Climbing Performance in U23 and Professional Cyclists during a
Multi-stage Race

Leo, Peter; Spragg, James; Simon, Dieter; Lawley, Justin S.; Mujika, Iñigo

doi:10.1055/a-1524-2656

Cited by 4 publications

(2 citation statements)

References 34 publications

(74 reference statements)

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“…For each athlete, we extracted the best average power output for a range of different durations from their training and racing history. It is well known that it is difficult to fit these models on racing and training data as it is unclear whether the data corresponds to truly maximal efforts (Puchowicz et al 2018 ; Leo et al 2021 , 2022b ). To alleviate this, we removed some efforts that could not have been maximal as well as outliers which are likely to be due to power-metre malfunctions (see Supplementary Information B.7 for more details).…”

Section: Contribution I: Fit Over Different Durationsmentioning

confidence: 99%

Modelling human endurance: power laws vs critical power

2023

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The power–duration relationship describes the time to exhaustion for exercise at different intensities. It is 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 a heated debate in the literature because it unrealistically represents efforts that are short (< 2 min) or long (> 15 min). We contribute to this debate 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 min 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 more naturally models fatigue than the latter.

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Section: Contribution I: Fit Over Different Durationsmentioning

confidence: 99%

Modelling human endurance: power laws vs critical power

2023

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“…For each athlete, we extracted the best average power output for a range of different durations from their training and racing history. It is well known that it is difficult to fit these models on racing and training data as it is unclear whether the data corresponds to truly maximal efforts (Puchowicz et al, 2018;Leo et al, 2021Leo et al, , 2022b. To alleviate this, we removed some efforts that could not have been maximal as well as outliers which are likely to be due to power-meter malfunctions (see Appendix B.7 for more details).…”

Section: Large-data Study In Cyclingmentioning

confidence: 99%

Modelling human endurance: Power laws vs critical power

Drake

Finke²,

Ferguson³

2022

Preprint

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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 viewed as the "gold standard" for assessing exercise capacity, e.g. in cycling, running, rowing, and 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 a mathematical result which suggests that the power-law model is a safer tool for pace selection than the hyperbolic model. 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.

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Power profiling and the power-duration relationship in cycling: a narrative review

et al. 2021

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Emerging trends in technological innovations, data analysis and practical applications have facilitated the measurement of cycling power output in the field, leading to improvements in training prescription, performance testing and race analysis. This review aimed to critically reflect on power profiling strategies in association with the power-duration relationship in cycling, to provide an updated view for applied researchers and practitioners. The authors elaborate on measuring power output followed by an outline of the methodological approaches to power profiling. Moreover, the deriving a power-duration relationship section presents existing concepts of power-duration models alongside exercise intensity domains. Combining laboratory and field testing discusses how traditional laboratory and field testing can be combined to inform and individualize the power profiling approach. Deriving the parameters of power-duration modelling suggests how these measures can be obtained from laboratory and field testing, including criteria for ensuring a high ecological validity (e.g. rider specialization, race demands). It is recommended that field testing should always be conducted in accordance with pre-established guidelines from the existing literature (e.g. set number of prediction trials, inter-trial recovery, road gradient and data analysis). It is also recommended to avoid single effort prediction trials, such as functional threshold power. Power-duration parameter estimates can be derived from the 2 parameter linear or non-linear critical power model: P(t) = W′/t + CP (W′—work capacity above CP; t—time). Structured field testing should be included to obtain an accurate fingerprint of a cyclist’s power profile.

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Climbing Performance in U23 and Professional Cyclists during a Multi-stage Race

Cited by 4 publications

References 34 publications

Modelling human endurance: power laws vs critical power

Modelling human endurance: power laws vs critical power

Modelling human endurance: Power laws vs critical power

Power profiling and the power-duration relationship in cycling: a narrative review

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