A mathematical model to determine optimum cadence for an individual cyclist using power output, heart rate and cadence data collected in the field

• Main Author: Reed, R. J.
• Published: University of Salford 2013
• Subjects: 658; Health and Wellbeing
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.594920

We aim to develop a methodology to determine individual optimum cadences for competitive cyclists using field data. Cadence is the number of pedal crank revolutions per minute or pedalling rate. Currently athletes tend to select a cadence intuitively (choosing a gear that permits a cadence that feels comfortable), with some advice from coaches. Literature defines optimum cadence based on gross efficiency. However only power output, heart rate and cadence measurements from the field are available to us. Hence we determine an optimum cadence as the cadence that minimises heart rate for a given power output. In so doing we consider heart rate a reasonable proxy for gross efficiency. We fit statistical models of power output, heart rate amd cadence, with heart rate lagged behind changes in power output, at various lags (though we believe 30 seconds is appropriate). We consider the effect of fatigue on optimum cadence through calculation of training impulses or TRIMPs, but do not consider the effects of fitness, gradient, or whether athletes are standing or sitting. Optimum cadences are found for two athletes (83 and 70 revolutions per minute respectively); these cadences are similar to athletes’ preferred cadences (82-92 and 65-75 rpm respectively). Optimum cadences do not vary by power output or heart rate in our study, and are relatively insensitive to TRIMP. Power output reduces by approximately 2% for cadences 10 rpm above or below optimum. The methodology we propose can be implemented by a wide range of competitive cyclists to calculate optimum cadence; cyclists need to collect power output, heart rate and cadence measurements from training sessions over an extended period (>6 months), and ride at a range of cadences within those sessions. Cyclists and their coaches can re-calculate optimum cadence, say every 6 months, to take account of possible changes in fitness.