Marginal gains in sprint cycling: quantifying the time-varying impact of aerodynamic drag reduction

Aerodynamic optimization has gained increasing attention in competitive cycling. It is widely believed that aerodynamics plays a more critical role at higher riding speeds, as the power required to overcome aerodynamic drag is proportional to the cube of the riding speed, making it increasingly dominant at higher riding speeds. This study challenges the applicability of this paradigm for sprint cycling. We demonstrate that neither riding speed nor the percentage of power output used to overcome aerodynamic drag can adequately reflect the importance of aerodynamics in sprint cycling, due to the significant role of transient dynamics in sprint cycling. To address this gap, we present a theoretical framework based on perturbation analysis to examine marginal gains in sprint time resulting from time-dependent parameter variations. Our analysis also explores the trade-off between power output and aerodynamic efficiency. Through several case studies of standing-start sprints, we establish a quantitative relationship between aerodynamic improvements and savings in sprint time. Furthermore, we propose a metric to explicitly quantify the time-dependent importance of aerodynamic drag on sprint performance. Overall, this study advances the understanding of performance optimization in sprint cycling and provides a practical tool for marginal gain analysis.