The Dynamics of Ski Skating (UMAP)

We discuss the dynamics of ski skating, in particular, the optimization problem: Maximize average speed for a given power. We begin with a mathematical model of ski skating. To simplify the analysis, we limit our attention to ski skating with no poles on a level plane. We also limit our attention to the physics of ski skating; we ignore most biomechanical considerations. In the early days of skating, ski instructors often said: "Take a long glide on a flat ski." Many skiers interpreted this to mean: "Take a passive glide, then give a short hard push to the side." As an application of our theory, we show that this advice is wrong. We show that the skier should start pushing to the side as soon as possible.

Table of Contents:

ABSTRACT

INTRODUCTION
Traditional Approaches
Our Goal and Outline

PRELIMINARIES
Notation
Newton's Law and Its Consequences

STRAIGHT-LINE SKIING
Model for Constant Snow Friction
Effect of Vertical Motion

SKI SKATING
The Skate Cycle
Constraints
Reducing to a Single Parameter
Average Speed
Optimization

EXAMPLES AND ADJUSTMENT OF MODEL

FINAL MODEL: INTERMEDIATE ATHLETE VS. ELITE ATHLETE

SUGGESTIONS FOR FUTURE WORK
Testing the Theory
Hills
More-General Push Functions
Three Dimensions
Multi-linked Chains
Poling
Friction of an Edged Ski

APPENDIX 1: MEASURING THE DYNAMIC COEFFICIENT OF FRICTION

APPENDIX 2: DIMENSIONAL ANALYSIS

REFERENCES

ACKNOWLEDGMENTS (DRIESSEL)

ABOUT THE AUTHORS