🚀 go-pugleaf

In article <800325178@news2.compulink.com>, drizzt <drizzt@cml.com> wrote:
>
>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.  

Oh, all right, since nobody else seems to be helping much...

First we'll assume Superman always has one foot on the ground or the 
other.  We can work out bounding later, but this is probably all you 
need.  Now, the maximum speed Superman can run is the point at which air 
friction, which works to slow him, is equal to the friction between his 
feet and the ground.  Since his foot is firmly planted, we use static 
friction.

The force of friction is
  
    Ff = mass * gravity * coefficient
 
       = m g k

The force of air friction goes with the square of his speed
 
    Fa = constant * area * densityofair * speed^2

       = C A d v^2

Superman's max speed is determined by
 
    m g k = C A d v^2
 
or  v = sqrt( mgk / CAD )

Superman is a pretty buff guy, say 100 kg (but only 10% body fat), 
gravity is 9.8 m/s^2, coefficient of friction between Nikes and the road 
is, well, according to the CRC Handbook, the coefficient of static 
friction between rubber and solids is 1-4, so let's say about 2, although 
the actual value will vary depending on the terrain.  The drag coefficient 
of a running man is probably around .8, his cross-sectional 
area is about a meter squared, and the density of air
is 1.2 kilograms per cubic meter.

v = sqrt( (100kg)(9.8m/s^2)(2) / (.8)(1m^2)(1.2kg/m^3) )
 
  = 45 m/s
 
  = 100 miles per hour

Very approximately, of course.  Feel free to plug your own numbers into 
the equation.