fitting power-duration model to track & field world records
Last time I described a running power model used by Péronnet and Thibault to apply a power-duration model to running world records. I pointed out some clear problems with their model. One was a clearly erronious estimate of wind resistance, substantially underestimating the metabolic cost of fighting wind resistance assuming reasonable parameters. Another was a strange presentation of acceleration work which looked suspiciously like two errors which essentially canceled each other. Here I'll follow a similar approach but with different parameters: P / M = K 1 η v + ½ [ C D A ρ / M + 1 / D ] v 3 where P is total power, M is total mass (runner + clothes), K 1 is a coeffient representing the metabolic cost of moving a unit mass a unit distance, η is a metabolic efficiency coefficient, C D is a coefficient of drag, A is the cross-sectional area of the runner in the direction of travel, and D is the distance traveled (amortizing the acceleration energy, where I assume a s...