Introduction: Mechanical power output in sprint cycling depends on pedaling rate, with an optimum at around 130 revolutions per minute (rpm). In this study, the question is addressed if this optimal pedaling rate can be understood from a Hill-type description of muscular dynamics. In particular, it is investigated how 1) the power-velocity relationship that follows from Hill's force-velocity relationship and 2) activation dynamics (from the perspective of which the optimal pedaling rate is near-zero) affect the optimal pedaling rate.
Methods: A forward dynamics modeling/simulation approach is adopted in this study. The skeletal model is a 2D linkage of rigid segments; it is actuated by eight Hill-type "muscles." Input of the model is the neural stimulation of the muscles, output is the resulting movement and variables dependent thereupon, such as pedal forces. For a wide range of isokinetic pedaling rates, the neural stimulation is optimized with respect to the average mechanical power output.
Results: Correspondence between experimental data and simulation results regarding 1) the (pedaling-rate dependent) muscle phasing, 2) pedal forces, and 3) the power-pedaling rate relationship is good. At the optimal pedaling rate predicted by the model (120 rpm), muscles contract at velocities well below those that maximize their power output. Finally, when a model is considered that lacks activation dynamics, it is found that both the optimal pedaling rate and the maximal power output increase substantially.
Discussion: From the results pertaining to the standard model, it is concluded that the optimal pedaling rate is not uniquely specified by the power-velocity relationship of muscle, as suggested in literature. From the results pertaining to the model lacking activation dynamics, it follows that activation dynamics plays a surprisingly large role in determining the optimal pedaling rate. It is concluded that the pedaling rate that maximizes mechanical power output in sprint cycling follows from the interaction between activation dynamics and Hill's power-velocity relationship.