On minimizing cyclists’ ascent times: Part II

We formulate an optimization of a bicycle ascent time under the constraints of the average, maximum, and minimum powers. In contrast to the first part of this study, we do not restrict the departure to flying starts with an initial speed determined by the model and its optimization. We allow for various initial speeds, from a standstill to a launched start. We accomplish this by generalizing the discontinuous piecewise constant speed model to a continuous piecewise linear speed model. Regardless of the initial speed, steepness, or profile of the ascent, the optimal strategy tends to a constant ground speed, in agreement with the conclusion of the previous, more restricted, formulation. This new formulation allows us to compare various initial-speed strategies and, hence, has a direct application to competitive cycling. Notably, in timetrials composed of flat and steep sections, it helps one decide whether or not to change the bicycle, which requires stopping and restarting, from one that is more appropriate for flats to one that is more appropriate for uphills.