Abstract
Models for human running performances of various complexities and underlying principles have been proposed, often combining data from world record performances and bio-energetic facts of human physiology. The purpose of this work is to develop a novel, minimal and universal model for human running performance that employs a relative metabolic power scale. The main component is a self-consistency relation for the time dependent maximal power output. The analytic approach presented here is the first to derive the observed logarithmic scaling between world (and other) record running speeds and times from basic principles of metabolic power supply. Our hypothesis is that various female and male record performances (world, national) and also personal best performances of individual runners for distances from 800m to the marathon are excellently described by this model. Indeed, we confirm this hypothesis with mean errors of (often much) less than 1%. The model defines endurance in a way that demonstrates symmetry between long and short racing events that are separated by a characteristic time scale comparable to the time over which a runner can sustain maximal oxygen uptake. As an application of our model, we derive personalized characteristic race speeds for different durations and distances.
Highlights
Scientists have been fascinated by trying to explain running performance and to predict its limitations for more than 100 years
Accurate models for running performance have been based on a combination of empirical data descriptions and underlying physiological processes, or they employed at least some empirical correction factors
A minimal power model for human running performance this requirement, and we shall validate its accuracy by comparing it to various record performances
Summary
Scientists have been fascinated by trying to explain running performance and to predict its limitations for more than 100 years. For men running events from 20 yards up to a few hundred miles he found a power law relation between distance d and duration T with T * d9/8 with a relative large error of up to 9% for distances from 100m to 50 miles (and larger errors for shorter and longer distances) [1]. In 1925 noted mathematician and physiologist A.V. Hill proposed a power model based on metabolic energy considerations to describe the maximal power output Pmax(T) over a given duration T by a hyperbolic function Pmax(T) = P0 + P1/T with constants P0 and P1 (known as the “running curve”) [2].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
