Re: What are the physics of snow skiing?

Snow skiing on a competitive level involves significant understanding of material science, fluid mechanics and basic kinematics. Again, I turn to The Physics of Sports edited by Angelo Armenti, Jr. Three articles discuss various elements of the physics of skiing. (Reprinted from The Physics Teacher 22, 109-110 (1984), The Physics Teacher 23, 1487-488 (1985) by Hignell and Terry, and The Physics Teacher 28, 72-76 (1990) by Bartlett). There is also a book available called Physics of Skiing at the Triple Point (by David Lind & Scott Sanders) that I have not read. I will hit a quick summary of some of the physics of skiing.

Material Science:
First, consider the friction between the ski and the snow. If you can minimize the friction, the skier will be able to go faster. The sliding friction is reduced by applying wax to the ski.
Two previous answers address the properties of ski wax, so I will just summarize in saying:

• the wax must repel water/snow at cold temperatures
• the wax must adher to the ski for a long time to useful
• the wax must reduce the sliding friction between the ski and snow.

solid lubricants

alpine ski wax

Fluid Mechanics / Aerodynamics:
Skis are designed to spread the weight, or more appropriately the normal force of the skier over a wider surface area. In this way, the skier does not fall into the snow. The problem is that more area can usually mean more friction in the real world, so the shape of the ski is important. Another requirement on the shape of the ski is maneuverability, balance and drag.

A ski moving on a snow surface and the skier moving through the air is a two part fluid dynamics problem.
At slow speeds the interaction of the ski and snow dominates, while at higher speeds because air drag goes as approximately speed squared, air resistance becomes important.

The cross sectional area of the object is a key factor in drag. So thinner skis will likely go faster than wider skis and a skier in a tuck position will present a smaller profile to the wind and will have less drag. For the skiier, reduction of the cross sectional area (or presentation to the wind) is usually the most significant way to reduce drag and move faster, but also reducing drag by having a more aerodynamic shape is important. Maybe you have seen the cool helmets that world class skiers wear that come to a point a few inches behind the head like an airplane wing (similar helmet bicycle profile)? This is to reduce drag.

Kinematics/ mechanics:
I also once upon time answered a question on ski jumping with some good links to other sites.

ski jumping

A key point from that answer is that the speed of the skier can be calculated approximately from basic kinematics using energy conservation.
Energy conservation means :

Energy_{at time} = Energy_initial

The energy equation has a potential energy and kinetic energy part (again very simple approximation, that works nicely)

Energy_{at time} = mass * g * current height + 0.5 * mass * speed².

The initial energy is determined by how high vertically the skier started her descent

Energy_initial = mass * g * starting height.

Using these three equations you can figure out the skier speed if you know her vertical height.

Of course this equation is overly simple. It assumes no loss or addition of energy which simply is not true.

Sincerely,

Tom "Snow Plow" Cull