Cross-country skiing motion equations,locomotive forces and mass scaling laws |
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Authors: | John F Moxnes Kjell Hausken |
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Institution: | 1. Department for Protection , Norwegian Defence Research Establishment , Kjeller, Norway john-f.moxnes@ffi.no;3. Faculty of Social Sciences , University of Stavanger , Stavanger, Norway |
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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. |
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Keywords: | differential equations cross-country skiing energy consumption muscle work power locomotion velocity forces friction aerodynamic drag gravity technical skills aerobic power scaling laws |
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