THE MECHANICS + BIOMECHANICS OF PLATFORM ANGLE: PART 7

On January 12 of this year I started a new direction for The Skier’s Manifesto with a critical examination of the mechanics of platform angle after concluding that this issue and its effect on dynamic stability is the single most important factor in skiing. The platform is the portion of the stack of equipment between the sole of a skiers foot and the base of a ski. I started my discussion with a review of some of the typical technical terms associated with platform angle mechanics.

In my last post, I examined rotational force applied to a ski. I noted that in the technical terminology of skiing this is referred to as steering. I identified a number of inconsistencies, ommissions and errors pertaining to steering that I will expand on in this post.

Technical discussions on steering typically show a ski rotating like a propeller about the center of its long axis. In my last post I demonstrated that the source of the rotational force or steering is the femur rotating in its joint with the pelvis and applying rotational force to the foot its lower (distal) end at the tibia.

The graphic below shows the axes of rotational force (steering) applied to a ski through the foot/ski boot interface by the leg. I’ve used a large ski boot and a short ski to illustrate the effect of the location of the axis of rotation.

Technical discussions of steering don’t always mention the source of steering force let alone show its location. In addition, no explanation is offered that would explain how a ski can rotate about its center like a propeller.

The graphic below shows a ski with the running center of the long axis with approximate location of the axis of rotation indicated. In this example the axis of rotation is approximately 11.5 cm behind the running center (C). On my own skis, the axis of rotation is approximately 13.5 cm behind the running center for my 335 mm ski boot.

When the ball of the foot is located on or close to the transverse center of the long axis of the running surface of a ski the axis of rotation will move progressively towards the shovel as a foot gets shorter and move progressively towards the tail as a foot gets longer. No one seems to mention this even though it raises a number of signficant issues, among them the effect on the edge hold and carving characteristics associated with platform dynamics.

Where is the Force Applied?

Technical discussions of platform mechanics typically don’t show or even mention the location of the force applied to a ski by the weight of a skier. Since the weight of the body is transferred to the foot from the lower end of the tibia the weight tends to be transferred to the foot close to the heel.

Some discussions of platform and steering mechanics even suggest that a skier should feel their weight under their heel when steering the skis. This would place the applied force on the transverse center of a ski, behind the center of the long axis and offset from the inside edge where it will create a torque or moment arm that will degrade platform mechanics.An analogy of the mechanics of rotational force applied to a ski by rotation of the leg is a vertical shaft (leg) rotated by a force with an arm (ski) projecting outward from the shaft.

As the arm gets longer the distance the end of the arm travels for every degree of rotation of the shaft will increase.

1. How will increasing the length of the arm effect the application of force applied to an object by the end of the arm distant from the shaft given a rotational force (torque) of a fixed magnitude applied to the shaft?
2. How would reducing the effective length of the arm acting on a ski affect platform mechanics, in particular edge hold and carving characteristics?

There is a way to reduce the effective length of the arm acting on the ski. Elite skiers can do it. This will be the subject of my next post.

THE MECHANICS OF PLATFORM ANGLE: PART 5

In my initial posts on the mechanics of platform angle I demonstrated the physical impossibility of making a ski carve an edge into hard pistes at high platform angles with the snow by a skier aligning opposing applied and reaction forces with the vector perpendicular to the transverse plane of the platform of the outside ski. The reason for this is that the component of shear or slipping force will progressively increase as the angle of the applied force Fa becomes increasingly aligned with the plane of the surface of the snow as shown in the examples in the graphic below.

In my previous post I said that a reader who commented on Part 3 correctly stated for a ski to hold and carve at high platform angles required two separate forces acting on the transverse plane of the platform; one force oriented at 90 degrees to the plane and a second force oriented parallel or 180 degrees to the transverse plane with the vector acting into the surface of the snow. I ended my post by asking the reader what the source of the 180 degree force was.

The graphic below shows the answer. Elite skiers can make the outside ski of a turn hold and carve at very high platform angles because they are able to apply two separate forces in a coordinated manner. The reason I say ‘able to apply’ is that many factors can severely limit or even prevent the coordinated application of these two forces; the most significant factor being interference from the structures of the ski boot with the associated coordinated joint actions of the foot and leg.The graphic above is for the purpose of illustrating the source of the 180 degree force acting on the transverse plane of the platform. As such, the graphic  is not accurate because it shows the plantar (sole) plane of the foot oriented on the transverse plane of the platform. The actual mechanics and biomechanics are much more involved. I’ll start to explore the various factors in my next post.

THE MECHANICS OF PLATFORM ANGLE: PART 4

In Part 3 of the mechanics of platform angle I suggested that some unidentified force or forces are at work that enable elite skiers to alter the angle of attack of the applied force R so that it is more aggressive in terms of cutting (carving) a step into the surface of the snow. I asked the reader what the components of the applied and reaction forces would look like.

One reader correctly identified two separate forces acting on the transverse plane of the platform of the outside ski; one oriented vertically at 90 degrees to the plane and a second force oriented parallel or 180 degrees to the transverse plane with the vector aligned into the snow.

The right hand graphic below shows the 90 and 180 degree components of the angular force acting on the platform in the left hand graphic.

The right hand graphic below is the same as the graphic above but with the angular force superimposed over the 90 and 180 degree components.

I am taking the discussion of platform mechanics in small steps in order to provide the reader with a chance to assimilate the issues and ask questions if my discussion is not clear.

