Physics of Skiing

Physics of Skiing

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Skiing is an old sport; the oldest artifacts date back over 4000 years. It was developed in the Scandinavian region, especially Norway, and didn't spread to the rest of Europe until the sixteenth or seventeenth century. It probably came over with Norwegian and German immigrants during the nineteenth century.
Skiing relies on many different forms physics. Newton's Laws of Motion, the transformation of potential energy into kinetic energy, air resistance, circular motion, even conservation of circular momentum is used as skiers pump upwards during a turn. Friction is by far the least understood of these forces. The surface of snow is a strange interaction between water, ice and water vapor, the three forms of water found on Earth. Snow changes properties and is difficult to measure and study in its natural environment.

Snow changes properties and is difficult to measure and study in its natural environment. Ice Crystals form when water vapor condenses around and freezes upon a foreign particle such as dust or sea salt. These Ice crystals then form various varieties of snow flakes.
Snowflakes can fall in many forms, including ferns, crystals and needles.

These snow flakes begin transforming as soon as they hit the ground. They begin to morph in a combination of melting, freezing, evaporation and sublimation*. They become needles, columns, and finally simple round pellets.

* Sublimation is when ice evaporates directly instead of melting first to water and then evaporating.

These pellets the bond again through a process of melting, freezing, evaporation and sublimation at their contact points, this creates a strong snow pack.

Snow Compaction and Work

One thing that slows a skier down is the compaction of the snow beneath a skier. Snow is mostly air and this allows a great degree of compaction. On packed trails, this compaction is negligible and contributes only slightly to the friction of the snow on the skis.

This diagram shows a skier who travels l distance on unpacked snow and sinks in h into the snow.

Logically, the distance the skier sinks in, h, is proportional to the skiers weight, FN. Work is defined as a force applied over a distance.

The work needed to propel the skier l distance through the snow is the same as the work done be the skiers weight along the height, h.

the force used to move the skier is defined as FFORWARD then


With different types of snow, a skier with the same weight will sink in different distances.

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For the reason, the coefficient of compressional friction, uc, is defined as:


Frictional Force is defined as f=u*FN

So the friction from compression, fc, can be defined as


An example of the conversion of Potential Energy, PE, to Kinetic Energy, KE, and then work done by friction to transfere this Kinetic Energy from the skier is given. This assumes there is no friction until the skier reaches the ungroomed section. The formula that describes the energy in this equation is:

PEinitial + KEinitial = PEfinal + KEfinal - fc *distance

Viscous Friction and Capillary Drag

Skis (as well as ice skate, sleds and other such winter equipment) glide because, some what ironically, of their friction. The friction that does exist between the ski and snow melts a little snow to create a very thin film of water.

The energy that creates this heat comes directly from the Kinetic Energy of the skier. The Kinetic Energy is reduced and thus also the speed is reduced. This loss of velocity to create the thin film of water is called Viscous Friction.

Capillary drag comes from the surface tension of water. The picture above shows how water clings to the bottom of a ski and stretches. The water is exerting a slight force on both the marble and the ski. In snow, columns of water form in the airspaces between the snow crystals. These myriad columns act like the water droplet pictured above and pull on the ski. The wetter the snow is and the thicker the film of water is, then the stronger the capillary drag is.

Dry Friction and Triboelectric Drag

At very cold temperatures, skis begin to slide less easily. This is because the coldness of the snow prevents the easy formation of the customary film of water. It turns out, even in extremely cold condition there is a extremely thin film of water.

Oxygen molecules at the surfaces of snow and ice crystals vibrate faster than those on the interior. This vibration creates an extremely thin layer of molecules, that, because of this vibration, behave like a fluid and provide for the basic slipperiness of snow and ice.
Even with a thicker layer of water lubricant, there is still some dry friction. Here is a graph of the total coefficient of friction compared to some of its components:

Skis rub constantly with the ground. Like with other substances, your hair and a pillow for example, the skis develop a static charge. This Static charge picks up any dust, pollen or other contaminants on the trail and adhere them to the base of the ski. This dirt on the base of the ski can create creates much more drag and abrasion. This static charge also attracts the ski base to the snow for greater friction. This is termed Triboelectric Drag.


Ski bases are created from the plastic polyethylene and created with a method termed sintering. All modern bases are sintered which means that they are porous and act like a sponge to the wax which is applied to them.

In general, softer ski waxes are used for warm temperatures. As the temperature drops there becomes a greater amount of dry friction between the snow and the wax. Harder waxes resist having sharp snow crystals imbed themselves into the wax which would slow the ski down.

