Combinations of Cycle Rate and Length for Minimizing the Muscle Power Requirement in Human Running

Abstract

The purpose of this study was to test the hypothesis that, in human running at a given speed, runners select the combination of cycle rate (CR) and cycle length (CL) that minimizes the power generated by the muscles. A 2-D model of a runner consisting of a trunk and two legs was defined. A force actuator controlled the length of each leg, and a torque actuator controlled the amplitude and frequency of the backward and forward swing of each leg. The sum of the powers generated by the actuators was determined for a range of CRs at each of a series of speeds. The CR and CL vs. speed relationships selected for the model were derived from a series of CR and CL combinations that required the least power at each speed. Two constraints were imposed: the maximum amplitude of the forward and backward swing of the legs (±50°) and the minimum ground contact time needed to maintain steady-state running (0.12 sec). The CR vs. speed and CL vs. speed relationships derived on the basis of a minimum power strategy showed a pattern similar to those reported for longitudinal (within-subjects) analyses of human running. The anatomical constraint set a limit on the maximum CL attainable at a given speed, and the temporal constraint made CL decrease at high speeds. It was concluded that the process for selecting CL-CR combinations for human running has characteristics similar to the process for solving a constrained optimization problem.