Re: drag coef. and falling bullets

[John Denker <jsd@MONMOUTH.COM>]

At 11:26 PM 1/19/00 -0800, Leon Leonardo wrote:

> As for Reynolds number, it seems that so long as the
> flow is turbulent, and well away from Mach one, the
> v^2 dependence is valid.

Yes, to within an approximation good enough for present purposes.  See
figure 7.4 on page 90 of _What Makes Airplanes Fly_ by Peter P. Wegener.

> What we have found is that if the bullet is released
> in water, regardless of its initial orientation, very
> quickly turns and falls sideways.

1) It's nice that you did the experiment.

2) Beware that the Reynolds number for the water experiment is grossly
different from the case you said you were primarily interested in.  You
might be much better off dropping bullets from a tall building.  A
multi-story indoor atrium or stairwell alleviates wind problems.  Let them
hit paper targets and see if you get point-first or broadside holes.

3) While you're at it, why not measure the velocity?  Let the bullet hit
two or more paper targets a few feet apart, and record the noise using an
oscilloscope in single-trace mode.

4) For the first few hundred yards of flight after leaving the muzzle, the
bullet should be spin-stabilized.  However, assuming it is fired in a
direction other than straight down, during its terminal fall it could be:
  -- spin stabilized at some cockeyed angle, or
  -- falling broadside as you describe, or
  -- tumbling.

> I wonder if the bullet will still be spinning when it
> hits the ground?

You can calculate that yourself.  Use a coefficient of skin-friction drag
on the order of 0.01 and see how long it takes to lose its spin.

> Problem is the drag coeff for such an approach
> assumes the bullet falls point first, which we've
> found, is not the case.

How much accuracy do you really need?  The range of plausible coefficients
is limited;  i.e. you might be able to just pick one and run with
it.  Using figure 7.3 on page 89 of Wegener, we have
  0.47 -- sphere -- representative of point-first flight
  1.17 -- cylinder -- representative of broadside flight

Additional numbers in the same range can be found in figure 7.10 on page
104, op. cit.

The troublesome extremes come from things like
 *) really streamlined (trout-shaped) objects, which have total drag that
is very low and dominated by skin-friction drag, which depends on wetted
area independent of frontal area.
 *) tumbling objects, which can have total drag that depends on the swept
area, which could be vastly larger than the physical area of the object.

> Do You Yahoo!?

Not in public.