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 confi rmed in running and swimming, when speed (V) is used instead of P; that is, (V - V-F) . t = D', where V-F is the Vat the fatigue threshold, and D' is the curvature constant. Therefore, we theoretically analyzed herein the con sequences of an athlete performing the initial part of an endurance event a t a V different from the constant rate that would allow the performance tim e to be determined by the hyperbolic Vt relationship. We considered not onl y the Vt constraints that limit the athlete's ability to make up the time l ost by too slow an early pace but also the consequences of a more rapid ear ly pace. Our analysis demonstrates that both the VF and D' parameters of th e athlete's Vt 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 whol e running distance is below VF, t:he athlete can never attain the goal of a chieving the time equivalent to that of running the entire race at constant maximal V(i.e., that determined by one's own best Vt curve); and 2) the "e ndurance parameter ratio" D'/V-F is especially important in determining the flexibility of the race pace that the athlete was able to choose intention ally.