Re: [Phys-l] Final velocity of bullets

[Brian Whatcott <betwys1@sbcglobal.net>]

At 11:01 AM 1/23/2007, you wrote:
> While real bullets tumble and are a more complex shape, I just ran a
> spreadsheet simulation using a 10 gram, 0.6cm spherical bullet.  At initial
> velocities of 1000 m/s (but with the same results at 500 m/s) I'm getting
> the same final velocity of the bullet fired anywhere from 5 degrees to 90
> degrees (within a very small range).  Namely, about 50 m/s.  I used a time
> increment of .01 seconds, a damping factor b = .5xCxrhoxA  with C = .5 and
> an overall b of .0000387.  I let g stay constant at 9.81 and assumed a
> v-squared dependency.  The flight times ranges from 12 to 27 seconds for the
> 1000 m/s initial velocity.  If you want to try this, the only complication
> is that the air-resistance induced acceleration changes sign after the
> bullet starts down.  I just adjusted that manually with each trial (changing
> angle).
>
> I think this might suggest that once the bullet starts tumbling (if it does)
> then the final velocity really doesn't depend on the angle fired.  Can
> anybody confirm or refute these calculations?
>
> Rick

NLREG has an iterative solver using the bullet trajectory as an example.
It provides much the same results, I find, for reasonably high elevations.

However, Rick will easily see that small elevations can deliver fast, lethal
bullets. That is the modus of the usual rifle, after all.
To expand on the point: if he will agree on the elevation value
for maximal range, then lower barrel elevations ought to land a bullet
with greater speed.
(usually)



Brian Whatcott    Altus OK    Eureka!