Part 1: Forces Effecting Movement on the Snow

Bombing down the Wishbone Couloir, Grand Turk (13,180′), Silverton, CO
Bombing down the Wishbone Couloir, Grand Turk (13,180′), Silverton, CO

In this three-part series I will cover the forces effecting movement on the snow in part one. In part two; base construction, material, and structure theory, and in part three; the role of wax, and health risks. While some of the physics can be complex, it’s actually easy to understand. With a basic understanding of the dynamics involved you can prepare your equipment and have a better understanding of how conditions impact riding.

The motion of a rider is determined by the physical principles of the conservation of energy and the frictional forces acting on the body. For example, in snowboarding, as the rider is accelerated down the hill by the force of gravity, the gravitational potential energy is converted to kinetic energy, the energy of motion. In theory, all of the potential energy would be converted into kinetic energy; in reality, some of the energy is lost due to friction.

One type of friction acting on the rider is the kinetic friction between the board and snow. The force of friction acts in the direction opposite to the direction of motion, resulting in a lower velocity and hence less kinetic energy. The kinetic friction can be reduced by applying wax to the base of the board which reduces the coefficient of friction. The shape, construction and material of a board can also greatly impact the forces acting on a rider.[1]Lind, D., & Sanders, S. (2003). The Physics of Skiing, Skiing at the Triple Point. Springer, New York


Part 1. Forces Effecting Movement on the Snow

Many forces effect movement across snow. The primary force effecting this movement is friction. There are two types of friction: kinetic and static. Kinetic friction slows an object already in motion and static friction prevents a stationary object from moving. Since it is harder to get an object in motion than it is to keep an object in motion, the coefficient of static friction is always greater than the coefficient of kinetic friction.

The temperature at which water freezes is increased with pressure. So when your snowboard or ski is in contact with the snow, the weight applied makes a micro-layer of snow beneath it melt as you glide across.[2]Baurle, L. (2006). Sliding Friction of Polyethylene on Snow and Ice, Dissertation, Retrieved November 29, 2014, from http://e-collection.library.ethz.ch/eserv/eth:28803/eth-28803-02.pdf This layer instantly refreezes once the base is no longer in contact with the snow. This action further reduces the two types of friction mentioned above.

Surfaces with liquid are more slippery. Everyday experience illustrates that; water on a floor, or rainwater on asphalt or concrete can create the same type of hazards that ice can. Liquids make a surface slippery because they are mobile, while a surface is relatively rigid. Skaters for instance glide across with a low coefficient because the ice melts under the skates’ edge pressure causing a micro layer of liquid. This is why in extremely cold temperatures (below -40°C), the snow or ice surface can seem like sandpaper. This phenomenon is known as Pressure Melting.[3]Thompson, J. (1948). M. Farraday Proceedings, Proceedings of the Royal Society of London pp151, Vol 10

Pressure melting is scientifically known as LeChatelier’s Principle. How does pressure melt ice you ask? Basically the same reason that ice floats; because when water freezes it expands. So, when pressure is applied to ice the reverse happens as it tries to take up less space. One way for ice to take up less space is for it to turn back in to water.

Each time a ski or snowboard passes over snow, the result is that a thin micro-layer of ice has been left behind from pressure melting. Once snow has been tracked by a base, it is no longer snow because it has melted and refrozen, this process is known as regelation. While the micro-layer is thin, and a person would hardly notice, when you multiply this by many skiers and riders it quickly becomes a thicker ice layer. This is why slopes at resorts are groomed each day.[4]Rosenburg, Robert. (2005). Why is Ice Slippery. Physics Today. Retrieved November 29, 2014, from http://lptms.u-psud.fr/membres/trizac/Ens/L3FIP/Ice.pdf This is also why skins tend to absorb some of the micro-layer of water, although in the simultaneous motion of gliding forward (when pressure is released), the water is quickly refrozen and mostly shed.

Fresh untracked powder, Eiseman Hut, Gore Range, CO.
Fresh untracked powder, Eiseman Hut, Gore Range, CO.

Snowboarding takes on many different forms of physics. There is of course Newton’s Laws of Motion, the transformation of potential energy into kinetic energy, air resistance, friction, and so on. 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. Ice crystals form when water vapor condenses and freezes around a foreign particle such as dust or sea salt. These Ice crystals then form various varieties of snowflakes.  These snowflakes can fall in many forms, including ferns, crystals, plates, stellar dendrites, and needles.

