Optimum take-off techniques for high and long jumps.

High jumpers run at moderate speeds and set down the foot, from which they take off, well in front of the body. Long jumpers run up much faster and place the foot less far forward, with the leg at a steeper angle. A simple model, which takes into account the mechanical properties of muscle, predicts optimum take-off techniques that agree well with those used by athletes. These predictions are remarkably insensitive to the numerical values assigned to the physiological parameters.