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Balanced carving turns in alpine skiing.

Serguei S Komissarov¹

¹Department of Applied Mathematics, The University of Leeds, Leeds, UK.

Sports Biomechanics

|August 4, 2020

Summary

Pure carving in alpine skiing and snowboarding is limited to gentle slopes due to torque balance assumptions. Current models suggest a critical slope angle, but advanced theories are needed for realistic racing scenarios.

Area of Science:

Sports Science
Physics of Sports

Background:

Alpine skiing and snowboarding involve complex dynamics during carving turns.
Existing models often simplify the balance of forces and torques acting on the skier.

Purpose of the Study:

To analyze the physics of pure carving turns in skiing and snowboarding.
To determine the speed and slope limitations for pure carving based on a simplified model.

Main Methods:

Developed a mathematical model for pure carving turns.
Assumed approximate balance between forces and torques during turns.
Simulated carving runs on slopes of constant gradient.

Main Results:

The model predicts lower and upper limits on skier speed based on sidecut radius and slope gradient.

Keywords:

Alpine skiing balance/stability modelling performance

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Pure carving is feasible only on slopes with a relatively small gradient.

The critical slope angle is influenced by snow friction and ski sidecut radius.

Conclusions:

The simplified torque balance assumption in the model is too restrictive for high-speed ski racing.
The model's upper speed and slope limits do not align with practical ski racing observations.
A more advanced theoretical framework is required to accurately model dynamic carving turns.