Equivalent Speed: A New Metric For Cycling Performance

Abstract

While Velocita Ascensionale Media (VAM) can predict performance on steep hills, no such metric for flat terrain exists. Cyclists instead rely on power meters and estimates of air density, drag-area (CDA), and coefficient of rolling resistance Crr to predict ideal speed (IS): the speed they can maintain on a flat windless road. We propose a new parameter-free metric, Equivalent Speed (ES), to predict IS given just speed data. Unlike average speed, V, ES (the distance-weighted average of speed, ν) approximates IS closely. ES assumes constant CDA on a closed loop course. Average drag is proportional to ν², so on a closed course in the absence of wind or braking and ignoring the constant energy lost to rolling resistance, power is given roughly by P∝ν²V. An approximation to third order changes in speed about ES is P∝ν³. Since IS is defined to be constant, V_(IS) = ν_(IS) and we find in this case P_(IS)∝V_(IS)³. ES is then the solution to P=P_(IS) for V_(IS).