6 Energy Transformation in Skiing

Newton’s Laws and Skiing

Newton’s First Law of Motion: A body will remain at rest or keep moving at a constant speed unless it is acted upon by a force (law of inertia).

Newton’s first law states that “an object in motion will stay in motion, and an object at rest will stay at rest unless acted upon by an outside force.” This means that if there were no outside forces acting on a skier, a single stride would keep the skier moving forward indefinitely. However, there are outside forces which act on skiers. Friction is one example of an outside force. Without friction (and an object in the skier’s path) a skier would not slow down after going down a hill.

Newton’s Second Law of Motion: If the external net force on an object is not zero, the object accelerates in the direction of the net force. The acceleration is directly proportional to the net force and inversely proportion to the net force and inversely proportional to the object’s mass.

Newton’s second law is often known as F=ma, or force equals mass times acceleration. This law explains the force a skier has when going down a hill. The heavier a person is, the faster they will travel down the slope due to a greater force production from their weight.

Newton’s Third Law of Motion: Every action has an equal and opposite reaction.

Newton’s third law of motion is also known as the action-reaction law. Newton’s third law says that “for every action there is an equal and opposite reaction.” This means that the skier is exerting a force on the ground, and the ground is exerting an equal and opposite force on the skier. An example of Newton’s third law is if a skier is forced to ski over some small trees. When the skier bends them over, the skier is exerting the same force on the trees as they are exerting on the skier. This might seem false because the trees are left bent, and the skier continues on unaffected. However, the skier is much more massive than the twigs, and therefore the effect on the trees is greater.

Attribution: Stephanie Akhigbe, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons

We see the application of Newton’s Three Laws of Motion in both skiing and snowboarding. Force is created by the skier on the snow as they travel from the chair lift to the top of the slope. Then gravity accelerates the skier down the hill at ever increasing speed, but another force (friction) is also at work to slow the skier. Friction is created when the bottom of the ski rubs against the surface of the snow. The skiers trade acceleration for control, using the friction between their skis and the snow. How the skier holds their skis on the snow impacts their speed. The frictional forces of the snow can be reduced by perfectly edging or floating across the snow. Edging the skis causes one side to dig in, slowing the skier down, but allowing them to make alternating right and left turns. In straightaways, keeping the ski flat on the snow causes the ski to sink less and maintains higher speed.

Energy Transformation in Skiing

Downhill skiing is a classic illustration of the relationship between work and energy. The skier begins at an elevated position, thus possessing a large quantity of potential energy (i.e., energy of vertical position). If starting from rest, the mechanical energy of the skier is entirely in the form of potential energy. As the skier begins the descent down the hill, potential energy is lost and kinetic energy (i.e., energy of motion) is gained. As the skier loses height (and thus loses potential energy), the skier gains speed (and thus gains kinetic energy). Once the skier reaches the bottom of the hill, the height reaches a value of 0 meters, indicating a total depletion of potential energy. At this point, the speed and kinetic energy have reached a maximum. This energy state is maintained until the skier meets a section of unpacked snow and skids to a stop under the force of friction. The friction force, sometimes known as a dissipative force, does work upon the skier in order to decrease the total mechanical energy. Thus, as the force of friction acts over an increasing distance, the quantity of work increases and the mechanical energy of the skier is gradually dissipated. Ultimately, the skier runs out of energy and comes to a rest position. Work done by an external force (friction) has served to change the total mechanical energy of the skier.

Along the inclined section of the run, the total mechanical energy of the skier is conserved provided that:

• there is a negligible amount of dissipative forces (such as air resistance and surface friction), and
• the skier does not utilize poles to do work and thus contribute to the total amount of mechanical energy

Provided that these two requirements are met, there would be no external forces doing work upon the skier during the descent down the hill. The force of gravity and the normal forces would be the only active forces. While the normal force is an external force, it does not do work upon the skier since it acts at a right angle to the skier’s displacement. In such situations where the angle between force and displacement is 90 degrees, the force does not do work upon the skier. Consequently, the force of gravity is the only force doing work on the skier and therefore the total mechanical energy of the skier is conserved. Potential energy is transformed into kinetic energy; and the potential energy lost equals the kinetic energy which is gained. Overall, the sum of the kinetic and potential energy remains a constant value.

Loading, Deflection and Angular Momentum to Maximize Ski Performance

• Loading of a ski refers to the snow pushing against it. Maximum forces typically build towards the bottom of an arc when the ski grips and steers out of the fall line.
• Deflection refers to the change in a object’s velocity when it collides with a surface (or force). A turn in skiing is like a million tiny deflections otherwise known as centripetal force. Centripetal force pushes the skier on a circular path. When the centripetal force is released the skier will travel at the same velocity along the tangent to that circle from the point of release. For the most part, gravity is responsible for creating a skiers momentum as they point their skis down the hill. The skier can only travel perpendicular to the fall line for a short period before friction from the snow and air resistance slows them down.
• Angular momentum is controlled with coiling and separation (i.e., turning the skis under a stable body), which hints to maintaining a stable upper body and not rotating with the turn, which would create too much angular momentum

How maximize momentum through turns and across the slope:

• Go faster – More speed means there is more force to work with.
• Tighten the radius using ski design – To tighten the arc we need to create a larger steering angle. We can do this by twisting the ski, however this usually corresponds with more slowing forces. Alternatively, we can roll the ski further on edge and use the skis’ design properties to create a steering angle that tightens the arc with fewer slowing forces.
• Move your center of gravity further inside – In skiing we do this through inclination. The inside leg bends and/or the outside leg to extends allowing gravity to pull the mass down and inside the arc. Conveniently this also tightens the arc, and when the arc tightens you can move the mass further inside:) As you continue tipping into the the turn, you’ll likely need to supplement with angulation to keep pressure on the working ski.
• Tip to tail through the arc – Pressure shifted slightly towards the front of the working ski will create more torque (or turning force) on the skier as the snow pushes the tips into the arc. This can be useful when there is not much pressure on the ski at the top of the arc. Once the ski is weighted, pressure through the middle of the side cut will allow the whole length of the edge to penetrate the snow. And finally, pressure slightly towards the tail can put a stop to this tip torque, helping the skis exit the direction change and accelerate out of the turn.
• Reduce friction – The most efficient turn occurs when the skier does a purely carved turn, in which the ski is pointing in the same direction as its velocity. In a purely carved turn there is no skidding, and the only snow resistance present is the very small sliding friction between ski and snow. As a result of this minimal level of friction between ski and snow, the speed reduction of the skier is minimized.

References

Energy Transformation for Downhill Skiing. The Physics Classroom. (n.d.). https://www.physicsclassroom.com/mmedia/energy/se.cfm

Newton’s Laws. (n.d.). http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/Sarah_Schlichting/NewtonsLaws.html

Loading, deflection & angular momentum to maximize ski performance. SkierLab. (2022, April 26). https://skierlab.com/loading-deflection-to-maximize-ski-performance/