Bend it Like Ligety

http://www.nytimes.com/newsgraphics/2014/sochi-olympics/giant-slalom.html

A few years ago, the International Ski Federation (FIS) changed the regulations for giant slalom (GS) skis to make them longer, straighter, stiffer, and generally harder to bend. The New York Times published an interactive article during the Sochi Olympics that highlighted American ski racer Ted Ligety’s unmatched ability to adapt to the new GS ski regulations. Most skiers were unable to adapt to the new regulation, and resorted to skidding the tops of their turns, but not Ted Ligety. As described by the New York Times, “the trace of his path is smoother and more serpentine than that of his foes, who ski in somewhat violent fits and starts, sliding into the turns and making adjustments that spray snow.”           

The first panel of the news-graphic says “through each turn, Ligety is so low that he is nearly sitting on the snow, and the edges of his skis for a nearly 90-degree angle with the snow.” This “nearly 90-degree angle” is crucial to the explanation of why he is so good at GS. So why does having a higher edge angle lead to a more bend ski? It has to do with the horizontal component of force applied to the middle of the ski by the skier’s legs.

If a skier is standing straight up, they have a 0^o edge angle and the skis do not bend at all. On a standard coordinate system, this downward vector would be at -90^o, and Cos(-90^o)=0. There is no horizontal component to the force on the ski when they are flat on the snow and the skier’s legs are straight beneath them. However, as the edge angle approaches 90^o, and the skier’s legs move from -90^o to 0^o on the standard coordinate plane, the horizontal component of their force approaches the total force that the skier is applying on their skis. Ted Ligety gets the best angles out of anyone, which explains why he can carve tighter arcs on the new equipment than anyone else can.