It was my intent to discuss the key move in the First Step to Balance on the Outside Ski; Impulse Loading of the Forefoot. However, it has become apparent that it is necessary to preface this subject with a discussion on the source of ground in relation to the outside foot in order to impart an appreciation of why a mechanism is required to extend ground from the running edges of the ski in order to create a platform for a skier to stand and balance on when the outside ski is on its inside edge.
In typical discussions of ski technique and the mechanics, biomechanics and physics of skiing, the prevailing mental model assumes that a skier is in balance (see REVISION TO FEATURE POST: CLARIFICATION OF DEFINITION OF SKIER BALANCE) if they are able to stand upright and exercise a degree of control over their skis. In studies of balance performed in gait labs, ground reaction force in the form of stable surface for subjects to balance on is assumed.
Mental models are a form of cognitive blindness. Once people assume they know something, they not only don’t question what they believe, they filter out information that conflicts with their mental model. And they typically fail to see the real issue even when it is in plain sight.
A man should look for what is, and not for what he thinks should be.
– Albert Einstein
The Skier Balance Paradox
Even though I quickly became a competent skier soon after I started skiing, I struggled to hold an edge on firm pistes and especially glare ice. It was disconcerting to see elite skiers hold an edge on ice with minimal effort while making controlled turns. When I sought the advice of the experts, they claimed that holding an edge on ice was matter of sharp edges and/or driving the knees into the hill. When I protested that after trying both and found it harder to hold an edge, the experts claimed that the ability of some skiers to do what I couldn’t was due to superior technique. They were just better skiers. No further explanation was needed.
The inability of experts to explain why a small number of skiers seemed able to balance on their outside ski and hold an edge even on ice provided me with the impetus to look critically at this issue with the objective of formulating an explanation based on principles of applied science.
The only plausible explanation for the ability of a skier to be able to stand and balance on their outside ski when it is on its inside edge is that some source ground (reaction force) must be present under ski that they are using to stand and balance on. Hence, the question, Where is the Ground?
On very hard pistes, ground as a source of reaction force, is limited to the running portion of the inside edge of the outside ski and the small portion of the base adjacent the edge with the edge and base supported on a small shelf cut into the surface of the snow/
In Figure 2.11 on page 26 of his book, Ultimate Skiing, LeMaster explains how the sidecut of a ski creates a smaller radius turn as the edge angle increases.
In Figure 2.12 on the following page, LeMaster shows misaligned applied (green arrow) and ground reaction (purple arrow) forces creating an unbalanced moment of force (yellow counter-clockwise rotation arrow) that rotates the ski down hill (out of the turn). LeMaster goes on to state that as the skier edges the ski more, the ski bites better. But he fails to offer an explanation as to how the skier can edge a ski more against an unbalanced moment of force acting to reduce the edge angle.
The mechanism that generates a moment of force that opposes the moment force shown by LeMaster in Figure 2.12 and has the effect of extending ground (reaction force) acting along the running length of the edge of the ski is the subject of this series of posts.
Edge Angle Sidecut FXs
A simple way to acquire an appreciation for the location of ground relative to the outside ski on edge is to make a simple model out of flexible piece of sheet plastic material a few mm thick.
The photo below shows a model I made from a piece of sheet plastic about 8 inches long. The upper portion of the plastic piece has a shorter sidecut with less depth than the sidecut in lower portion of the piece of plastic piece. Both the model and sketches that follow are for illustrative purposes to demonstrate the effects of sidecut geometry on edge angle and a source of ground. Although the basic principles are the same, it is not intended that they be viewed as an accurate representation of actual ski geometries The symmetrical geometry is for the benefit of the simplifying what is already a complex issue.
There is a relationship between the depth and length of a sidecut in that the greater the ratio of the depth to the length of a sidecut, the lower will be the edge angle it forms with the surface in relation to the camber radius. In the sketch below, the upper rectangular ski shape will maintain a vertical relationship with a surface regardless of the camber radius.
There is also a relationship between the edge angle a ski with sidecut will form with a uniform surface and the radius of the camber with the edge angle formed with a uniform surface. The edge angle will increase (become more vertical) with a decrease in the radius of the camber. This explains why GS skis that are longer and have less sidecut depth than SL skis can attain much higher edge angles.
The photo below shows how the aspect of the model I made with the smallest sidecut ratio forms a steep angle with a uniform surface when bent to sufficient camber radius to allow the sidecut to become compliant with a uniform surface.
When viewed from the rear of the model, the location of ground in relation to the structure of a ski with sidecut and camber should become readily apparent.
The graphic below shows what a photo taken at a low enough vantage point to the snow would capture looking straight on at a ski carving a turn with its edge compliant with the surface of the snow. This may seem foreign, even extreme to some. But when the edge of a ski is compliant with a uniform surface, the curve of the sidecut becomes linear.
The left image below depicts the schematic model of the ski shown in the second graphic with the camber angle sufficient to make the edge in contact with the uniform surface compliant with it. The angled line represents the surface of the snow. The schematic model of the ski represents the proximate end profile associated with a high load GS turn. A photograph in Figure 1.18 on page 17 of the Skier’s Edge shows a similar profile in Hermann Maier’s outside (left) ski which is at a very high edge angle.
The graphic on the right shows some penetration of the running surface of the edge of the ski in conjunction with the forces commonly shown in the prevailing mental model that are used to explain how forces acting on the outside are balanced.
The reality is of the applied forces acting on the ski are shown in the vertical profiles in the graphic below as captured by digitized force plate data. Once the foot is loaded on a surface there is what is called a Center of Pressure as shown by the peaks in all 3 graphs. But when the foot is in compliance with a uniform surface, some pressure is expressed by the entire contact surface of the foot. So, the point application of applied force in opposition to a point application of GRF as depicted in the right hand graphic above is a physical impossibility.
Viewing a transverse vertical profile of a ski on edge from the perspective of ground as a source of GRF for a skier to stand and balance on puts the issue of skier balance in a whole new, albeit unfamiliar, perspective. But it is a reality that must be dealt with in order to engage in realistic narratives on the subject. Overly simplistic explanations of skier balance attributed to a basic alignment of opposing forces do not serve to advance the sport of skiing as a credible science.
I concur with LeMaster’s position that the platform angle a ski forms with resultant and GR forces must be at 90 degrees or slightly less in order for the edges to grip. In my next post, I’ll start to introduce mechanical principles that explain how this can be accomplished.
It is the ability of racers like Mikaela Shiffrin to stand and balance on their outside that enables them to consistently dominate World Cup competition.