# SKI LEVERS

In a simplistic schematic form, the transverse aspect of a decambered ski acts in the capacity of a dual-pivot, offset lever. The model I will use to illustrate this assumes that the load W is transferred by the central load-bearing axis (LOAD TRANSFER) to an axis lying on the transverse center of the portion of the ski underfoot. It also assumes that foot is in neutral and that this has extended the central load-bearing axis from the lower aspect of the tibia to the base of the heel and from there to the plane of the base of the ski.

From a practical perspective, it is exceedingly difficult to immobilize the joints of the foot, let alone immobilize the subtalar joint in a neutral configuration with any degree of precision. But since the predominant view of the experts in skiing is that the foot functions best when it’s joints are immobilized in neutral, my schematic model  assumes this is actually possible in the name of simplicity. Since a vertical alignment of the heel bone with the supporting surface is often cited as an objective in the fabrication of insoles, boot fitting and lower limb alignment, it is reasonable to assume that neutral means subtalar joint or STJ neutral.

The graphic below depicts the ski as a dual-pivot, offset lever. For the sake of simplicity, the effective length of the lever offset create by the width of the sidecut at the tail and fore body of the ski are represented as being equal.

(Click on graphics to enlarge the image)

The graphic below shows a section through the ski where W would be transferred to when the foot is immobilized in neutral.

In the above schematic, W is the load transferred to the ski by the COM of the skier. C is the central axis of the ski. P is the pivot created by the edge of the ski that is engaged with the snow.  R is the resistance of the snow acting on the portion of the base of the ski within the sidecut area. In the configuration shown in the above graphic, the length of the lever is measured from the point of the transfer of W to the pivot P created by the active inside edge (aka – Ground Zero).

The graphic below depicts the 3 classes of levers. The First Class Lever is the classic teeter-totter mechanism, one that most children experience at an early age.

Of the 3 classes of levers, only First and Second Class levers have practical application to the ski as a dual pivot, offset lever.

The center pivot format of the First Class Lever represents the configuration that exists when W is transferred to the center of transverse center axis of the ski as it will be when the foot cannot pronate at ski flat between edge changes.

The first problem that arises is that R is in phase with W. In this configuration, both forces are cooperating to rotate (invert) the ski towards the outside of the turn. Without an opposing force or effort, W and R will invert the ski and foot as a unit as shown in the graphic below. This will occur even in the absence of resistance R that is created by the sidecut of the ski.

In addition to the preceding, no vertical force is present acting in opposition to the GRF at P. So the edge will not grip. In the mechanics of sidecut, the inside edge of the outside ski is Ground Zero. Opposing forces W and GRF must be aligned at 90 degrees to the transverse plane of the base of the ski in order to enable the sidecut to cut into the snow as the ski rotates into the snow about P. This alignment must be maintained at all times during the turning phase.

The central load-bearing axis (DOT 9: LOAD TRANSFER) is a straight line between head of the femur and the lower aspect of the tibia. A neutral configuration of the subtalar joint extends the lower aspect of the central load-bearing axis to the base of the heel. An unbalanced moment of force results when W is offset with P on the inner (inside turn) aspect of the outside foot.  The top down load transfer of  W through the central load-bearing axis induces a state of inversion stress as unit inversion of the element underfoot and the foot are translated through subtalar joint coupling to external vertical axial rotation of the leg as a whole.

The graphic below shows the 3 degrees of freedom of the foot/ankle complex of the foot. The line joining the arcs of Inversion-Eversion and Lateral-Medial Axial Rotation indicates coupling through the subtalar joint which acts in the capacity of a torque converter.

Inversion Stress

A state of inversion stress exists when the centre of the load W is transferred to the centre axis of outside ski when it is on its inside edge and W is offset laterally from the P. This creates a moment arm with the inside edge acting in the capacity of a pivot P. The load W applied by the foot to the moment arm causes the ski to invert. Inversion occurs either as a unified movement of the ski equipment stack/foot-leg system or as a combination of ski equipment stack inversion in conjunction with a degree of subtalar joint inversion of the foot and leg within the confines of the ski boot. In either case, inversion of the foot involves translation through the subtalar joint of an inversion moment of force into a lateral axial moment of force of the outside leg. This is accompanied by a degree of hip adduction of the leg against the closed kinetic chain created by the edged ski. This combination creates medial compression of the knee joint in combination with a degree of lateral axial rotation of the tibia against a well stabilized femur.

A state of inversion stress results from the inability of the central load-bearing axis to complete the transfer of load W through the load transfer elements of the foot to a source of contiguous GRF.

In the First Class ski lever format that exists when W is on the outside turn aspect of the moment arm created by an offset with P, it is virtually impossible for pronation of the outside foot of a turn to be induced by the load transfer of W to the foot, let alone for pronation to be prevented or precisely controlled as is implied by some authorities in skiing. To suggest that it can, is absurd.