These snowflakes 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. These pellets then bond again through a process of melting, freezing, evaporation and sublimation at their contact points. Hence, the type of snow plays a large role on the type of friction we might encounter. The difference between manmade snow, and natural snow is enormous and incomparable. [5]Colbeck, S.C.  (1992). The Friction of Snow Skis. Retrieved November 29, 2014, from http://arc.lib.montana.edu/snow-science/objects/issw-1992-018-027.pdf[6]Ambach, W., & Mayr, B. (1981). Ski Gliding and Water Film. Cold Regions Science and Technology, Vol. 5, pp. 59-65.[7]Barnes, P., Tabor, D. & Walker, I.C.F. (1971). The Friction and Creep of Polycrystalline Ice, Proceedings of the Royal Society of Landon, Vol. A324, pp. 127-155.[8]Bowden, F.P., (1953). Friction on Snow and Ice, Proceedings of the Royal Society of London, Vol. 217A, pp. 462-478.

The dynamics of a base sliding on snow

In a very fast explanation and formula here is what is happening when a base slides on a slope. The reaction force from the snow (R) is a different angle to the force from our weight. So, there is a component of this reaction force created by our weight in the direction of the slope (FM). The friction force (FF) is calculated by multiplying the coefficient of friction (μ) by the reaction force from the snow (R). Because the pressure of the snowboard has made a thin layer of snow melt, μ is very low, and in most conditions the slope angle (θ) will not need to be very high before FM is larger than FF and the board begins to slide. In essence, when FM is greater than FF the snowboard will slide.[9]Bowden, F.P., & Hughes, T.P. (1939). Mechanism of Sliding on Ice and Snow, Proceedings of the Royal Society of London, Vol. 172A, pp. 280-298.[10]Colbeck, S.C., (1988). Kinetic Friction of Snow, Journal of Glaciology, Vol. 34(116), pp. 78-86.[11]Kuroiwa, D., (1977). Kinetic Friction on Snow and Ice, Journal of Glaciology, Vol. 19(81), pp. 141-152.[12]Spring, E., (1988). A Method for Testing the Gliding Quality of Skis, Tribologia, Vol. 7(1), pp. 9-14.

diagram

The effect on powder

In softer, deeper snow – like that typically experienced in the backcountry it takes more force to get compression. It takes more energy to get glide, and hence the reason you cannot go as fast in powder conditions.

The effect on wet snow

In wet snow, such as spring conditions the base (ski or snowboard) will not slide as well due to the amount of water under the base. When the amount of water is so great that no air can in to the micro-layer it creates a vacuum pulling the base to the snow and not allowing it to slide as easily.

Kinetic Friction

Kinetic Coefficients of Friction (μ)

Material μ 

Ice on ice μ = 0.035
Waxed ski on snow μ = 0.05
Brass on ice μ = 0.075
Rubber on wet cement μ = 0.97
Rubber on dry cement μ = 1.02

Kinetic friction is caused by the rough surface of the moving object rubbing with the rough surface of the non-moving object. If force is continuous on the moving object, small pieces of each object will be chipped away and energy in the form of heat.[13]Bueche, F.  (1965). Principles of PhysicsMcGraw-Hill This is why your hands warm up when you rub them together. A number called a coefficient of friction expresses the resistance between two materials. The coefficient of friction of a waxed base to snow is about 0.05.[14]Tipler, Paul A., & Mosca, Gene (2008). Physics for Scientists and Engineers, Text, W. H. Freeman and Company The coefficient of friction of a waxed snowboard on snow is an estimate because there are different kinds of waxes, conditions, snow, bases, and ways to wax a base. Depending on those factors the coefficient can range from 0.3 to 0.001.[15]Tipler, Paul A., & Mosca, Gene (2008). Physics for Scientists and Engineers, Text, W. H. Freeman and Company Using the kinetic coefficient of friction you can calculate the frictional force against the objects movement and then how far the object will move before it slows to a stop.

Two examples of coefficient of friction on a snowboard:

Waxed Snowboard

Let’s assume ‘snowboard A’ has a coefficient of friction of 0.05, a rider with a mass of 63.5 kilograms (140 pounds), gliding at 5 meters per second (roughly 10 miles per hour) the rider would glide 25.5 meters before stopping without adding additional thrust.

Unwaxed snowboard

Now let’s assume ‘snowboard B’ has no wax, a coefficient of friction might increase to 0.15. At this coefficient of friction, the same rider, at the same speed would only glide 8.51 meters. This is almost 17 meters of glide less than if the coefficient had been 0.05. Thus, with more friction the rider must apply significantly more effort to maintain speed and distance.


