In article dtIDb.370160$Dw6.1208036@attbi_s02, Lawrence L'Hote says...

FWIW Frictional losses are very significant at high velocities(i.g. shuttle
reintry). When I was in infantry school at Ft. Jackson during the last
'action' in S.E. Asia I had an opportunity to get one of those info cards
that came in each case of 50 cal. machine gun ammo. On that card, range,
angle, velocity data were given WITH atmospheric effects. If I just used
the equations listed above and optimum 45 deg angle I calculated the range
of the 50 cal. to be IIRC miles but the tables showed about 20% what I
calculated w/o allowances for air resistance. If one is really interested
in this stuff you might look at some of the work Galileo(1564-1642) did with
cannon trajectories years before Newton(1642-1727) Just Google _Galileo
projectile motion_ or some such.

Funny story, true:

I was in my first year at the Univ or Arizona, and was taking an
intro level mechanics course. The instructor was doing a simple
problem like this, which of course neglected any air friction
effects.

He solved it and got the answer, and then as an aside, said,
"of course this is all wrong. The resistance of the air
on the projectile is complicated, it goes like the fourth
power (IIRC) of the velocity. Which one of you can tell me
why I know this?"

The class was very small and it had come out that he had
worked in the shah's army in iran. So I took a SWAG and
piped up, "because you were an artillery officer."

"Correct."

Jim

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