Analysis of the upper limitation of the most convenient cadence range in cycling using an equivalent moment based cost function

The article presents the study of the pedalling rates obtained by minimizing a cost function based on a kinetic approach and which can be estimated with more easily achievable experimental data as input than other cost functions. Simulations based on data available in the literature were used to compare the cadences obtained by minimizing well-known joint moment-based cost functions and the proposed cost function. The influence of the power output and of the body mass index on the pedalling rates that minimize the cost function was investigated. Experimental tests performed by four competitive cyclists in the field were used as comparison for the results based on simulations. From simulations emerged that results obtained with the cost function proposed in this work were similar to those based on the absolute average joint moments. We found that the upper limit of the more convenient pedalling rate range decreases linearly with the body mass index, while it increases non-linearly with power output. Furthermore, a polynomial regression of the correlation of the pedalling rate obtained through the method and body mass index and power was found. Experimental results confirmed that the proposed model, finding an approximation of the minimum of muscular effort (not including negative muscular work), is able to estimate the upper limit of an optimal range of cadence. All tested cyclists freely choose to pedal at a cadence under this limit.