Comprehensive Statistical Analysis of Skiers’ Trajectories: Turning Points, Minimum Distances, and the Fundamental Diagram

In recent years, an increasing number of accidents at ski resorts have raised significant safety concerns. To address these issues, it is essential to understand skiing traffic and the underlying dynamics. We collected 225 trajectories, which were analyzed after a correction process. To obtain a quantitative classification of typical trajectories we focus on three main quantities: turning points, minimum distance, and the fundamental diagram. Our objective was to analyze these trajectories in depth and identify key statistical properties. Our findings indicate that three factors-turning angle, curvature, and velocity change-can be used to accurately identify turning points and classify skiers' movement styles. We found that aggressive skiers tend to exhibit larger and less stable turning angles, while conservative skiers demonstrate a more controlled style, characterized by smaller, more stable turns. This is consistent with observations made for the distribution of the minimum distance to other skiers. Furthermore, we have derived a fundamental diagram which is an important characteristic of any traffic system. It is found share more similarities with the fundamental diagram of ant trails than those of highway traffic.