Characterisation of the Contact between Cross-Country Skis and Snow: A Macro-Scale Investigation of the Apparent Contact

Abstract

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.

A novel free-gliding ski tribometer for quantification of ski-snow friction with high precision

“…A handlebar is mounted on each side for manoeuvrability when changing skis and configuring the sled. A 3D-printed shoe was designed in-house (described as the "measurement boot" in [23], and mounted to the sled in order to replicate the loading condition of a commercially available elite-level ski boot while skiing. The shoe size is adjustable and the distance between them can be adjusted to accommodate ski tracks of different widths.…”

“…However, determining the propagation of the vibrations to the tribological interface between the ski and the snow requires further investigation. High-amplitude and low-frequency vibrations do, e.g., cause the sled to bounce, leading to a cyclic loading/unloading which affects the ski-camber profile and, in turn, the nominal contact area and pressure [22,23], while the small-amplitude, high-frequency vibrations merely affects the uncertainty in the COF determined. However, since all repeated runs in the current study show similar vibration patterns, the precision of the tribometer should not be affected.…”

Characterisation of the Contact between Cross-Country Skis and Snow: A Micro-Scale Study Considering the Ski-Base Texture

“…We have, therefore, chosen to adopt a multi-scale framework. In fact, our intention is to establish a two-scale model by combining a model governing the macro scale [14] with a micro-scale model. In this section, we present the theory and the assumptions for the approach employed for estimating the real area of contact, the average interfacial separation, corresponding to the volume of the void space between the ski-base surface and the snow, and the average reciprocal interfacial separation, which all are related to the micro-scale of the problem.…”

“…Other models, [10][11][12], including the authors' previous work [13,14], have only considered the apparent area of contact, an approach that completely neglects the influence of the preparation of the ski base. Recently, Lever and colleagues [15], utilised a setup involving a rotating disc to observe the thermal and mechanical characteristics of polyethylene in sliding contact with snow.…”