How fast does a bullet return to earth?

[satelital]

My question is based on a stray bullet that was shot on new years, and we discovered the it had hit the surface of our tennis court with such force that it made a hole aprox. the same size as the bullet it's self. A group of friends discussed different opinions as to how fast the bullet comes down oposed to the speed it leaves the gun, or said in other words, does it come down faster than it went up?

If anyone has a general answer (taking into consideration we do not have the exact launch speed, wind, bullet weight, etc.)

Thanks

Satelital

 

[ahrkron]

In a perfect vacuum, the bullet would return (to the height from which it was shot) with the same speed it had when it left the gun's barrel; in an atmosphere, part of its energy will be lost in collisions with gas molecules.

 

[Vodka]

it would take the same amount of time for it to go back as it would coming down. since gravity is constant [close to the surface of Earth for all practical purposes, anyways] it'll act upon the bullet with the same amount of 'pull' [for lack of better word :P]

its terminal velocity depends on on its size and mass, but i doubt it would reach. bullets are pretty aerodynamic tho, so they do go pretty fast. but you could expect it would land with roughly the same speed as it left.

 

[suyver]

Originally posted by Vodka
its terminal velocity depends on on its size and mass, but i doubt it would reach. bullets are pretty aerodynamic tho, so they do go pretty fast. but you could expect it would land with roughly the same speed as it left.

I disagree: the speed of a bullet leaving the gun is typically (much) faster than the speed of sound: ~1000 m/s. Compare this to the terminal velocity of a skydiver: ~100 m/s. I'd say that there is no way that a free-falling bullet would break the sound-barrier (~300 m/s), so somewhere arround ~100-200 m/s seems like a reasonable estimate of a free-falling piece of metal.

 

[schwarzchildradius]

I agree, it definitely does not come down as fast as it went up. If it is shot from horizontal in a vacuum, it will reach the ground at the same time as another body dropped at the height of the gun. In air, the dropped body would hit the ground first because the fired bullet is slowed down more.
There are equations for particle paths for air resistance that include atmospheric density and the velocity of the particle etc, but they are large.

 

[Integral]

Originally posted by suyver
I disagree: the speed of a bullet leaving the gun is typically (much) faster than the speed of sound: ~1000 m/s. Compare this to the terminal velocity of a skydiver: ~100 m/s. I'd say that there is no way that a free-falling bullet would break the sound-barrier (~300 m/s), so somewhere around ~100-200 m/s seems like a reasonable estimate of a free-falling piece of metal.

This is a question about the terminal velocity of a bullet, a dense streamlined object designed to travel at high speeds through the air. Why would we base estimates of this on the terminal velocity of the human body? While I do not know what the terminal velocity of a bullet is, I am sure equal to or 2 twice that of a human body is on the very low end of the possibilities.
edit.
http://www.loadammo.com/Topics/March01.htm is a good link.

Actually the terminal velocity of a human is more like 120MPH this is about 54 m/s while that of a bullet seems to be anywhere from 100~400m/s depnending on the size and mass of the slug. (Note the high end is for a 14" Naval gun!)

 

[FZ+]

It is rather obvious that the bullet will land at a lower velocity - simple conservation of energy, and second law of thermodynamics.

 

[suyver]

Originally posted by Integral
Actually the terminal velocity of a human is more like 120MPH this is about 54 m/s while that of a bullet seems to be anywhere from 100~400m/s depnending on the size and mass of the slug. (Note the high end is for a 14" Naval gun!)

400 m/s would mean that the free-falling bullet breaks the sound-barrier. Do you have a link proving this (I find it hard to believe)? I could not find this info in the link you provided.

 

[Integral]

Major Julian Hatcher in his book Hatcher’s Notebook estimates that a 12 inch shell weighing 1000 pounds and fired straight up would return with a speed of 1,300 to 1,400 feet per second and over 28 million foot pounds of striking energy.

That is from the last paragraph of the link, calling a 1/2 ton of steel a bullet is a stretch. That is called a shell, Looks like the reference is given.

 

[krysith]

Regarding the possibility of the bullet breaking the sound barrier in its fall - it is possible for objects to break the sound barrier while falling - just ask Joe Kittinger (google if you don't know who he is). However, of course, he exceeded the sound barrier at a very high height, where the air was thin.

