RT Journal Article SR Electronic T1 Modelling human endurance: Power laws vs critical power JF bioRxiv FD Cold Spring Harbor Laboratory SP 2022.08.31.506028 DO 10.1101/2022.08.31.506028 A1 Drake, Jonah A1 Finke, Axel A1 Ferguson, Richard YR 2022 UL http://biorxiv.org/content/early/2022/10/29/2022.08.31.506028.abstract AB 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 hyperbolic (a.k.a. critical-power) model which formalises this belief is the dominant tool for describing and predicting high-intensity exercise performance, e.g. in cycling, running, rowing, or swimming. However, the hyperbolic model is now the focus of two heated debates in the literature because: (a) it unrealistically represents efforts that are short (< 2 minutes) or long (> 15 minutes); (b) it contradicts widely-used performance predictors such as the so-called functional threshold power (FTP) in cycling. We contribute to both debates by demonstrating that the power–duration relationship is more adequately represented by an alternative, power-law model. In particular, we show that the often observed good fit of the hyperbolic model 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. We also prove mathematical results which suggest that the power-law model is a safer tool for pace selection than the hyperbolic model and that the former better models fatigue than the latter. Finally, we use the power-law model to shed light on popular performance predictors in cycling, running and rowing such as FTP and Jack Daniels’ “VDOT” calculator.Competing Interest StatementThe authors have declared no competing interest.