Twack! Boom! What distance?


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4v50 Gary
January 21, 2004, 09:49 PM
Was reading an account from the Civil War. A fellow is seated heating his coffee. The Col. looks and him and is aghast when the fellow falls face down into the fire. He then hears the boom and feels that the distance was 3/4 of a mile.

The caliber or make of the weapon is unknown.

Can anybody figure out the distance?

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Badger Arms
January 21, 2004, 10:21 PM
No. Sound travels at a known velocity of about 1100fps. Therefore, if one can measure the time between the shot leaving the gun, and hitting its target, one can come to a reasonable assumption. Of course, you have to figure in flight time of the bullet because the bullet will be in the air and slowing down with the sound wave close on its heels. For a 3/4 mile shot with an initial velocity of 1600fps, I would assume that the bullet and sound wave would arrive nearly simultaneously. The sound wave would overtake the bullet in flight. Measuring this by ear is impossible. Sure, maybe within plus or minus one mile you could guess then you'd surely be right!

This presumes several things. First, you have to know the initial velocity of the bullet as well as it's time of flight. For that, you'll need to know the Ballistic Coeficient of the bullet. Also, you must know that the sound you are hearing is indeed the shot and not an echo or sonic boom. I'd assume that the reporting party did not know the velocity or BC of the bullet but might have known the lightning trick.

With Lightning, you can measure distance because the first cue is visual. You SEE the bolt and can therefore begin to count. When you hear the thunder, just multiply the number of seconds by 1100 feet and you're there. The same does NOT apply to bullets, but can apply to muzzle flash!

Bottom line, he was wrong.

4v50 Gary
January 21, 2004, 10:24 PM
Thanks Badger Arms.

I was leery of the account when I read it too. Another factor to consider is air density and acoustic shadow. Forgot which battle it was, but it couldn't be heard by friendly forces that was a few miles away yet it could be heard distinctly by other forces 50 miles away.

redneck
January 21, 2004, 10:34 PM
3/4 of a mile....duh....why would I argue with the guy that was there :neener:


Speed of sound is roughly 1100 feet per second. So if you know how long it was between the thunk and the bang, and you take some liberties with assuming the projectile and its initial velocity, its not too hard.

You know how far the bullet was ahead of the sound. I'd have to say that since it was probably a maxi ball it probably started out at about 1500 fps, and if we figure that its speed at best is reduced by 1/3 every second.
A little calculus says that it would have to travel 33 miles at those rates for the sound to overtake the bullet. So it very well could have been a LONG way.
If you know the difference you can figure it out pretty quick.

Redlg155
January 21, 2004, 10:47 PM
I'd have to say that since it was probably a maxi ball it probably started out at about 1500 fps, and if we figure that its speed at best is reduced by 1/3 every second. A little calculus says that it would have to travel 33 miles at those rates for the sound to overtake the bullet. So it very well could have been a LONG way.


You lost me on that one. I'm no mathematician, but looking at the ballistic calculator on Handloads.com (http://www.handloads.com/calc/) ,
a lyman .58 cal 460grain minnie ball travelling at 1500 fps would only be travelling at 1212 fps at 100 yards. At 160 yards we are looking at 1095 fps, less than the speed of sound. I entered 35 Degrees F as the temperature.

Good Shooting
Red

redneck
January 21, 2004, 10:52 PM
Thought about it a little more, we know (OK Gary knows ;) ) which guns were most commonly used back then. We know it was black powder so there is going to be a definite upper limit to what the initial velocity would have been probably 2000. And you can figure maybe 1400 fps as the lower limit maybe, for the proposed group of rifles ?
They all would have about the same ballistic coefficient, so really all you need to know is the time interval between splat and pow and you can figure out some fairly reasonable limits for what the distance would have been. Given roughly the same ballistic coefficients and the fairly narrow range of velocities the range for the distance might not even be that big.

4v50 Gary
January 21, 2004, 10:58 PM
The trouble is that there were no standards when it came to heavy scoped target rifles. Each was a custom gun of different caliber that had a special bullet mold, sizer, paper patch cutter that was tailored for that gun. They all took a certain powder charge too that made it unique from any other gun.

redneck
January 21, 2004, 11:00 PM
Red I was going by time
Figured its velocity would decrease by 1/3 every second.
So if you integrate the velocity : 1500-(1500X1/3T) = 1500T-(5/2)T^2.
Integrate the velocity for the speed of sound to get its displacement 1100=1100T , and set them equal and you get roughly 160 seconds before the sound has travelled the same distance as the projectile (not theoretically possibly due to gravity, bullet would never be airborn for 160 seconds so its safe to say that sound would never overtake the projectile,with the numbers I used)
I don't think I was too accurate with my guessing, but you see how I was figuring things.
I don't think the problem is too far fetched. But then I did spend the whole day studying for a midterm in differential equations and boundary problems and my brains a little fried. Most soldiers back in the civil war probably weren't tortured with 5 quarters of calculus (good lord do I hate math now!) so the fella who saw it happen probably didn't have a chance in hell of guessing how far it really was. I've got a graphing calculator too, which probably doesn't tip the odds anymore in the soldiers favor ;)

Mal H
January 21, 2004, 11:01 PM
The answer to that one is very simple and Badger Arms got it correct in the very first word of his reply.

Too many variables and the values of all of them are unknown.

Joe Demko
January 21, 2004, 11:02 PM
Was it necesarily such a sophisticated gun? At 3/4 of a mile how would the survivor have had any idea what kind of gun it was? Can't discount the possiblity of lucky or random shot from a plain vanilla musket, IMO.

redneck
January 21, 2004, 11:26 PM
I think I misunderstood the question at first. I thought you were asking if it was possible for any of us to figure it out, not if it was possible for someone then to figure it out.
Like I said, I think today we could make a pretty good guess. Back then, I'd say there was no way in hell.

I made a mistake in that equation I put up there too, the velocity would be an exponential decay problem so I set that up wrong. I don't care, I'm going to bed now, math sucks :D

4v50 Gary
January 21, 2004, 11:29 PM
I'm going to bed now, math sucks

Exactly why I tossed the question out here to the forum. :D

Dave R
January 22, 2004, 12:07 AM
Were there any rifles in the Civil War era that shot much faster than 1100fps? I'm not aware of any.

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