Estimation of critical power with nonlinear and linear models

Glenn A. Gaesser, Tony J. Carnevale, Alan Garfinkel, Donald O. Walter, Christopher J. Womack

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117 Scopus citations


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). PCestimates 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 PCfor all models except the three-parameter nonlinear (PC= 197 ± 30 W); PCfor 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 PCestimate that comes.

Original languageEnglish (US)
Pages (from-to)1430-1438
Number of pages9
JournalMedicine and science in sports and exercise
Issue number10
StatePublished - Oct 1995
Externally publishedYes

ASJC Scopus subject areas

  • Orthopedics and Sports Medicine
  • Physical Therapy, Sports Therapy and Rehabilitation


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