2 00 3 Physics of Skiing : The Ideal – Carving Equation and Its Applications

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. In addition, we should mention that the paper contains a lengthy didactic presentation of a specific example of vector calculus. Nevertheless, rather general statements governing the dynamics of a skier's trajectory can be obtained on the basis of an elementary analysis. 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 ideal-carving equation which describes the physics of a carved turn under ideal conditions. The laws of Newtonian classical mechanics are applied. The parameters of the ideal-carving equation are the inclination of the ski slope, the acceleration of gravity, and the sidecut radius of the ski. The variables of the ideal-carving 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.