Most endurance sports aim to get from point A to point B as quickly as possible. Throughout the course, athletes need to overcome the resistive forces that are present in their specifc sport. Cross-country skiing is no exception to this, and there are mainly three resistive forces acting on a skier: the aerodynamic drag force, the friction force, and the gravitational force in the inclined parts of a track. The present work focuses on the resistive force of friction between the ski and the snow. At the highest level of ski sports, a signifcant efort is made to reduce the ski-snow friction, and a slight reduction in friction can signifcantly impact the race outcome. Several aspects are considered when skis are chosen and prepared to minimise friction: ski-camber profle, ski-base material, ski-base texture, and ski-base preparation. Depending on the prevailing snow and weather conditions, the dominating friction mechanisms may vary, so the choices of skis and preparations must be carefully considered and tested accordingly. Herein, the multi-scale nature of ski-snow friction is modelled using a contact mechanical point of view. The macro-scale referees to the ski-camber profle and the more signifcant deformations when loaded. This is incorporated through ski-camber profle measurements, where a measured ski is used in a boundary element-based con tact mechanical model to simulate the contact between the ski and the snow. During simulations, the ski-camber profle is modelled as a rigid geometry which is in contact with elastic snow. The resulting apparent contact pressure and contact area can be used to characterise skis. The ski-base texture is categorised as the micro-scale. On this scale, the elastic modulus is modelled as ice, several times stifer than the snow at the macro-scale. When the contact is simulated, the ski-base textures are charac terised using the contact mechanical response parameters: real contact area, average interfacial separation, and average reciprocal interfacial separation. The multi-scale nature of the ski-snow contact is coupled through the apparent pressure, which acts as a load condition for the micro-scale contact simulation. The micro-scale parameters can be evaluated along the entire ski, considering both scales. A full-scale ski-snow tribometer was developed throughout the work, with the main goal of correlating the characteristics obtained from the multi-scale simulation to ski-snow friction. The tribometer was built to mimic an athlete on skis while performing the G7 in terms of load magnitude, positioning, and transfer interface. To do so, an athlete`s plantar pressure distribution was measured and analysed using different variations of the G7 position. The neutral position, resembling a load position of 55% of the athlete`s foot, was chosen as the load point for the ski tribometer. A replica of a ski boot was developed for the tribometer, herein called the measurement boot, to make it possible to use skis equipped with a regular NNN-binding system on the ski tribometer. The impact on the ski-camber profle from using the measurement boot was also studied, and results showed that since a ski boot transfers the load on a larger area, compared to the conventionally used metal block designed, the ski will collapse to a greater extent. The ski-tribometer can be equipped with a pair of regular skis and is built to ft in normal classic ski tracks. The ski tribometer was designed to be loaded with regular Olympic weights to enable various loads. During feld measurements, the ski tribometer is accelerated using a downhill slope, and the velocity and position are measured using an RTK-GNSS system. The retrieved data, in terms of time, altitude, and velocity, was used to calculate a mean coefcient of friction for reaching individual runs while accommodating aerodynamic drag, centripetal force, and slope angle. During the winter period of January-February 2024, a measurement campaign was carried out to evaluate the infuence of the simulated apparent and real contact area in cold conditions and challenging tracks. Eight skis with diferent apparent contact areas were stone ground with three diferent ski-base textures, with the purpose of developing different amounts of real contact area. Results from the friction tests indicate a different optimum combination of apparent and real contact area at the snow temperatures of -3, -8.5 and -13 °C. At the warmer conditions -3 and -8.5 °C, a small apparent and real contact area exhibited the lowest friction, and at a snow temperature of -13 °C, the opposite trend was observed, where a large apparent and contact area exhibited the lowest friction. A regression model was developed for each condition based on the apparent contact length and the total real contact area. Using the developed ski-snow contact models, a pair of skis and their ski-base texture can be characterised, and the frictional performance in cold conditions with challenging tracks can be estimated using the regression model. This method makes ski and ski base texture selection possible before testing, thus contributing to a more efficient way of conducting ski selection.
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