Heavy paratroopers

There was a bit of a kerfuffle in the comments section on this matter not so long ago. My dad has now weighed in:

“I know its old stuff now but here’s my two pennyworth on falling parachuters. Large persons do indeed fall faster than small ones, but on account of their size rather than their weight. Terminal velocity is reached when the air resistance force becomes equal to the weight. Approximating a person to a sphere of radius a (more appropriate with some than others [yes yes dad you could stand losing a few pounds yourself — d^2] ) the person’s weight is proportional to a-cubed, whereas the air resistance is proportional to a (Stokes Law). As a result, the terminal velocity becomes proportional to a-squared.”

This is, as far as I am concerned, the official view of the physics community on the subject. Any physicist wanting to disagree, go ahead, but please be aware that you are disagreeing with Mr Davies Sr and therefore wrong. I am treating the paragraph above as the definitive truth on heavy versus light paratroopers and their rates of descent. If anyone who reads this site is a paratroop or ex-paratroop and remembers falling more quickly than their heavier comrades-in-arms, I might revise this view, but not otherwise (recreational skydivers, keep your views to yourselves).

In semi-related news, I’d be interested in anyone’s opinion on the subject of which is more of a stretch; to assume that a person is a rational utility-maximiser, or to assume that he’s a sphere of radius a. Actually, from now on, it is probably official policy of this site that homo economicus is spherical, except in contexts where we have to work on the economics of overcrowding, in which case we’ll assume he’s a cuboid or other tessellating polyhedron.


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