels at 147 feet per second, or 44 meters per second. The formula for kinetic energy is ½ mv². So the formula is ½ times 0.145 kilograms times the square of 44 meters per second. This works out to 140 joules.

Here is baseball player Andrew McCutchen being hit by a 100 mph fastball:

That, it turns out, is only a little less energy than a shot from a 22 caliber rifle. The .22LR bullet weighs about 3 grams (a tenth of an ounce) and has a muzzle velocity of 335 meters per second (about 750 mph) which works out to 168 joules.

Of course a bullet impact will have a very different effect. The baseball did not deliver all of its energy to McCutchen – the ball retained some kinetic energy as it bounced off. A baseball will generally not penetrate into the body. A bullet will usually penetrate (but not always) and do internal damage. But the bullet can also go right through, taking some of its kinetic energy with it. Do a YouTube search for “ballistic gelatin” and you will see many videos showing what various bullets can do.

Nevertheless, the point is that a 100 mph fastball didn’t even seem to faze Andrew McCutchen. When people say that no one needs a powerful gun, or one that can shoot more than 7 rounds without reloading, this is what they’re missing. The goal is to take down the assailant, and a couple rounds from a .22LR is not very likely to get the job done. It doesn’t have stopping power. And what if there are more bad guys?

Other examples of sports projectiles include:

A Tiger Woods drive, 46 grams at 180 mph for a total of about 150 joules, like a fastball;
A Pujols home run, which leaves his bat at 120 mph with 200 joules of kinetic energy.
A hockey puck, weighing 165 grams going 120 mph, with 240 joules.

Any fan has seen players hit by these projectiles. Sometimes they go down, but often they do not.

Here’s a chart with some common sports projectiles and bullets, and please note that these are rough numbers. For firearms there’s a great ballistics calculator from Winchester.

With not much more energy than the hockey puck, a .380 pistol fires a 6 gram bullet at 640 mph, with 245 joules. This is a fairly popular caliber of handgun, especially for small handguns. Anyone who has watched a fair bit of hockey has seen a player hit with a hard shot without being seriously injured.

Taking it a step up, the 9mm bullet weighs about 7.5 grams and leaves the muzzle at about 800 mph for muzzle energy of 467 joules, or about twice as much as a well hit hockey puck. There is plenty of criticism out there that even the 9mm is underpowered and lacks stopping power.

See: Man survives 9mm head shot – Firearm Blog. More on that story here: Daniel Tice – Cleveland blog. And here: Bullet bounces off head – Akron Beacon Journal. As an aside, notice that a SWAT sniper’s AR-15 jammed during this event.

Gun controllers think that firing one bullet should be more than enough to resolve any conflict. This is unrealistic. The next link has a discussion of stopping power (and read the comments at bottom of that article too).

One key point here is that the AR-15 has far less muzzle energy than typical hunting rifles like the .308, less than half of the 30-06, and about a third of the energy of a shotgun blast. So a shotgun fired half as fast as an AR-15 will do more damage.

The AR-15′s .223 bullet is very light. Its strength is velocity. Despite the mass shootings where they have been used at close range, their real strength is not close quarters but shooting distant targets, especially in target shooting competitions. Because of its high velocity, it is affected less by wind and gravity. You can see in the graphic below that the lower velocity 7.62×39 bullet (yellow – used by the AK-47 and a number of other rifles) falls more quickly and is pushed further to the right by a crosswind than the AR-15′s .223 round (red).

Now consider the kinetic energy remaining in the bullet at distance – the first chart is for the .223 round from an AR-15, and the second is from a 7.62×39 (AK-47):

At 300 yards, the bullets have lost more than half its energy. At 500 yards they have less than a quarter of the energy they had when leaving the muzzle, and not much more than a hockey puck. Keep in mind that the goal is to take down the target. Since one round may not have adequate stopping power, especially at a distance, and since the shooter does not always hit his or her target, being able to fire multiple rounds is important. And there may also be more than one bad guy.

A person may be using a rifle for lawful and appropriate purposes, such as hunting or self-defense in a WROL situation (like the aftermath of Hurricane Katrina or the Korean merchants in the Rodney King riots). If someone is attacking you and you can shoot them from 300 yards away, that’s a lot better than waiting until they’re close enough to hurt you. And a single shot from an AR-15, or even 5 shots, may not be enough to stop the bad guy at such a distance. So having a 30-round magazine is appropriate in such situations.

Which might explain why our soldiers and law enforcement carry 30-round magazines on their rifles. They think it’s necessary and appropriate. If it is for them, it can also be so for civilians.

As an aside, here’s a great and odd video showing various calibers and ammo types.