🚀 go-pugleaf

 
>I assume that there would have to be a maximum because there is only so 
>much friction between his shoes and the ground

The friction is proportianal to the force superman imparts.  If he can
impart very large force down, as well as back, then he could essentially
ensure that his shoes don't slip when he pushes off.  (How he could generate
a force down greater than his own mass*gravity is not clear unless you
invoke some superability.  If he can only run, then the normal force cannot
be greater than his weight.  Then, I suppose you could estimate the ability
of the shoe to hold when he pushes off by multipying some friction coefficient
times this weight (he couldn't run very fast at all if he was using greased
shoes or running on wet ice!).  This gives you the maximum force he can apply.
Then you
can calculate his accelleration using that force.  To get a maximum speed, you
will have to make some assumptions about a quadratic drag law (air friction)
and see at what speed the air drag balances the force.  Essentially, you can
think of a car, instead of a runner.  If the car is not heavy enough it will
just spin its wheels instead of going faster.  Of course if you fitted 
superman with a spoiler...

>Also, as a person 
>runs faster, they have to hop higher and higher off the ground and they 
>can only fall so fast back to the ground.There has to be a delay 
>between each step.

I don't think so.  You could push your legs back down.   Don't need to rely
on gravity to do it for you.
-- 


Keith Alverson
Massachusetts Institute of Technology
Earth, Atmospheric, and Planetary Sciences Deptartment
54-1419
Cambridge MA 02139
USA

tel: 617-253-9345
fax: 617-253-4464
internet:keith@puddle.mit.edu