Physics of Downhill Ski Racing

Gliding is the art of maintaining the flattest ski in order to achieve the lowest possible friction. The forces associated with gliding are fairly straightforward: gravity, friction, and air resistance. Air resistance has several inputs that add to the total resistive force. Friction is caused by the lack of a perfectly smooth surface between the skis and snow on a microscopic level. Think of it as the Rocky Mountain range trying to slide over the Himalayas. On a microscopic level this is what friction is.

Two factors contribute to the resistive frictional force; a normal force and the friction coefficient. The normal force is the force holding the person up keeping them from falling towards the center of the earth. On level ground the normal force acts straight up against the acceleration of gravity. On a slope, the normal force is equal to the force of gravity proportional to the cosine of the angle of the slope to horizontal. This portion of gravity attempts to accelerate the person toward the center of the earth, the normal force resists this acceleration. The remaining component of gravity accelerates the body down the hill parallel to the slope, a linear acceleration.

It is the coefficient of friction that speed skiers and racers try to reduce to a minimum. The normal force is a constant since it is related to their body weight, which does not change during the course of the race. The coefficient of friction is already reduced from everyday levels because of the snow, but it is the goal of racers to reduce this to an absolute minimum to maximize speed.

The coefficient of friction is a unit less ratio of the force of friction to the normal force. The real value for the coefficient is often determined experimentally....

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...and the force normal to the shear plane. These two forces again result in the same resultant force but are rotated into the shear plane. The angle of rotation into the shear plane is phi in above second diagram. Phi is the edge angle minus the angle in the triangle of the normal force(N) and the friction force(F) on the ski divided by 2. This can be seen in the first diagram. The centripetal force can be found using the above equations in the second diagram:

Fc=Fs*cos(phi)+Fn*sin(phi)

Fn=Fs/tan(O-b-F)

The Fc is the failing point at which the racer begins to slide the ski and lose speed. When a racer does balance the speed, radius, and other factors to maximize the centripetal force and acceleration, up to 2.5 Gs of acceleration can be achieved. Downhill ski racing is a ballet and balancing act of the laws of physics to be the fastest person down the hill.