Testing glide properties is an essential component in ski preparation and equipment development as well as the race day selection thereof (KarlOf et al., 2007). Ideally, such testing finds the coefficient of friction between the skis and snow. However, this coefficient—often stated as a material property—is better categorized as a systems property and depends not just on the materials, but on system variables like temperature, velocity, atmospheric conditions, and geometric properties (Wikipedia, 2016; Bowden & Bowden, 1950). The ski-snow friction is particularly complex and includes dry, wet, and mixed-friction regimes (Colbeck, 1992; KarlOf, Axell, & Slotfeldt-Ellingsen, 2005; Nachbaueret al., 2016). All current approaches to glide testing measure something other than the friction coefficient itself (typically distance or time) and then draw conclusions about the average ski-snow friction on the basis of such proxy data. Unfortunately, such data are influenced by both the friction between the ski and the snow and wind drag. This combined result is biased by the profile of the test track, which often favors preparations that perform well at certain speeds or in certain phases of acceleration or deceleration. To fully understand the glide performance of a ski, the effects of wind drag and the profile of the test track must be removed. Kirby and KarlOf (2013) have developed a novel approach to monitoring changes in velocity on the test hill with optical flow, which, for the first time, allows nearly continuous monitoring of glide performance with a resolution of less than a cm. With such high-resolution data, new patterns of glide performance became apparent, but the results were still confounded by the wind drag and the test-track profile. In the present study, we overcome these issues by re-expressing data—collected with the system described above—in terms of velocity-distance and acceleration-distance data. This parameterization combined with the known slope-distance profile of the test track allows us to compute the driving force due to gravity at each distance along the test track. Driving force minus mass times acceleration results in the combined resistive forces due to wind drag and snow friction at each point along the test track. Reparameterizing the resistive forces with velocity as the independent variable results in resistive force as a function of velocity. Assuming that the wind drag at each speed remains constant between runs (a reasonable assumption with a professional glide tester and no wind), one friction-velocity dataset can be subtracted from another, cancelling out the force due to wind drag and leaving only the difference in ski-snow friction between the two pairs of skis. Dividing by the normal force results in the differential friction coefficient as a function of velocity. We have applied this approach to real test data using a highly qualified professional tester and matched pairs of test skis, and we discuss how this novel approach to glide testing might be employed to determine the glide characteristics under different conditions, the consequences for racing strategy and tactics, and the ideal shape of the test hill.
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