On minimizing cyclists' ascent times (Q6632481)

The authors formulate a strategy to minimize the time of climbing an uphill with a bicycle. They consider that the ascent profile, including distance and steepness, is known. The weight of the cyclist, together with the bicycle, as well as fitness level, quantified by the power output, are also known. The aforementioned strategy is formulated with these and other information, such as the air, rolling and drivetrain resistances. The formulation is based on power considerations, which is the key metric in training and race preparation. Most modern racing bicycles have power meters.\N\NThe article begins with a phenomenological model to estimate the power required to maintain a given speed. The model is analogous to the one used and discussed in [\textit{L. Bos} et al., ``Modelling of a cyclist's power for time trials on a velodrome'', Preprint, \url{arXiv:2201.06788}] and [\textit{L. Bos} et al., ``Modelling of a cyclist's power for time trials on a velodrome'' Sports Engineering 27, Paper No. 9 (2024; \url{doi:10.1007/s12283-024-00451-x})].\N\NSubsequently, the authors seek the riding strategy that results in the least ascent time and show that under stated constraints and assumptions it is the constant speed. This result is illustrated for several distinct ascent profiles and is compared to another plausible strategy. Comments on possible future developments are added. The article ends with five Appendices providing supplementary information about the methods, comments on numerical optimization, and insights into empirical adequacy of the model.