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Numerical simulation of cross-country skiing
Peter Carlsson1, Mats Tinnsten, Mats Ainegren
1Department of Engineering and Sustainable Technology, Akademigatan, Östersund, Sweden. peter.carlsson@miun.se
Summary
This study presents a MATLAB program for simulating entire ski races, considering various forces and track conditions. The model accurately predicts race times and performance metrics.
Area of Science:
- Sports Science
- Computational Physics
- Biomechanics
Background:
- Ski racing performance is influenced by numerous dynamic factors.
- Accurate simulation models are crucial for understanding and optimizing race outcomes.
- Previous models may not fully capture the complexity of ski race physics.
Purpose of the Study:
- To develop a comprehensive numerical simulation program for ski races.
- To model a two-dimensional ski track using cubical splines.
- To analyze the impact of various physical forces and environmental conditions on race performance.
Main Methods:
- Utilized MATLAB for developing the simulation program.
- Modeled the ski track geometry using cubical splines.
- Applied the Runge-Kutta method to solve differential equations of motion.
- Incorporated forces: gravity, normal, wind drag, friction, and skier propulsion.
Main Results:
- The program simulates a complete ski race from start to finish.
- Outputs include total race time, forces, speed profiles, and intermediate times.
- The model allows for variations in wind, snow glide conditions, and skier power.
Conclusions:
- The developed simulation program provides a robust tool for analyzing ski race dynamics.
- It can be used to explore the effects of different parameters on race results.
- Preliminary simulations demonstrate the program's capability in predicting race performance.
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