Physics of Skiing


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The sport of skiing has been around for thousands of years, originally existing solely as a form of transportation. Today the sport is entirely dependent upon the laws of physics, and has even had advancements through reliance on physics. There are two types of Nordic Skiing. These are Classic (or diagonal) and Skate Skiing. Usually these two forms are raced separate. To be fair, there are actually two slightly different forms of skate skiing; V1 and V2. As these can get very very complicated and precise in the technique, I will focus mainly on classic skiing, which is also the type of skiing that most people are familiar with.

Cross-Country Skiing is the most basic form of skiing, even preceding downhill skiing. Primitive skis may have even been used about 3000 B.C. in Norway. There have been cave drawing found that seem to depict men on skis. Skiing has its roots in Scandinavia; Vikings used skis as a form of transportation in the 10th century A.D.

Early skis were made of wood, and even the word ski comes from the Norse word skith a stick of wood. Norse skies were very rudimentary, little more than snowshoes. Glide was little to none. It was not until the early 1800s when Sondre Norheim changed the face of skiing and gave skis glide that the sport was introduced to the world.

Competitive skiing started in the late 1800s, again in Norway. In the 1932 Winter Olympics at Lake Placid, Nordic Skiing as we know it was added. Today the sport has evolved to be both extremely competitive and leisurely.

In the past 30 years the sport has changed dramatically, adding skis made of synthetic materials, and utilizing waxes for improved speed. Physicists have been at the front line of all this; from determining the coefficent of friction for both the wax and the ski, to helping skiers change their technique based on the laws of physics.

To maximize speed, Nordic skiing is more about form than probably any other sport. Brute strength and athletic prowess certainly have their advantages, but these pale in comparision to proper technique.

While the shape of classic skis is slightly different than that of skate skis, the real difference is that classic skis have a "kick zone." This is a spot directly underneath the foot that has kick wax applied to it. Kick wax is a sticky poly-hydrocarbon that in theory is only supposed to provide a sticky surface from which to push back from.

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If the skier cannot push backwards, by Newton's Third Law, he cannot go forwards. Thus the more push back against the foot, the more thrust forward.

Another form of wax is glide wax, usually made of fluorocarbons. On classic skis this is applied to everywhere on the ski except the kick zone. This is because glide wax is exactly the opposite of kick wax; glide wax reduces the frictional coefficient between the skis and the snow whereas the kick wax increases it. Different kick and glide waxes are used at different temperatures and different snow conditions.

Certainly one of the most important and difficult tasks of race skiing is to find the balance between the kick and glide. If there is too much kick, the skier ends up running the entire race; not enough kick and striding is out of the question.

Classic Forms

There are three forms of Classic:

Classic Stride

Classic Stride is the most traditional form. It is skied in a track and is left kick, glide, right kick, glide. When the left arm plants the pole, the right leg is at the furthest back that it will go. As the arm comes back, the opposite leg comes forward. Conversely, the arm and leg on the same side come forward and backward as one, as if there was a string tied to them. When the arm is thrown back, as in the picture above, the opposite foot "plants" the ski, allowing the wax to set, thus increasing the frictional coefficient, and giving a much better kick. Notice in the picture above that the left arm and left leg are both back and that the right arm and leg are both forward. This is because of Newton's Third Law; the action of throwing the arm and leg forward, causes an action in the opposite direction, slowing the skier down. Good technique dictates letting both the arm and leg go backwards with the reaction thus setting up for the next kick.



Double Pole

Double Poling is used at higher speeds (gentle downhills or flat terrain) because the mass of the skier is distributed over both skis, thus reducing the kinetic friction. Compare this to the stride where one ski has almost all the mass. Another advantage of double poling is that it uses abdominal and lower back muscles, which are very strong and don't often get used in race (other than with this motion) so the muscles are fresh!

One important point of double poling is to only bend at the midsection. The effect of this is that the Potential Energy is higher when standing up and lower when bent over forward. This is because the center of mass is much higher when standing up than bent over. The Potential Energy is transformed into linear kinetic energy by placing the weight on the poles. Potential Energy (U) is equal to the mass times gravity time height (U = mgh). Another way to improve form is to raise up on your toes (as she is about to do in the picture above). This raises the height almost 0.1m which translates into almost a 10% increase in Potential Energy.

Another tip that is directly from Physics is to thrust the lower legs forward as soon as the push from the pole is ending. The effect of this is that the action of moving the mass of your legs forward causes a reaction backward, giving more push through the poles. This is Newton's Third Law in action: the action moving forward, causes a reaction backwards, which gives more power forward.



Double Pole Kick

To be fair, this isn't necessarily a different form, yet simply a mix of both types. It is the double pole motion with an added kick by one leg, usually alternating legs so that one doesn't tire out too quick. The kick is done at the time when the arms are being lifted from just after the extension of the double pole.

There is better grip when doing a double pole kick because the action of bringing the arms forward during the kick, causes there to be more down force on the ski, thus increasing Ff (the Frictional Force).



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