Experimental validation of the 3-parameter critical power model in cycling

Eur J Appl Physiol. 2019 Apr;119(4):941-949. doi: 10.1007/s00421-019-04083-z. Epub 2019 Jan 29.


Purpose: The three-parameter model of critical power (3-p) implies that in the severe exercise intensity domain time to exhaustion (Tlim) decreases hyperbolically with power output starting from the power asymptote (critical power, ẇcr) and reaching 0 s at a finite power limit (ẇ0) thanks to a negative time asymptote (k). We aimed to validate 3-p for short Tlim and to test the hypothesis that ẇ0 represents the maximal instantaneous muscular power.

Methods: Ten subjects performed an incremental test and nine constant-power trials to exhaustion on an electronically braked cycle ergometer. All trials were fitted to 3-p by means of non-linear regression, and those with Tlim greater than 2 min also to the 2-parameter model (2-p), obtained constraining k to 0 s. Five vertical squat jumps on a force platform were also performed to determine the single-leg (i.e., halved) maximal instantaneous power.

Results: Tlim ranged from 26 ± 4 s to 15.7 ± 4.9 min. In 3-p, with respect to 2-p, ẇcr was identical (177 ± 26 W), while curvature constant W' was higher (17.0 ± 4.3 vs 15.9 ± 4.2 kJ, p < 0.01). 3-p-derived ẇ0 was lower than single-leg maximal instantaneous power (1184 ± 265 vs 1554 ± 235 W, p < 0.01).

Conclusions: 3-p is a good descriptor of the work capacity above ẇcr up to Tlim as short as 20 s. However, since there is a discrepancy between estimated ẇ0 and measured maximal instantaneous power, a modification of the model has been proposed.

Keywords: Anaerobic alactic metabolism; Endurance; Hyperbolic model; Non-linear model; Physical work capacity; Power–time relationship.

MeSH terms

  • Adult
  • Energy Metabolism / physiology*
  • Exercise / physiology*
  • Exercise Test*
  • Humans
  • Male
  • Oxygen Consumption / physiology
  • Physical Endurance / physiology*
  • Task Performance and Analysis
  • Young Adult