biomechanics

THE MECHANICS + BIOMECHANICS OF PLATFORM ANGLE – PART 11

In my preceding post I said 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. The reason I conducted a thorough investigation and analysis of the forces is that as a problem solver this is my standard protocol. Protocol aside, the need for a thorough investigation of every aspect affecting athletic (skier) performance was known as far back as 1983.

….. 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……

There are many sports skills which require that sports objects, implements, equipments, and apparatus be utilized. (implements such as ski boots and skis)

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 directions for improvement given to the performer must be based on scientific and technical analysis of the total skill.

Analysis of Sport Motion (May 1, 1983): John W. Northrip

Planes of Forces

The ability to conduct a thorough investigation and analysis of the forces associated with platform angle mechanics and biomechanics requires as a minimum, a basic understanding of the engineering aspects of the associated forces. In the case of platform mechanics and biomechanics, knowing the plane or planes in which a force or combination of forces are acting is essential.

The Force Plane in the Perfect Fit

The objective of achieving a perfect fit of the foot and leg of a skier is create a perfect envelopment of the foot and leg of a skier with the rigid shell wall of a ski boot so that force is applied evenly to the entire surface of the foot and leg to create a unified mass with the ski so that the slightest movement of the leg will produce edging and steering forces. In this format force(s) applied to the base plane by the leg will be distributed to a broad area with limited ability to apply coordinated forces to a specific area of the ski. Sensory input is also limited by the uniform force applied to all apects of the foot by the perfect fit format creating what amounts to the skiing equivalent of the Bird Box.

Platform Planes

In the mechanics and biomechanics of platform angle there are potentially three horizontal planes in which forces can be applied as shown in the graphic below. The left hand image shows the rotational force applied to a torque arm plane elevated about the base and plantar planes. In the perfect fit format in the right hand image the leg is shown as a rigid strut extending to the base plane where rotational force is applied.When the foot and leg of a skier are perfectly fit within to the rigid shell of a ski boot any force applied by the leg can only applied to the base plane of the ski where the force is distributed over a broad area. Steering and edging forces applied to the ski by the leg lack precision because they cannot be applied to specific areas or applied in a coordinated manner.

In the above graphic the whole leg rotational effort applied to the base plane by foot in the two examples is shown with no resistance. In my next post I will discuss what happens when resistance is added that opposes the rotational force applied to the base plane.

THE MECHANICS + BIOMECHANICS OF PLATFORM ANGLE – PART 10

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.

THE MECHANICS + BIOMECHANICS OF PLATFORM ANGLE: PART 10 – SUPPLEMENTAL INFORMATION


Because of the complex issues I am about to start discussing in the next series of posts I am providing supplemental reference information to assist the reader in understanding the issues associated with platform angle mechanics and biomechanics and underlying process of dynamic stability.

Background of events leading up to the outside ski platform ground balance solution

In late 1989, after gaining valuable insights from the medical textbook, The Shoe In Sport, I had formulated a hypothetical model that explained the macro details of the mechanics and biomechanics of platform angle and the mechanism of user CNS postural balance control.

Insights from The Shoe in Sport:

Correct positioning of the foot is more important than forced constraint and “squeezing” the foot.

Forward sliding of the foot should not be possible. 

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). 

The comment about the importance of correct positioning of the foot and the ski boot  representing an interface between the human body and the ski gave me insights that led to the discovery of key mechanical of the foot whose position in relation to the inside edge and X-Y axes of the ski affects the transfer and control of steering and platform forces to the ski and control.

When I wrote the application for US Patent No 5,265,350 in late 1991 and early 1992 I described the mechanics and biomechanics of plantar angle in great detail knowing this information would be freely available to the entire world to use once the patent was published. The only exception was the information covered by claims. Known mechanics and biomechanics are not in themselves patentable.

Patents and Research

It is important to note that patents, even when granted, do not apply to the use of a patented device for the purpose of pure research. Knowing this at the time I wrote the patent, I described the Birdcage research vehicle in sufficient detail with many figures to enable the device to be constructed at minimal cost so research could be conducted by others as soon as possible for the purpose of advancing the knowledge base and science of alpine skiing.

