Bullet Theory (Not JFK related).

June 10, 2007 4:23 PM

An empty field. Nothing for miles and miles and miles. And a gun. I shoot the gun. The bullet blasts out of the barrel and doesn't stop until....well, that's my question. Few more details inside.

How far does a bullet travel if you assume that it hits nothing, there isn't any wind resistance and whatever else you need to make this as easy on you as possible when doing my thinking for me.

Further, how far would it be before it is rendered ineffective (i.e. bullet wound) but still in motion? Like I could just swipe it out of the air with my bare hand and receive nothing more than a sting and some redness on the fingers?

I hope I'm clear in my question.

Thanks all.

posted by ryecatcher to science & nature (19 comments total)

No wind resistance? Does that mean no friction at all? What about gravity?
posted by mzurer at 4:25 PM on June 10, 2007

First Google result for "How far does a bullet travel":

A rifle bullet, when fired or dropped from a height of about 5 feet, will take just over half a second to hit the ground. This time won't change if the bullet is fired with a higher velocity.

So how far does the bullet travel? We can now go back to our original equation involving the horizontal speed of the bullet: The bullet has a horizontal constant speed of 88,400 cm/s, and will hit the ground after 0.55 s:

The bullet will travel a distance of 486.2 metres.

posted by Jairus at 4:27 PM on June 10, 2007

Rifle Bullet Trajectories

I googled 'how far would a bullet travel no air resistance'

I've not checked out their working though.
posted by knapah at 4:28 PM on June 10, 2007

Damn you Jairus!
posted by knapah at 4:29 PM on June 10, 2007

HA HA HA
posted by Jairus at 4:30 PM on June 10, 2007

It would stop in the same amount of time it takes to fall to the earth. It wouldn't be much different from dropping a bullet from shoulder height.

If there is no resistance from the air, the bullet's movement would only be slowed by its impact with the ground, so there would be no point in its flight that you could reach out and touch it without it hurting you.
posted by 517 at 4:34 PM on June 10, 2007

If there is no resistance from the air, the bullet's movement would only be slowed by its impact with the ground, so there would be no point in its flight that you could reach out and touch it without it hurting you.

Unless, of course, you fire the bullet upwards, and you climb a tower really really fast and grab it within a few meters of its maximum height. Someone will show you how to do the math. I learned how in 10th grade, but damned if I can remember, and damned if I am going to look it up for you.
posted by Kwantsar at 4:45 PM on June 10, 2007

yea, the bullet is always going to fall due to gravity (-9.80 m/s^2), no matter how fast you fire it.
posted by unexpected at 4:47 PM on June 10, 2007

yea, the bullet is always going to fall due to gravity (-9.80 m/s^2), no matter how fast you fire it.

Not if you have a big enough gun.
posted by b1tr0t at 4:52 PM on June 10, 2007

Rifle bullets basically are affected by gravity, atmospheric resistance, crosswinds, and other drag/turbulence effects such as those created by their spin.

If you fire a rifle bullet on the moon, where it is airless, and at the same time drop an identical rifle bullet from the height of the rifle muzzle, the time-of-flight of the two bullets will be identical.

If you know the muzzle velocity of the bullet you can use this time to calculate the distance traveled. Since there is nothing to stop the fired bullet it will still be traveling at its muzzle velocity when it hits the ground because of gravity.

If you are interested in learning about the way a bullet behaves in air, people have devised calculators to help you learn about these numbers. You do need to know the bullet's ballistic coefficient, a number that helps quantify the bullet's interaction with the atmosphere.
posted by ikkyu2 at 4:52 PM on June 10, 2007

All of this changes, of course, if the bullet travels far enough that the curvature of the planet its fired on causes the ground to fall away from it. I mention this not as a snark, but as a way to introduce Newton's famous thought experiment that led him to deduce the structure of the solar system and the mechanics of gravity.
posted by ChasFile at 5:03 PM on June 10, 2007

The assumption that the bullet's falling time is going to be the same whether it's fired or simply dropped is also only valid if it's fired exactly horizontally.

Another way in to thinking about orbital mechanics is to ponder exactly what "horizontal" means on the surface of a ball.
posted by flabdablet at 6:20 PM on June 10, 2007

Wait, if you take out wind resistance, I don't think the second part of your question would work. If you ignore gravity pulling the bullet to the ground, wind resistance would be the thing slowing it down to the point where you could "swipe it out of the air."
posted by edjusted at 8:15 PM on June 10, 2007

Another way in to thinking about orbital mechanics is to ponder exactly what "horizontal" means on the surface of a ball.

Simply fire the bullet such that the initial force vector is perpendicular to the initial gravity vector.

