Bivariate optimization of pedalling rate and crank arm length in cycling

The contribution of this paper is a bivariate optimization of cycling performance. Relying on a biomechanical model of the lower limb, a cost function derived from the joint moments developed during cycling is computed. At constant average power, both pedalling rate (i.e. rpm) and crank arm length are systematically varied to explore the relation between these variables and the cost function. A crank arm length of 170 mm and pedalling rate of 100 rpm correspond closely to the cost function minimum. In cycling situations where the rpm deviates from 100 rpm, however, crank arms of length other than 170 mm yield minimum cost function values. In addition, the sensitivity of optimization results to both increased power and anthropometric parameter variations is examined. At increased power, the cost function minimum is more strongly related to the pedalling rate, with higher pedalling rates corresponding to the minimum. Anthropometric parameter variations influence the results significantly. In general it is found that the cost function minimum for tall people occurs at longer crank arm lengths and lower pedalling rates than the length and rate for short people.