A metabolic limit on the ability to make up for lost time in endurance events.

It has been repeatedly demonstrated that the tolerable duration (t) of high-intensity cycling is well characterized as a hyperbolic function of power (P) with an asymptote that has been termed the "fatigue threshold" and with a curvature constant. This hyperbolic P-t relationship has also been confirmed in running and swimming, when speed (V) is used instead of P; that is, (V - V(F)). t = D', where V(F) is the V at the fatigue threshold, and D' is the curvature constant. Therefore, we theoretically analyzed herein the consequences of an athlete performing the initial part of an endurance event at a V different from the constant rate that would allow the performance time to be determined by the hyperbolic V-t relationship. We considered not only the V-t constraints that limit the athlete's ability to make up the time lost by too slow an early pace but also the consequences of a more rapid early pace. Our analysis demonstrates that both the V(F) and D' parameters of the athlete's V-t curve play an important role in the pace allocation strategy of the athlete. That is, 1) when the running V during any part of the whole running distance is below V(F), the athlete can never attain the goal of achieving the time equivalent to that of running the entire race at constant maximal V (i.e., that determined by one's own best V-t curve); and 2) the "endurance parameter ratio" D'/V(F) is especially important in determining the flexibility of the race pace that the athlete was able to choose intentionally.