You could stipulate that the bullet be fired with an initial force vector parallel to the surface tangent at the point of launch, however this would fail on planets that are not perfectly round.
posted by b1tr0t at 9:10 PM on June 10, 2007

In your question you menion no wind velocity. If that is the case, what would slow the bullet down?

The answer is: nothing. You could fire it straight up and that will slow it -- but it will regain that velocity on its way back down.

In fact, in an infinite field (ignoring its a planet and all the orbit stuff for now) no matter which direction you fire the gun, it will hit the ground going as fast or faster than the speed at which it left the muzzle.

Now we can bring the planet aspect back into it and show why thats irrelevant except to add that if you fire it fast enough it will go into orbit or achieve escape velocity. So, now the slightly revised statement is: If the bullet hits the ground at all, ever, it will hit that ground at a velocity faster than that which it left the muzzle.
posted by vacapinta at 10:19 PM on June 10, 2007

I think I get what you're trying to ask, and basically, it comes down to this. Your bullet will travel (if there is no wind resistance) at the speed in which it left the muzzle of the gun until gravity (which is acting upon it regardless of forward velocity) makes it touch the ground. This amount of time is exactly the same as the time it would take to simply drop the bullet from an equal height (presuming that you fired it exactly perpendicular to the force of gravity. For simplicity's sake we will presume as such). There would be no point in time where you could simply swat it out of the air, even factoring in wind resistance, before it fell to the ground.

Moreover, the answer differs greatly depending on what kind of gun you use. A bullet travelling at 773-956 feet per second (apparently the muzzle velocity of a .45 caliber bullet, like one Dirty Harry would fire) will travel a much shorter distance than a .32 Winchester Special coming out of a hunting rifle, travelling at (apparently) 2250 feet per second.

So, presuming that you fire your Collt .45 from shoulder height, which is (convieniently) 2 meters high, your bullet will hit the ground in .144 seconds (I think. it's been years since I calculated something like that.) If you've got a fast gun, it's going 956 fps, and you'll get 137 feet before it hits the ground. Naturally, everything changes if you aim up or aim down at all.

(Realize that this calculation is not even close to actually accurate, but is actually a pretty wide ballpark, because i'm disregarding pretty much every important factor, like curvature of the earth, topographics, the bullet's spin, wind, etc., as well as imagining perfect (in the sense of ease of calculation). This is not the real world answer, this is more the high school physics answer. Not to mention, I haven't calculated something like this since I took intro physics two years ago, so there's also a solid chance i'm straight wrong about something.
posted by The Esteemed Doctor Bunsen Honeydew at 11:48 PM on June 10, 2007

There was a Mythbusters episode that covered a similar question (about firing a gun into the air):

Episode 50 — "Bullets Fired Up"

* Original airdate: April 19, 2006

Bullets Fired Up

Bullets fired into the air maintain their lethal capability when they eventually fall back down.

Busted , Plausible, and Confirmed

In the case of a bullet fired at a precisely vertical angle (something extremely difficult for a human being to duplicate), the bullet would tumble, lose its spin, and fall at a much slower speed due to terminal velocity and is therefore rendered less than lethal on impact. However, if a bullet is fired upward at a non-vertical angle (a far more probable possibility), it will maintain its spin and will reach a high enough speed to be lethal on impact. Because of this potentiality, firing a gun into the air is illegal in most states, and even in the states that it is legal, it is not recommended by the police. Also the MythBusters were able to identify two people who had been injured by falling bullets, one of them fatally injured.

To date, this is the only myth to receive all three ratings at the same time.

link
posted by chuckdarwin at 2:19 AM on June 11, 2007

Couple things to make life more difficult...

It matters entirely what kind of bullet it is. Some bullets are meant to deform (hollowpoints), where some are not. Some brass, some are lead composites, some are iron/steel, some are wood. Again, all deform at a different rate and have different densities.

Also---is it a high-velocity-low-density round like a .22? Or a low velocity high density round like a .44? If you look at a box of .22 long mags, it'll tell you that the bullet will travel something like 3200 feet. Our .22-270 will take out a deer no problem at around 400-600 yards.

Or is it a shotgun pellet, which is flat and not spinning?

Oh, and just another reason to dislike the mythbusters (I'm never satisfied w/ their nearly scientific method), a little girl in a trailer park near me was hit by a falling bullet fired vertically on the 4th of july a couple years ago...didn't kill her but it put her in a coma for a couple days, and it hurt her pretty bad.
posted by TomMelee at 5:38 AM on June 11, 2007

General Ballistic Trajectory assuming no air resistance.

Part of this more comprehensive site.

If you're going to assume no air resistance, why not go all-out and assume no dirt and rock resistance, too? If you do that, the bullet will stop when gravity pulls it in to the center of the Earth, I suppose. Or maybe it won't stop at all, but will orbit the Earth's center forever.
posted by Kirth Gerson at 7:06 AM on June 11, 2007