The limits of the possible: models of power supply and demand in cycling

This paper outlines a general strategy for mathematical modeling of cycling performance. This strategy involves formulating one expression describing the power available for external work from physiological sources. The variables used in this expression include maximal aerobic power (VO2max), fractional utilisation of VO2max, mechanical efficiency, maximal accumulated oxygen deficit, and the time constants relating to the expression of aerobic and anaerobic capacities. A second expression describing the power demand of cycling is then constructed. The variables used in this expression include the mass, projected frontal area and drag characteristics of the system, the coefficient of rolling resistance, environmental variables such as temperature, barometric pressure, relative humidity, wind speed and direction and the slope of the course. The two expressions are equated and solved using an iterative procedure. Two series of trials were used to assess the predictive accuracy of the model, one using track endurance performances and the other a 26 km road time-trial. The correlations between actual and predicted times have been excellent (0.92-0.95, p < or = 0.0001), with small mean differences (0-1.83% of mean performance time) and mean absolute differences (1.07-3.24%). The model allows us to make predictions about the effect of equipment changes and environmental factors, to compare performances under very different conditions, and to predict the limits of the possible in cycling performance. A range of options designed to improve cycling performance is described.