Modeling the ski–snow contact in skiing turns using a hypoplastic vs an elastic force–penetration relation

Abstract

A ski-snow interaction model is presented. The force between ski and snow is decomposed into a penetration force normal to the snow surface, a shear force parallel to it, and friction. The purpose of this study was to investigate the benefits of a hypoplastic vs an elastic contact for penetration in the simulation of skiing turns. To reduce the number of influencing factors, a sledge equipped with skis was considered. A forward dynamic simulation model for the sledge was implemented. For the evaluation of both contact models, the deviation between simulated trajectories and experimental track data was computed for turns of 67 and 42 m. Maximum deviations for these turns were 0.44 and 0.14 m for the hypoplastic contact, and 0.6 and 7.5 m for the elastic contact, respectively. In the hypoplastic contact, the penetration depth of the ski's afterbody maintained nearly the same value as the part under maximum load, whereas it decreased in the elastic contact. Because the shear force is proportional to the penetration depth, the hypoplastic contact resulted in a higher shearing resistance. By replacing the sledge with a skier model, one may investigate more complex skier actions, skiing performance, or accident-prone skiing maneuvers.

Effects of Counter-rotation Position on Knee/Hip Angulation, Center of Mass Inclination, and Edging Angle in Simulated Alpine Skiing

“…Among them, recreational skiers (intermediate and expert levels) and racing athletes try to create a larger edging angle by increasing the COM inclination using knee and hip angulations to perform faster speeds and shorter radius turns Mössner et al, 2014). At this time, most skiers prefer counter-rotation position for greater variation of angulation, COM inclination, and edging angle (LeMaster, 2010, Lind & Sanders, 2004.…”

“…Conversely, hip angulation is affected not only by the radius of the slope or turn, but also by the counter-rotation position. Therefore, the skier must slide by increasing the hip angulation through the counter-rotation position to effectively transmit force to the inner edge of the outer ski, which is in contact with the snow surface and acts on the reaction force Mössner et al, 2014).…”

“…Because of the experimental difficulties and characteristics of the sport, such as high-speed and wide range of motion, as well as environmental factors, such as cold and sloping snow, kinematic studies of alpine skiing have been conducted through the studies using a ski simulator (Koo, Lee, Kweon, Hyun, & Eun, 2014;Lee, Roh, & Kim, 2016;Nam & Woo, 2007), or using a robot Mössner et al, 2014;Yoneyama et al, 2009) or through the studies that simulate Alpine skiing in a laboratory setting to generalize the results to actual situations (Böhm & Senner, 2008;Demšar, Duhovnik, Lešnik, & Supej, 2015;Nedergaard et al, 2014). The purpose of this study was to investigate the differences of segments rotation movement between 3 different positions and their effects on knee and hip angulation, COM inclination and edging angle changes.…”

Comparison of Three-dimensional Kinematic Changes of the Lower Extremity between the Two Different Braking Distances of Snowplow in Alpine Skiing

“…The plowing force is generated when skidding occurs on the side of the ski plate, which can be defined as the friction force. The friction force is generated in between the ski plate edge and the snow surface, and can be divided into penetration and shear forces (Mössner et al, 2014;Figure 6). When skidding occurs, the penetration depth increases as the edging angle increases because the penetration force of the ski plate acting vertically on the snow surface becomes larger.…”

“…Therefore, the shear force increases as well owing to the coefficient of friction (μ) increasing proportionally to the penetration force (Mössner, Nachbauer, Innerhofer & Schretter, 2003). In , friction force; ε, penetration depth of the ski edge; θ, edging angle; α, attack angle of the ski; V, the displaced volume of snow by the ski; and A, contact area between the ski and the snow projected to the undisturbed snow surface of the hill (Mössner et al, 2014). rotation axis, we can infer that the shorter the braking distance during snowplow, the greater the contribution of the ankle joint to the snowplow angle than to the edging angle.…”