# What would the ideal amount of gravity be for an Olympic sprinter?

The goal here is to get the sprinter running as fast as possible. How much of an effect would more or less gravity have on the top speed of an Olympic sprinter, say...

Usain Bolt?

• 6 ft 5 in (1.95m)

• 207 lbs (94 kg)

• running at 44.72 km/h (27.8 mph)

Obviously too much gravity and he'll be slowed down by weight, but too little gravity and he'll arc up into the air with every step and end up in the triple jump instead of the 100m.

So, what value for the acceleration of gravity maximizes a sprinter's top speed?

You may assume the sprinter has as long a distance as he wants to achieve this top speed.

Zero gravity means zero normal force $F_N$ (unless the runner was tethered to the planet's surface) which means zero friction force $F_{friction}$ because:
$$F_{friction} = \mu F_N$$