Modelling human endurance: Power laws vs critical power - Drake, J.; Finke, A.; Ferguson, R. (Journal of Science and Cycling, 2023)
The power-duration relationship describes the time to exhaustion for exercise at different intensities. It is generally believed to be a "fundamental bioenergetic property of living systems" that this relationship is hyperbolic. Indeed, the critical- power model which formalises this belief is the dominant tool for studying endurance exercise, e.g. in cycling, running, rowing, or swimming. However, this model is now the focus of a heated debate because it unrealistically represents efforts that are short (< 2 minutes) or long (> 15 minutes). We contribute to this debate by demonstrating that the power--duration relationship is not hyperbolic (and thus cannot be adequately described by a "critical power`` parameter). Rather, the power-duration relationship is more adequately represented by an alternative power-law model. In particular, the oftenobserved good fit of the critical-power model to exercise durations between 2 and 15 minutes should not be taken as proof that the power-duration relationship is hyperbolic. Rather, in this range, a hyperbolic function just happens to approximate a power law fairly well. Additionally, we show that the power-law model sheds light on the strengths and limitations of many popular rules of thumb for performance prediction such as Jack Daniel`s "VDOT" tables in running and FTP in cycling. For instance, for the latter, it explains why the 95-% rule for estimating a cyclist`s 60-minute power output from a 20-minute effort is too optimistic.