By Anne-Marie Robertson, 2007.
Understanding the forces involved in a dynamic ski turn and how these relate to modern ski design helps to explain why we make the movements we do to maximize ski performance.
A ski pointed straight down a fall line will accelerate towards the bottom of the slope because of gravity. Another force must be applied in order to turn the skis away from the fall line. Centripetal force is what keeps the skis travelling in a curved path. Because of inertia, the skier’s mass wants to keep going in a straight line, i.e. at a tangent to the curved path (imagine what happens when you swing something on the end of a string in a circle, and then let it go).
Gravity is also acting to pull the skier’s mass in the downhill direction. The combination of these explains why a skier feels like he/she is being pulled to the outside of a turn, and why the skier’s weight is naturally transferred to the edge of the outside ski. In a dynamic turn, the combination of centripetal force and gravity acting on the skis is usually referred to as ‘pressure’.
A formula for centripetal force is:
centripetal force = mass x (velocity) squared over radius [refine equation]
The force comes from edge grip between the skis and the snow. In comparison, for a car turning a corner, the force comes from friction between the tyres and the road surface. If the car is going too fast, or the road is wet or icy, the tires cannot hold and the car skids. In skiing, if the edge is released, or if the slope is too icy for the edges to penetrate and grip, there is not enough centripetal force and the skis skid to the outside of the turn.
Because velocity is squared in the equation, speed has a greater influence on centripetal force than the other variables. The higher the speed, the heavier the skier and the tighter the turn radius, the greater the centripetal force required.
Modern skis are designed with a shaped side cut. Skis also have camber (i.e. they aren’t flat, at least when they’re new) so that the skier’s weight is more evenly distributed over the length of the ski. When a ski is tipped up onto its edge and flexed (or ‘bent’ or ‘reverse cambered’) so that the whole edge is in contact with the snow it forms an arc. If the skis are edged while moving they will turn in that arc. The centripetal force is created by the edge angle. The higher the edge angle the more the ski has to bend to contact the snow and the tighter the turn radius. Rotating the femurs also ‘twists’ the edges into the snow, increasing centripetal force and tightening the turn radius.
The equation above is a simplified version of what is happening in a ski turn. For example, as already mentioned, gravity is acting on the skier and so as he or she turns into the fall line, the skis accelerate. Velocity is not constant so the force or pressure increases through the turn. To get more complicated, to maintain edge grip the ski has to be able to penetrate the snow to some degree and also hold without the snow itself giving way. So, for different snow conditions there is a ‘critical edge angle’ – depending on the shear strength or hardness of the snow. This determines whether the skis will carve or skid and explains why it is difficult to carve a turn on ice and why in some types of softer snow it is not always possible to leave two completely clean lines as tracks.
Applied to the dynamic turn
In a dynamic turn, to balance against the forces acting on the ski, the skier inclines his or her mass inside the arc of the turn. This further increases the edge angle and also has a similar effect to banking on road corners. At high edge angles, angulation at the hip is required to physically keep the outside ski in contact with the snow. To maintain centripetal force, i.e. edge grip, there has to be some downward pressure on the ski. Angulation moves the centre of mass back slightly towards the outside ski, where most of the gripping force should be acting. Think of what happens when a car goes too fast around a corner that is not banked, and the inside wheels lift off the ground. Unlike a car, a skier is not completely rigid and can adjust body parts to balance.
As the skis pass back under the centre of mass during the transition of one turn to the next, edge angle decreases and the centripetal force is released – sometimes felt as a ‘ping’ at the end of a carved turn.
Many articles have been written about the forces involved in skiing. Some are extremely complicated and mathematical. Discussing forces with students can be confusing for them, but using analogies from everyday life can be useful for understanding. In high-level skiing managing the forces and using the ski design is vital to obtain optimum ski performance.
References and Acknowledgments
- NZSIA Alpine Instructors Manual
- Jones, Bill (2006)
- Raguso, Victor (2000)
- Williams, Mark
- Photo from Ski Racing New Zealand