In THE MECHANICS + BIOMECHANICS OF PLATFORM ANGLE: PART 8, I stated that after a thorough investigation and analysis of the forces associated with platform angle mechanics I reached the conclusion that rotational (steering) force should be applied to an isolated area of the inner shell wall of the ski boot by the medial aspect of the head of the first metatarsal as shown in the graphic below.Applying rotational or steering force to the medial (inner) aspect of the head of the first metatarsal requires the application of an effort by the skier that attempts to rotate the foot inside the confines of the ski boot. The application of rotational effort to the inner aspect of the vertical wall of the boot shell opposite the head of the first metatarsal will result in a reaction force that pushes the lateral (outside) aspect of the heel bone against the outer corner of the vertical shell wall as shown in the graphic below. The robust structure of the bones of the first metatarsal, midfoot and heel bone serve as a structural element in transferring rotational force to opposing aspects of the shell walls in an eccentric torque couple.The outline of the boot shell in the above graphic was generated from a vertical plane photo of an actual ski boot. The interference created by the inner wall with the localized application of rotational force to the shell wall by the medial aspect of the head of the first metatarsal should be obvious.
The radius of the moment arm acting on the outer aspect of the heel area of the shell is much smaller than the radius of the moment arm acting on the inner aspect of the shell opposite the head of the first metatarsal and many times shorter than the length of the moment arm acting at the shovel of the ski. The result is that rotational force applied to the eccentric torque arm couple by rotation applied to the ankle will attempt to rotate the torque arm and the axis of rotation at the ankle joint about an axis of rotation at the lateral aspect of the heel as shown in the graphic below. This mechanism enables a skier to apply much greater rotational force into a turn at the center of the ski than can be applied at the shovel. This has signficant implications for platform angle mechanics. In addition to the above, the plane of the rotational force applied by the medial aspect of the head of the first metatarsal and lateral aspect of the heel bone to the shell wall is elevated above the plane of the rotational force at base of the ski below.
In my next post I will discuss what happens when the reaction force from the snow that opposes the 180 degree force applied to the base plane of the ski becomes sufficient to arrest rotation of the ski about its axis of rotation at the ankle joint.
For the sake of simplicity I have started the discussion of the mechanics of platform angle with opposing static forces acting across the platform edge/snow surface (i.e. ground) interface. The use of static forces and drills to illustrate platform mechanics is not realistic because skiing involves the acceleration and deceleration of a body (i.e. mass). A realistic discussion must consider all significant external and internal forces and the effects of momentum and inertia. A key component of any discussion of this nature is the orientation of the platform or transverse base angle of the outside ski in relation to the vector of opposing applied and reaction forces and the angle of the vector with the plane of the surface of the snow. The mechanism of control of the platform angle must also be considered.
The objective of the initial posts on the mechanics of platform angle is to create a set basic principles to serve as a frame of reference for multi disciplinary dialogs on the mechanics, neurobiomechanics and physics of skiing.
In my last post I discussed how the shear or slip component of an applied angular force acting on a surface or body will increase in magnitude as the angle of attack decreases and becomes more aligned with the plane of the surface while the normal component of the applied and force will decrease in magnitude. As this happens the tendency of the force applied to the snow that would cause it to penetrate into the surface and cut a step will decrease. As the platform angle with the snow becomes increasingly more perpendicular and the vector of the applied force becomes more aligned with the plane of the surface of the snow the component of shear force will increase and the ski will slip regardless of a perpendicular orientation of the platform with the applied force R.
Platform Forces: A different perspective
The force diagram below shows how the angle of the point of application of force applied to the inside edge of the platform that would cause it to cut a step into the surface of the snow becomes progressively less aggressive as the vector of the opposing forces becomes more aligned with the plane of the surface of the snow.The graphic below shows another way looking at angular forces acting on a surface. This graphic only shows the components of the applied and reaction forces. The advantage of showing the components is the magnitude of the normal and shear or slipping forces can be shown in relation to each other. I’ve taken some liberties in showing the normal GRF force as having greater potential magnitude than any force applied by the platform of the ski.
As the angle of the platform with the surface of the snow increases (becomes closer to perpendicular) the magnitude of the normal force will decrease. As it does the magnitude of the shear (slipping) force will increase in lock step. As the magnitude of the shear (slipping) force increases, the potential magnitude of the GRF shear component will decrease and the platform will tend to slip and not cut a step into the surface of the snow.
Since we know that elite skiers and racers can carve a step or ledge into the surface of very hard pistes at high platform angles it is reasonable to assume that some unidentified force or forces are at work that are altering the angle of attack of the applied force R so that it is more aggressive in terms of carving a step into the surface of the snow as shown in the graphic below. What would the components of the applied and reaction forces look like?As always, comments, suggestions and objective criticisms are welcome. In Part 4 we will look for the elusive forces that make skis carve at high platform angles.
I believe the single most important factor affecting a skiers’ balance and directional control of a ski is the ability of the balance system to effect dynamic balance of the angle of the platform of an edged ski with the surface of the snow . So I am going to focus my efforts on explaining the mechanism of dynamic balance.
Skiing is an interaction of the skier with the snow. Since the interface of the interaction is the inside edge of the ski and the snow I’ll start here with an explanation of the principles of the associated mechanics.
Snow = Ground
Snow is an extension of ground. Hence we speak in terms of ground reaction force or GRF. In moving over the snow a skier is interacting through a layer of snow with the ground. In the name of consistency firm pistes will be the reference for the discussion of forces.
The interface with the ground is the base plane of a ski in particular the juncture of the transverse base and sidewall planes. In this interaction the angle of the base plane with the surface plane of the snow is the plane of balance for the skier in terms of the management of angular forces.
Edging Forces are not Normal
In order for the platform of a ski to hold and not slip under the weight of a skier the edge and the adjacent portion of the base must cut a step or ledge into the surface of the snow. But the portion of the ski that must cut a step into the surface of the snow is not a knife edge. It is more like a knife blade on the flat with the blade aligned perpendicular to the angle of attack of the force applied by the skier.
Typical force diagrams in technical discussions of skiing only show opposing angular forces with a platform perpendicular to the vector of the forces. The opposing angular forces R and GRF are said to cause the platform of the ski to cut a step or ledge into the surface of the snow as shown in the graphic below. One problem is that sketches such as the one below don’t show the perpendicular (Normal) or horizontal (Shear or Slip) components of the opposing angular forces R and GRF.
When an applied force is Normal to a surface (perpendicular) the penetration or cutting action is maximal. But when a force applied to a surface is less than perpendicular it will have components of Normal and Shear or Slip forces such as shown in the graphic below. At an angle of attack of 45° the Normal and Shear components of the applied and GRF forces will be equal. But as the angle of attack decreases and becomes more aligned with the plane of the surface the Shear or slip components will increase in magnitude and the Normal components of the applied and GRF forces will decrease in magnitude.
As this happens the tendency of an applied force acting on a body like the platform of a ski that would cause it to penetrate into the surface of the snow and cut a step will decrease as the angle of the platform with the snow increases. As the platform angle increases so will the tendency of the ski to slip and not hold an edge. The components of opposing applied and GRF forces acting on a solid body or surface are determined mathematically by sine/cosine. They are not negotiable. Nor can their impact on ski platform mechanics be ignored.
In my next post I will discuss the real force that makes the platform of a ski cut a step or groove into the surface of the snow that the edge of the ski tracks in.