The influence of slope and speed on locomotive power in cross-country skiing Kjell Hausken ⇑ Faculty of Sciences, University of Stavanger, 4036 Stavanger, Norway article info Article history: Available online 15 November 2014 PsycINFO classification: 2330 2540 Keywords: Velocity Incline Work Air drag Efficiency Friction abstract Purpose: A model was developed for cross-country skiing where locomotive power depends on speed and slope as variables, and further depends on snow friction, gravitation, mass, air drag, wind, and air density. Model parameters were estimated experimentally. Methods: Two differential equations were developed for how loco- motive power depends on speed and slope. The equations are of the logistic form with a threshold determined by the skier’s tech- nique, intensity, mass, metabolic rate, gross efficiency, and lactate threshold. Three parameters were estimated by minimizing the average summed square difference between the simulated speed, using the model, and experimental speed of an elite male skier in a 4218 m track. Distance and height along the track were measured using a measuring wheel and an inclinometer generating 52 data- points. Research assistants measured time from start at 14 differ- ent positions. Parameter values were determined from the literature. Results: We illustrated how speed and slope impact loco- motive power. The model was shown to be superior to a model where locomotive power is a function of speed only. The joint dependence of locomotive power on speed and slope is crucial in the non-stationary conditions where the skier passes high and low points along the track where both speed and slope change rap- idly. Conclusion: The model is useful to predict the impact of alter- ing a subset of the 23 variables and parameters on the remaining variables, for example the impact of changed friction or terrain slope on the skier’s speed and thus time to complete a ski race. Ó 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.humov.2014.08.016 0167-9457/Ó 2014 Elsevier B.V. All rights reserved. ⇑ Tel.: +47 51 831632; fax: +47 51 831550. E-mail address: kjell.hausken@uis.no Human Movement Science 38 (2014) 281–292 Contents lists available at ScienceDirect Human Movement Science journal homepage: www.elsevier.com/locate/humov