Physics of Skiing: The IdealCarving Equation and Its Applications
Authors: U. D. Jentschura, F. Fahrbach
Comments: 14 pages, 9 figures, LaTeX
Subjclass: Classical Physics; Popular Physics
Ideal carving occurs when a snowboarder or skier, equipped with a snowboard or carving skis, describes a perfect carved turn in which the edges of the ski alone, not the ski surface, describe the trajectory followed by the skier, without any slipping nor skidding. In this article, we derive the idealcarving equation which describes the physics of a carved turn under ideal conditions. The laws of Newtonian classical mechanics are applied. The parameters of the idealcarving equation are the inclination of the ski slope, the acceleration of gravity, and the sidecut radius of the ski. The variables of the idealcarving equation are the velocity of the skier, the angle between the trajectory of the skier and the horizontal, and the instantaneous curvature radius of the skier's trajectory. Relations between the slope inclination and the velocity range suited for nearly ideal carving are discussed, as well as implications for the design of carving skis and raceboards. [This short article is not meant to be understood as a paper on the foundations of physics, but purely concerned with the application of Newtonian mechanics to the dynamics of skiing. We neglect relativistic corrections, as well as quantum mechanical effects.]
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http://arxiv.org/abs/physics/0310086
