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

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.