  We prove that, given an average power, the ascent time is minimized if a
cyclist maintains a constant ground speed regardless of the slope. Herein,
minimizing the time is equivalent to maximizing -- for a given uphill -- the
corresponding mean ascent velocity (VAM: velocit\`a ascensionale media), which
is a common training metric. We illustrate the proof with numerical examples,
and show that, in general, maintaining a constant instantaneous power results
in longer ascent times; both strategies result in the same time if the slope is
constant. To remain within the athlete's capacity, we examine the effect of
complementing the average-power constraint with a maximum-power constraint.
Even with this additional constraint, the ascent time is the shortest with a
modified constant-speed -- not constant-power -- strategy; as expected, both
strategies result in the same time if the maximum and average powers are equal
to one another. Given standard available information -- including level of
fitness, quantified by the power output, and ascent profile -- our results
allow to formulate reliable and convenient strategies of uphill timetrials.
