Bullet Dropped vs Fired

[WWLabRat]

I'm not an expert, nor claiming to be such, in any field, much less physics. My knowledge is very basic, not much higher than what you would learn at a typical high school. My question is actually inspired after watching an episode of Mythbusters (Episode #125 "Knock Your Socks Off") where they tested to see if a bullet fired would hit the ground at the same time as a bullet dropped from equal height.

 

I don't find it surprising that their results were effectively correct. What I'm wondering though, is if the same thing would happen if they were able to test this in a vacuum. Granted they get about as close as possible to a vacuum by being indoors and reducing the presence of wind. However there is still air present, and thus friction. A dropped bullet would only be moving through two dimensions as it falls (due to one end weighing more than the other) whereas a fired bullet would be moving through three.

 

Another variable would be the rifling from the barrel of the gun, though minimal, would still slightly reduce how much mass there is with the fired bullet when compared to the dropped bullet. This would also skew the findings of their experiment. After all was said and done, they found that in their experiment, there was a 39.6 millisecond difference between time the dropped bullet and the fired one.

 

So, simply put, my question is: When in a vacuum, would a bullet fired and a bullet dropped hit the ground at the same time?

[ajb]

Yes the same thing would happen.

The equations of motion here are that of projectile motion. In the explanation of the bullet dropped Vs fired one usually ignores air resistance. Technically you only get projectile motion when the only force acting is gravity.

Anyway, importantly the horizontal and vertical motion decouple and so do not influence each other.

[WWLabRat]

What keeps molecules, in the air, from affecting a bullet in such a way that their absence in a vacuum goes unnoticed?

[ajb]

What keeps molecules, in the air, from affecting a bullet in such a way that their absence in a vacuum goes unnoticed?

A fast streamlined bullet and not a very long path of flight.

 

For the purposes of the fired or dropped bullet you will not see a significant deviation due to air resistance. The deviation will get swamped in any other errors in your measurements and so assuming a vacuum is okay.

[WWLabRat]

If the range on the average pistol is too short, would it be different if, just theoretically, a firearm were able to fire a bullet horizontally for a significant distance?

[ajb]

If the range on the average pistol is too short, would it be different if, just theoretically, a firearm were able to fire a bullet horizontally for a significant distance?

I don't quite follow your question. The bullet exhibits (approximate) projectile motion. The neglects air resistance and the Earth's curvature, which is okay here.

A fast streamlined bullet and not a very long path of flight.

Let me amend this. If the bullet is slow and heavy the effects of air resistance will be small and so can be neglected. In reality, one will have to take air resistance in account.

[WWLabRat]

Sorry, I'm being a little dense here. I get that due to the bullet's shape and being aerodynamic means that it's not affected really affected by friction in the air. I understand the very basics of the bullet travelling through the air, that the air moves around it on all sides equally while the rifling from the barrel it was fired from helps to keep the round in a spiral motion to keep it stabilized while in flight. And I'd imagine with the speed at which the bullet is travelling that it would create small pockets of empty space in its wake, much the same way as a jet ski travelling through water. After the bullet leaves the barrel, it would immediately lose some of its speed and its velocity would start to change as gravity pulls it downwards. The dropped bullet, from the time it was dropped would tumble, end over end, until it hit the ground. The only real deciding factor in what happens to the bullet would be whether it was dropped pointed at the ground or at the same horizontal level as the fired bullet. For argument's sake, it'll be released at the same angle as the fired bullet.

 

As an example, say the constants in the experiment were the caliber, the type of round used, the firearm used, and the level of the firearm. And, much in the same way as on Mythbusters, we remove wind, control the humidity, and keep everything at room temperature. We fire and drop the bullets at the same time (the bullet dropped being released as the bullet fired leaving the barrel) and everything goes as expected. There are two variables that could be presented at this time that would create another 3 experiments. The variables would be whether or not the experiment takes place in a vacuum and the height at which the bullet is dropped/fired. I mention the second variable because by firing from a higher perch, the dropped bullet has a chance to hit terminal velocity, where the air resistance matches that of the gravity acting on the bullet. With the increased height, there's also the a point where the lateral speed would slow to the point where it's not being carried forward and the entirety of the velocity would have since been shifted in the direction of the ground. By this point the rotation of the bullet should have also slowed to where it's not able to cancel out the friction of the air around it. Or at least that's my thought. However in a vacuum, even with the increased height, there would be no opposing force to act against the gravity and the bullets would hit the ground at the same time.

 

I'm sorry, I don't know all the math behind it, so forgive me for not being able to provide mathematical proofs to back this up...

[ajb]

You can certainly add air resistance to the equations and solve these. The trouble is you need to do this numerically, but it is not particularly hard. I am sure a quick google will give you more details here.

 

You can read a bit about it at www.scienceblogs.com/dotphysics/2009/10/09/mythbusters-bringing-on-the-physics-bullet-drop/

 

I think that for light fast bullets the effects of air resistance will be more important than for heavy slow bullets. If I recall, Myth Busters used large caliber bullets with a relatively slow velocity to minimise the air resistance.

 

As for the effects of the bullet spinning and air turbulence I do not know. I assume people have modeled this.

Edited August 31, 2013 by ajb

[WWLabRat]

In mythbusters they used a pistol and what looks like either 9mm or 45 rounds. Not a relatively large round, especially when compared to the powder propelling it out of the chamber.

[ajb]

In mythbusters they used a pistol and what looks like either 9mm or 45 rounds. Not a relatively large round, especially when compared to the powder propelling it out of the chamber.

0.45 I think they used, what I mean is slow and heavy.

[WWLabRat]

So then what about hollow points? Am I correct in assuming that they would not only have a lower mass/weight, but would also have slightly different flight mechanics?