In order for the inside edge to grip and serve as a pivot for the sidecut to rotate about and cut into the snow surface, the transfer of the load W must be completed and an opposing force or effort provided by the skier to restrain inversion of the outside ski and foot.

# THE EFFECT OF LIFT PLATES ON SKI MANEUVERS

In THE EFFECTS OF LIFT PLATES – CONTINUED, I used a simple model to show how the presence of joints with rotational capability below the lower end of the mechanical line at the tibia affect the initial length of the torque arm acting on the outside foot stabilized in a neutral position and the force vector of the mechanical line as the foot rotates about its long axis about a pivot under the inner aspect of the foot. In this post, I am going to set this basic model in the context of the forces acting on a skier in the arc of a turn.

When it comes to discussions of the forces involved in ski maneuvers, most of the force diagrams I have been able to find by others are those that show components of gravity (G) and centrifugal forces (C) with a resultant force (R) acting at the inside edge of the outside ski. If a force diagram is really sophisticated, it might show a ground reaction force (GRF) acting in opposition to the resultant force (R) similar to what is shown in the annotated photo below.

The inference of such simplistic explanations is that, far from being complicated, the forces involved in skiing are really quite simple.

Gravity (G) and centrifugal force (C) are components of a resultant force (R). The resultant force merely has to be shown aligned in opposition to a ground reaction force (GRF) at the inside edge of the outside ski in order to satisfy an explanation of the mechanics of  edge hold. Forces applied by the foot? No need to complicate things. Keep it simple. Ignore them. If other forces are ignored they aren’t important.

Riser plates? Torques? Ignore them too. It would be nice if things were that simple. But when things like centre of pressure (CoP) and the torsional effects of lift plates are added to the discussion, it quickly begins to become obvious that the forces in skiing are anything but simple. Significant forces other than gravity and centrifugal force are present. And they do affect the skier.

In THE EFFECTS OF LIFT PLATES – CONTINUED, I used a simple model to show how the presence of joints with rotational capability below the lower end of the mechanical line at the tibia affect the initial length of the torque arm acting on the outside foot stabilized in a neutral position and the force vector of the mechanical line as the foot rotates about its long axis about a pivot under the inner aspect of the foot. In this post, I am going to set this basic model in the context of the forces acting on a skier in the arc of a turn as shown in the above sketch.

The sketch below shows the forces applied to the outside foot and ski of a turn by the foot through the mechanical line in conjunction with a resultant force acting at the inside edge before a load is applied. This situation would exist if a skier were to get caught inside and lose contact of the outside ski with the snow. The tendency of a limb that unloads from a force applied to it is to release muscle tension and unwind into a supinated position. In the situation described in the sketches the foot has been stabilized in a neutral configuration with arch supports or custom insoles and/or a form fitted liner or possibly a form fitted shell. When the foot is in a neutral position the force applied to the foot will act on the proximate centre of a line that runs through the ball of the 2nd toe and the heel.

The sketch below shows force applied to the outside foot causing the rotation described in THE EFFECTS OF LIFT PLATES – CONTINUED. There is way more going on than shown in the sketch. But I will get to the other issues in future posts.

The sketch below shows and overlay of the first and second sketches to show the changes. As rotation occurs in the subtalar joint the force vector of the mechanical line shifts towards the outside of the turn. As it does the transverse angle of the ski base flattens. These changes will tend to cause the ski to slip out of the turn forcing the skier to increase the angle of the resultant force R by increasing the angle of inclination.

Increasing the angle of inclination makes a bad situation worse because the forces become more aligned with the slope of the hill thus increasing the magnitude of the forces that tend to make the ski slip out of the turn.

The NY Times video – Ligety on GS commented, “The trace of his (Ligety’s) path is smoother than that of his foes, who ski in somewhat violent fits and starts, making adjustments that spray snow.” What are Ligety’s foes doing that is different from what Ligety is doing? The forces on Ligety’s outside ski are consistently rotating into the turn. The forces on the outside ski of his foes are rotating out of the turn. But changes in the consistency of the snow texture and the forces acting on the outside ski cause changes in the edge angle. The animated video clip below show this effect.

Changes in edge angle cause the outside ski to oscillate into and out of the turn. Ligety’s foes, which includes the majority of World Cup racers, are unable to develop a dynamically tensioned base of support on their outside foot and ski because the forces they are applying are on the wrong side on the inside edge and they are unable to apply a countering torque with internal rotation of the outside leg from the pelvis. The result is the outside ski is unstable. It makes small oscillations in response to perturbations in ground reaction force necessitating a corresponding series of small adjustments by the racer. Edge angle oscillation can also cause the ski to suddenly hook into turn without warning causing a fall. In a future post I will include some video clips showing edge angle oscillation.