Muzzle Velocity vs. Barrel Length (Updated and bumped)

Update (10/8/2015): Go ahead and copy and use the graph I generated (the one immediately below), but please credit Ballistics by the Inch as the source of the data on which it was based.

Update (8/22/2015):

I was somewhat disappointed with the graph that I found the other day because it didn't include other common defensive pistol rounds such as .38 Special, so I decided to make my own graph, set out immediately below:

Comparison of muzzle energy for common defensive handgun calibers

As with the other graph, the data came from Ballistics by the Inch. I don't know how the author of the graph I'd used the other day assembled his data, so I will go through my method. Ballistics by the Inch published tables setting out muzzle velocity for various brands and/or loads of ammunition for given barrel lengths (ranging from 2 inches to 18 inches). The bullet weights varied among the different loads, and each obviously had different muzzle velocities. Since this graph is only intended to give a rough comparison, I simply averaged the velocity for each brand/load for the given length of barrel to give me an average velocity at that barrel length. Then I average the bullet weight for that particular caliber (which sometimes varied considerably) to arrive at an average hypothetical bullet weight. Plugging the average velocity and average bullet weight into the muzzle energy formula should provide an average muzzle energy. These were used to generate the graph above.

Some notes on the data. For the most part, the ammunition used by Ballistics by the Inch tended to be high quality (Cor Bon figured prominently) defensive ammunition. So, I would expect that the velocities are probably higher than what you could expect from less expensive "plinking" ammo. Also, some data was missing. For instance, the dip in the muzzle energy with .38 Special at the 17 and 18 inch lengths is because data was not available for one of the higher muzzle velocity rounds tested, so the average had to be calculated at those lengths without the data. Ballistics by the Inch had two different data sets for .380 (what appeared to be an "original" and a "2010"). I only used the "original" data set. The 9 mm data set included both regular 9 mm and +P loads; these I analyzed separately (and there are separate lines above in the graph). I didn't notice that any other loads were designated as +P, so all other calibers were considered together. Although I have included most of the calibers tested, I did not include those that I thought were likely to be more rare (some of the .32 revolver calibers, for instance), and the 9mm Makarov was left out because there was only a single load tested.

As I originally noted, there are some interesting groupings; and, with the additional loads considered, some additional groupings and interesting information appears.

First, at the bottom, as you can see, .22 LR and .25 ACP pretty much overlap. At a finer level of detail, the .25 was slightly better out of the extremely short barrels (2 and 3 inch), but performed slightly worse at longer barrel lengths.

.32 Auto doesn't appear on the scale of the foregoing graph to much better than .22 or .25, but there is a significant difference when viewed at a smaller scale.

Although .38 Special performs better than the .380 through most of the continuum of barrel lengths, it actually was worse at 2 inch, suggesting that a .380 would be better as a pocket pistol. From what I could tell, the .38 Special loads were standard loads, so a .38 Special +P might perform more on the level of a standard 9 mm load.

As noted below, in my original post, .45 ACP, .40 S&W, and 9mm +P form overlap, suggesting approximately equal muzzle energy and, thus, performance.

.357 Sig and 10 mm also overlap on the graph, again suggesting essentially equal performance. Unfortunately, for those who have touted the 10 mm as the equal of the .41 Magnum, that is only true at the shorter barrel lengths; and the 10 mm clearly falls behind once you get to a 5 inch barrel.

Not too surprisingly, .45 Colt and .44 Special largely mirror each other's performance. It is notable, though, the appreciable increase in performance from longer barrels, confirming that these are both cartridges well suited for shooting from a carbine.

The final overlapping grouping, and one that frankly surprised me, are the lines for .357 Magnum, .41 Magnum, and .44 Magnum. At least with the defensive loads tested by Ballistics by the Inch, the performance of these three cartridges was nearly identical (the .357 consistently running just slightly less muzzle energy than the other two calibers), and followed the same trajectory of increased performance from longer barrels; again, pointing out that these are great cartridges for use in a carbine. More shocking to me, though, was that the .41 Magnum outperformed the .44 Magnum! Again, these are factory defensive loads, so it is possible that hunting loads or handloads would be very different.


Original Post (8/20/2015):

Barrels by the Inch has done everyone a great service over the years compiling data on velocity and energy for given barrel lengths. In addition to the web-site, they also run a blog; and I was taking a look at a graph on the muzzle energy of common defensive pistol rounds:

If you can't see it very well, use this link.

There is some interesting information from this. First, the top line is from a .357 Magnum. It clearly is the round that benefits the most from being shot out of a carbine length barrel. It also suffers the most from being fired from a short (snub) barrel. In fact, the .357 Magnum doesn't really come into its own until you start using a at least a 4 inch barrel. So, there is no point in carrying a short-barreled or snub-nosed revolver in .357 Mag.

The bottom line is the .380 ACP, which registers very little change between a short barrel and a carbine. Thus, if you are shooting .380 ACP, there is no point in getting anything with a longer barrel.

The next line up is for the standard 9 mm. As you see, by the time you get down to carrying a "mouse gun" with a 2-inch barrel, the muzzle energy of the .357 Mag. is no more than a 9 mm (and probably less in reality, because you will have to contend with the loss of energy due to the cylinder gap).

The next group of lines (the gray, light green, and aqua) is one of the most interesting of all because those lines represent the muzzle energy of 9mm+p, .40 S&W, and .45 ACP, respectively. As you can see, the three lines overlap each other along the entire continuum. Meaning, there is no advantage to using .40 S&W over .45 ACP or 9mm +p. If you are going to beat the frame to death with hot loads, you might as well have the round advantage offered by the 9 mm.

The next two lines are also interesting because they are also nearly identical, and they are for the .357 Sig and 10 mm respectively. 

As a final observation, with the exception of the .357 Mag., muzzle energy on all these pistol rounds appear to pretty much max out at around 13 inches; and there is little incremental increase in performance past 5 inches.