INTRODUCTION: This work models the influence on time of descent of the choice radius line in ski racing with constant speed and with accelerations due to gravity, ski-snow friction, aerodynamic drag and turn radius. This will help in the selection of line and in the development of technique that can take advantage of the best lines. It also has the potential to assist in the design of courses and equipment that could control the loads on ski racers. There have been several researchers who have measured paths in ski racing (Reid et al. 2008). In the experimental work, while different racers who are taking different turn radii can be compared, it is impossible isolate the influence of the choice of line from technique, strength, snow and equipment factors. METHOD: Lines with different turn radii are fit to hypothetical courses with different offsets and gate spacing. Preliminary work is done on a segmented geometrical model with turns of different radii and the same center with straight traverses, using constant speed. This approach is advanced using a CAD program to determine the time for different lines with constant speed. Finally a program is developed that using discrete steps allows the inclusion of the accelerations from gravity, ski-snow friction, energy dissipation in the turns, and aerodynamic drag. The dissipation of energy in the turns is modeled after the experimental results of Reid (2008). RESULTS: The model with constant speed shows the smaller radius has a greater advantage with greater offset and lower speeds. Fig. 1 shows the time for one turn and one traverse when the turning poles are 9 m apart. Several offsets are shown. The time differences are in the hundredths to tenths of seconds for turn radii between half and three meters. When accelerations are included the time is dependent on the function used to estimate the loss in the turns. An optimal turn radius, i.e., finite radius for minimum time, can be found, which depends on the course, slope, conditions, and the dissipation-radius function. One simulation with 9 m pole spacing and 5 m off set initially at 7 m/s shows the optimal radius to be between 2 and 3 meters. DISCUSSION: In the model with velocity constant small radii are always faster. Radius based dissipation results in a finite optimal turn radius. The smaller radius traverse is steeper, which tends to compensate for the dissipation. CONCLUSION: The radius for minimum time depends on the dissipation-radius relation.
© Copyright 2012 Science and Skiing V. 5th International Congress on Science and Skiing, Dec. 14 - 19, 2010, St. Christoph am Arlberg. Published by Meyer & Meyer Sport (UK) Ltd.. All rights reserved.