The Relationship between Pedal Force and Crank Angular Velocity in Sprint Cycling

Purpose: Relationships between tangential pedal force and crank angular velocity in sprint cycling tend to be linear. We set out to understand why they are not hyperbolic, like the intrinsic force-velocity relationship of muscles. Methods: We simulated isokinetic sprint cycling at crank angular velocities ranging from 30 to 150 rpm with a forward dynamic model of the human musculoskeletal system actuated by eight lower extremity muscle groups. The input of the model was muscle stimulation over time, which we optimized to maximize average power output over a cycle. Results: Peak tangential pedal force was found to drop more with crank angular velocity than expected based on intrinsic muscle properties. This linearizing effect was not due to segmental dynamics but rather due to active state dynamics. Maximizing average power in cycling requires muscles to bring their active state from as high as possible during shortening to as low as possible during lengthening. Reducing the active state is a relatively slow process, and hence must be initiated a certain amount of time before lengthening starts. As crank angular velocity goes up, this amount of time corresponds to a greater angular displacement, so the instant of switching off extensor muscle stimulation must occur earlier relative to the angle at which pedal force was extracted for the force-velocity relationship. Conclusion: Relationships between pedal force and crank angular velocity in sprint cycling do not reflect solely the intrinsic force-velocity relationship of muscles but also the consequences of activation dynamics.