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Rich
2003-May-13, 09:39 PM
OK, if the title didn't get anyone's attention I don't know what to do.

My wife's grandfather mentioned this to me a couple weeks ago and I thought you all would get a kick out of it. While not strictly astronomy related it is physics, and he'd get a kick out of an actual mathematical answer (which I can't really provide).

So anyway...
My wife's grandfather was a American B-24 crewman and was shot down and interred in a POW camp early in the war. One of the raging debates the POWs held, for lack of other amusement, follows: What would happen to a bullet, from a tailgunners perspective, that was fired while an aircraft was flying a steady course at the muzzle velocity of the bullet?

The aircrews fell into three camps; one group believed the bullet would appear to fall almost straight down from the gunners perspective, another group felt the bullet would appear to slowly drop away in an arc from the muzzle, and the final group said it didn't matter what speed the plane is flying at the bullet would always appear to take a "normal" path. All defended their positions mercilessly, fisticuffs were exchanged on (rare) occasion, bets were placed but never redeemed. It seems they all took this subject quite seriously, in the most comic terms they could think of.

So, what's the right answer?

Senor Molinero
2003-May-13, 10:45 PM
It's all a matter of "frame of reference". From the POV of the tail gunner, the bullet (tracer, no doubt) would appear to fly "normally" WRT to his position. An observer on a plane flying a parallel course would observe the same. An observer on the ground would see the bullet left behind the plane and descending vertically relative to the ground.

daver
2003-May-14, 12:37 AM
The aerodynamic forces on the bullet are going to be different.

To a first approximation (B-24 flying in a vacuum) there would be no difference in bullet behavior (the bullet flies away at bullet speed, falls at g).

To a second approximation, the bullet will maintain energy better--it's not going to lose horizontal velocity to air resistance.

To a third approximation, the bullet might fall faster. I thought i read somewhere that bullets actually get a bit of lift from air flow. The bullet from the fast plane will not have this lift, and would tend to fall a bit faster. This effect is a bit more questionable.

Nanoda
2003-May-14, 09:39 AM
Put me in camp three. (Well, don't actually...) Both the above posts appear right to me.
Also, since any following fighters will be travelling as fast or faster than the bomber (I'm assuming they can still do that), they will feel the impact from said bullets with the usual force. So everybody's happy. (In a physics kinda way. I doubt those slinging bullets are having much fun).

Glom
2003-May-14, 12:00 PM
I'm glad you asked this. This is covered in one of the chapters of M4 and I have the exam next week.

(Where are subscripts when you need 'em?)

avg is the velocity of the aircraft relative to the ground and is mI, where m is muzzle speed.

bva is the velocity of the bullet relative to the aircraft and is -mI-gtēJ.

bvg = bva + avg
This is intuitive. If we know the speed of an object in a frame A and the speed with which frame A moves in frame B, the speed of the object in frame B must be the speed it has in frame A plus the latent speed it has for just being in frame A, which is the speed of frame A in B.

Therefore, bvg = -gtēJ or in other words, it proceeds to fall vertically.

The gunner would see it follow a ballistic path, while the guy in the field would see it fall vertically. Think about it. The bullet has momentum Mm realative to the ground, where M is its mass. The gun gives it an impulse of -Mm so those momenta cancel in the ground frame. But in the frame of the plane, the bullet has zero initial momentum. It is given -Mm by the gun and so moves accordingly.

Donnie B.
2003-May-15, 06:17 PM
To a first approximation (B-24 flying in a vacuum)...
Now that's a good trick!

Might as well lop off the wings and save weight, while you're at it... :P

traztx
2003-May-15, 08:28 PM
If you are on an jet traveling at 800 k/h and toss a magazine to your friend in the seat behind you...

To you both... the magazine hits him at oh... .3 m/s.

From a ground reference point, your 800kph friend just ran into a magazine that was moving at 799.9997 k/h.