Centre of Pressure

THE SKI BOOT FLEX INDEX INSTABILITY PROBLEM

It has been known for decades that an unbalanced moment of force or torque will be present on the outside ski when the center of pressure of the load applied to the ski by a skier is acting along the center of the transverse axis of the ski where it is offset from GRF acting along the inside edge. Ron LeMaster acknowledges the existence of an unbalanced moment of force on the ouside ski in both The Skier’s Edge and Ultimate Skiing (Edging the skis). LeMaster states in Ultimate Skiing;

The force on the snow is offset from the center of the skier’s and creates a torque on it that tries to flatten the ski.

Ron didn’t get the mechanics right. But he correctly shows the unbalanced torque acting on the ankle joint. LeMaster tries to rationalize that ice skates are easy to cut clean arcs into ice with because the blade is located under the center of the ankle. While this is correct, ice skaters and especially hockey players employ the Two Stage Heel-Forefoot Rocker to impulse load the skate for acceleration. Hockey players refer to this as kick.

In his comment to my post, OUTSIDE SKI BALANCE BASICS: STEP-BY-STEP, Robert Colborne said:

…..In the absence of this internal rotation movement, the center of pressure remains somewhere in the middle of the forefoot, which is some distance from the medial edge of the ski, where it is needed.

The load or weight of COM is transferred to distal tibia that forms the ankle joint. This is the lower aspect of the central load-bearing axis that transfers the load W from COM to the foot. What happens after that depends on the biomechanics. But the force will tend to be applied on the proximate center of the stance foot. This is a significant problem in skiing, (one that LeMaster doesn’t offer a solution for) when the ski is on edge and there is air under the body of the ski. The unbalanced torques will move up the vertical column where they will manifest at the knee against a well stabilized femur.

But this unbalanced torque creates another problem, one that is described in a paper published in 2005 by two Italian engineers (1.) that describes how this load deforms the base of the boot shell.

The Italian study found large amounts of deformation at mean loads of up to 164% body weight were measured on the outer ski during turning. The paper suggests that the ski boot flex index is really a distortion index for the boot shell. The lower the flex index, the greater the distortion potential.

For the ski-boot – sole joint the main problem is not material failure, but large amounts of local deformation that can affect the efficiency of the locking system and the stiffness of the overall system.

Values of drift angle of some degree (>2-3°) cannot be accepted, even for a small period of time, because it results in a direct decrease of the incidence of the ski with the ground.

My post GS AND KNEE INJURIES – CONNECTING THE DOTS (2.) cites studies that found that knee injuries are highest in GS in the shortest radius turns where peak transient forces are highest.

As shown in Figure 2a FR (sum of centrifugal and weight forces) and F GROUND (ground reaction force) are not acting on the same axis thus generating a moment MGR that causes a deformation of the ski-boot-sole system (Figure 2b) leading to a rotation of the ground reaction force direction. The final effect is to reduce the centripetal reaction force of the ground, causing the skier to drift to the outside of the turn (R decreases, causing the drift event).

An imperfect condition of the ski slope will emphasize this problem, leading to difficulties maintaining constant turning radius and optimal trajectory. The use of SGS ski-boot in competitions requires a particular focus on this aspect due to the larger loads that can be produced during races.

I have added a sketch showing that the moment arm M R created by the offset between the F Ground and F R is in the plane of the base of the ski where it results in an Inversion-lateral rotation torque.

The importance of sole stiffness is demonstrated with a simplified skier model…..…ski boot torsional stiffness with respect to ski longitudinal axis in particular is very important as it deeply influences the performance of the skier during turning…. A passage over a bump or a hollow may generate a sudden change in ground reaction force that may lead to a rapid change in the drift angle delta. The ski boot must be as stiff as possible going from the lower part of the boot to the ski (i.e. lower shell-joint-sole system)

As explained in the method section using the simplified model, values of some degree cannot be accepted, even for a small period of time, because the skier stability and equilibrium could be seriously compromised especially when the radius of curvature is small. A non perfect condition of the ski slope will emphasize the problem, leading to big difficulties for maintaining constant turning radius and optimal trajectory.

This excellent paper by the two Italian engineers concludes with the following statements:

Authors pushed forward the integration of experiments and modeling on ski-boots that will lead to a design environment in which the optimal compromise between stiffness and comfort can be reached.

