On a Mathematical Model of Ski Skating

Kenneth R. Driessel, Adjunct Scholar

Department of Mathematics

Colorado State UniversityI shall discuss the dynamics of ski skating. In particular, I shall discuss the following optimization problem: Maximize average speed for a given power. I shall first need to develop a mathematical

model of ski skating. Scientists should limit the scope of inquiry in order to achieve greater certainty about the questions answered. So I limit my attention to steady periodic skiing with no poles on a level plane. I also limit my attention to the physics of the motion (that is, I ignore most bio-mechanical considerations). In preparation for this lecture, I suggest that you think about the following questions: What is a typical average speed for an intermediate skier? What is a typical power for an amateur athlete? What are the important forces in ski skating? What are typical parameters associated withe these forces? If you have time I also suggest that you look at the references given below.This will be an elementary talk; calculus and freshman physics are the main prerequisites.

Alexander, R. (1992) The Human Machine

Driessel, K., Fink, P. and Hentzel, I. 'The Dynamics of Ski Skating', UMAP Journal, 25, No. 4, 2004, pp. 375-410 (Also available at http://members.hpnx.com/driessel )

McMahon, T. (1984) Muscles, Reflexes and Locomotion

Svensson, E. (1994) Ski Skating with Champions

Whitt, f. and Wilson,F. (1974) Bicycling Science