On maximizing VAM for a given power: Slope, cadence, force and gear-ratio considerations

Abstract

The velocit\`a ascensionale media (VAM) is measurement that quantifies a cyclist's climbing ability. It depends on both the ground speed of a bicycle-cyclist system and the slope of an incline. To maximize the ascent speed, the solution to the brachistochrone problem determines that the optimal curve for the incline is a straight line, which is a hill with a constant slope. The maximum obtainable VAM value by a cyclist increases monotonically with the slope of the incline, but is limited by the maximum sustainable power. These properties -- which are theorems stemming from a standard mathematical model to account for the power required to propel a bicycle -- constitute a mathematical-physics background upon which various strategies for the VAM maximization can be examined in the context of the maximum sustainable power as a function of both the gear ratio and cadence. Recently established records provide an empirical support for these analytical results, which are based on theoretical considerations.