[ajb]

I don't think there would be much difference assuming masses to be equal.

[studiot]

Bullets are tested in apparatus known as a ballistic pendulum.

 

You might like to watch this video.

 

http://www.youtube.com/watch?v=l87Dr2lJEOk

[Mr Monkeybat]

Although there is all sorts of interesting fluid dynamics going on around a fired bullet if the weapon is pointed exactly horizontal so is the tip of the bullet so the air pressure above the bullet is the same as that bellow the bullet leading to no net effect on the bullets vertical motion.

[J.C.MacSwell]

Although there is all sorts of interesting fluid dynamics going on around a fired bullet if the weapon is pointed exactly horizontal so is the tip of the bullet so the air pressure above the bullet is the same as that bellow the bullet leading to no net effect on the bullets vertical motion.

If you can assume the bullets alignment remains horizontal, and the vertical component of the velocity changes from 0 due to gravity, the pressure below the bullet will become greater than the pressure above it. A lift component will result which will slow a bullets fall relative to that of a dropped bullet, which should have a lesser, also upward, vertical drag component.

[WWLabRat]

Bullets are tested in apparatus known as a ballistic pendulum.

 

You might like to watch this video.

 

http://www.youtube.com/watch?v=l87Dr2lJEOk

 

All that this video shows is the velocity of a projectile, not it's motion relative to the ground or to a similar projectile that is dropped. Also, the video seems to sound more like an advertisement rather than actually discussing motion.

[ccwebb]

When talking about the flight path of an object, you can not compare it to the horizontal plane if you are trying to measure lift. You have to measure it to the Angle of Attack, that is the 'horizontal line' (cord line) of the object compared to the relative wind. The relative wind is the direction of airflow to the object. Rifling is a stabilizing effect reducing drag. Since drag and thrust are opposite forces of each other, reduce drag and thrust becomes greater. Or the bullet goes further, it is still dropping.

 

Bullets do not generate lift, as an airfoil would, they fall. Hence why missiles have wings.

[WWLabRat]

I always thought that missiles have the wings to help stabilize it during flight. Being that they generally are not "fired" from a barrel and generate their own propulsion, they wouldn't have or need rifling, but would still need something to stabilize them. Also I thought that they needed this stabilization to keep navigational systems in check. I am more likely than not incorrect on one or both of these points. I'm far from being a munitions/explosive ordinance expert.

[ccwebb]

True, all fins help stabilize aircraft. The fins in the back part of the rocket/missile provide the stabilization you are referring to. Lift is produced by moving/displacing air, this can be accomplished in one of two ways: with wings or with thrust. (or of course with some combination in-between). Rockets get all of their lift from their engine. A glider plane gets a small amount of lift from its thrust, and thus needs very big wings to make up the rest of lift. Missiles have powerful engines, but not as powerful as rockets. Hence why they have additional wings to help, though tiny.

 

Since bullets can not have wings, fins, or stabilizers, the rifling effect is need to help it stay accurate. It is still falling the moment it leaves the barrel.

 

Ajb was correct in post #2, the same effect would happen in a vacuum. I would guess that the 39.6 millisecond difference you quoted was due to what little resistance there was with the air.

[ewmon]

Let me horn my way in here and say that the results (ie, time to reach the ground) between a fired and dropped bullet is mixed.

 

For example, a bullet fired from a rifled gun will spin rapidly and acquire gyroscopic stability, causing the bullet to remain horizontal. As the fired bullet begins to drop, the angle of attack through the air changes, which provides lift to the bullet. A bullet simply dropped through air acquires no lift, only the drag due to its downward fall.

 

In another example, a bullet fired from a non-rifled gun will not spin or acquire the gyroscopic stability, and so, the aerodynamic forces may cause the bullet to turn downward, point first, in which case, it will present a smaller cross-sectional area, which will cause it to fall faster than the dropped bullet that is "keyholing" its way through the air.

 

There are many factors at play here. I have only mentioned a few.

[ccwebb]

ewmon-

 

I'm sorry, but I am going to have to respectfully disagree. The fired bullet is following a parabolic flight path. The angle of attack does not change because the relative wind does not change. The bullet does not generate lift.

[ewmon]

Okay, I'll accept parabolic.

 

So, why doesn't the bullet's spin stabilize the bullet? The angles are exaggerated in the diagram below, and it exists for bullets fired horizontal, although rather slightly. The gyroscopic effect diminishes the bullet's tractability by the air, and the bullet attitude will remain mostly horizontal, while (as you said) its trajectory angles downward, so the angle of attack is non-zero which produces lift, making it drop more slowly.

 

I compared it to a non-spinning bullet, which is more tractable, and will angle downward, typically presenting a smaller cross-sectional area, and thus less drag, and it will drop faster.

 

Edited October 2, 2013 by ewmon

[WWLabRat]

Okay, I'll accept parabolic.

 

So, why doesn't the bullet's spin stabilize the bullet? The angles are exaggerated in the diagram below, and it exists for bullets fired horizontal, although rather slightly. The gyroscopic effect diminishes the bullet's tractability by the air, and the bullet attitude will remain mostly horizontal, while (as you said) its trajectory angles downward, so the angle of attack is non-zero which produces lift, making it drop more slowly.

 

I compared it to a non-spinning bullet, which is more tractable, and will angle downward, typically presenting a smaller cross-sectional area, and thus less drag, and it will drop faster.

 

Can you include the diagram?

[ewmon]

I can see the diagram in your quote. It's background is blue. You can't see it?

 

Here's its URL —

 

http://www.nennstiel-ruprecht.de/bullfly/fig15.gif

 

It actually shows the Magnus Effect and the resulting sideways drift, but the gyroscopic stability is clearly shown.

[WWLabRat]

For some reason it wasn't showing on my other computer... Odd. My apologies.