Re: Falling pellets

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

Jim,

The viscosity of air has very little to do with the terminal velocity of a
lead pellet as large as 1 mm in diameter beyond determining that the
Reynold's number is very large for any appreciable speed.  I calculate a
terminal velocity of 15 to 20 m/s based on equating the dynamic drag (1/2
C_drag rho A v^2) to the weight of the pellet.  At this velocity the
Reynold's number is on the order of a thousand and the drag
coefficient is approximately 0.5.

John

On Sat, 19 Dec 1998, James G. Pengra wrote:

> Folks,
>        Here's a problem for you. I was interested in the risk due to the
> falling pellets from a shotgun discharged toward the zenith. I assumed that
> they would come down with nearly terminal velocity, so Stokes' Law should
> give a reasonable estimate of their speed. For lead pellets with a diameter
> of 1 mm, I calculated (to my surprise) that the terminal velocity would be
> 337 m/sec. There is a web site
> <http://www.imagina.com/webpages/bbroadside/Big_Table_Metr.html> which
> gives the muzzle velocity of various ammunition, which says that the exit
> velocity from a 12-gauge shotgun is around 345 m/sec. Hmm? In the
> calculation I used the viscosity of air at 18 degrees C (1.827 x 10^(-5)
> N-sec/m^2), and did the calculation in both mks and cgs to make sure I had
> not messed up the units.
>        Somehow, my sense is that falling pellets should not be very
> dangerous if they hit you on exposed skin. However, if this calculation is
> anywhere near correct, falling shotgun pellets would be very dangerous
> indeed. What's wrong here?
>
> --Jim Pengra, Walla Walla, Washinton 99362  mailto:pengra@whitman.edu

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