The 4 traditional materials combined to make ski wax are:

* petroleum jelly are constituted by light branched hydrocarbon molecules like that shown below on the right. These make a softer wax with a oily feel.
* paraffin are constituted by long, straight hydrocarbon molecules like that shown below on the left. These can be both heavy and light but the lighter paraffins are used because of their lower melting point.. Paraffins make a hard wax more suitable to cold conditions.
* microwax: are constituted by heavy, branched hydrocarbon molecules. Microwax is harder than both paraffins and petroleum jelly.
* Fischer Tropsch wax is derived from coal tar and is the hardest and heaviest of all the waxes.

Cheaper, common waxes are composites of these ingredients. For better performance, higher end waxes combine these constituents with secret ingredients and these newer materials:

* Graphite reduces triboelectric drag by minimizing the static electricity build up on the ski. Graphite also conducts heat from the contact points at the tip and tail of a ski to its middle. In warm weather, this prevents the formation of thicker water films and thus reduces capillary drag.
* Flourocarbons repulse water and decrease the capillary a viscous friction on warm days.

Kick wax is used to create friction to allow classic cross country skiers to push off the snow with one foot and glide with the other. Kick wax is designed have a high static coefficient of friction and a low kinetic coefficient of friction. The soft, tacky wax embeds the show crystals in its base through the force of the skiers downward kick. When the kick is finished, the skier transferes his weight to the other leg to make the next quick. Without any downward force, the forward motion of the ski lightly wipes the wax clean and ready to glide.


Lind, Dave and Sanders, Scott P. The Physics of Skiing: Skiing at the Triple Point. AIP Press, New York, 1996.

Why Do Wings Fly?

Simple Newtonain Physics

The reason wings create lift is illustrated by Bernoulli's Equation:
where P is pressure, p is air density, and v is velocity.

Simple Newtonian Physics

Aerodynamic lift of a wing can be explained and calculated through simple application of Newtonian physics. Air flow following the contours of a wing in normal flight departs in a downward direction. In this redirection of flow, downward momentum is produced. Upward reaction force (or lift) must be equal, according to Newtonian physics, to the downward rate of change of air momentum. Inclination of a wing lower wing surface deflects some air downward there, while greater downward deflection is produced as flow follows the downwardly-curving upper surface. In the downwardly-curving flow, an upward pressure gradient exists which opposes atmospheric pressure to cause upper surface pressure reduction. Bernoulli's law is satisfied with velocity changes related to pressure changes when oncoming air accelerates over the wing leading edge into the reduced pressure above the wing and decelerates in encounter with increased pressure below the leading edge. The pressure difference also accelerates air upward around the leading edge. These accelerations occur in accordance with Bernoulli's law, but the greater upper surface velocity is more easily explained as resulting from pressure difference, rather than causing it as popular theories teach. (Craig)

The following is the equation for lift:
where L is lift, C is the coefficient of lift, p is air density, v is velocity, and s is the plan form area (surface area). 1/2pv² is known as dynamic pressure.

Short Thin Wings

General aviation, or private pilot, aircraft are built with short stubby simple wings. These planes are designed to withstand light loading and a moderate to heavy amount of air turbulance, which is more than most of these airplanes' passengers can stomach. Normal wing configurations consist of ailerons, flaps, and the main wing. Simple to build and easy on the wallet, these wings are perfect for personal, and recreational aircraft. Pictured above is a piper Cherokee (PA-32) in flight, below is another Cherokee (PA-28) sitting at the Palmer Airport.

Rounded Wings

Rounded wings are designed to give maximum stability in flight and smooth stabile responses from flight control surfaces. The rounded trailing edge gives the air more time to smooth out after the leading edge has disrupted its uniform state. Wing configuration still consists of flaps, ailerons, and the main wing. Larger, more stable planes were a necessity as military and civil demands increased for goods to reach destinations in a timely manner, no matter what the weather conditions. Pictured is one of Northern Air Cargo's C-118 (military) to DC-6 B (civil) conversion freighters that moves freight with in Alaska after its service as a U.S. Air Force Cargo Plane.

Angular Wings

Angular wings came about as the airlines industry was looking for ways to maximize efficiency and minimize cost. The sweeping back of the wings is more fuel efficient and economical, but still stabile with the help of extra flight control surfaces other than the ailerons and flaps. Pictured above is a Boeing 727-100 freighter N190AJ on climb out after take-off. Barely visible on the tops and bottoms of the wings are gates that open and close in flight to assist in maneuvering and slowing down.

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