Can a skier make a circular turn without any active movement?

TL;DR

This paper presents a simple model showing that a skier can perform a stable circular turn without active movement, relying solely on the physics of the system, which could inform more natural skiing techniques.

Contribution

The study introduces a minimal model demonstrating stable ski turns without active skier control, providing new insights into skiing mechanics and technique development.

Findings

Stable turns can be achieved without active skier movement.

The model calculates the supporting force from the ground.

Conditions for stability depend on velocity and turn radius.

Abstract

A skier's motion was analyzed by a simple model consist of point mass $m$ and a single rod connected to a single ski plate. We studied the conditions for the stable ski turn as functions of the linear velocity and the radius of the turn. The solutions for the stable ski turn in our model do not require any extra skier's movement to complete a stable circular turn. The solution may then give the skier the most comfortable skiing method without any active movement to control the ski. The generalized force supporting the point mass from the ski plate was calculated. We obtained the force from the ground (rebound force) without any geometrical structure of the ski plate. Adding an active movement to the direction of the ski plate, the conditions for the stable ski turn were also analyzed. Our result gives some insight for the skier who wants to develop technique.