# Analysis of sit-ski alpine skiing trajectories based on an inverted pendulum model

## TL;DR

Researchers used an inverted pendulum model and sensor data to study how sit-ski athletes navigate turns in alpine skiing, finding correlations between skiing time and distance metrics.

## Contribution

A novel combination of an inverted pendulum model and advanced kinematic testing to analyze sit-ski trajectories during gate turns.

## Key findings

- There is a significant positive correlation between single-gate skiing time and minimum and lateral distances.
- The inverted pendulum model's simulated center of mass trajectory showed strong consistency with actual skiing times.
- Optimizing turning radius, speed, and distance can reduce skiing time, validating the model's utility for individualized trajectory optimization.

## Abstract

This study analyzes sit-ski alpine skiing trajectories during gate-turning phases using an inverted pendulum model combined with an advanced kinematic testing system involving inertial sensors and drone video analysis. Data were collected from 11 elite sit-ski athletes during runs on a designated slope segment. The inertial sensor system showed static accuracy of 2° and an average deviation of 0.008 m, while drone video analysis had a mean relative error of 1.36% ± 0.94%. Analysis of 33 gate turns revealed a mean skiing distance of 13.61 ± 2.87 m and mean time of 0.88 ± 0.19 s, with significant positive correlation (\documentclass[12pt]{minimal}
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\begin{document}$$\:p$$\end{document}< 0.05) between single-gate skiing time (\documentclass[12pt]{minimal}
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\begin{document}$$\:p$$\end{document}< 0.01) and lateral distance (\documentclass[12pt]{minimal}
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\begin{document}$$\:p$$\end{document} = 0.01). Simulation with the inverted pendulum model yielded a COM trajectory length of 97.93 ± 2.31 m, 1.66 ± 3.61 m shorter than actual values (\documentclass[12pt]{minimal}
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\begin{document}$$\:p$$\end{document} = 0.16), and a simulated time of 6.36 ± 0.64 s, showing strong consistency (ICC = 0.85 for time, ICC = 0.45 for trajectory length). These results confirm that optimizing the balance of turning radius, speed, and distance reduces skiing time, supporting the model’s effectiveness in individualizing trajectory optimization for sit-ski alpine skiing.