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Taking On McGyver

Here's a fun interview with the Mythbusters. I don't get this, though:

My favorite episode, that I think the science is the most right, is ''Bullets Fired Up'': Will a bullet that you fire directly into the air kill you when it comes back down? We tried it in several different ways, and every single way we tried it -- from a shop experiment, to a scaled outdoor experiment, to a full-size outdoor experiment where we fired a full clip of 9mm rounds into the air out in the desert -- confirmed the same results. If it's coming straight down, it won't kill you. But if you fire it on an angle of even two degrees, it stays on a ballistic trajectory and it will kill you. So when you see someone in a movie fire their automatic rifle on kind of a spray up into the sky, probably all of those bullets are actually deadly. The amount of data we collected on it was more than anybody up to that point had ever achieved on firing bullets into the air.

I don't get what they're saying here. Why would it come down any harder if it's at a slight angle? How did they determine whether or not "it would kill you"? If it's in a vacuum, it should come down with exactly the same vertical velocity component it had when it left the gun (except reversed), but the atmosphere complicates things. It seems to me that any bullet fired in the air is going to be coming down at terminal velocity, unless the potential energy is so high that it doesn't have time to get to terminal velocity before it hits the ground, but that's pretty hard to believe. When it leaves the muzzle of the gun, it's supersonic, but I would think that it won't be able to be going that fast when it falls back down, because of air drag. This seems like something that should be simulatable with CFD (it might even be possible to do it analytically, if the bullet was round).



Big D wrote:

I saw that one, and it made sense at the time.

The terminal velocity of an "unpowered" bullet is pretty much nothing... and if a bullet is fired *directly* up, it keeps going until it loses all momentum, and then falls at terminal velocity.

But if fired at an angle, the bullet never sheds all of its momentum. It retains enough forward trajectory to wound or kill when its ballistic arc reaches the ground.

Rand Simberg wrote:

I understand that. What I don't understand is how an angle as small as two degrees can make that big a difference from straight up. The sine of two degrees is 0.04, so a bullet will only have four percent of the muzzle velocity in the horizontal. Will that really kill someone?

Peter O wrote:

But remember, the cosine is much larger, and the bullet impacts with full (vertical and horizontal) velocity on whatever is in the way.

The difference between straight up and any real angle also involved those atmospheric effects you mentioned. The straight up bullet began to tumble and experience significant air drag on the way down, while a bullet at an angle kept a ballistic profile, so it came down a lot faster.

mz wrote:

Umm and why would it go any faster horizontally than it goes vertically? I would tend to think the opposite, that it would come in almost vertically.

Imagine it is fired at a 45 degree angle: the gravity acts on the y velocity (it gets shifted to potential energy and back again) but the drag acts on both.

The magnitude of total drag is probably directly proportional to total velocity squared:
drag_tot propto v_tot^2 = v_x^2 + v_y^2
in subsonic flight and the proportion to which it affects the x and y velocity, directly to the actual velocities:
drag_x propto drag_tot * v_x/v_tot
drag_x propto v_x * v_tot and
drag_y propto v_y * v_tot

So, in the early part the total velocity is high and both velocities get their share in drag and slow down. In the top arc part, vertical velocity is low but so is total velocity so the horizontal velocity is not lowered that much, but still some. And in the end part drag affects both again but only v_y is kept constant because of gravity. So the trajectory should get steeper and the x velocity should be LESS than the y terminal velocity.

Of course, the bullet is not a sphere and it has a spin that probably keeps it oriented tip to the original firing direction, which could make for all kinds of weird phenomena...

4% of a rough original muzzle velocity of 400 m/s is 16 m/s, 60 km/h or 35 mph. Can hurt but probably not penetrate skin?
And there is no mechanism that would add to the horizontal velocity. So, the horizontal velocity definitely drops from that.

Saying the total velocity is subsonic doesn't gauge lethality much yet. Even M 0.3 = 100 m/s could still be deadly.

Dawson Lewis wrote:

Peter O gave the answer they gave in the show, which I have seen at least twice. When the bullet tumbles drag reduces the speed to the terminal velocity of a tumbling object in the air which is below the speed needed to kill. Hurt like heck but not kill.

An angled bullet stays going tip first and get get a higher terminal velocity. So it retains much of it's velocity.

Essentially it is the difference between the speed of dropping "flat" object versus a pointed object.

Larry J wrote:

I remember that episode. They interviewed a doctor who had treated a couple (IIRC) of people who had most likely been shot by bullets randomly fired into the air. I'm not certain but one of those cases might have been fatal. It's uncertain what angle the bullets were fired but there is evidence that firing even at a high angle can be dangerous. Two degrees off of vertical sounds like a stretch, though. I suspect as other commenters noted that if the bullet retains enough horizontal velocity to keep it from tumbling then it could still be fatal.

Dale Amon wrote:

Synchronicity strikes again, almost. I had almost the same discussion a few weeks ago on Samizdata when we discussed the hypersonic rail gun and compared it to a regular gun fired at different ballistic trajectories.

The tumbling versus still spinning thing is one I have never previously heard of though, but I guess I can see what they
are getting at... but I wonder if the bullet actually does stop spinning at apogee. Why would it in one case and not the other? The angular momentum is not affected by trajectory.

As an experiment I just spun my pen as I tossed it in the air... it tipped over and went gravity gradient on the way
down, still spinning.

Jonathan wrote:

I saw part of that MB episode. I think they oversimplified the issue, either out of ignorance or because of the constraints of their show format. The variable that they didn't adequately address was the aerodynamics of bullets, which determine how rapidly bullets decelerate and destabilize (tumble). IIRC the MB guys used a 9mm pistol and an M1 rifle. All or almost all pistol bullets are blunt and have flat bases, so whatever pistol bullets they used were probably representative. However, rifle bullets vary considerably in shape. Typical military and hunting bullets for the M1 have flat bases. Match bullets have tapered bases, are stable at longer ranges and probably have longer absolute ranges. I suspect that the MB guys used only flat-base rifle bullets in their tests.

Tests like these have been run before. I believe that Julian Hatcher, an Army officer who worked in weapons development between the wars, published results of similar tests. (Googleable, I'm sure.) Ballistics software that takes account of the aerodynamic differences between specific bullet types is readily available. I suspect it would be easy to run accurate computerized simulations.

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This page contains a single entry by Rand Simberg published on February 20, 2008 7:48 AM.

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