Biomechanics

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.

WHAT DOES HIRSCHER HAVE IN COMMON WITH BRIGNONE, WORLEY AND SHIFFRIN?

The short answer to this question is that the 4 racers share a stance with the muscles of the biokinetic chain in isometric contraction during what I term the Load Phase of a turn sequence and the ability to use the elastic recoil energy created during the Load Phase for acceleration.

One of the key visual cues of an isometric stance is an extended outside leg with small angles at the knee and ankle and a forward position of the pelvis. Another key visual cue is high hands with arms reaching forward as if the racer is trying to reach forward and hug a large barrel.

The screen shot below is of Marcel Hirscher in the December 16, 2018 Alta Bada GS that he won by 2.53 seconds.

The screen shot below is of Tessa Worley in the 2018-19 Soelden GS.

Reductionist Anatomy

A longer answer to the question posed by the title of this post, one that I will expand on in future posts, is that Hirscher, Brignone, Worely and Shiffrin are examples of the application of the principles of an emerging paradigm that is challenging the fundamental way in which muscular anatomy has long perceived muscles as separate systems with specific functions. In the new paradigm that has arisen out of recent discoveries muscles function in conjunction with the myofascial network as a wholly integrated system; one that responds and adapts to the stresses imposed on it. Since these discoveries are almost ten years old the odds are that the dominant technique of Hirscher, Brignone, Worely and Shiffrin is not by chance.

In previous posts, I described a stance based on isometric contraction as the SR Stance. SR is an abbreviation for the Stretch Reflex. Technically, a better term for the stretch reflex is the stretch-shorten cycle

The reason I chose SR for the name of the stance is that isometric contraction and the stretch reflex are not part of the narrative of ski technique. I discuss the three forms of muscle contraction in my post I-C-E: SR (2.) which I have recently updated.

The reason a ski stance based on isometric contraction provides a huge competitive advantage has to do with recent finding discussed in a 2009 article (1.) in which ultrasound imaging that allowed for quantitative assessment of the mechanisms for elastic energy storage and return at the ankle joint during human walking found that the Achilles tendon stores elastic energy as the mid stance phase progresses until the energy peaks in late midstance and is released to produce a rapid recoil with very high peak power output. The researchers named this the Catapult Mechanism (3.).

An important feature of the ankle ‘catapult mechanism’ is that the stretch and recoil of the Achilles tendon allows muscle fibers to remain nearly isometric producing high forces with very little mechanical work. In the isometric state, muscles expend much less metabolic energy to produce force when compared to muscles shortening in concentric (positive work) contractions.

Recent research has also found that during explosive movements, the contractile elements of a muscle remain in an isometric state to increase tension in the non-contractile components in an effort to produce higher levels of force. The enhanced stiffness from the contractile component can help the connective tissue rapidly store mechanical energy during the lengthening (recoil) phase delivering greater power output during the shortening phase. (4.), (5.)

What all this means is that the power advantage seen in racers like Hirscher, Brignone, Worely and Shiffrin results from an integrated system. But the human body can only function as an integrated system under conditions which allow multi-plane movement, something conventional ski boots intentionally interfere with.

In my next post I will start from what I see as the fundamental element of a ski stance based on isometric contraction and progress upward from there.


  1. It Pays to Have a Spring in Your Step – 2009 Gregory S. Sawicki1, Cara L. Lewis2, and Daniel P. Ferris2 – 1. Department of Ecology and Evolutionary Biology, Brown University, Providence, RI; and 2. School of Kinesiology, University of Michigan, Ann Arbor, MI
  2. https://wp.me/p3vZhu-1wT
  3. Fascial Fitness: Fascia oriented training for bodywork and movement therapies – Divo G. Muller, Robert Schleip 
  4. Cutting Edge: Training the Fascial Network (Part 1) by Pete McCall M.S.
  5. Cutting Edge: Training the Fascial Network (Part 2) by Pete McCall M.S.

 

ANALYZING SKIER/RACER PERFORMANCE

In my last post (1.), I showed photos of Tessa Worely, Federica Brignone and Mikaela Shiffrin with their outside legs extended with small angles at their knees and ankles and asked Why is their outside leg extended? What advantage does it give these racers? How does it affect their ability to load and control their outside ski? So far there has only been one comment that didn’t address the questions I posed.

……… the study of biomechanics by physical educators must include cause as well as effect relationships which exist between sequential joint motions of the performer and the motion of the inanimate objects which he or she wears, rides or manipulates.

All factors must be studied in terms of the skill objective. If problems are noted in the performance of the skill, where did they originate? Within the performer? Within the sport object? Both? What precise changes must be made to obtain the skill objectives? The answer to the last question leads directly to what is known as quality teaching. The directions for improvement given to the performer must be based on scientific and technical analysis of the total skill.

The above excerpts are from a book published in 1983 called ANALYSIS OF SPORT MOTION by John W. Northrip. 

….. quality teaching – coaching of neuromuscular skills in physical education should always be preceded by an analytical process where the professional physical educator synthesizes observations and theory from scientific and technical perspectives……It must be remembered that the teaching of physical education is an art with a basis in science.

 Adjustments during the teaching process to improve performance must be made in sequential motion pattern of the involved joints. Therefore, the student of physical education must have functional knowledge of anatomic kinesiology.

Fast forward to 1987.

Few forms of athletics place as high demands on the footwear used in their performance as alpine skiing. It (the ski boot) functions as a connecting link between the binding and the body and performs a series of difficult complex tasks. 

Dr. med. H.W. Bar, Orthopedics-Sportsmedicine, member of GOTS, Murnau, West Germany (2.)

In my next post I will attempt to provide an explanation of the effect of extending the outside knee and ankle in the load phase of a turn and the role of equipment in enabling (or preventing) this action using the knowledge I have gleaned over the past 40 years.


  1. WHAT DO BRIGNONE, WORLEY AND SHIFFRIN HAVE IN COMMON?
  2. Der Schu im Sport