The possibility of measuring accurately the skier kinematics on the ski slope, not addressed in the presented study, could represent a further step in the understanding of skiing dynamics and thus could provide even more insightful ideas for the ski-boot design process.

I first recognized the shell deformation, boot board instability issue in 1980, at which time I started integrating rigid structural boot boots into the bases of boot shells I prepared for racers. The improvement in ski control and balance was significant. The instability of  boot boards associated with shell/sole deformation with 2 to 3 degrees of drift at modest loads of up to 164% body weight has significant implications for footbeds.


  1. AN INNOVATIVE SKI-BOOT: DESIGN, NUMERICAL SIMULATIONS AND TESTING – Stefano Corazza 􀀍 and Claudio Cobelli Department of Information Engineering – University of Padova, Italy – Published (online): 01 September 2005 – https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3887325/
  2. http://wp.me/p3vZhu-zx

THE MECHANICS OF BALANCE ON THE OUTSIDE SKI: THE ROCKER/TURNTABLE EFFECT

The Two Phase Second Rocker (Heel to Ball of Foot) described in the previous post is dependent on inertia impulse loading. A good discussion of the basics of inertia and momentum is found in Inertia, Momentum, Impulse and Kinetic Energy (1.)

Limitations of Pressure Insoles used in Skiing

A paper published on May 4, 2017 called Pressure Influence of slope steepness, foot position and turn phase on plantar pressure distribution during giant slalom alpine ski racing by Falda-Buscaiot T, Hintzy F, Rougier P, Lacouture P, Coulmy N. while noting that:

Pressure insoles are a useful measurement system to assess kinetic parameters during posture, gait or dynamic activities in field situations, since they have a minimal influence on the subject’s skill.

acknowledge limitations in pressure insoles:

However, several limitations should be pointed out. The compressive force is underestimated from 21% to 54% compared to a force platform, and this underestimation varies depending on the phase of the turn, the skier’s skill level, the pitch of the slope and the skiing mode.

It has been stated this underestimation originates from a significant part of the force actually being transferred through the ski boot’s cuff. As a result, the CoP trajectory also tends to be underestimated along both the anterior-posterior (A-P) and medial-lateral (M-L) axes compared to force platforms.

Forces transferred through the cuff of a ski boot to the ski can limit or even prevent the inertia impulse loading associated with the Two Phase Second Rocker/Turntable Effect. In addition, forces transferred through the cuff of a ski boot to the ski intercept forces that would otherwise be transferred to a supportive footbed or orthotic.

Rocker Roll Over

In his comment to my post, OUTSIDE SKI BALANCE BASICS: STEP-BY-STEP, Robert Colborne said:

In the absence of this internal rotation movement, the center of pressure remains somewhere in the middle of the forefoot, which is some distance from the medial edge of the ski, where it is needed.

Rock n’ Roll

To show how the Two Phase Second Rocker rocks and then rolls the inside ski onto its inside edge at ski flat during edge change, I constructed a simple simulator. The simulator is hinged so as to tip inward when the Two Phase Second Rocker shifts the center of pressure (COP) from under the heel, on the proximate center of a ski, diagonally, to the ball of the foot.

The red ball in the photo below indicates the center of gravity (COG) of the subject. When COP shifts from the proximate center to the inside edge aspect, the platform will tilt and the point of COP will drop with the COG in an over-center mechanism.


A sideways (medial) translation of the structures of the foot away from the COG will also occur as shown in the graphic below. The black lines indicate the COP center configuration of the foot. The medial translation of the foot imparts rotational inertia on the platform under the foot.

Two Phase Second Rocker: The Movie

The video below shows the Two Phase Second Rocker.

Click on the X on the right side of the lower menu bar of the video to enter full screen.

The graphic below shows to Dual Plane Turntable Effect that initiates whole leg rotation from the pelvis applying multi-plane torque to the ski platform cantilevering reaction force acting along the running edge of the outside ski out under the body of the ski. A combination of over-center mechanics and internal (medial or into the turn) application of rotation of the leg from the pelvis, counters torques resulting from external forces.


  1. http://learn.parallax.com/tutorials/robot/elev-8/understanding-physics-multirotor-flight/inertia-momentum-impulse-and-kinetic
  2. http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0176975

 

 

 

 

CARVE, MEET BIRDCAGE – BIRDCAGE, MEET CARV

July 1991: Birdcage Research Vehicle – Cost approximately $140,000

Secret  Toshiba Prototype Portable Computer used for Birdcage studies – Value? Priceless!

