Minimum barrel length for handgun... technical question.

[Mystery]

Looking at barrel length in handguns, most sub/compacts are between 3" to 4".
The North American Arms NAA-22S .22 Short has only 1.13" barrel.

So my question is, to be effective, what's the shortest barrel length?
I assume it has to be at least longer than the cartridge but what's the science behind barrel length?.

[Darth_Uno]

The longer the barrel, the more velocity the bullet will have as gas expands behind it before it's lost out of the open muzzle.

This isn't normally an issue for "bad breath" distance shooting, but some rounds are specifically made to perform better out of short barrels.

[Stephanie B]

Looking at barrel length in handguns, most sub/compacts are between 3" to 4".
The North American Arms NAA-22S .22 Short has only 1.13" barrel.

So my question is, to be effective, what's the shortest barrel length?
I assume it has to be at least longer than the cartridge but what's the science behind barrel length?.

Ballistics by the Inch (http://www.ballisticsbytheinch.com/index.html) is probably a good place to start. This chart (http://www.ballisticsbytheinch.com/22.html) has .22 cartridges.

In short, the longer the barrel, the faster the muzzle velocity. That's not a hard-and-fast rule, but it's a general one.

[Robinson]

It depends. :)

Some cartridges can take more advantage of a longer barrel than others. For example, a .357 Magnum really benefits from a longer barrel, whereas 9mm depends a bit less on barrel length. But even with 9mm, going down to a really short barrel will cost velocity and increase muzzle blast.

You might actually pick up some useful information by spending some time in the Ammunition sub-forum.

[peterb]

So my question is, to be effective, what's the shortest barrel length?
I assume it has to be at least longer than the cartridge but what's the science behind barrel length?.

Barrel length determines how long(time)the bullet is affected by the pressure of the expanding gases from the burning powder. Once the bullet leaves the muzzle the gas pressure drops to zero and the bullet starts to slow down.

In simple terms, a longer barrel lets the bullet accelerate for a longer time, resulting in higher muzzle velocity.

The effect tends to be greater in higher-pressure loads.

On the short extreme, no barrel at all results in very low velocities:
“ SAAMI states: “Smokeless powders must be confined to propel a projectile at high velocity. When not in a firearm, projectile velocities are extremely low.” At distances of 10 meters, bullets launched from “cooked-off” ammo would not penetrate the normal “turn-out gear” worn by fire-fighters.”
http://bulletin.accurateshooter.com/2013/11/what-happens-when-ammo-burns-saami-video-reveals-truth/

[OlongJohnson]

At some point, the pressure of the gas becomes just about equal, and then eventually less than the force required to drive the bullet down the barrel. The bullet holds steady speed and then eventually actually slows down in the barrel. Look at the numbers on BBTI for, for example, .44 Magnum. There isn't really much reason, ballistically speaking, to have a barrel longer than 14-15 inches. From there to the longest barrel lengths they tested, the results are basically random variation up and down. Although you'll save some headaches if you keep your carbine over 16 inches.

A .44 Magnum cartridge takes about as much powder as a .223, but the barrel cross section is ~3.7x as great. So for a given barrel length, that powder is expanding into ~3.7 times the volume. That's why straight wall (most pistol) cartridges need faster powders, and overbore cartridges need slower powders. A .243 Win with heavy-for-caliber bullets generally works well with the same powders that work well in a .330 Win Mag or even 7mm Rem Mag. (One asterisk on that statement is that some of the slower powders used in the big magnums have low density, so you can't really get enough of them in the little .243 case to work well.) Bigger, more overbore rifle cartridges continue to add velocity up to 28- and 30-inch barrel lengths. Longer than that, the gains are small and practicality in the field decreases rapidly.

Another good example is 9mm. A heavy-for-caliber 147gr round (less powder, lower velocity) has achieved as close as matters to all you're going to get by 6 or 8 inches, while a 115gr +P (more powder, higher velocity) can continue to gain up to carbine-length barrels.

Here's another good link, although it's focused on rifles:
http://www.sadefensejournal.com/wp/?p=1093