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Re: [Phys-l] Final velocity of bullets



Ok, here is one for the theoreticians out there.

Of course a rifle bullet is spinning as well as translating. For the
sake of argument, suppose the bullet spins two revolutions as it moves
through a 75 cm long barrel. (these numbers are somewhat arbitrary, but
reasonably close to actual -- please replace with better numbers if you
have them).

Is the bullet still spinning when it reaches its maximum height?

Or, put another way, does a bullet reach terminal velocity before or
after the air friction stops the bullet from spinning and then produces
the tumbling?

Oren Quist, South Dakota State

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of Brian
Whatcott
Sent: Tuesday, January 23, 2007 12:14 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Final velocity of bullets

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!


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