Universität zu Köln

Zhang, Buchuan (2025). An Integrated Modelling and Simulation Framework for Alpine Skiing Dynamics: Combining Empirical Data and Cellular Automaton Approaches. PhD thesis, Universität zu Köln.

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Abstract

This doctoral dissertation advances the understanding of alpine skiing dynamics by developing an integrated framework that combines conceptual modelling, empirical trajectory analysis, and advanced simulations to explore skier movement and efficiency under diverse environmental and physical conditions. Motivated by the increasing importance of safety and slope management in modern skiing, this research addresses a critical gap: the lack of comprehensive models that capture both the environmental forces acting on skiers and their behavioural responses on the slopes. The research unfolds in four interrelated stages. First, it introduces a foundational modelling concept designed to simulate skier traffic on alpine slopes, using principles inspired by pedestrian and vehicular flow models but adapted to the unique dynamics of skiing. In the second phase, the focus shifts to the extraction and correction of real-world skier trajectory data. Leveraging video footage from various skiing environments, the study applies rigorous correction techniques to address distortions caused by camera angles, lens effects, and perspective errors. The third stage conducts a comprehensive statistical analysis of the corrected trajectory data. Here, the research identifies key behavioural markers such as turning points, defined by combinations of velocity shifts and curvature changes; minimum distances between skiers, which reveal patterns of interaction and implicit safety margins; and the fundamental diagram, illustrating the relationship between skier density, speed, and flow. Notably, the findings draw intriguing parallels between skier traffic and other self-driven systems, such as pedestriancrowds and ant trails, highlighting underlying universal principles. Building upon this empirical foundation, the fourth phase develops a cellular automaton (CA)-based simulation model that integrates six crucial factors: slope angle, surface friction, boundary constraints, terrain curvature, aerodynamic drag, and directional inertia. Results demonstrate that slope angle serves as the primary driver of speed, while surface friction and aerodynamic drag increase resistive forces, thereby reducing overall efficiency. Boundary effects, although minimal on wide slopes, play a significant role in shaping lateral motion and path optimization. Terrain curvature affects turning dynamics, especially on irregular or challenging surfaces, while directional inertia enhances straight-line motion but limits a skier’s adaptability when responding to slope variations. In conclusion, the research offers valuable contributions to sports science, particularly in improving slope design, enhancing safety protocols, and informing athlete training strategies. Beyond practical applications, the findings also enrich our theoretical understanding of human-environment interactions in high-speed, outdoor sports settings.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Zhang, Buchuan bzhang@thp.uni-koeln.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-786534
Date:	2025
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics
Subjects:	Physics
Uncontrolled Keywords:	Keywords Language Alpine Skiing Dynamics UNSPECIFIED Empirical Motion Data Analysis UNSPECIFIED Cellular Automaton Simulation UNSPECIFIED Environmental Force Modelling UNSPECIFIED Slope Safety and Management UNSPECIFIED Self-driven Systems Modelling UNSPECIFIED
Date of oral exam:	22 July 2025
Referee:	Name Academic Title Schadschneider, Andreas Prof. Dr. Schreckenberg, Michael Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/78653