How many feet per second is the speed of sound?

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grimjaw

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I'm trying to do some guestimations on rimfire ammunition at longer ranges (150-200 yards). I've heard anecdotal evidence that if a projectile moving a supersonic speed falls to subsonic speed, especially if it the fall is rapid, it has an affect on trajectory. I don't know if that is true, maybe someone will come along and enlighten me.

I read up a little bit on the speed of sound, and I understand that it changes depending on medium pressure (?) and thus decreases with altitude in air. 761 mph is the speed of sound at sea level, but at 11000+ feet, it's 660 mph. I'm using the 761 mph number to do my math.

761 miles = 4018080 feet
1 hour = 3600 seconds

Speed of sound at sea level = ~1116.13 feet per second

Are those correct calculations?

jmm
 
Sure. :)

Speed of sound is dependent on a bunch of other variables like temperature and humidity, but ~340m/s is a good number for napkin math.

Allowing for .3048 m/ft, that comes out to 1115ft/s.
 
I recently spent some time working up a subsonic load for the AR15.
I found that last week, with a temperature about 110 degrees, in Las Vegas, I started getting a supersonic crack at around 1140 fps. This isn't a solid number but right now, here, it is very close.
 
There is no exact answer. The speed of sound is not fixed. It varies based on atmospheric conditions (temp, air pressure, humidity).
 
I recently spent some time working up a subsonic load for the AR15.
I found that last week, with a temperature about 110 degrees, in Las Vegas, I started getting a supersonic crack at around 1140 fps. This isn't a solid number but right now, here, it is very close.
Click to expand...
Wow! I didn't know you could download a .223 to subsonic velocities considering it's usually smoking at about 3000fps. That's cool to know. How does it shoot with those loads?
 
its around 1100 f/s, it will vary a bit depending on atmospheric conditions like temp and humidut, but its not a wild variation.

the reason you want a supersonic bullet ot stay supersonic is to keep it from passing through the shock wave. a supersonic projectile has a shock wave traveling BEHIND it. if the bullet slows down to subsonic velocities it passes through the shockwave which can alter its course slightly.
 
The speed of sound does NOT vary with pressure. It is independent of pressure. It does vary with temperature. http://en.wikipedia.org/wiki/Speed_of_sound I know this from freshman aerodynamics class five years ago.

The difference between winter and summer, or night and day, will be more than the difference between florida and colorado.

In addition to that, the air passing over the bullet may exceed mach 1 even if the bullet is travelling well under that speed. This means a semiwadcutter can have a supersonic crack at much lower speeds than a streamlined bullet. Keep that in mind when you develop subsonic loads.
 
trapperjohn, thanks for the explanation. That is what I was trying to avoid. The ballistics tables I've seen for .22WMR show that for 40gr projectiles you'll be hitting ~1100fps somewhere between 150-200 yards. I don't have a place that I can set up 200 yard paper targets, so it's hard for me to see just what kind of accuracy hit I'll take from that "shock wave", if any.

prophet, thanks for the correction and info.

jmm
 
In addition to that, the air passing over the bullet may exceed mach 1 even if the bullet is travelling well under that speed. This means a semiwadcutter can have a supersonic crack at much lower speeds than a streamlined bullet. Keep that in mind when you develop subsonic loads.
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Nitpick. :p
 
The problem is the transonic barrier, when the projectile drops from super to subsonic, there is a lot of buffeting on the projectile, not exactly a good thing for accurcay because the buffeting is not uniform, every porjectile is differnt.
 
What about through other mediums, i.e. liquid and solid? And combinations of them? Say, tomato soup versus chili? :o :p

For that matter, what about different gases? Is it different for hydrogen and xenon?

What exactly causes sonic booms and cracks? Is it something along the lines of supercavitation of the medium itself?

:confused:
 
Somewhere back in my old computer code I have the formula for calculating the speed of sound (Mach). IIRC it is dependent on several variables including altitude (air pressure). Probably it was a multi-step computation, you first have to compute air pressure based on altitude ASL and then use that as an input.

I could go look it up if someone really really needs to know the exact formula.
 
the naked prophet said:
The speed of sound does NOT vary with pressure. It is independent of pressure. It does vary with temperature. http://en.wikipedia.org/wiki/Speed_of_sound I know this from freshman aerodynamics class five years ago.
Click to expand...

If you want to really get technical, the "only vary with temperature thing" depends on air being an ideal gas, which it isn't. Not that that fact makes a significant difference.
 
For most considerations, air at atmospheric pressure (or even a few atmospheres) is close enough to an ideal gas for most approximations. Considering the accuracy and consistency of our chronographs and loads, +/- 10 fps is way more than the error you get from approximating air as an ideal gas.

The reason that the speed of sound varies with altitude is that the temperature varies with altitude. This website explains it pretty well, with a simple, correct equation. Although that wikipedia page is technically correct, it isn't the formula that I learned in school, and any joker can change it at any time. If you really want to be sure, get an aerospace book. I've got a few for sale ;)
 
Ken - I imagine the source grimjaw is referring to used the term 'medium' to mean the substance through which the sound is traveling.

That source would be incorrect as the naked prophet points out since pressure is proportional to density in an ideal gas and that ratio is therefore a constant, not a variable, in determining the SOS.

Although, strictly speaking, that is not true. Considering an ideal gas only, if you take pressure to the extreme, say 0 force units/area, then the SOS is 0 because 0 pressure implies no medium for the sound to travel through. So saying the SOS does not vary with pressure is not entirely accurate. But for the purposes as used here, it is.
 
A lot of .22LR ammo comes out of the barrel very close to the speed of sound, so temps will for sure make the difference one way or the other. If you are firing a suppressed .22, this really comes into play, and you can literally hear the difference on a cold day that warms up. The difference firing a suppressed .22LR that is subsonic and crack-less is quite striking.
 
"Wow! I didn't know you could download a .223 to subsonic velocities considering it's usually smoking at about 3000fps. That's cool to know. How does it shoot with those loads?"

Why couldn't you ?
It shoots great, out to about 75 yards. The wind really played havoc with them at 100 yards. At 50 you could cover the group with a dime easily.
The discussion of working up this load can be found in the ammo/terminal effects section of the www.silencertests.com forum.
The load is a 77 grain Sierra Match King boatail hollow point and IMR Trail Boss powder loaded to just below the speed of sound.
With the suppressor, the report is Hollywood quiet.
If you go to that forum, you will see that my next project is a 100 grain bullet, subsonic.
 
I can also suggest anyone bored enough that wants to learn more can look for books, scientific journal entries, and tech papers dealing with light-gas guns (LGG's) as it is a fundamental of their design (driving force of a dyanamic light atomic gas accelerating a projectile into a hard vacuum environment for velocities upwards of 4-5 miles per second (21000fps+)).

There are some reprints that are available but a tad math intensive. In general discussions like this that don't require designing canard wings or ramjets so I think ideal formulas can be presented, and used to get reasonable approximations as it eliminates the added complexities of taking every little variable and fudge factor into account.
 
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