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Reply to "Effect of elevation on performance"

I don't really know what's been done recently, but I'll remind you of the work we did some 24 years ago, which we applied to the Boston Marathon course.

To a first approximation, the effect of elevation is given simply by the elevation difference between a course's start and finish. Ken Young realized this a long time ago, and it's why we base the aidedness of a course for record purposes on its net drop. In an attempt to go beyond this first order approximation, I presented a formula for "Hill Effect to Second Order" which was published in the January 1989 issue of Measurement News, available at http://www.runscore.com/course...mentNews/033_89a.pdf

A year later, Alan Jones and I applied this to the Boston Marathon course in an article titled "Uphills, Downhills and the Boston Marathon" published in the March 1990 issue of MN, available at http://www.runscore.com/course...mentNews/040_90a.pdf This article also included a derivation of the 2nd order hill formula, which I hadn't included in my 1989 article. And in that same March 1990 issue, Pete Riegel used the formula to work out optimal pacing for the Boston Marathon course. Pete and I also applied the formula to a number of other courses around that time.

My 2nd order formula was based on the assumption that the energy cost of running, per unit distance, is a nearly linear (but slightly convex) function of slope -- an assumption that seemed to be borne out fairly well by energy cost measurements on treadmills, for the range of speeds used in distance running. It was also based on a simplified physiological model, assuming that the runner has a fixed energy store, which can be used maximally by expending energy at a constant rate. Clearly, this ignored a lot of effects (such as physiological changes in a given runner during the course of a race). But, overall, it seemed pretty reasonable.
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