Formulas

f=μN
F=ma
v2=v02+2ax

Unit Definitions

f – frictional force
μ – kinetic coefficient of friction (0.05)
N – normal force of the object (9.8m)
F – opposite of the frictional force
m – mass of the object moving (63.5 kg)
a – acceleration or deceleration
N = normal force
v – ending velocity of the object (0)
v0 – starting velocity of the object (5 m/s)
x – distance to reach the ending velocity

Calculation

Finding Frictional Force:

  • 63.5 x 9.8 = 622.3N = normal force
  • f=μN
  • 622 x 0.05 = 31.1N = f

Finding Deceleration Rate:

  • F=ma
  • -31.1N = 63.5 x a
  • a = -0.49m/sec2

Finding Distance Before Stopping (x):

  • v2=v02+2ax
  • 02=52+2(-0.49)(x)
  • x = 25.5m before stopping

Static Friction

Static friction is overcome when a rider applies a force greater than the force of static friction. Static friction is also measured with a coefficient to find the force needed to move the object (the frictional force). The frictional force is found with the formula f ≤ usN, where us is the static coefficient of friction.[16]Tipler, Paul A., & Mosca, Gene (2008). Physics for Scientists and Engineers, Text, W. H. Freeman and Company If the object is on a hill, the normal force that is usually the weight of the object becomes the weight multiplied by the cosine of the slope angle.

Water Suction

The third force effecting the base/snow interface zone is water suction. In temperatures of about 26°F and lower, the heat of kinetic friction meets the snow under the snowboard, and produces a thin layer of water. This layer is only about a one thousandth of a centimeter thick. However, If the temperature is above 26°F the layer is thicker and can create a suction effect on the base.

Conclusion

The forces effecting movement on the snow are sometimes complex and involve many laws of physics to decipher. If you can grasp the basic concept of what has been covered, it will make base preparation and waxing easier to understand. Friction on the base in particular plays a large role. In Part Two, I will go in to polyethylene base material, base structure theory, the snowboard base material. In Part Three I will be covering, waxing, wax structure, precautions, and health risks.


Part 2: Snowboard Base Construction

Part 2: Snowboard Base Construction

Part 3: Snowboard Waxing

Part 3: Snowboard Wax

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References   [ + ]

1. Lind, D., & Sanders, S. (2003). The Physics of Skiing, Skiing at the Triple Point. Springer, New York
2. Baurle, L. (2006). Sliding Friction of Polyethylene on Snow and Ice, Dissertation, Retrieved November 29, 2014, from http://e-collection.library.ethz.ch/eserv/eth:28803/eth-28803-02.pdf
3. Thompson, J. (1948). M. Farraday Proceedings, Proceedings of the Royal Society of London pp151, Vol 10
4. Rosenburg, Robert. (2005). Why is Ice Slippery. Physics Today. Retrieved November 29, 2014, from http://lptms.u-psud.fr/membres/trizac/Ens/L3FIP/Ice.pdf
5. Colbeck, S.C.  (1992). The Friction of Snow Skis. Retrieved November 29, 2014, from http://arc.lib.montana.edu/snow-science/objects/issw-1992-018-027.pdf
6. Ambach, W., & Mayr, B. (1981). Ski Gliding and Water Film. Cold Regions Science and Technology, Vol. 5, pp. 59-65.
7. Barnes, P., Tabor, D. & Walker, I.C.F. (1971). The Friction and Creep of Polycrystalline Ice, Proceedings of the Royal Society of Landon, Vol. A324, pp. 127-155.
8. Bowden, F.P., (1953). Friction on Snow and Ice, Proceedings of the Royal Society of London, Vol. 217A, pp. 462-478.
9. Bowden, F.P., & Hughes, T.P. (1939). Mechanism of Sliding on Ice and Snow, Proceedings of the Royal Society of London, Vol. 172A, pp. 280-298.
10. Colbeck, S.C., (1988). Kinetic Friction of Snow, Journal of Glaciology, Vol. 34(116), pp. 78-86.
11. Kuroiwa, D., (1977). Kinetic Friction on Snow and Ice, Journal of Glaciology, Vol. 19(81), pp. 141-152.
12. Spring, E., (1988). A Method for Testing the Gliding Quality of Skis, Tribologia, Vol. 7(1), pp. 9-14.
13. Bueche, F.  (1965). Principles of PhysicsMcGraw-Hill
14. Tipler, Paul A., & Mosca, Gene (2008). Physics for Scientists and Engineers, Text, W. H. Freeman and Company
15, 16. Tipler, Paul A., & Mosca, Gene (2008). Physics for Scientists and Engineers, Text, W. H. Freeman and Company

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