# THE MECHANICS OF PLATFORM ANGLE: PART 3

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.

1. Agnew Drake says:

My guess would be that the answer is multifactorial. I have raised 2 issues for your input:

1] the angle of point of application of force applied to the inside edge of the platform [ 180 degrees – 90 degrees – platform angle] seems to vary between 45-60? degrees [the sweet spot where we all experience solid contact with the snow]. More OR less angle promotes increasing slippage as the angles recede from this sweet spot.

2] the COM of the professional racer is forward onto the MTP 1 joint of the foot insuring that the initial contact point of the ski with the snow occurs solidly and anteriorly keeping the fore-body of the ski carving a step into the snow. The photos of ski racers on your blog have the tips of their skis solidly in the snow seeming to lead the charge, but in reality demonstrate the application of the angle of point of application of force along the entire length of the front half of the ski. If this is too much relative to the back of the ski, then tail slippage will occur. With a weight back skier, there will be an elevating force vector trying to bring the ski back to the surface of the snow. This raises interesting questions about the stiffness of the ski, the length of the ski, the width of the ski underfoot, the side-cut of the ski.

Bob Drake

1. Hi Bob,

My response to issue 1). If your comment is implying that there are two separate forces acting on the base plane of the platform, one with a vector 90 degrees to the base plane and a second force with a vector 180 degrees to the base plane, you are correct.

The force with a vector 90 degrees to the base plane is a factor of the G force loading on the COM of skier. But the force with a vector 180 degrees to the base plane is within the control of the skier. The magnitude of the force is limited by the nature of the constraint applied to the foot. The ability of a skier to control the magnitude of the force with a vector 180 degrees to the base plane determines the sweet spot angle or what I refer to as the ‘platform balance angle’ which must be 90 degrees to the vector of the force 90 degrees to the base plane of the platform or slightly less than 90 degrees (i.e. angled inward).

Issue 2). The position of the hips (pelvis) is the best indicator of the position of the COM of a skier/racer. Ankle-knee extension moves the pelvis anteriorly ensuring high loading of the first MTP. So you are correct. You are also correct in stating that the tips (shovel or forebody) of the ski leads the charge. A carved turn starts at the tip with the edges engaging and cutting a step into the snow that the edges that follow track in. The ability of an elite skier/racer to make a very clean carve with a narrow signature provides evidence of the tip leading the charge.

“……force with a vector 180 degrees to the base plane…” You are correct that “….application of the angle of point of application of force along the entire length of the front half of the ski.” The highest force or load is under the first MTP which is on the running center of the ski and over or close to the narrowes part of the ski. The edge at tip having much less loading engages and hooks across the line of the skier.

There are a lot more things to discuss. But for now, if a skier/racer has dynamic stability of the platform under the outside foot the balance system will take care of fore-aft loading.

In my next post I will discuss the source of the force with the vector 180 degrees to the base plane of the platform.

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