Modelling of a cyclist's power for time trials on a velodrome

We formulate a phenomenological model to study the power applied by a cyclist on a velodrome-for individual timetrials-taking into account the straights, circular arcs, connecting transition curves, and banking. The dissipative forces we consider are air resistance, rolling resistance, lateral friction and drivetrain resistance. Also, in general, the power is used to increase the kinetic and potential energy. However, to model a steady ride-as expected for individual timetrials-we assume a constant centre-of-mass speed and allow the cadence and power to vary during a lap. Hence, the only mechanical energy to consider is the increase of potential energy due to raising the centre of mass upon exiting each curve. Following derivations and justifications of expressions that constitute this mathematical model, we present a numerical example. We show that, as expected, the cadence and power vary only slightly during a steady ride. In addition, we examine changes in the required average power per lap due to modifications of various quantities, such as air density at a velodrome, laptime and several others. Such an examination is of immediate use in strategizing the performance for individual pursuits and the Hour Record.