On Bicycles, and.... what else is there?

One issue in using VAM to predict power is the effect of variation in grade. I looked at this back in November, 2009 . Grade variation leads to speed variation (at constant power) and speed variation results in an increase in energy dissipated to wind resistance. The analytic result I got was: Δ p / p 0 ≈ 3 f [ < Δ grade ² > / ( grade 0 + C RR )² ] × [ ( 1 - f ) / ( 1 + 2 f ) ]² where f is the fraction of power from wind resistance, <Δ grade ²> is the variance of grade with respect to time (this is to first order the variance with respect to position), and C RR is the coefficient of rolling resistance. Using iBike data from a ride up Old La Honda (iBike directly measures grade, rather than indirectly via altitude), I concluded at constant power up Old La Honda the grade variation would lead to a 0.44% increase in power. I can convert this to the effect on VAM by multiplying by the fractional effect of power on VAM : Δ VAM / VAM 0 ≈ 3 f [ < Δ grade ² ...

This Tour de France has experienced truly epic increases in people calculating how much power riders generate on climbs, typically towards assessing whether Chris Froome is practicing illicit performance enhancement. One of the more popular practioners of this assessment is VeloClinic, for example in his Haiku-esque Tumblr page . In previous years, there has been a good deal of discussion about VAM, Ferrari's statistic of rate of vertical ascent. Since climbing primarily involves mass overcoming gravity, VAM is related to power/mass, but but it's only a crude instrument, since the more gradual the climb, the greater the fraction of power going into wind resistance and rolling resistance. Additionally, it is possible to sustain higher VAM for shorter climbs compared to longer ones: on shorter climbs you can use your anaerobic energy reserves more rapidly, increasing the energy per unit time, which is power. Furthermore, at higher altitude oxygen concentrations in the atmos...