How long does it take a bullet to come down, if you shoot straight up?

[fws]

Interesting question. Just to get an idea one could go through the following exercise:

Assumptions/Simplifications:
a) Bullet is fired exactly straight upwards.
b) Wind does not matter as it will only move the point of impact but not influence the downward velocity vector.
c) Let’s assume a 158 grain, .357 bullet with a coefficient of drag (Cd) of about 0.8, which is about right for elongated cylindrical objects like a wadcutter. (This is not the BC).
d) Let’s assume the bullet is not tumbling as this would seriously complicate our relatively simple computation.
e) Let’s assume constant, standard atmospheric pressure (even though it would change with altitude).

Based on the formula for terminal velocity

V = Square root ((2*weight)/(Cd*air density*cross sectional area))

the above bullet would travel with about 51 ft/s. Could it penetrate a skull? Don’t know.

FWS

 

[fws]

Oops, that was not even the question. How long it takes to come down should mostly depend on the initial muzzle velocity.

 

[John_galt]

Assuming all of the projectiles attain a terminal velocity, initial muzzle velocity would only affect the time it took for the bullet to return to earth, not its velocity in free fall. In free fall back to earth it will attain a terminal velocity and for the most part maintain it. The weight of the bullet has much more to do with the velocity when falling than the original muzzle velocity. I think this would be especailly true when you factor in the real world effects of air resistance and flight characteristics. Air resistance slows it down so it reaches terminal velocity sooner. It will be almost impossible for it to fly with the same characteristics of a fired bullet with axial rotation perpendicular to its flight, it will tumble in some fashion and decrease the terminal velocity because of increased air resistance.

OK my head hurts now. Has anyone been shooting up in the air nearby here? I think a bullet just dropped out of the sky and hit me in the head or I am thinking about htis too much. Either way it hurts.

 

[ricklin]

Childhood memories

This thread reminds me of an experience I had when I was about 10-12 years old.
We enjoyed making things that went bang, our favorite was empty BB gun C02 cylinders, packed full of match heads!! Don't try this at home before the flames start, please remember, I was 12.

We took one of our "creations" to a large parking lot at a closed up grocery store. We always wondered whether the C02 cylinders exploded, or flew away like rockets.
We discovered they did fly like rockets! We pointed one straight up, touched it off and waited, and waited, and waited. We started walking home. We were about a half block away from the parking lot when our "rocket" landed on the gravel street about ten feet away from us. The cylinder was intact, the small end we packed the match heads through was blown out a bit, and it was quite warm.

I have always wondered just how high that sucker went before it came back to earth. Even given our youth we decided that this particular bit of fun with the C02 cylinders should not be repeated.

Ahh....... the memories of a sometimes misspent youth. We all survived, and with all of our digits and appendages intact.

 

[Guns and more]

If you're given the mass of the bullet and it's initial velocity, this isn't all that hard of a problem if you ignore air resistance and only care about gravity.

The mass of the bullet has nothing to do with it. An anvil and a bullet fired at the same velocity will reach the same altitude. (we're ignoring air resistance remember) I'm gonna run when the anvil comes down.

 

[fws]

Right on, Guns and More. As we know, in a perfect vacuum a feather and a stone fall at the same rate. If we include air resistance, it is the Coefficient of drag in combination with size and mass that matter mostly. Something shaped more aerodynamically will have a higher terminal velocity.
FWS

 

[buenhec]

Well they aired the Mythbusters episode today. A 9mm bullet went up 5000 feet, a 30-30 10,000 feet. The 9mm round trip took 37 seconds and came down at 150 FPS. It penetrated 2" of dirt and did not penetrate the skull of a Pig. It also keyholed on the way down. One Doc they interviewed said in some cases it had definately killed people, in some it barely pierced the skin. Almost forgot, the shots were fired straight up and were found 300 feet away due to air currents.

 

[Guns and more]

Correct, the bullets assumed a sideways orientation on the way down.
Shooting at an angle of less than 90 deg. is another story.

 

[Jim Watson]

As I recall, Hatcher's tests included one marginally stable .30-06 bullet that would sometimes drop back base first and sometimes turn over and fall more or less nose first. 1 min 6 seconds, 1 min 46 seconds.

He figured that a .30-06 150 gr FMJ would climb to about 9000 feet in 18 sec and fall back in 31 seconds. The same round fired in vacuum would go up 113,000 feet, 84 sec up, 84 sec back down. So when you start your little Internet Discussions saying "ignoring air resistance" you have completely departed the real world.

 

[krs]

In the 1980's a guy who was pasting a poster onto a billboard in San Jose, CA suddenly slumped and fell from his scaffold to the ground. He was dead, and the paper reported that a followup autopsy had found that he'd been shot and that the bullet had entered the top of his head.

The paper went on to say that in an interview a police spokesman surmised that the guy's death was the result of someone across the valley firing a gun into the air but they'd been unable to track down a source or even a report of gunfire near the time it happened.

What goes up must come down...

 

[krs]

Ricklin,

What you did, in a rudimentary way, was enter the hobby of rocketry. Kids and adults are involved in such pastimes even today, sometimes on a rather grand scale. There's a club in Arizona that routinely fires rockets complete with rear viewing cameras, altimeters, and assorted other intsruments to heights in excess of 40,000 feet as a hobby activity.

What was that guy's name in 1937? No, not Werner.....

 

[rcmodel]

surmised that the guy's death was the result of someone across the valley firing a gun into the air

Had the bullet been fired perfectly or even nearly straight up, they would only have suffered a bruise or bump on their head.

People who get killed or seriously injured by a falling bullet do so because the bullet was fired in a ballistic arc, and was still stable and flying point first when it came back down at fairly high velocity.

This is the same principal used by military forces around the world in indirect fire from machine guns, artillery, and mortars.

Indirect fire was even a tactic employed by groups of military riflemen long ago.
That's why the old bolt-action military rifles had ladder sights that went up so dang far.

rcmodel

 

[Jim K]

The Mythbusters findings were as would be expected.

A bullet fired straight up will come back down with its maximum velocity at terminal velocity (some 200 fps), which is not enough to achieve deep penetration on a human body, but could cause injury.

A conventional bullet will come down base first. In the absence of wind, there are no forces that would cause it to tumble or turn over in the air. It just stops and then starts back down.

But "a bullet fired in the air" has no meaning. Unless there is some special condition (under water, in a vacuum tank) ALL bullets are "fired in the air."

Jim