<p>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 (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:p\)</EquationSource> </InlineEquation>< 0.05) between single-gate skiing time (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\it\text{t}}_{\text{s}}\)</EquationSource> </InlineEquation>) and the minimum distance (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\it\text{d}}_{\text{m}\text{i}\text{n}}\)</EquationSource> </InlineEquation>) (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\:\rho\:\)</EquationSource> </InlineEquation> = 0.74,<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\:p\)</EquationSource> </InlineEquation>< 0.01) and lateral distance (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\({\it\text{d}}_{\text{l}\text{e}\text{v}}\)</EquationSource> </InlineEquation>) (<InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\:\rho\:\)</EquationSource> </InlineEquation> = 0.73,<InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\:p\)</EquationSource> </InlineEquation> = 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 (<InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\:p\)</EquationSource> </InlineEquation> = 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.</p>

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

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2025年12月4日

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Xu Zhiyi,
Lu Jie,
Xu Qinghua,
Lin Mingjie,
Liu Tao,
Wang Xiangdong

摘要

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 ( \(\:p\) < 0.05) between single-gate skiing time ( \({\it\text{t}}_{\text{s}}\) ) and the minimum distance ( \({\it\text{d}}_{\text{m}\text{i}\text{n}}\) ) ( \(\:\rho\:\) = 0.74, \(\:p\) < 0.01) and lateral distance ( \({\it\text{d}}_{\text{l}\text{e}\text{v}}\) ) ( \(\:\rho\:\) = 0.73, \(\:p\) = 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 ( \(\:p\) = 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.