A physiologically motivated analytic model for optimal bicycle gearing

The performance of a cyclist can be optimized by selecting the most appropriate gear ratio for a rider’s physiological profile, bike-rider setup, and environmental conditions. Currently, there is no analytic model available to guide gear ratio selection, and the aim of this study is to fill this gap. We study the kinematics of a cyclist using a physiologically motivated human power model. Analytic expressions for the position and velocity of the cyclist as functions of time are presented. We show how these formulas can be used to optimize the choice of gear ratio, taking into account the transient behavior of sprint-like efforts. The model can be used to guide gear ratio selection in a variety of cycling disciplines.