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### Mechanics of the Turning Snow Ski

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Abstract

A snow ski turning at a constant radius and a constant speed is analyzed through a model of the skier/snow/ski dynamic system. The skier is modeled as a rigid body pivoted at the ski; the cutting properties of the snow are empirically modeled from ice cutting data; the ski is represented as a Euler-Bernoulli beam. The force of interaction between the ski and the snow at each longitudinal section of the ski is a function of the angle between the ski and the snow surface and the depth of ski penetration into the snow. Solutions to the equations of motion of the turning skier/ski system are obtained by specification of the trajectory of the ski center and then computation of the ski/skier system orientation and the forces required to obtain that trajectory. There is no unique relationship between the system orientation and the trajectory. A “tangential compensation force,” F, directed tangent to the ski trajectory at the ski center, is imposed to minimize the error in the equations of motion in a least-squares sense. The increasing efficiency of each trajectory is predicted by decreasing this tangential compensation force. The closer the tangent to the ski at the midpoint in length is to the tangent to the trajectory, the more efficient the turn. A state of “carving” in a turn, in which segments of the ski length ride in the track in the snow created by preceding ski segments, occurs when the skew angle between the ski longitudinal axis at the midpoint and the ski trajectory is less than approximately 0.15 rad, in the skis examined in this study, and when the ski tail is pressed into the snow. A ski with a softer afterbody carves a turn at larger skew angles, but with less efficiency, than a ski with a stiffer afterbody.

Keywords:

ski design, skiing mechanics, skiing, snow, sport mechanics, ski, ski areas, sports equipment, skiing trauma, skiing safety

Author Information:

Lieu, Dennis K.
Graduate student, University of California, BerkeleyCA,

Mote, C. D.
Professor and vice chairman, University of California, Berkeley, CA

Committee/Subcommittee: F27.65

DOI: 10.1520/STP46631S