What the study found
The study finds that, for a cyclist trying to gain a given height in the least time, the best strategy is to climb the steepest constant-grade hill possible. For a fixed average-power constraint, the minimum-time ascent path between two points is a straight line ridden at constant speed, which is equivalent to constant power along that line.
Why the authors say this matters
The authors say this helps frame cycling ascent strategy in terms of the power available to the cyclist, which they describe as a necessary condition for examining other aspects of climbing. They also link the result to VAM, or velocità ascensionale media, a measure of climbing ability.
What the researchers tested
The article examines the brachistochrone problem for cycling ascents, meaning the path that minimizes ascent time. It considers given start and end points and assumes a fixed average-power constraint.
What worked and what didn't
Under the conditions studied, the straight line between the start and end points was the minimum-time ascent path. On that path, constant speed corresponds to constant power. This differs from the classical brachistochrone for descent under gravity, which is a cycloid with non-constant speed.
What to keep in mind
The abstract notes that steepness is limited by factors such as pedalling efficiency, feasible cadence, balance, preventing the front wheel from lifting, and avoiding rear-wheel skidding. It also says the article is focused on the consequences of power available to the cyclist, and limitations are otherwise not described in the available summary.
Key points
- VAM is described as a measure of a cyclist’s climbing ability.
- For a given height gain, the authors say minimizing time is equivalent to maximizing VAM.
- With a fixed average-power constraint, the minimum-time ascent path is a straight line between the start and end points.
- Along that straight line, constant speed is equivalent to constant power.
- The result is contrasted with the classical descent brachistochrone, which is a cycloid.
Disclosure
- Research title:
- Fastest cycling ascent is a straight line under fixed average power
- Authors:
- Len Bos, Michael A. Slawiński, Raphaël A. Slawinski, Theodore Stanoev
- Institutions:
- Memorial University of Newfoundland, Memorial University of Newfoundland, Mount Royal University, University of Verona
- Publication date:
- 2026-04-23
- OpenAlex record:
- View
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