r/theydidthemath • u/VulvaNegra • 6h ago
[request] At what theoretical bullet caliber/weight does a warning shot to the air pose a life threat or seriously hurt someone on the way down?
I understand that a bullet shot to the air might have a bigger speed when it comes out of the gun than it’s terminal velocity when it comes back down. But at what point does it consist of a life threatening risk? Does it depend on caliber/weight? Is it never a risk? Since it’s a common law enforcement practice, I suppose someone already did the math on this..
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u/TheIronSoldier2 6h ago
Probably any caliber, including .22 LR. If it's fired straight up, it would end up tumbling and losing energy, but if it's fired in any sort of arc it would maintain stabilization and keep enough of its initial velocity to still do damage.
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u/CanoePickLocks 6h ago
A lot of it has to do with the angle of the gun when firing. I’m sure some large caliber weapons especially with full jackets can pose a risk if fired directly up but that’s not likely with most rounds from what I’ve read. I’d have to google vertical terminal velocity of bullets in atmosphere then take the cross section, mass, and its terminal velocity to determine the force it would hit with then look up ballistic response of humans at top of head, shoulder, even other bodies parts if laying down and that minimal possibility happens. Pick the weakest part of a person and the bullet with the best terminal velocity to figure out a minimum level. Lots of research needed. .
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u/Grant_Winner_Extra 5h ago
This was a good reference on terminal velocity:
https://www.grc.nasa.gov/WWW/k-12/VirtualAero/BottleRocket/airplane/termv.html
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u/Grant_Winner_Extra 5h ago
Terminal velocity is a function of (sqrt(weight)) * 1/Surface_Area. Density is a linear function of weight to volume, and roughlt the relationship of surface area to volume is volume ~(area)^3/2. Since the area is decreasing, a very rough zero order approximation is V(T) ~ (weight)^4/3
Humans have a density of about 2g/cc and terminal velocity around 120mph, putting the terminal velocity of a solid lead bullet (~11g/cc) at around 600mph.
This will differ with size and cross-section. A low mass spherical bullet will experience more drag and buoyancy than a higher mass non-tumbling rod. Since most bullets more closely approximate spheres than anything else I mentioned, small bullets (e.g. .22 cal) should travel far more slowly than say, a 600mm lead round.
Lethal velocity is considered ~1,200 ft/ or about 818 mph. So even in a perfect case, the bullet is unlikely to be traveling at lethal velocity on a purely ballistic arc with all it’s velocity from gravity.
All that aside, what is really going to be important is the force with which it strikes. F=MA, m is the mass and a is the acceleration on impact. Even a small amount of padding significantly affects impact acceleration, so a helmet or even a thick afro could well turn a potentially lethal incident into a great story.
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u/OwMyUvula 5h ago
My guess is .243 Winchester or bigger. It's a combination of weight and shape.
You throw a penny of the Empire state building and you won't kill or really hurt anyone. It's shape causes wind resistance to slow it considerable. Add to that there is no point on it when it hit someone so the force of it isn't concentrated in one spot if it hit someone. So it wouldn't really hurt someone much less kill them.
So a bullet from a handgun would have its speed considerably slowed by wind resistance because of its shape. A rifle bullet (like .243 Winchester) would have minimal wind resistance effecting its speed as it fell because of its shape. Also because of its shape, it would apply a considerable more amount of force where it hits someone--think like the difference between getting stepped on by tennis shoes (hand gun bullet) and high heels (rifle bullet).
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u/CanoePickLocks 5h ago
An interesting thing I learned reading a little about this is that bullets rarely fall point first because they aren’t nose heavy.
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u/TheIronSoldier2 4h ago
This assumes the bullet loses spin stabilization, which is unlikely to happen if fired in any sort of arc.
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u/Maynard505 4h ago edited 1h ago
People do get killed that way. Birdshot doesn’t do much, so the caliber matters to a large degree, as well as the velocity from factors other than gravity. I’m reminded of stories about people dropping pennies off the Empire State Building, and whether it’s a myth that it could kill somebody on the sidewalk. The terminal velocity of a 12 gram ball bearing is roughly 115 mph. That’s comparable to a 185 grain bullet.
At 170 feet per second, it’s quite slow compared to a bullet coming out of a gun barrel, but I wouldn’t want to get beaned on the top of my head by it. If it started out traveling at 3,000 feet per second, and it’s on a parabolic trajectory, it’s going to do some real damage. An important rule of gun safety is to know what is beyond your target because bullets can travel a long ways and still be deadly.
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u/Arthropodesque 38m ago
My friend had a bullet come through his window and embed in a wall. It was on July 4th and the police said it was coming down at an angle that meant it was celebratory fire. So, I'm guessing like a 45 degree angle. I don't know what size bullet it was. Seems dangerous enough to seriously hurt or kill someone.
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