Bullets falling back to earth

About a year ago there was a thread on how far a bullet would travel. Someone, Mike Graham IIRC, posted the balistics for a 22 long rifle bullet. Since I still had that data on file, I ran it through my balistics program for a near vertical shot. Here are the results:

----- Given the velocity of a 22lr bullet at the muzzle and 100 yards as

1280 1017 fps respectively, I convert to metric and get 390.14m/s and 309.98m/s at muzzle and 91.44m. From these values, I calculate the drag coefficient, km (dV/V per meter), of .002515. Using this result and the muzzzle velocity, V0, I can calculate the point, x1, at which the upward velocity is 0 and the point, x2, at which the bullet has returned to the level of the muzzle. Thus, assuming an 85 degree angle of elevation, x1= 86.4 x2= 133.7 The positions, velocities and times at the muzzle, x1 and x2 are then Show_flight V0 km 85 Bflight 0 x1 x2 x y Vx Vy t 0 0 34 389 0 86 729 5 0 9 134 0 1 ²61 25 Summarizing, the bullet reaches a maximum height of ~730meters where its horizontal velocity has dropped from 34m/s to only 5m/s. Back at the initial height, the horizontal velocity is now 1m/s, it took almost twice as long to come down as it did to go up and its velocity is less than 1/6 of its muzzle velocity. Due to the complexity of the math in getting these results, the high school physics approach to this problem ignores air friction, i.e. sets km=0. If we do this, we get x1= 1348.5 x2= 2697.1 Show_flight V0 0 85 Bflight 0 x1 x2 x y Vx Vy t 0 0 34 389 0 1349 7707 34 0 40 2697 0 34 ²389 79 Note that this simplified approach gives a maximum altitude over ten times too high. Also note that without air resistance, the horizontal velocity would remain constant, the bullet would take the same time to come down as to go up and would be travelling at its muzzle velocity when it got back down. Although the "no air resistance" approach is a good introduction to some of the concepts involved, it is not adequate to solve balistics problems in the "real world".

On Wed, 17 Dec 2003 12:28:47 -0500, Jeff Wisnia brought forth from the murky depths:

No, he was just a bit senile, not Alzheimy.

P.S: You don't need to REPLY ALL when you reply, just send your replies to the newsgroup. Most of us are smart enough to need only one copy to comprehend it.

-- Remember: Every silver lining has a cloud. ----

Comprehensive Website Development

Can the New Jersey shoot straight up?

---------------------------

Idiots. You work it green - my whole city used to be plumbed with wooden pipes, drilled in this manner. A few of them still get dug up occasionally. Any half-competent green woodworker can show them how to do it (do it green, go down the pith)

-- Smert' spamionam

Well, if the gun's stabilization was turned off and the gun was aimed to as high an angle as possible and the ship was wallowing in a heavy, beam-on, sea and the guy on the trigger was really good then, maybe.

But then, down below in the shop, the lathe would NOT be level! [The Horror.....]

Firing a 16" at that much roll? Wouldn't that present a serious danger of getting said lathe wet? Along with everything else?

On Thu, 18 Dec 2003 01:31:05 GMT, Doug Smith brought forth from the murky depths:

ROTFLMAO! I would imagine the Mess to be more of a mess, too.

-- Remember: Every silver lining has a cloud. ----

Comprehensive Website Development

> Embedded software/hardware/analog Info for designers:

I guess then, it couldn't do a lot of damage. Maybe only kill you.

STeve

I saw this discussion quite a while back in a gun newsgroup. People said it was impossible, but I have read stories of it, one while I lived in New Orleans, and the lady struck by the falling bullet died.

I guess, as Mr. George Cawthorn stated, you don't have to get overboard about the amount of damage a falling bullet can do. It can kill you, but probably wouldn't go through your roof or your car fender.

Steve

I think it can launch cruise missiles at a high angle, and some of the smallest guns might shoot straight up, but the 16-inch guns have a maximum elevation of 45º. I have a photo of a cutaway diagram of the New Jersey's

16-inch guns, that at one point says, "Guns can be inclined individually from -5 degrees to 45 degrees, at a rate of 12-degrees per second." There are 3 turrets with 3 guns each, 1700 tons rotating weight per turret, and basic rounds are either 2700-pound AP or 1900-pound HC. Minimum crew size is 77 men per turret and fire rate is two rounds per minute per gun. The maximum range of an HC round is "41622 yards when fired with the normal propelling charge of 660 pounds, with a muzzle velocity of 2690 feet per second".

