On modelling bicycle power for velodromes: Part I: Formulation for individual pursuits

Abstract

For a moving bicycle, the power can be modelled as a response to the propulsion of the centre of mass of the bicycle-cyclist system. On a velodrome, an accurate modelling of power requires a distinction between the trajectory of the wheels and the trajectory of the centre of mass. We formulate and examine an individual-pursuit model that takes into account the aforementioned distinction. In doing so, we provide details of the invoked physical principles and mathematical derivations, with an emphasis on their limitations. We assume that a velodrome consists of two parallel straights and two semicircular arcs. We neglect the effects of the track inclination along the straights and assume the track inclination along the curves to be constant. For either segment, we consider two distinct black-line speeds. For the latter, the lean-angle expression is derived based on a noninertial frame of the cyclist. Among conclusions quantified by this model is the fact that a constant-cadence approach to an individual pursuit does not minimize the required power.