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Estimation of critical power with nonlinear and linear models

GAESSER GLENN A.; CARNEVALE, TONY J.; GARFINKEL, ALAN; WALTER, DONALD O.; WOMACK, CHRISTOPHER J.
Medicine & Science in Sports & Exercise: October 1995
Applied Sciences: Biodynamics: PDF Only

ABSTRACT

Sixteen young, healthy males each performed five to seven randomly assigned, exhaustive exercise bouts on a cycle ergometer, with each bout on a separate day and at a different power, to compare estimates of critical power (PC) and anaerobic work capacity (W') among five different models: t = W'/(P - PC) (two-parameter nonlinear); t = (W'/(P - PC)) - (W'/(Pmax - PC)) (three-parameter nonlinear); P ± t = W' + (PC't) (linear (P · t)); P = (W'/t) + PC (linear (P)); P = PC + (Pmax - PC)exp(−t/τ) (exponential). The data fit each of the models well (mean R2 = 0.96 through 1.00 for each model). However, significant differences among models were observed for both PC (mean · standard deviation (SD) for each model was 195 ± 29 W through 242 ± 21 W) and W' (18 ± 5 kJ through 58 ± 19 kJ). PC estimates among models were significantly correlated (r = 0.78 through 0.99). For W', between-model correlations ranged from 0.25 to 0.95. For a group of six subjects, the ventilatory threshold for long-term exercise (LTE Tvent; 189 ± 34 W) was significantly lower than PC for all models except the three-parameter nonlinear (PC = 197 ± 30 W); PC for each model was, however, positively correlated with LTE Tvent (r = 0.69 through 0.91). The three-parameter nonlinear model, with t appropriately designated as the dependent variable, is preferred first, on statistical grounds; second, because the assumption is not made that P is infinite as t approaches 0; and third, because it produces a PC estimate that comes closest to a physiological parameter, LTE Tvent, that reflects the capacity for sustained aerobic power output.

©1995The American College of Sports Medicine