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Cross-country skiing motion equations, locomotive forces and mass scaling laws

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  • John F. Moxnes
  • Kjell Hausken

Abstract

This article presents differential equations for locomotive force and velocity during cross-country skiing. A muscle's work power is modelled. Thereafter, a locomotive force that depends on the skier's velocity is constructed. The external forces aerodynamic drag, friction forces and the force of gravity are incorporated in order to provide the equation of motion. Some allometric mass scaling relations are established and used to analyse the effect of a skier's mass on velocity. The model is tested by using a GPS instrument. We compare analytically and experimentally determined skiing distances and velocities as functions of time, and under different conditions. The article provides tools useful for practising athletes and coaches.

Suggested Citation

  • John F. Moxnes & Kjell Hausken, 2008. "Cross-country skiing motion equations, locomotive forces and mass scaling laws," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 14(6), pages 535-569, April.
    • Handle: RePEc:taf:nmcmxx:v:14:y:2008:i:6:p:535-569
    DOI: 10.1080/13873950802164643
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    Cited by:

    1. Kjell Hausken, 2017. "Exhaustive Classification and Review of Techniques and Research Program for Techniques for Skate Skiing, Classical Skiing, and Ski Mountaineering," The Open Sports Sciences Journal, Bentham Open, vol. 10(1), pages 160-178, October.

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