Modeling the expenditure and reconstitution of work capacity above critical power

Med Sci Sports Exerc. 2012 Aug;44(8):1526-32. doi: 10.1249/MSS.0b013e3182517a80.


Purpose: The critical power (CP) model includes two constants: the CP and the W' [P = (W' / t) + CP]. The W' is the finite work capacity available above CP. Power output above CP results in depletion of the W' complete depletion of the W' results in exhaustion. Monitoring the W' may be valuable to athletes during training and competition. Our purpose was to develop a function describing the dynamic state of the W' during intermittent exercise.

Methods: After determination of V˙O(2max), CP, and W', seven subjects completed four separate exercise tests on a cycle ergometer on different days. Each protocol comprised a set of intervals: 60 s at a severe power output, followed by 30-s recovery at a lower prescribed power output. The intervals were repeated until exhaustion. These data were entered into a continuous equation predicting balance of W' remaining, assuming exponential reconstitution of the W'. The time constant was varied by an iterative process until the remaining modeled W' = 0 at the point of exhaustion.

Results: The time constants of W' recharge were negatively correlated with the difference between sub-CP recovery power and CP. The relationship was best fit by an exponential (r = 0.77). The model-predicted W' balance correlated with the temporal course of the rise in V˙O(2) (r = 0.82-0.96). The model accurately predicted exhaustion of the W' in a competitive cyclist during a road race.

Conclusions: We have developed a function to track the dynamic state of the W' during intermittent exercise. This may have important implications for the planning and real-time monitoring of athletic performance.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Adult
  • Exercise / physiology*
  • Exercise Test
  • Fatigue / physiopathology
  • Humans
  • Male
  • Models, Biological*
  • Oxygen Consumption / physiology*
  • Physical Endurance / physiology*
  • Work Capacity Evaluation*