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.

1 Answer

Zero friction == zero forward movement possible through running.

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:

$$F_{friction} = \mu F_N$$

Naively, more gravity == more frictional force == more "push off" to get you started running. On the other hand as you suggest, at some point gravity would be too strong that no human could ever stand. Seems that at least up to 1.5 times Earth gravity is doable from The Biology of Human Survival: Life and Death in Extreme Environments by Claude A. Piantadosi (2003):

Adaptation to Sustained G Forces

The mechanisms of homeostasis and adaptation to sustained G forces are unique, and they have important implications for prolonged human space flight. It is not surprising that chronic G-force tolerances are far below the acute tolerance limits, and the plot of G tolerance versus time is the familiar hyperbola. The human G-tolerance curve approaches its zero time asymptote at about 9 G, and its lifetime asymptote is about 1.5 G. Although this curve outwardly appears to be smooth, it is important to realize that human G tolerance, like other physiological strains, is limited by different physiological factors at different levels of G stress. Human volunteers have tolerated 1.5 G for seven days with no apparent ill effects. However, after just twenty-four hours at 2 G, evidence of significant fluid imbalance is detectable. At 3 G to 4 G fatigue is limiting, and above 4 G cardiovascular factors limit G tolerance.