The following unedited text is excerpted from the patent.

……. the teaching of this (patent) application is that force must be applied and maintained only to specific areas of the foot and leg of the user while allowing for unrestricted movement of other areas.

The performance of such mediums (skate blades and skis) is largely dependent on the ability of the user to accurately and consistently apply forces to them as required to produce the desired effect.

In addition, in situations where the user must interact with external forces, for example gravity, the footwear must restrain movements of the user’s foot and leg in a manner which maintains the biomechanical references with the medium with which it is interacting.

Precise coupling of the foot to the footwear is possible because the foot, in weight bearing states, but especially in monopedal function, becomes structurally competent to exert forces in the horizontal plane relative relative to the sole of the footwear at the points of a triangle formed by the posterior aspect and oblique posterior angles of the heel, the head of the first metatarsal and the head of the fifth metatarsal. In terms of transferring horizontal torsional and vertical forces relative to the sole of the footwear, these points of the triangle become the principal points of contact with the bearing surfaces of the footwear. 

The most important source of rotational power with which to apply torque to the footwear is the adductor/rotator muscle groups of the hip joint. In order to optimally link this capability to the footwear, there must be a mechanically stable and competent connection originating at the plantar processes of the foot and extending to the hip joint. Further, the balanced position of the skier’s centre of mass, relative to the ski edge, must be maintained during the application of both turning and edging forces applied to the ski. Monopedal function accommodates both these processes. 

Yet a further problem relates to the efficient transfer of torque from the lower leg and foot to the footwear. When the leg is rotated inwardly relative to the foot by muscular effort a torsional load is applied to the foot. Present footwear does not adequately provide support or surfaces on and against which the wearer can transfer biomechanically generated forces such as torque to the footwear. Alternatively, the footwear presents sources of resistance which interfere with the movements necessary to initiate such transfer. It is desirable to provide for appropriate movement and such sources of resistance in order to increase the efficiency of this torque transfer and, in so doing, enhance the turning response of the ski.

In skiing, the mechanics of monopedal function provide a down force acting predominantly through the ball of the foot (which is normally almost centred directly over the ski edge). In concert with transverse torque (pronation) arising from weight bearing on the medial aspect of the foot which torque is stabilized by the obligatory internal rotation of the tibia, the combination of these forces results in control of the edge angle of the ski purely as a result of achieving a position of monopedal stance on the outside foot of the turn. 

The edge angle can be either increased or decreased in monopedal function by increasing or decreasing the pressure made to bear on the medial aspect of the foot through the main contact points at the heel and ball of the foot via the mechanism of pronation. As medial pressure increases, horizontal torque (relative to the ski) increases through an obligatory increase in the intensity of internal rotation of the tibia. Thus, increasing medial pressure on the plantar aspect of the foot tends to render the edge-set more stable.

There are many figures that illustrate the concepts expressed in the above text which I will include in future posts.

The photo below shows the strain gauges (black disks) fit to the 1991 research vehicle. These gauges recorded first metatarsal forces under and to its inner or medial aspect and the outer and rearmost aspects of the heel bone.

I’ve learned a lot since the above information was made public after the patent was issued on November 30, 1993.

In Part 10, I will discuss the mechanism by which forces applied by the ball of the foot to what I call the Control Center of the platform provide quasi ground under the outside foot and leg in the load phase of a turn for a skier to stand and balance on.

