The equation of motion of a runner, exerting a maximal effort

Furusawa, Hill and Parkinson (1) have shown that the acceleration of a runner and the maximum speed he can obtain depend upon two factors, ( a ) the maximum force he can exert in propelling himself, and ( b ) the frictional resistance of his muscles. They have experiment these factors in a mathematical equation, which they have tested by experiment. The experimental results fit the equation very satisfactory and allow the values of the constants to be determined. The maximum velocity attained depends upon a balance between the propelling force, which is constant up to the onset of fatigue, and the internal resistance, which increases as the speed rises until it balances the propelling force. In spite of the accuracy with which experiment has been found to verify the equation, this internal resistance has to some degree a hypothetical existence. The object of the present paper is to give it greater reality by showing how an actual external resistance can be added on to it and produces exactly the calculated effect.