Birdcage Co-Designer and Team Science Leader, Alex Sochaniwskyj, P. Eng.

After interviewing a number of candidates in the spring of 1991 for the science component of the MACPOD project to develop a ski boot based on anatomical principles, I chose Alex Sochaniwskyj, P. Eng. as the most qualified candidate and one of the most intelligent and creative persons I have ever had the privilege of meeting.

Alex provided the CV that follows in his letter in support of my nomination for the Gold Medal in the categories of Applied Science and Engineering in the 1995 British Columbia Science & Engineering Awards.

Alex Sochaniwskyj, P. Eng.

Alex is a professional engineer with 12 years of biomedical and rehabilitation engineering research experience in the Human Movement and Motor Functions Research Programmes at the Hugh MacMillan Rehabilitation Centre in Toronto, Ontario, Canada. The principle aim of these labs is to provide detailed information and objective analysis of movement, dynamics and motor function of persons with various physical disabilities. The information is used to objectively assess the effects of a variety of therapeutic and surgical interventions.

Alex holds a Bachelor of Science degree from the University of Toronto in Human Physiology and a Bachelor of Applied Science from the University of Toronto. Most recently, Alex has worked with several companies including ADCOM ELectronics Limited in Toronto, where he was responsible for the design and development of video conferencing and multi-media communication systems, and the Arnott Design Group, where he focused on physiological human factors in product system design, prototyping and testing.

Currently, as a principal at designfarm inc., he consults to design and manufacturing firms on the development of programs to evaluate human physiological, biomechanical, ergonomic and environmental response for product and interface design, and the planning of comprehensive technology implementation strategies for the integration of computing, telecommunication and telepresence technologies. Alex is also a Certified Alias Instructor in the Information Technology Design Centre in the School of Architecture and Landscape Architecture at the University of Toronto, where he teaches courses in computer literacy, three-dimensional design, modelling, simulation and animation.

Alex is a member of the Association of Professional Engineers of Ontario (APEO), the Institute of Electrical and Electronics Engineers (IEEE), the Association of Computing Machinery (ACM) and the University of Toronto, Department of Rehabilitation Medicine Ethics Review Committee. He is co-author of numerous publications in refereed medical and engineering journals and has produced several video productions regarding biomedical and rehabilitation engineering.

              – March 24, 1995

Team Birdcage


2000 – Novel Pedar In-Shoe pressure technology used by Synergy Sports Performance Consultants – Cost, approximately $60,000 with 2 Sony VAIO laptop computers

 


2017 – CARV: Cost? Approximately $300 US – See footnote re special price

 

Birdcage to CARV: “Where have you been? I’ve been waiting 26 years for you. Welcome! The future of skiing has arrived.”


FOOTNOTE
CARV is currently taking pre-orders at $249 at 
 http://carv.ai

THE MECHANICS OF BALANCE ON THE OUTSIDE SKI: WHERE IS GROUND?

It was my intent to discuss the key move in the First Step to Balance on the Outside Ski; Impulse Loading of the Forefoot. However, it has become apparent that it is necessary to preface this subject with a discussion on the source of ground in relation to the outside foot in order to impart an appreciation of why a mechanism is required to extend ground from the running edges of the ski in order to create a platform for a skier to stand and balance on when the outside ski is on its inside edge.

In typical discussions of ski technique and the mechanics, biomechanics and physics of skiing, the prevailing mental model assumes that a skier is in balance (see REVISION TO FEATURE POST: CLARIFICATION OF DEFINITION OF SKIER BALANCE) if they are able to stand upright and exercise a degree of control over their skis. In studies of balance performed in gait labs, ground reaction force in the form of stable surface for subjects to balance on is assumed.

Mental Models

Mental models are a form of cognitive blindness. Once people assume they know something, they not only don’t question what they believe, they filter out information that conflicts with their mental model. And they typically fail to see the real issue even when it is in plain sight.

A man should look for what is, and not for what he thinks should be.

                                                                                                                 –  Albert Einstein

The Skier Balance Paradox

Even though I quickly became a competent skier soon after I started skiing,  I struggled to hold an edge on firm pistes and especially glare ice. It was disconcerting to see elite skiers hold an edge on ice with minimal effort while making controlled turns. When I sought the advice of the experts, they claimed that holding an edge on ice was matter of sharp edges and/or driving the knees into the hill. When I protested that after trying both and found it harder to hold an edge, the experts claimed that the ability of some skiers to do what I couldn’t was due to superior technique. They were just better skiers. No further explanation was needed.