THE MECHANICS + BIOMECHANICS OF PLATFORM ANGLE: PART 9

In my previous post I the described a mechanism by which whole leg rotational or steering force can be applied to a vertical extension of the platform by inner (medial) aspect of the head of the first metatarsal. The associated user biomechanics have a number of requirements the structures of a ski boot must meet in order to apply this force. These include, but are not limited to the following:

  • in the load phase in what is called ‘the bottom of the turn’ the foot must be able to rapidly pronate with minimal interference from the structures of the ski boot.
  • force applied to the vertical extension of the platform must be localized on (medial) aspect of the head of the first metatarsal and not from other structures of the foot, including the inner (i.e. medial) aspect of the big toe and the medial boney structures of the ankle and midfoot.
  • the big toe must be able to be aligned straight ahead on the anatomical center of the long axis of the foot without significant interference from the structures of the ski boot including structures of the liner.

In addition to the above, there must also be minimal interference with the ability of the Achilles tendon to transfer high loads to the head of the first metatarsal (i.e. ball of the foot) to the platform underneath as the 90 degree component of edge cutting force. The magnitude of force, especially peak impulse force, that a skier can apply to the head of the first metatarsal has a direct effect on the degree of force that can be applied to the medial aspect the head of the first metatarsal.

Data from the 1998 University of Ottawa study of pressures under the feet of elite skiers (1.) found that maximal forces ranged from a low of 522 N to a high of 1454 N; a difference of 279%. The data also found significant differences in the maximal forces recorded between the left and right feet of all elite skier test subjects for all turn types except dynamic parallel.

Table 1 below from the shows the forces generated from the pressure data acquired in University of Ottawa study.

The large differences seen between a range of elite skiers and especially between left and right feet of the same skier has significant implications for the ability to apply force to a vertical structure with the head of the first metatarsal, a force not considered in the University of Ottawa pressure study or any study I am aware of.

To the best of my knowledge my 1992 skier force study that used a research vehicle called The Birdcage is the only study even today that examined force applied by the medial aspect of the head of the first metatarsal to a vertical structure of the platform of a ski boot/ski. The Birdcage studies also examined the interaction and effect of vertical plantar forces applied to the platform in conjunction with horizontal force applied to a vertical extension of the platform.

Center of Force

Sometimes call Center of Pressure in gait/balance studies, Center of Force (COF) or Center of Pressure (COP) do not represent a point application of a force vector. COF and COP are point centers of force applied to an area of a surface or body. (2.)(3.)(4.)

In platform mechanics, the sole of the foot applies force to a large area of the platform. The closest point to the inside edge of the outside ski where the Center of Force can act is under the head of the first metatarsal. Force applied to the platform of the ski will always apply a force to the running surface of the inside edge. Even if CoF is aligned over one aspect of the GRF acting on the inside edge of the outside ski it is impossible for COF of the outside foot to be aligned over the entire sidecut arc of the inside edge in contact with the snow. Since the foot cannot access GRF (i.e. ground) under the entire length of the inside edge of the outside ski, ground needs to be brought out under the platform.

In order to successfully solve a problem all aspects of a problem must be identified and their implications understood. The solution to the platform/ground problem is finding a way to extend the ground under the entire running surface of the inside edge of the ski out under the platform. In my next post I will begin to explain how this is tied to the ability to apply robust force with the head of the first metatarsal to a vertical extension of the inner aspect of the platform.


  1. ANALYSIS OF THE DISTRIBUTION OF PRESSURE UNDER THE FEET OF ELITE ALPINE SKI INSTRUCTORS – Dany Lafontaine, Mario Lamontagne, Daniel Dupuis & Binta Diallo,
    Laboratory for Research on the Biomechanics of Hockey, University of Ottawa, Canada: Proceedings of the XVI International Symposium on Biomechanics in Sports (1998), Konstanz, Germany, p.485.
  2. WHAT THE TWO HIGH PRESSURE COPS IN THE UNIVERSITY OF OTTAWA STUDIES MEAN – https://wp.me/p3vZhu-1fV
  3. IMPLICATIONS OF THE UNIVERSITY OF OTTAWA PRESSURE STUDIES – https://wp.me/p3vZhu-1e2
  4. AN INDEPENDENT STUDY IN SUPPORT OF THE UNIVERSITY OF OTTAWA FINDINGS – https://wp.me/p3vZhu-1gR

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.

Platform Paradoxes

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.