Abstract
The problem of maximizing the distance run in a given time is considered as a problem in optimal control. The parameters involved are the resistive force, the maximal propulsive force available, the energy supply rate, the initial energy level and a fatigue constant. The latter is the proportionality constant relating the additional rate of energy loss due to fatigue at time t to the energy already spent in running up to time t. The constrained optimization problem is reduced to a single variable problem in the first switching time, the time at which the runner changes from maximal thrust to constant cruising speed. An algorithm is presented for the determination of the maximum distance. Short and long race approximations are also presented. Methods are described for determining the parameters. Predictions of the model are compared with current world track records for both men and women for distances up to 274.48 km (the maximum distance run by a man in 24 hours). The mean absolute error for 24 men's records is 2.35% and for 16 women's records is 1.61%.
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