  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.