In order to see whether the bullet could exceed the sound barrier, let's look at the energy gained and lost per distance fallen. The bullet will gain energy +E=d*g*m, and lose energy -E=d*Cd*p*v^2*A/2.

d=distance fallen
g=9.8m/s^2
m=mass of bullet
Cd=drag coefficient
p=density of air
v=velocity while falling
A=frontal area (from which Cd is generated)

Setting -E=+E, and solving for v, we find that v=((2*g*m)/(Cd*A*p))^1/2.
Cd at transonic speeds is about 0.45 for a bullet with an A of 5.8x10^-5 m^2 (a 7.62mm rifle bullet, AK-47). p at sea level is about 1.275 kg/m^3. m for a 7.62 mm bullet is about 0.01 kg. The terminal velocity calculated by this equation is about 76 m/s, well below transonic speed. Using the subsonic drag coefficient of 0.3, we get a terminal velocity of 94 m/s. So the bullet would come down at nowhere close to transonic speed. Nevertheless, a bullet hitting you at 94 m/s has a kinetic energy of 88 Joules, spread over a small area. It won't hurt as much as a regular bullet shot, but it will still hurt you. I'd wear a helmet if I were firing bullets in the air - people die all the time from "celebratory firing".

 

[Integral]

Perhaps you did not notice..

The shell that may be breaking (is breaking according to analysis similar to yours) is from a 12" navel gun. m= ~2.2x10³kg

 

[AnthreX]

in my opinion the bullet shot up would be faster than the bullet dropping by the gravity force. when shooting up the potential energy should be greater than the potential energy of the bullet falling. even though when falling the gravity acts on it.

 

[McNamara]

A bullet is said to travel 33,000 MpH which would obviously lose it's velocity at an upward angel. Depending on the angel in which it was shot it, it's hard to tell exactly how fast it made contact with your tennis court. To determine the speed of the bullet would be a large process involving you figuring out the approximate angel of entry, the type of bullet, gun, atmospheric pressure and other weather factors as well as where the person shot the gun from. You would probably need to make some sort of quadratic sketch to find this out. Sorry I couldn't actually answer the question however, this should help you if you so choose to go to these great lengths.

 

[ZapperZ]

A bullet is said to travel 33,000 MpH which would obviously lose it's velocity at an upward angel. Depending on the angel in which it was shot it, it's hard to tell exactly how fast it made contact with your tennis court. To determine the speed of the bullet would be a large process involving you figuring out the approximate angel of entry, the type of bullet, gun, atmospheric pressure and other weather factors as well as where the person shot the gun from. You would probably need to make some sort of quadratic sketch to find this out. Sorry I couldn't actually answer the question however, this should help you if you so choose to go to these great lengths.

Wow! Talk about digging up the dead! Did you know that you're responding to a post from 2004?

Zz.

 

[russ_watters]

Coincidentally, Mythbusters just did an episode on this very topic and found that bullets have a terminal velocity of only 100mph. Very, very surprising.

For one thing, their aerodnamics don't help because they fall on their side.

http://kwc.org/mythbusters/2006/04/episode_50_bullets_fired_up_vo.html

 

[Rach3]

Coincidentally, Mythbusters just did an episode on this very topic and found that bullets have a terminal velocity of only 100mph. Very, very surprising.

For one thing, their aerodnamics don't help because they fall on their side.

http://kwc.org/mythbusters/2006/04/episode_50_bullets_fired_up_vo.html

Mythbusters are made-for-tv idiots. Look at their pathetic excuse for physical reasoning:

Adam calculated that the ballistics gel is 650x more dense than air, so, according to his theory, if a bullet fired into ballistics gel goes 1ft, it would go 650 ft through air.

Rubbish!

 

[russ_watters]

Read a little further. They constructed a vertical wind tunnel and dropped bullets into it.

 

[WhyIsItSo]

If it is shot from horizontal in a vacuum, it will reach the ground at the same time as another body dropped at the height of the gun. In air, the dropped body would hit the ground first because the fired bullet is slowed down more.

I don't agree. The horizontal velocity of the fired bullet is irrelevant in this instance.

