Alpine Ski Track Design Combining Conjugated Harmonic Functions and Terrain Surfaces

This article proposes a methodology that allows for optimized adaptation of the terrain surface on steep mountain slopes for the implementation of alpine ski tracks. It is a mathematically based stepwise model that generates bands of harmonic surfaces by studying the best adaptation to the natural terrain, considering and assessing earthwork balances, longitudinal and transverse drainage (stream crossings), allowable slope ranges, and comfort criteria for alpine skiing. Conjugated harmonic surfaces have important characteristics that make them attractive for multiple technical applications. This is the first time that these surfaces have been applied within a methodological procedure to optimize the diversity of characteristics described in the design of alpine ski tracks. A case example at a ski resort in the Spanish Pyrenees will be illustrated in the article.