Steep constant-grade climbs minimize cycling ascent time

What the study found: The study says that to minimize the time needed to gain a given height, a cyclist should climb the steepest constant-grade hill possible. For a fixed average-power constraint and given start and end points, the minimum-ascent-time path is the straight line connecting the points, ridden at constant speed, which along that line is equivalent to constant power.
Why the authors say this matters: The authors describe VAM, or velocità ascensionale media, as a measure of a cyclist’s climbing ability, and the findings indicate a way to think about maximizing it. They also note that power available to the cyclist is a necessary condition for examining other aspects of climbing strategy.
What the researchers tested: The article examines the brachistochrone problem, which is the problem of finding the trajectory of minimum ascent time, in the context of cycling ascents. It considers start and end points and a fixed average-power constraint.
What worked and what didn't: The result given is that the straight line between the points is the minimum-time ascent path under the stated power constraint. The abstract contrasts this with the classical descent brachistochrone under gravity, which is a cycloid and does not have constant speed.
What to keep in mind: The abstract says the steepness limit is affected by factors such as pedalling efficiency, feasible cadence, maintaining balance, preventing front-wheel lift, and avoiding rear-wheel skidding. It also says the article is focused on the consequences of available power, so other aspects of climbing strategy are not examined here.

Key points

• The study says the minimum-time ascent for a cyclist is a straight line between the start and end points under a fixed average-power constraint.
• The authors state that this straight-line ascent is ridden at constant speed, which is equivalent to constant power along that path.
• The paper links the finding to VAM, described as a measure of cycling climbing ability.
• The abstract contrasts the cycling ascent result with the classical gravity-driven descent brachistochrone, which is a cycloid.
• The abstract notes practical limits on steepness, including pedalling efficiency, cadence, balance, front-wheel lift, and rear-wheel skidding.