Observed velocity v(t) for current world record races in the men's 100 m (Usain Bolt, 9.58 s), 400 m (Michael Johnson, 43.18 s), mile (Hicham El Guerrouj, 3:43.13), and 10,000 m (Kenenisa Bekele, 26:17.53).
Physical model representing anaerobic metabolism. Working muscle is conceived as a reservoir for X-factor, added at rate described by A and removed at rate described by C. Muscle ceases to function when reservoir fills.
(a) Two pacing strategies that cover the same distance (areas under the two curves are the same): an “original” strategy (solid line) and a “perturbed” strategy (dotted-dashed line). (b) X-factor generated during the course of the race by the perturbed pacing strategy (area under dashed curve) is more than the X-factor generated by the original pacing strategy (area under solid curve). (c) X-factor accumulated in the working muscle by the end of the race may or may not be larger for the perturbed compared to the original strategy, depending on the details of the perturbation (area under dashed curve may or may not be larger than area under solid curve). (d) A case in which perturbed strategy is superior to original strategy.
Two perturbations to the optimal pacing strategy of maximum acceleration followed by optimal deceleration. (a) Perturbations of this type are inferior to the optimal pacing strategy. (b) Perturbations of this type are inadmissible.
Comparison of maximum available power (MAP), energy depletion (ED), and X-factor models to data from world-record races. (A) Velocity profiles predicted by the three models compared to velocity profile of the current men's 400-m world-record race (Michael Johnson, 43.18 s). Each of the eight data points represents the average velocity for a 50-m segment of the race. (b) Velocity profiles compared to the current men's 800-m world-record race (David Rudisha, 100.91 s). Each of the four data points represents the average velocity for a 200-m segment of the race.
Number of positive and negative splits for the subset of IAAF-ratified world records for which halfway times are recorded by the IAAF. 1
Comparison of split times in the men's 400-m world record with split times predicted by various models.
Comparison of split times in the men's 800-m world record with split times predicted by various models.
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