## On modelling bicycle power-meter measurements

**Tomasz Danek, Michael A. Slawinski, Theodore Stanoev**

We combine power-meter measurements with GPS measurements to study the model that accounts for the use of power by a cyclist. The model takes into account the change in elevation and speed along with adverse effects of air, rolling and drivetrain resistance. The focus is on estimating the resistance coefficients using numerical optimization techniques to maintain an agreement between modelled and measured power-meter values, which accounts for the associated uncertainties. The estimation of coefficients is performed for two typical scenarios of road cycling under windless conditions, along a course that is mainly flat as well as a course of near constant inclination. Also, we discuss relations between different combinations of two model parameters, where other quantities are constant, by the implicit function theorem. Using the obtained estimates of resistance coefficients for the two courses, we use the mathematical relations to make inferences on the model and physical conditions. Along with a discussion of results, we provide two appendices. In the first appendix, we illustrate the importance of instantaneous cadence measurements. In the second, we consider the model in constrained optimization using Lagrange multipliers.

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