ARTICLE | doi:10.20944/preprints202307.0346.v1
Subject: Engineering, Mechanical Engineering Keywords: Cross-Country Skiing; Sports Equipment; Multi-Scale; Contact Mechanics; Ski-Camber Profile; Ski-Base Texture
Online: 5 July 2023 (15:37:49 CEST)
At the highest level of endurance sports, the differences in finishing times are small, so equipment is constantly being constantly improved to enhance the athletes' performance. For instance, one dominant resistive force in connection with cross-country skiing is the friction between the skis and snow and since the 1930s, research designed to understand and reduce this friction has been ongoing. The mechanisms involved in ski-snow friction include compaction, micro-ploughing, adhesion, viscosity, and water-bridging. Of these, adhesive and viscous friction have been most studied, while much less is presently known about compaction, micro-ploughing, and water-bridging. At the macro-scale, the ski-camber profile plays a key role in determining whether, with respect to friction, a particular cross-country ski is suitable for use under a given set of conditions. Through its influence on where ski-snow contact occurs, this ski-camber profile has a profound impact on adhesive and viscous friction, micro-ploughing, the formation of water bridges, and the rate of compaction. Different contact zones with different apparent areas of contact and pressure have been found to be most suitable for different conditions. In addition, the micro-scale texture of the ski base is also an important determinant of ski-snow friction. Topographical measurements of this texture can be achieved with white-light interferometer and recent characterisation has focused on the mechanical properties of contact. In numerous tribological studies the interactions between features at different scales are modelled. In most tribological systems, features on several scales influence friction and ski-snow contact is certainly no exception. Accordingly, the current investigation was designed to evaluate the multi-scale properties of different combinations of two skis with two different base textures. The real area of contact and the average interfacial separation and total average reciprocal interfacial separation between the ski and snow were taken into consideration. We found that different macro- and micro-scale properties of the ski favour different mechanisms of friction. Both the profile of the ski camber and texture of the base play decisive roles in determining viscous friction. At the same time, the texture of the ski base exerts a greater impact on the average real contact pressure, real contact area and minimal average interfacial separation between the ski and snow than does the ski-camber profile.
ARTICLE | doi:10.20944/preprints202208.0512.v1
Subject: Engineering, Mechanical Engineering Keywords: Contact Mechanics; Cross-Country Skiing; Cross-Country Ski; Load Conditions; Ski-Camber Profile; Sports Equipment
Online: 31 August 2022 (02:26:22 CEST)
In cross-country skiing the time difference between a race winner and the person coming second is typically very small. Since much of the energy is spent on overcoming resistive forces, a relatively small reduction of these can have a significant impact on the results. The resistive forces come partly from the friction in the tribological interface, between the ski and the snow, and as with many tribological applications the characterisation of its origin, plays an important role in determining the frictional properties. Also in cross-country ski friction, there are several scales impacting the frictional performance, with the major contributors being the ski-camber profile and ski-base structure. Macro-scale measurements of the ski's camber profile under load, are often used to determine how adequate the ski is for a specific condition. The characteristic properties usually obtained are, the force required to collapse the ski to a certain camber height, the topography of the kick-wax zone, and by simple means a determined lengths of the frictional interface, i.e., the apparent contact length. To this date, there are some mathematical models, but there is no robust way of determining the macro-scale contact properties between a cross-country ski and a counter surface using simulations. In the present paper an Artificial neural networks (ANN) is trained to predict the ski-camber profile for various loads placed at different positions, and a well established deterministic approach is used to simulate the contact between the ANN-predicted ski-camber profile and a linearly elastic body with a flat surface, representing the snow. The results suggest that this method is feasible for the determination of the apparent contact characteristics of different skis. Moreover, we show that the apparent contact area does not linearly depend on the load, and that the elastic properties of the counter surface also has a large impact on the apparent contact area and the average apparent contact pressure.
ARTICLE | doi:10.20944/preprints202304.0091.v1
Subject: Engineering, Mechanical Engineering Keywords: Winter sports; Sports equipment; Snow; Cross-country skiing; Ski friction; Ski-base texture
Online: 6 April 2023 (10:57:19 CEST)
In winter sports, the equipment often comes into contact with snow or ice, and this contact generates a force that resists motion. In some sports, such as cross-country skiing, this resistive force can significantly affect the outcome of a race, as a small reduction in this force can give an athlete an advantage. Researchers have examined the contact between skis and snow in detail, and to fully understand this friction, the entire ski must be studied at various scales. At the macro scale, the entire geometry of the ski is considered and the apparent contact between the ski and the snow is considered and at the micro scale the contact between the snow and the ski base ski-base textures. In the present work, a method for characterising contact between the ski-base texture and virtual snow will be presented. Six different ski-base textures will be considered. Five of them are stone-ground ski bases, and three of them have linear longitudinal textures with a varying number of lines and peak-to-valley height, and the other two are factory-ground “universal” ski bases. The sixth ski base has been fabricated by a steel-scraping procedure. In general, the results show that a ski base texture with a higher Spk-value has less real contact area, and that the mutual differences can be large for surfaces with similar Sa-values. The average interfacial separation is, in general, correlated with the Sa-value, where a “rougher” surface exhibits a larger average interfacial separation. The results for the reciprocal average interfacial separation, which is related to the Couette type of viscous friction, were in line with the general consensus that a “rougher” texture performs better at high speed than a “smoother” one, and it was found that a texture with high Sa and Spk values resulted in a low reciprocal average interfacial separation and consequently low viscous friction. The reciprocal average interfacial separation was found to increase with increasing real contact area, indicating a correlation between the real area of contact and the Couette part of viscous friction.