The relation between temperature, ballistics and sonic booms

November 15, 2008 2:11 AM

Need to get a double-check on some extracurricular science number crunching. A friend and I were wondering about how much effect cold temperatures would have on the speed of sound, and I had the idea to see if some handgun calibers could go from subsonic to supersonic at reasonably cold temperatures. After some extensive calculations, I think I have a pretty good set of numbers, but I want to make sure I'm not wrong.

Anyway, the practical formula for the speed of sound in dry air, as given by Wikipedia (http://en.wikipedia.org/wiki/Speed_of_sound#Practical_formula_for_dry_air) is: c = 331.3*sqrt(1+T/273.15), where c is in meters per second and T is in degrees Celsius (yes, I know T is supposed to be in Kelvin but I don't have a theta key).

Working backwards from that, the equation for the temperature at which the speed of sound is a given velocity is: T = (((c/331.3)^2)-1)*273.15. Now that we have that equation, here's some of the temperatures I got for various calibers. The temperatures stated are the temperatures below which a given round is supersonic, all speeds are stolen from Wikipedia unless otherwise stated, and I tried to find the most common bullet weights.

9mmx19 NATO (military spec): 385 m/s, 95.73 degrees C
.45 ACP FMJ, 230 gr.: 250 m/s, -117.61 degrees C
.38 Special, 158 gr.: 290 m/s, -63.86 degrees C
.40 S&W, 164 gr.: 350 m/s, 31.70 degrees C
.44 Magnum, 240 gr.: 470 m/s, 276.59 degrees C
.22 LR, 40 gr.: 330 m/s, -2.14 degrees C
And just for fun: 5.56mmx45 NATO, 62 gr.: 940 m/s, 1,925.79 degrees C

The one that I find most interesting is .22 LR. I was really skeptical about how close it is to 0 degrees C, so that's why I made this post. This means at reasonable conditions, a really cold day or the inside of a walk-in freezer, a completely suppressed .22 LR pistol, firing a standard .22 LR 40 grain round, which would normally be subsonic, would actually produce a sonic boom, which would make a good deal of noise and possibly give you away. Not nearly as much as an unsuppressed gun, but more than it would otherwise. Of course, there's a few other issues, like the effects of humidity (although at these low temperatures, it might not be as much of an issue due to the air drying out from the cold), the actual volume of the sonic boom created and whether or not it would be enough to give someone away, but these are things that either require more math skills than I can rustle up at this late hour or actual testing. If these numbers check out, I might just take this over to the Mythbusters message board and put it up there for them to test the next time they decide to do a firearms special, since I don't have access to a suppressed .22 LR pistol or a freezer large enough and with an understanding enough owner to let me shoot a gun inside of it.

posted by Punkey to science & nature (5 comments total)

well at 0 degrees, the speed of sound would be 331.3, so if that bullett really travels at 330, that seems like a reasonable temperature.

A couple questions from a non-sciency guy though...

Does the gun fire warm up the air around it in a meaningful way?

Does the cold air make the bullet travel slower too?
posted by chndrcks at 7:02 AM on November 15, 2008

Sounds worth testing. If you have a firing range with indoor and outdoor targets you could try over the winter. (I know nothing about firing ranges.)

The threshold for the .40 S&W is about 90 F, a hot summer day. So that weapon would be subsonic in the heat of the day but supersonic in the evening.
posted by fantabulous timewaster at 7:23 AM on November 15, 2008

Your maths looks good to me. I know the supressors aren't hugely common on higher calibre weapons or rifles due to the pointlessness of trying to supress the gas escape sound when also using supersonic ammunition. (Though snipers can use them to disguise the sound anyway, as can hunters)

Suppressors do slow the bullet down slightly due to the reduced gas pressure so that would mean you'd have to get slightly colder to compensate for your supressed 40gr .22 LR in a cold room to get it up to supersonic.

You can also get ammunition with a smaller charge specifically designed to slow the bullet down and make it subsonic (such as 174gr 9mmx19), often intended to used in conjuction with a suppressor. Some gun clubs on the continent mandate the use of suppressors and subsonic ammunition when on the range specifically to reduce the sound pollution for neighbours of the club, and it's not at all a bad thing for your own ears either!

Note, supressors aren't nearly as good as portrayed in the films - the metallic noise of the bolt action is pretty loud still, though the lack of 'bullet crack' and reduced flash makes the gun fire less shocking and damaging to eardrums in an enclosed space.
posted by ArkhanJG at 10:38 AM on November 15, 2008

Oh, I know about the difference between movie suppressors and real suppressors, that's part of why I wanted to look at .22 LR as a test bed instead of .40 S&W. I suppose you could just make a sealed barrel that you have to screw open and closed, but as far as things that don't require custom builds, .22 LR would be the easiest to get quiet enough that you could tell the difference between the sound of the action moving and the bullet going supersonic. As far as things like suppressors slowing things down and temperature fluctuations, I'm going to add changes in air density due to altitude as well, as I think that equation is only good for sea level. Anyway, thanks for checking over my math, all.
posted by Punkey at 11:12 AM on November 15, 2008

I do quite a bit of target shooting, and there is a very large range of muzzle velocities for various types of .22 LR ammunition, some supersonic under standard-day conditions and some subsonic. It is accepted among serious target shooters that the best accuracy is achieved with ammo that is subsonic out of the barrel. The reason is that as a body slows from supersonic to subsonic, it goes through the condition known as transsonic, where the supersonic shock wave dissipates. This transsonic regime can be quite turbulent, and the turbulence can wreak havoc on accuracy.

If you do any testing, remember that once a bullet leave the barrel, it loses velocity rapidly. Even if its muzzle velocity is well into the supersonic range, it may be subsonic after only a few feet. Rifle bullets, because of their relative streamlining, will retain speed much farther from the muzzle than pistol bullets.

If your question has more to do with suppressors, there's a quirk with suppressors you should be aware of. To be effective, a suppressor needs to have a certain level of internal pressure. This pressure is usually achieved by trapping combustion gases from the first shot. Therefore, with many suppressors, the noise of the first shot is hardly suppressed at all. Kind of blows another Hollywood myth…

An interesting story on bullets and sound propogation:

I once had occasion to work adjacent to a strafing range where A-10's would make frequent passes with their 30mm gatling gun. At 3000 rounds per minute, this gun sounds almost exactly like a gas-powered chain saw, with each burst about one second (fifty rounds) in duration. We were much closer to the target than we were to the aircraft when they fired.

On each firing pass, we would actually hear the "buzz" of shots three times…twice in rapid succession, then a short pause, then the third. We knew exactly when the gun was being fired because it left a plainly-visible smoke trail. Finally we figured it out: the first two reports were the bullet stream going past us supersonic, then almost immediately impacting in the target area. Finally, after a short delay, the actual sound of the gun firing reached us. The whole effect was very bizarre.
posted by dinger at 11:33 AM on November 15, 2008 [2 favorites]