  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.