-jiw

Right, but normal firing conditions are worst case. That's because the axis of rotation diverges from the line of flight (normal bullet path is a parabola). This divergence allows aerodynamic forces to disturb the gyroscopic action, causing the bullet to nutate around the line of flight. This saps rotational energy, and causes the bullet spin to slow faster than if the forces were aligned.

A bullet fired vertically *does* have all forces aligned. The line of flight does line up with the spin axis. So the bullet loses rotational energy much slower than when fired horizontally. Add to that the bullet doesn't have to spin as rapidly to maintain stability when the bullet is moving slowly (because the disturbing aerodynamic forces are less). So a vertically fired bullet has the best chance of maintaining gyroscopic stability.

That's probably true, but a tumbling bullet isn't as aerodynamically clean as one falling base or point first. So if stability isn't maintained, terminal velocity will be even lower.

Gary

But we are finely tuned enough to notice the results of non-zero accelerations. The integral of vt dv/dt is distance traveled in a given amount of time. When that distance is zero, as it is when we're sitting on a chair, then dv/dt must also be zero. In other words, in a static system, acceleration must be zero.

Gary

Another factor is the time of flight. Under "normal" firing conditions, fired at, say, a 1000 yd. target, the .30 cal. bullet only has to retain sufficient angular momentum for less than 2 seconds. When fired straight up, the time increases to over 60 seconds.

Also the .30 caliber bullet fired straight up will be traveling in the trans and subsonic range of speeds for a portion of it's flight, whereas the 1000 yd bullet won't.

R, Tom Q.

On Mon, 15 Dec 2003 09:03:45 +0800, "Dean" wrote something ......and in reply I say!:

A lead ball say around 1-1.5" diameter will stop at around 190-200 mph. I would not think a bullet would fall "bullet shaped", and would not get much faster, if as fast. I would imagine larger objects would have less air problems (more mass per surface area) and get a bit faster even if not as dense in materials. Shape also matters. A humman will fall a lot faster if arrowing down than if spreadeagled.

I have watched a fascinating thing about a guy who worked with falcons. He had one that could fall at over 220mph, due to its shape (teardrop) and they had not finished testing. So a feather _can_ drop faster than a brick!

I also saw a thing about cats. They apparentoy have quite a high surival rate from apartment falls. Up to about 2 storeys they have no trouble. From there until 7 storeys they get increasingly hurt and killed. After that, they reach terminal velocity (funny I thought _terminal_ velocity was about 0, but anyway) and have time to realise that they are not going to go any faster. They relax, and spread out, and may even slow down. They get broken legs and cracked ribs and that's that.

Anumals were injured during the making of this production. The show claimed that this was based on vet practice records, not actual experiments.

**************************************************** sorry remove ns from my header address to reply via email

I was frightened by the idea of a conspiracy that was causing it all. But then I was terrified that maybe there was no plan, really. Is this unpleasant mess all a mistake?

On Wed, 17 Dec 2003 04:39:59 GMT, "Bob Swinney" wrote something ......and in reply I say!:

But we are not talking about acceleration from gravity. We are talking about acceleration of an object (a bullet falling in air).

**************************************************** sorry remove ns from my header address to reply via email

I was frightened by the idea of a conspiracy that was causing it all. But then I was terrified that maybe there was no plan, really. Is this unpleasant mess all a mistake?

On Wed, 17 Dec 2003 14:41:01 GMT, "Bob Swinney" wrote something ......and in reply I say!:

Ahah! But it is! The earth travels in a circular orbit. In physics, velocity is understood to have direction. IIRC, your arse has not changed speed but is constantly changing velocity. You are right. You do not notice it.

**************************************************** sorry remove ns from my header address to reply via email

I was frightened by the idea of a conspiracy that was causing it all. But then I was terrified that maybe there was no plan, really. Is this unpleasant mess all a mistake?

On Tue, 16 Dec 2003 15:13:16 -0800, "lane" wrote something ......and in reply I say!:

In my young, teenage, girl hunting days I would been worried by that statement.......

**************************************************** sorry remove ns from my header address to reply via email

I was frightened by the idea of a conspiracy that was causing it all. But then I was terrified that maybe there was no plan, really. Is this unpleasant mess all a mistake?

Are you trying to say Integral of v(t)dt?

Ted

Not in air.

Ted