In a cross-country skiing competition, the time difference between the winner and the skier coming in at second place is typically very small. Since the skier spends much of the energy on overcoming resistive forces, a relatively small reduction in these forces can have a significant impact on the results. The resistive forces come partly from the friction, at the tribological interface between the ski and the snow, and as with many tribological processes, the characterisation of its origin plays an important role in determining the frictional properties. Furthermore, 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-camber profile under loading are often used to determine how adequate the ski is for use under specific conditions. The characteristic properties usually assessed are the force required to collapse the ski in order to obtain a certain camber height, the topography of the kick-wax zone, and the length (determined by simple means) of the frictional interfaces associated with the rear- and front glide zones, i.e., the apparent contact length. These measurements are, however, commonly performed by loading the ski against a much stiffer counter surface than snow and this affects the quantification of the characteristic properties. To date, some mathematical models have been proposed, but there is no reliable approach for determining the macro-scale properties of the contact between a cross-country ski and a counter surface using simulations. In the present paper, an Artificial Neural Network (ANN) has been trained to predict the ski-camber profile for various loads applied at different positions. A well-established deterministic approach has been employed to simulate the contact between the ANN-predicted ski-camber profile and a linearly elastic body with a flat upper surface, representing the snow. Our findings indicate that this method is feasible for the determination of relevant macro-scale contact characteristics of different skis with snow. Moreover, we show that the apparent contact area does not linearly depend on the load and that the material properties of the counter surface also exert a large impact when quantifying the apparent contact area and the average apparent contact pressure.

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 textures. In the present work, a method for characterising the 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 longitudinal linear textures with a varying number of lines and peak-to-valley heights, 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 $S_{pk}$ value has less real contact area, and that the mutual differences can be large for surfaces with similar $S_a$ values. The average interfacial separation is, in general, correlated with the $S_a$ 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 $S_a$ and $S_{pk}$ 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 the viscous friction.

Of the medals awarded during the Winter Olympics Games, most are awarded for sports involving cross-country (XC) skiing. The Double Poling (DP) technique, which is one of the sub-techniques used most frequently in XC skiing, has not yet been studied using simulations of the ski–snow contact mechanics. This work introduces a novel method for analysing how changes in the distribution of pressure on the sole of the foot (Plantar Pressure Distribution or PPD) during the DP motion affect the contact between the ski and the snow. The PPD recorded as the athlete performed DP, along with an Artificial Neural Network trained to predict the geometry of the ski (ski-camber profile), were used as input data for a solver based on the boundary element method, which models the interaction between the ski and the snow. This solver provides insights into how the area of contact and the distribution of pressure on the ski-snow interface change over time. The results reveal that variations in PPD, the type of ski, and the stiffness of the snow all have a significant impact on the contact between the ski and the snow. This information can be used to improve the Double Poling technique and make better choices of skis for specific snow conditions, ultimately leading to improved performance. Graphical Abstract

This study evaluates the negative effects of grip wax application on the dynamic ski–snow coefficient of friction and subsequent performance during the double poling cycle in cross-country skiing. Utilising a linear ski tribometer, friction tests were performed on classic cross-country skiing skis prepared with no, thin, and thick grip wax under controlled laboratory conditions. The dynamic coefficient of friction was estimated under various load conditions, reflecting dynamic skiing motions. Results indicated a clear increase in coefficient of friction with the addition of grip wax, with significant differences observed between thin and thick applications. Specifically, compared to skis with no wax, the coefficient of friction for skis with thin and thick wax layers experienced a negative increased by 1.8% and 3.2% during double poling, and by 1.7% and 2.6% whilst gliding, respectively. These friction increases were associated with higher power requirements during skiing or a consequent time loss. This underscores the need for meticulous application of grip wax application, tailored to the snow conditions, ski camber profile and racecourse demands, to minimise impact on gliding performance whilst maintaining sufficient static coefficient of friction for effective use of the diagonal stride technique. Furthermore, the skier should utilise a skiing technique to minimise the risk of encountering load conditions that increase the coefficient of friction. Overall, this research provides quantitative insights into the trade-offs between grip enhancement and friction-related performance losses in cross-country skiing.

In elite endurance sports, marginal differences in finishing times drive ongoing equipment improvement to enhance athlete performance. In cross-country skiing, researchers, since the 1930s, have faced the challenge of minimising the resistance caused by friction in the contact between skis and snow. This study was designed to evaluate the multi-scale interaction between the macro-scale ski-camber profile and the micro-scale ski-base texture. Considerations included real contact area, average interfacial separation, and total reciprocal interfacial separation between the ski and snow, which are properties that are intimately coupled to ski–snow friction. We found that both the profile of the ski camber and the texture of the ski 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 the ski-camber profile.

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.