Modeling road-cycling performance

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Abstract
This paper presents a complete set of equations for a “first principles” mathematical model of road-cycling performance, including corrections for the effect of winds, tire pressure and wheel radius, altitude, relative humidity, rotational kinetic energy, drafting, and changed drag. The relevant physiological, biophysical, and environmental variables were measured in 41 experienced cyclists completing a 26-km road time trial. The correlation between actual and predicted times was 0.89 (P < or = 0.0001), with a mean difference of 0.74 min (1.73% of mean performance time) and a mean absolute difference of 1.65 min (3.87%). Multiple simulations were performed where model inputs were randomly varied using a normal distribution about the measured values with a SD equivalent to the estimated day-to-day variability or technical error of measurement in each of the inputs. This analysis yielded 95% confidence limits for the predicted times. The model suggests that the main physiological factors contributing to road-cycling performance are maximal O2 consumption, fractional utilization of maximal O2 consumption, mechanical efficiency, and projected frontal area. The model is then applied to some practical problems in road cycling: the effect of drafting, the advantage of using smaller front wheels, the effects of added mass, the importance of rotational kinetic energy, the effect of changes in drag due to changes in bicycle configuration, the normalization of performances under different conditions, and the limits of human performance.

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