Application of calculus of variations to maximize the mean ascent speed (VAM)
If one wishes to maximize the mean ascent speed, one needs to choose an appropriate uphill to do so. Herein, we show that, for a constant power, the maximum is achieved by riding along as steep of a hill as possible. Invoking the calculus of variations, we also show that the inclination should be as steady as possible.
Bos, L., Slawinski, M.A., Stanoev, T. (2020) On maximizing VAM for a given power: Slope, cadence, force and gear-ratio considerations, 2006.15816 [physics.pop-ph]