The inability of experts to explain why a small number of skiers seemed able to balance on their outside ski and hold an edge even on ice provided me with the impetus to look critically at this issue with the objective of formulating an explanation based on principles of applied science.

The only plausible explanation for the ability of a skier to be able to stand and balance on their outside ski when it is on its inside edge is that some source ground (reaction force) must be present under ski that they are using to stand and balance on. Hence, the question, Where is the Ground?

On very hard pistes, ground as a source of reaction force, is limited to the running portion of the inside edge of the outside ski and the small portion of the base adjacent the edge with the edge and base supported on a small shelf cut into the surface of the snow/

In Figure 2.11 on page 26 of his book, Ultimate Skiing, LeMaster explains how the sidecut of a ski creates a smaller radius turn as the edge angle increases.

In Figure 2.12 on the following page, LeMaster shows misaligned applied (green arrow) and ground reaction (purple arrow) forces creating an unbalanced moment of force (yellow counter-clockwise rotation arrow) that  rotates the ski down hill (out of the turn). LeMaster goes on to state that as the skier edges the ski more, the ski bites better. But he fails to offer an explanation as to how the skier can edge a ski more against an unbalanced moment of force acting to reduce the edge angle.

The mechanism that generates a moment of force that opposes the moment force shown by LeMaster in Figure 2.12 and has the effect of extending ground (reaction force) acting along the running length of the edge of the ski  is the subject of this series of posts.

Edge Angle Sidecut FXs

A simple way to acquire an appreciation for the location of ground relative to the outside ski on edge is to make a simple model out of flexible piece of sheet plastic material a few mm thick.

The photo below shows a model I made from a piece of sheet plastic about 8 inches long. The upper portion of the plastic piece has a shorter sidecut with less depth than the sidecut in lower portion of the piece of plastic piece. Both the model and sketches that follow are for illustrative purposes to demonstrate the effects of sidecut geometry on edge angle and a source of ground. Although the basic principles are the same, it is not intended that they be viewed as an accurate representation of actual ski geometries  The symmetrical geometry is for the benefit of the simplifying what is already a complex issue.

sidecut-1

There is a relationship between the depth and length of a sidecut in that the greater the ratio of the depth to the length of a sidecut, the lower will be the edge angle it forms with the surface in relation to the camber radius. In the sketch below, the upper rectangular ski shape will maintain a vertical relationship with a surface regardless of the camber radius.

There is also a relationship between the edge angle a ski with sidecut will form with a uniform surface and the radius of the camber with the edge angle formed with a uniform surface. The edge angle will increase (become more vertical) with a decrease in the radius of the camber. This explains why GS skis that are longer and have less sidecut depth than SL skis can attain much higher edge angles.

side-cut-factor

The photo below shows how the aspect of the model I made with the smallest sidecut ratio forms a steep angle with a uniform surface when bent to sufficient camber radius to allow the sidecut to become compliant with a uniform surface.

sidecut-2

When viewed from the rear of the model, the location of ground in relation to the structure of a ski with sidecut and camber should become readily apparent.

The graphic below shows what a photo taken at a low enough vantage point to the snow would capture looking straight on at a ski carving a turn with its edge compliant with the surface of the snow. This may seem foreign, even extreme to some. But when the edge of a ski is compliant with a uniform surface, the curve of the sidecut becomes linear.

The left image below depicts the schematic model of the ski shown in the second graphic with the camber angle sufficient to make the edge in contact with the uniform surface compliant with it. The angled line represents the surface of the snow. The schematic model of the ski represents the proximate end profile associated with a high load GS turn. A photograph in Figure 1.18 on page 17 of the Skier’s Edge  shows a similar profile in Hermann Maier’s outside (left) ski which is at a very high edge angle.

The graphic on the right shows some penetration of the running surface of the edge of the ski in conjunction with the forces commonly shown in the prevailing mental model that are used to explain how forces acting on the outside are balanced.

 

side-cut-angle

The reality is of the applied forces acting on the ski are shown in the vertical profiles in the graphic below as captured by digitized force plate data. Once the foot is loaded on a surface there is what is called a Center of Pressure as shown by the peaks in all 3 graphs. But when the foot is in compliance with a uniform surface, some pressure is expressed by the entire contact surface of the foot. So, the point application of applied force in opposition to a point application of GRF as depicted in the right hand graphic above is a physical impossibility.