THE SHOCKING TRUTH ABOUT POWER STRAPS AS A REFERENCE

Most of the views of the series on the Mechanics of Platform Angle are accompanied by views of The Shocking Truth About Power Straps which contains quotes from the medical textbook The Shoe in Sport (published in German in 1977 as Der Schu im Sport). This medical textbook has been invaluable to my efforts.

Here are some pertinent quotes by Dr. E. Stussi,  Member of GOTS – Chief of Biomechanical Laboratory ETH, Zurich, Switzerland

From a technical (skiing) point of view, the ski boot must represent an interface between the human body and the ski. This implies first of all an exchange of steering function, i.e., the skier must be able to steer as well as possible, but must also have a direct (neural) feedback from the ski and from the ground (snow). In this way, the skier can adapt to the requirements of the skiing surface and snow conditions.

These conditions can be met if the height, stiffness, angle and functions (rotational axes, ankle joint (AJ)/shaft) of the shaft are adapted, as well as possible to the individual skier.

The modern ski boot must be designed from a functional point of view, i.e., the design must take into consideration the realities of functional anatomy (axes etc.).

It (the design) should not make compromises at the expense of other joints (length of shaft, flexibility and positioning).It (the ski boot) must represent the ideal connecting link between man and ski (steering and feedback).

Biomechanical Considerations of the Ski Boot (Alpine)

The question for this post is what is the source of the 180 degree force? Please consider Dr. E. Stussi’s comments above when contemplating an answer to this question.

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.

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.

THE MECHANICS OF PLATFORM ANGLE: PART 1

In order to engage in an interactive productive dialog on issues pertaining to ski technique and related equipment a frame of reference based on validated, non-negotiable principles of physics, mechanics and (neuro)biomechanics as well as a schedule of defined reference terms such as exists in the sciences of mechanics, anatomy and physics is essential. Defined technical reference terms help ensure all participants in a discussion are on the same page.

I decided to start the new direction of The Skier’s Manifesto with a critical examination of the mechanics of platform angle starting with a schedule of the technical terms associated with platform angle and their definitions. Additional technical terms and their definitions will added in future posts according to the content of the discussion. The intent at this point is to start with a basic discussion of forces applied to a rigid body and/or surface (in this case, the surface of the snow) and then expand the scope of the discussion in future posts. Agreement on terms and definitions is important. So please comment if you feel one or more the following terms are inappropriate or inaccurate or should be expanded and/or refined.

Technical Terms associated with Platform Angle

• Platform Angle: the angle of the transverse aspect of the body of the ski underfoot with the surface of the snow.
• Edge Angle: the angle of the edge of the ski in relation to the plane of the transverse aspect of the body of the ski adjacent the edge.
• Force: an unopposed interaction that will change the motion of an object. A force has both magnitude and direction, making it a vector quantity.
• Force Vector: the magnitude and direction of a force.
• Applied Force: a force applied to a rigid body or surface.
• Reaction Force: a force that opposes a force applied to a rigid body or surface.
• Normal Force: a force acting perpendicular to a rigid body or surface that is resisting a force applied to it.
• Angular Force: a force applied to a rigid body or surface that is not normal (perpendicular) to the rigid body or surface to which the force is applied.
• Angle of Attack: the angle an angular force forms with the rigid body or surface to which it is applied to.
• Resultant Force: also known as Net Force, is a single force associated with torque obtained by combining a system of forces and torques acting on a rigid body.

Technical discussions of the forces associated with the angle of the platform with the snow typically show opposing resultant and ground reaction forces implying a state of balance of the forces acting on platform created by the outside ski underfoot.

Schematic diagrams showing forces acting on the platform created by the body of the ski underfoot often show two opposing forces in alignment with each other acting close to or at the axis point created by the inside edge of the outside ski. Or diagrams may simply show opposing forces aligned with each other implying the existence of a state of equilibrium.

In my next post I will discuss whether the above force diagrams accurately reflect a state of equilibrium of the forces acting on the platform of the outside ski. Please join the conversation.

THE EFFECT OF PENDULUM ACTION ON THE INSIDE SKI

Part 1 left off with the inside ski flat on the surface of the snow after it had completed its rotation about its current (uphill) edge when pressure was applied to the ski by stepping on it. The current or uphill edge was the point where snow reaction force S was acting. The pressure W, applied under the heel of the inside leg and foot, on the proximate center of the ski, was offset from S resulting in a moment arm that tended to rotate the ski downhill. This rotation was opposed by a force exerted against the inner aspect of outside of the boot shaft  by the inside leg being abducted (moved outward) by the thigh as shown in the insert in the graphic of Ana Fenninger below.

When the ski rotates into contact with the snow surface, rotational momentum wants to maintain the rotation.

If the piste is firm or icy, there will be little or no penetration into the surface as the ski moves beyond full contact with the snow surface as it changes edges.

One way or another, there will be a translation of the plane of the base  of the ski into a different plane as it changes edges and begins to rotate about the inside edge of what will become the outside ski of the new turn. Translation is part of the event that I call Roll Over.

If the pressure stays in the center of the ski as it changes edges and translation starts, there will be a problem. Even though COM will eventually pass the axis of rotation of the new edge, translation will be resisted by the Pressure applied to the center of the ski. This is the literal Moment of Truth. If the Pressure stays on the center of the ski, force exerted on the inside of the inner side of the boot shaft will cause translation to occur against the Pressure that continues to rotate the ski out of the turn. What has to happen for Pressure and Translation to be in phase, so Roll Over can occur, will be the subject of Part 3.