期刊
MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL SYSTEMS
卷 14, 期 6, 页码 535-569出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/13873950802164643
关键词
differential equations; cross-country skiing; energy consumption; muscle; work power; locomotion; velocity; forces; friction; aerodynamic drag; gravity; technical skills; aerobic power; scaling laws
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 tinder different conditions. The article provides tools useful for practising athletes and coaches.
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