Screen Shot 2015-12-20 at 9.59.06 PM

Viewing a transverse vertical profile of a ski on edge from the perspective of ground as a source of GRF for a skier to stand and balance on puts the issue of skier balance in a whole new, albeit unfamiliar, perspective. But it is a reality that must be dealt with in order to engage in realistic narratives on the subject. Overly simplistic explanations of skier balance attributed to a basic alignment of opposing forces do not serve to advance the sport of skiing as a credible science.

I concur with LeMaster’s position that the platform angle a ski forms with resultant and GR forces must be at 90 degrees or slightly less in order for the edges to grip. In my next post, I’ll start to introduce mechanical principles that explain how this can be accomplished.

It is the ability of racers like Mikaela Shiffrin to stand and balance on their outside that enables them to consistently dominate World Cup competition.

INTEREST IN MY POST, ‘WHAT THE TWO HIGH COP PRESSURES IN THE OTTAWA STUDIES MEAN’


I started this blog with the objective of stimulating thinking and discussion among serious skiers, racers, ski pros and coaches about the mechanics, biomechanics and physics of skiing. Ingrained and accepted beliefs in skiing, that have little or no basis in science, have created resistance to ideas that question these beliefs .

The response to a post serves as a barometer of the type of audience my blog is connecting with. Since my post on excessive ramp angle as a stance killer stimulated interest in my post on the meaning of high COP pressures reported in University of Ottawa studies, I have decided to delay my post on my vision of a standard specification for boot boards and instead provide links to two papers below that are related to the Ottawa studies.

In the first paper (1), the authors correctly identify the moment of force created on the outside foot and ski of a turn by an offset in the alignment of the opposing force applied to the ski by the weight of a skier Fr with the ground reaction force F Ground as shown in Figure 2 below from the paper. The resulting drift angle creates medial compression of the associated knee joint.

BB MoF

In the second paper (2), the authors also correctly identify the moment of force created on the outside foot and ski of a turn by an offset in the alignment of the force applied by the weight of the skier with the ground reaction force, GRF as shown in Figure 1 below from the paper. Sketches a) and b) show the effect of greater width of the ski underfoot in increasing the length of the moment arm.

Waist 2

The authors of both of the papers recognize the problem; an offset in the alignment of opposing applied and ground reaction forces sets up a moment arm that causes the outside ski to rotate out of the turn. Each of the papers attempts to resolve the problem in a different manner.

Do either of the approaches presented in the 2  papers cited above address the problem?

…… to be continued.


1. An innovative ski-boot: Design, numerical simulations and testing

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3887325/

https://www.researchgate.net/publication/259878372_An_innovative_ski-boot_Design_numerical_simulations_and_testing

2. The Waist Width of Skis Influences the Kinematics of the Knee Joint in Alpine Skiing 

https://www.researchgate.net/profile/Matej_Supej/publication/281541462_The_Waist_Width_of_Skis_Influences_the_Kinematics_of_the_Knee_Joint_in_Alpine_Skiing/links/560cdf1e08aea68653d38633.pdf?inViewer=0&pdfJsDownload=0&origin=publication_detail

GOOD COP, BAD COP

The science of the study of human balance is well established. Studies of balance use two key metrics; COM (Centre of Mass) and COP (Centre of Pressure). The following text is excerpted from Human balance and posture control during standing and walking – D A Winter PhD, P. Eng. – Gait & Posture: 1995; Vol 3: 193-214, December. (1)

Centre of Pressure (COP) is the point location of the vertical ground reaction force vector. It presents a weighted average of all pressures over the surface of the foot that is in contact with the ground. It is totally independent of COM. If one foot is on the ground, the net COP lies within that foot. If both feet are in contact with the ground, net COP lies somewhere between the two feet depending on the relative weight taken by each foot.

The location of COP under each foot is a direct reflection of the neural control of the ankle muscles (my emphasis added).

Increasing plantarflexion activity moves COP posteriorly (ergo, toward the back of the foot). Increasing inverter activity moves COP laterally (ergo, towards the outside of the foot). COP is often mistakenly equated with COG (Centre of Gravity). COP is calculated with software from pressure data obtained from a force plate or in-shoe pressure insole. (my emphasis added)

Because it is calculated COP can reside in the arch of the foot even though it may not be in contact with the ground.  – my comment

“Centre of Mass (COM) is a point equivalent of the total body mass in the global reference system (GRS). It is the weighted average of the COM of each body segment in 3-dimensional space. It is a passive variable controlled by the balance control system. The vertical projection of COM onto the ground is often called the Centre of Gravity (COG).