Both the "stationary" object dropped and the bullet fired begin with zero vertical velocity. They will accelerate downwards at the same rate, therefore hit the ground at the same time.

 

[WhyIsItSo]

I note this thread started some two years ago, however it is an interesting question. Friction due to air resistance is a very tricky thing according to my research. A great many factors will affect this value.

In the original post, there was not suffcient information to say, for example, if the bullet still had kinetic energy from being fired, or if all the speed that was left was its terminal velocity. For the latter case:

Assumptions:
1. Take the ideal case (unlikely) that the bullet is falling in a consistently "nose-down" attitude.
2. Air pressure is 1.29Kg/m^3
3. Use a .45 Cal bullet, mass 300g, drag coefficient 0.228. The "nose down" attitude gives us a cross-sectional area of 0.0001026m^2.
4. Still day.
5. Ignoring humidty.

Process:
We can use the Quadratic drag formula.

v_{terminal} = \sqrt{\frac{2mg}{CP_{air}A}}

As I right this, LaTeX isn't working, so that is saying terminal velocity =
square root ((2mg)/(CPA)).
m = mass
g = acceleration (gravity)
C = drag coefficient
P = air pressure
A = cross-sectional area

That comes out to about 442m/s = 1,448ft/s = 987mph.

Gun enthusiasts are probably thinking that number is higher than the muzzle velocity of most guns, which means that in this "ideal" scenario, a bullet fired straight up wouldn't get high enough to attain terminal velocity on the way down.

Much more realistic would be to assume the bullet is more or less sideways on the way down. This will result in a drag coefficient more like 0.6 (a sphere is about 0.5), and a cross-sectional area very roughly twice the nose-on area, or say 0.0002052m^2 Plugging those numbers in gives:

192m/s = 630ft/s = 430mph.

That should be good enough as a "useless information" tidbit at your next BBQ.

 

[Farsight]

This is interesting, from "Hatcher's Notebook":

http://www.recguns.com/Sources/XD1.html

"Out of more than 500 shots fired after adjusting the gun--only four shots hit the platform. One of the shots was a service 30.06, 150 grain flat based bullet, which came down base first...it left a mark about 1/16 inch deep in the soft pine board...

It was concluded from these tests that the return velocity was about 300 feet per second. With the 150 grain bullet, this corresponds to an energy of 30 foot pounds. Previously, the army had decided that on the average, an energy of 60 foot pounds is required to produce a disabling wound. Thus, service bullets returning from extreme heights cannot be considered lethal by this standard...

This supports the observations of those who wrote during WW2, that after a heavy battle, a number of bullets were found slightly embedded in tar rooftops, all pointed towards the sky.

 

[DaveC426913]

A bullet is said to travel 33,000 MpH

This is a wildly inaccurate number - it's at least an order of magnitude too high.

 

[WhyIsItSo]

This supports the observations of those who wrote during WW2, that after a heavy battle, a number of bullets were found slightly embedded in tar rooftops, all pointed towards the sky.[/i]

Interesting. If a bullet fired vertically does not change attitude througout its flight, therefore falls back "butt-first", its drag would be pretty high. Assuming 0.6...

BTW, I just realized I was taking a .45 as 300 grams NOT grains as I should have. Correcting that now...

Plug that into my "formula" gives a terminal velocity of 69m/s = 226ft/s = 154mph.

A 30.06 will have different characteristics. The largest my research tells me is 220 grains. Plugging the relevant numbers in...

79m/s = 259ft/s = 177mph.

For 150 grain bullet...

65m/s = 213ft/s = 145mph.

If one takes the drag coefficient to be 0.3...

92m/s = 302ft/s = 206mph.

It would seem to be a little low for drag for a flat surface, but that is what it takes to get about 300ft/s terminal velocity for a 150 grain 30.06 bullet falling butt-first!

Guess my numbers are wrong. The part I'm not sure of is the drag coefficient. Oh well...

 

[phun]

I didn't think drag coefficient depended on the mass..?

 

[Mongo]

Ok, what everyone seems to be missing is trajectory. All bullets fired do not return to Earth at terminal velocity. Gravity is a constant, and a bullet fired on a flat trajectory, ) degrees elevation, it will hit the ground at the same time as a bullet dropped next to the chamber at the same time. Now, this doesn'tmean the bullet fired will hit with the same force, it also has a consicerable amount of force behind it, and the mass is coniderably greater.

