THE MECHANICS OF PLATFORM ANGLE: PART 2


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.

2 comments

  1. Hey David. …have followed you for years from Sugarloaf here in Maine. Great info/library! The direction you are heading I would recommend John Howes book‘Skiing Mechanics Revised’ includes dynamics of shaped skis. Like you an engineer. John has done a lot of your work for you and is absolutely defendible. Pricey on line but a real tomb of knowledge if you can handle the math. I have a copy…. would be glad to send it to you. Like where you are Going! And thx for all your work. More then a few ‘Gems’!

    1. Thank you for your comments and encouragement. At one point I had a library of just about every book ever written including Howe’s book. The reason I started thus blog is that for reasons I con’t understand I couldn’t find any book, article or reference that discussed the mechanism by which elite skiers set up a dynamic platform under the outside ski that they can stand and balance on. As far as I can recall Howe never addressed this issue. I can probably get a copy of his book from our local library.

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