ArticleEuropean journal of applied physiology2024
Modelling human endurance: power laws vs critical power.
Article in European journal of applied physiology, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers, 1 of them a synthesis that pooled it.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
6 citing papers in PubMed, 1 synthesis or guideline pooled it, 11 citations in OpenAlex.
- The 3-min all-out test in cycling: a systematic review and meta-analysis on its reliability and validity.European journal of applied physiology · 2026Pooled it
- RACLET: the Ramp Above Critical Level Endurance Test to evaluate critical velocity in running.European journal of applied physiology · 2026Article
- Association of Physical Capacities with Peak Match Intensities and Match-to-Match Variability: An Exploratory Study in Young Male Football Players.Sports (Basel, Switzerland) · 2026Article
- Modelling the relative precision of whole-kidney dosimetry in molecular radiotherapy using a power law approach.Radiation protection dosimetry · 2026Article
- Blue plaque review series: A.V. Hill, athletic records and the birth of exercise physiology.The Journal of physiology · 2025Article
- Article
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
3 authors at 1 institution in 1 country.
Funding
No grant is acknowledged in the PubMed record.
Abstract
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.
Indexed as
Identifiers
What Socratic holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the Socratic graph.