So, the question waas, how did a bullet fired into the air penetarate your tennis court, simple, that's what bullets do. Has nu\othing to do with terminal velocity or gravity. I also saw the episode of myth busters, and they were going under the asumption that a round was fired streight up, which is nearly impossible.

All artillary is fired on trajectory, in an arch, and they still have devistating impacts. These objects are not particularly fast, but are moving faster then terminal velocity.

SO to restate, the bullet did what bullets fired on a trajectory do.

 

[Andrew Mason]

Now, this doesn'tmean the bullet fired will hit with the same force, it also has a consicerable amount of force behind it, and the mass is coniderably greater.

I am not sure why you say the mass of the fired bullet is considerably greater. They must have the same mass.

All artillary is fired on trajectory, in an arch, and they still have devistating impacts. These objects are not particularly fast, but are moving faster then terminal velocity.

They are fired on an arch trajectory in order to maximize range. If they are explosive shells that are being fired, the damage they do doesn't depend so much on their speed.

It seems that http://nfttu.blogspot.com/2005/12/celebratory-gun-firing-good-idea-or.html" . I wonder what the experience in Gaza was when they celebrated the election of Hamas?

AM

 

[HallsofIvy]

Ok, what everyone seems to be missing is trajectory. All bullets fired do not return to Earth at terminal velocity. Gravity is a constant, and a bullet fired on a flat trajectory, ) degrees elevation, it will hit the ground at the same time as a bullet dropped next to the chamber at the same time. Now, this doesn'tmean the bullet fired will hit with the same force, it also has a consicerable amount of force behind it, and the mass is coniderably greater.

No, what you are missing is that everyone else is taking into account air resistance. Without that, there is no "terminal velocity" and a bullet dropped will hit the ground at the same time as a bullet fired on some trajectory. With air resistance, however, that's not true- given enough time to reach terminal velocity, a bullet will, eventually, return to Earth with terminal velocity straight down (since there is no horizontal force, the horizontal component of "terminal velocity" will be 0.
It is true that the fired bullet, in your "airless" scenario will hit with more force since it has a horizontal component of velocity also. But I am mystified as to why you think the mass of the fired bullet will be "considerably greater" than the mass of the same bullet dropped.

 

[DaveC426913]

But I am mystified as to why you think the mass of the fired bullet will be "considerably greater" than the mass of the same bullet dropped.

Relativistic effects?

 

[phun]

I didn't think drag coefficient depended on the mass..?

oops it does

 

[Danger]

[semi-rant]Firing into the air in almost any circumstance is incredibly stupid. I'm not going to get involved in the calculations aspect of it, because I don't know math. What I do know is that one should absolutely NEVER shoot without knowing that there's an acceptable backstop for the round. It's nearly impossible to fire straight up, so you can't know where it's going to land. As Krysith and Andrew pointed out, people are injured or killed by this practice all the time. Even if terminal speed is only 100mph or so, that can still be lethal if it hits someone in the head. It's far more likely, moreover, that midrange-trajectory ballistics will apply rather than straight gravitational effects. People, especially when alcohol is involved, don't pay a lot of attention to where they're pointing guns as long as it's significantly above horizontal.
I also don't always trust the math and physics as presented, either, if it conflicts with experience. Some gun magazine article that I read decades ago laughed at the folly of trying to hunt at over 50 yards with a handgun. It went through the math showing that a .44 magnum could be snagged by a guy with a catcher's mitt at 100 yards. Maybe, but I've killed gophers at 150+ yards with mine (not often, mind you; I'm not that good a shot). Even an innocent little .22LR bullet can kill someone at over a mile away.
I don't intend, as stated, to enter into the scientific analysis of the situation; I merely want to stress that one should treat firearms (and other projectile weapons) as potentially lethal under any conditions and use them accordingly.[/semi-rant]

 

[WhyIsItSo]

Ok, what everyone seems to be missing is trajectory. All bullets fired do not return to Earth at terminal velocity.

In my defence, I had a CYA clause

In the original post, there was not suffcient information to say, for example, if the bullet still had kinetic energy from being fired, or if all the speed that was left was its terminal velocity. For the latter case: