cbd@iham1.UUCP (Carl Deitrick) (11/02/84)
The other night a friend and I were talking about his recent hunting trip when the subject of ballistics ( I use the term loosely ) came up. That discussion reminded me of an article I saw someplace that claimed ( in summary) that the forward motion of a body did not change the effect of gravity on that body. The example cited in that article was a bullet fired from a gun held level and not pointed at any obstacle that would stop the bullet. The article claimed that the fired bullet would hit the ground as quickly as a bullet dropped manually from the height of the gun muzzle. Is this true? Did I maybe suffer from a momentary brain flutter and misinterpret the article? If I didn't, is the author full of bat guano? Please reply by mail. Thanks. Carl Deitrick ihnp4!iham1!cbd
herbie@watdcsu.UUCP (Herb Chong, Computing Services) (11/03/84)
This is true. Gravity has only a vertical component that acts downward
equally on the fired bullet and the dropped bullet. We assume perfectly
horizontal surface and negligible downward air resistance as well as
uniform gavitational field. Most first-year dynamics texts will have
you prove this or something like this (monkey dropping coconuts and
a hunter shooting them as they fall is the one I had to prove).
Herb...
I'm user-friendly -- I don't byte, I nybble....
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BITNET: herbie at watdcs,herbie at watdcsujhputtick@watrose.UUCP (James Puttick) (11/03/84)
One thing to keep in mind, though, is that the earth's surface is curved. Thus, if fired from a given height, in the time it takes the bullet to fall that height because of gravity, it will have travelled part of the way along a tangent to the earth, and thus will be a little above the earth at this new point. At low speeds, this extra distance is negligible. At fast enough speeds, though, the new point could be the same height above the ground as the firing point. The result is that the bullet goes into orbit. :-) Now, if only we could forget about air resistance...
jlg@lanl.ARPA (11/07/84)
> One thing to keep in mind, though, is that the earth's surface is > curved. Thus, if fired from a given height, in the time it takes the > bullet to fall that height because of gravity, it will have travelled > part of the way along a tangent to the earth, and thus will be a little > above the earth at this new point. At low speeds, this extra distance > is negligible. At fast enough speeds, though, the new point could be > the same height above the ground as the firing point. The result is that > the bullet goes into orbit. :-) > Now, if only we could forget about air resistance... Speaking of air resistance, there is another effect on the bullet. Due to air viscosity there are strong dissipative forces on the bullet which depend only on the speed of the bullet - not its direction. The result is that gravity is opposed by air resistance more for a moving bullet than for a dropped bullet. This also is a VERY small effect. To demonstrate that a fired bullet actually falls as fast as a dropped object, suspend a metal object from an electro-magnet. Then aim a 'firearm' (popgun, dart gun, etc.) at the object in such a manner that the electro-magnet is turned off when the bullet leaves the gun. Aim the gun exactly at the target. Since both the object and the bullet fall the same distance during the flight time of the bullet, the object will always be hit.
chongo@nsc.UUCP (Landon C. Noll) (11/08/84)
> Now, if only we could forget about air resistance...
But anyone who has taken their first physics class learns how to neglect
air resistance with ease! :-)
chongo <the earth has no atmosphere, neglecting air resistance> \/++\/
--
"Don't blame me, I voted for Mondale!"
John Alton 85'chris@politik.UUCP (Christopher Seiwald) (11/09/84)
> Now, if only we could forget about air resistance...
Ballistics is mostly concerned with the effect of air resistance.
Computing the path of a bullet on the moon is relatively simple (high
school algebra; most bullets don't go fast enough to take advantage of
curvature of the planet). Computing the path of a bullet on the earth
is harder (college calculus). It involves (acceleration due to)
gravity, the ballistic coefficient, viscosity of the air (function of
temp and pressure), and, of course, muzzle velocity.
Does anyone know the actual equations for computing that path?
--
----
Christopher Seiwald
dual!ptsfa!politik!chrisgwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (11/11/84)
> Ballistics is mostly concerned with the effect of air resistance. > > Does anyone know the actual equations for computing that path? To properly take into account the spin of the projectile, velocity dependence of drag, and other details is by no means a trivial task. The equations of motion do not have a closed-form solution, so it must be calculated through numeric approximation. One of the first digital computers, the ENIAC, was employed for computing firing tables. If you make various simplifying assumptions (e.g., neglect spin and lift, make drag proportional to speed and directly opposed to it, etc.), then you can write down an analytic solution. Whether it is useful or not depends on how well the assumptions fit reality. This is nothing new; nearly all exact solutions are to simplified models.