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In article <800325178@news2.compulink.com> drizzt@cml.com (drizzt) writes:
>
>My original question as to how fast superman could run seems to have been 
>misunderstood because a few people wrote me suggesting that on the moon 
>or in outer space, he could run at the speed of light.  That would be 
>flying and not RUNNING.  I'm more concerned with Superman being able to 
>push off of the ground with a pair of Nike airs without falling down due 
>to inertia and how long he has to wait before taking each step because 
>gravity takes time to pull him back down from each step.  
>
>On the other hand, if this speed IS fast enough so that his suit might 
>burn up or something, THEN all the stuff with fluid dynamics and etc are 
>relevant.  But I think his maximum speed won't reach that high.  
>
>Because I have a VERY limited knowledge of physics, I would like some 
>guesses from people as to how much friction there is between Superman's 
>shoes and the ground (asphalt maybe) and how high he will hop with x 
>amount of force from his legs.
>
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Ok, I'm sucked into this.  Assuming that Superman can move his legs as fast
as he wants, then there is no reason to assume that there is any waiting time
between steps.

Here's my back of the matchbox calculation using simple physics concepts.
Superman's weight is given by W = mg, where m, g are his mass and the gravit-
ational constant, respectively.  The amount of force that he can impart to
the ground perpendicular to his weight (parallel to the ground) is the
force used to accellerate him (assuming no energy losses).  This force can
be expressed in terms of Coulomb's friction law F1 = qW = qmg, where q is
the dynamic friction coefficient (assume that he is just slipping at maximum
speed).  Note that no dynamic impact factors are being considered here.

There is also a drag force imparted on Supie by the air as he moves through it.
Assuming that force varies quadratically with his velocity (for low air speeds),

we get F2 = CApv^2, where C is a drag coefficient, A is his projected area to
the air, p is the density of air, and v is his velocity.  This drag force acts
opposite to the direction of motion. 

Now, when Superman reaches his maximum velocity, F1 = F2.  If you make the
substitutions, you get

v = sqrt(qmg/CAp)

For q = 0.5, m = 90 kg, g = 9.81, C = 1.0, A = 2 m^2, and p = 1.118 kg/m^3,
you get v = 14 m/sec, which means he could run 100 m in 7.14 sec (take that,
Ben Johnson).

I'm sorry if it was a homework assignment....

Rick.   

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