I decided to choose math in skiing. Skiing has a lot of components that have to do with math and physics such as speed, mass, radius, and friction. I wanted to learn more about the mechanics of skiing because skiing is something i feel very passionate about. It is an activity i par take in almost every day during the winter, but its something i know little about.
- Speed, mass, and friction can all be described in the picture below. The amount of mass that a skier has the more friction their skis will create against the snow, causing the speed of the skier to slow down. So the more mass a skier has the faster the skier will move down the mountain.
Radius: The turning radius of a ski varies as the turn is being executed with the edge angle being used by the skier and with the amount of reverse camber in the ski during the turn. The greater the amount of pressure on the ski the greater the arc of the turn will be. Also the more playable the ski is the more of an arc the ski will be able to create. With a stiff ski it will take more force to get the ski to make the arc that is desired.
- The sidecut radius of a ski is a design feature of a ski found by assuming the ski edge is an arc of a circle and determining the radius of that circle.
The following calculation descibes the radius of a circle if you know the parameters of a sector of the circle. A sector is found by cutting off the edge of a circle, or disc, with a straight cut that is perpendicular to the radius.