Development and field validation of an omni-domain power-duration model

J Sports Sci. 2020 Apr;38(7):801-813. doi: 10.1080/02640414.2020.1735609. Epub 2020 Mar 4.


Purpose: To validate and compare a novel model based on the critical power (CP) concept that describes the entire domain of maximal mean power (MMP) data from cyclists.Methods: An omni-domain power-duration (OmPD) model was derived whereby the rate of W' expenditure is bound by maximum sprint power and the power at prolonged durations declines from CP log-linearly. The three-parameter CP (3CP) and exponential (Exp) models were likewise extended with the log-linear decay function (Om3CP and OmExp). Each model bounds W' using a different nonconstant function, W'eff (effective W'). Models were fit to MMP data from nine cyclists who also completed four time-trials (TTs).Results: The OmPD and Om3CP residuals (4 ± 1%) were smaller than the OmExp residuals (6 ± 2%; P < 0.001). W'eff predicted by the OmPD model was stable between 120-1,800 s, whereas it varied for the Om3CP and OmExp models. TT prediction errors were not different between models (7 ± 5%, 8 ± 5%, 7 ± 6%; P = 0.914).Conclusion: The OmPD offers similar or superior goodness-of-fit and better theoretical properties compared to the other models, such that it best extends the CP concept to short-sprint and prolonged-endurance performance.

Keywords: Athletic performance; anaerobic threshold; critical power model; cycling; mathematical modelling; maximal mean power data; power-duration profile; wʹ.

Publication types

  • Validation Study

MeSH terms

  • Adult
  • Bicycling / physiology*
  • Competitive Behavior / physiology*
  • Exercise Test
  • Female
  • Humans
  • Male
  • Models, Statistical*
  • Physical Endurance / physiology*