A simulation of cross-country skiing on varying terrain by using a mathematical power balance model

John F Moxnes,¹ Øyvind Sandbakk,² Kjell Hausken<sup>3

1</sup>Department for Protection, Norwegian Defence Research Establishment, Kjeller, Norway; ²Human Movement Science Program, Norwegian University of Science and Technology, Trondheim, Norway; ³Faculty of Social Sciences, University of Stavanger, Stavanger, Norway

Abstract: The current study simulated cross-country skiing on varying terrain by using a power balance model. By applying the hypothetical inductive deductive method, we compared the simulated position along the track with actual skiing on snow, and calculated the theoretical effect of friction and air drag on skiing performance. As input values in the model, air drag and friction were estimated from the literature, whereas the model included relationships between heart rate, metabolic rate, and work rate based on the treadmill roller-ski testing of an elite cross-country skier. We verified this procedure by testing four models of metabolic rate against experimental data on the treadmill. The experimental data corresponded well with the simulations, with the best fit when work rate was increased on uphill and decreased on downhill terrain. The simulations predicted that skiing time increases by 3%–4% when either friction or air drag increases by 10%. In conclusion, the power balance model was found to be a useful tool for predicting how various factors influence racing performance in cross-country skiing.

Keywords: skiing, power balance, metabolic rate, work rate, air drag, friction coefficient