“Balance is a generic term describing the dynamics of body posture to prevent falling. It is related to the inertial forces acting on the body and the inertial characteristics of body segments.  The CNS is totally aware of the problems of controlling a multisegment system and interlimb coupling that can facilitate balance control.

“In the literature there is a major misuse of the COP when it is referred to as ‘sway’, thereby inferring that it is the same as the COG. Unfortunately some researchers even refer to the COP directly as the COG.”

In the mechanism of balance control, COP is the equivalent of the Balance Police. It keeps COM from breaching the limits of there base of support by outpacing COM in the race to the limits of the base of support within the foot or feet. In quiet standing, the force of gravity disturbs equilibrium by pulling COM forward. This causes the ankle to dorsiflex. As COM moves forward, it starts to overtake COP. In order to prevent a forward fall, the CNS signals muscles that plantarflex the ankle to increase their contraction. This increases the force of COP and pushes COM rearward. As COP shifts rearward, the CNS reduces the contractive force of plantarflexion so that COP passes COM in the race to the rear of the foot.

A similar process is employed by the CNS to prevent a sideways fall. Here, the force of gravity disturbs equilibrium towards inner or medial aspect of the foot. This causes the foot to pronate. To oppose the disturbing force, the CNS signals muscles to contract that invert the foot.

It is important to recognize that it is the external forces that disturb equilibrium  that cause the foot to pronate.

The same process is at play in skiing. However, since the sideways balance strategy involves inverter muscles, it is only possible to establish a balance platform (DOT 4: PLATFORM) on the outside foot of a turn and only then under specific conditions. In the skier/ski equipment system, COP is the point where the Resultant Force acting on a skier at ski flat that pulls COM downward towards the snow is opposed by muscles that the CNS recruits to oppose the pending collapse of the skeletal system and prevent a fall.

COP is calculated from pressure data obtained from a force plate or in-shoe pressure insole such as  the Novel Pedar system or Tekscan. Since COP reflects neural control of ankle muscles when a foot (the whole foot) is in contact with the ground or a stable source of (ground) reaction force, the use of the term COP is not technically correct in a situation where a ski is on edge unless a platform exists as described in DOT 4: PLATFORM. Until the ski lies flat on the snow between edge changes and there is full foot contact ground reaction force the appropriate term to describe the force applied by the foot to snow through the stack of ski equipment is centre of force or COF.

In a turn, COP is a good COP when it is on the right side of the law: ergo, when COP lies under the head of the 1st metatarsal and R is aligned between the inside edge underfoot and the limits of sidecut. The sketches below show the progression of COF at ski flat that moves COP to the head of the 1st metatarsal. If COP arrives at the head of the 1st metatarsal before the outside ski has attained a significant edge angle and COP remains in this position through the turn COP is a good COP.

Sketch 1 below shows the 2 key mechanical points in skiing (red cross)

Centres of key pts

Sketch 2 below shows the Centre of Force (COF) under the heel of the inside foot at the start of the transition between turns. The red dashed line shows the approximate trajectory of COF as it moves forward and becomes COP at ski (foot) flat between turns as the external forces cause the foot to pronate.

 

COP 1

Sketch 3 below shows the forward progression of COP towards the head of the 1st metatarsal.

COP 2

Sketch 4 below shows the successful transition of COP to the head of the 1st metatarsal where it lies over top of the inside edge of a ski of appropriate width.

COP 3

 

Sketch 5 below shows axis on which COP and R must align in order to engage the external force R to drive edging and turning mechanics.

COP 4

Sketch 6 below shows R on the same axis as COP.  In this configuration the alignment of R described under DOT 4: PLATFORM will enable multiplane torques generated by pronation to be directed into the turn.

COP 5

In sketch 7 below COP has failed to make a transition to the head of the 1st metatarsal. When COP fails to make the transition to the head of the 1st metatarsal at ski flat between edge change before the new outside ski attains a significant edge angle, a moment arm will be setup between the inside edge and COP that will create an inversion moment of force or torque with an associated external vertical axial rotation of the whole leg.

COP 6

 

In sketch 8 below COP has reversed direction. Once an inversion moment arm has been set up on the outside ski there is no way to undo it. The odds are great that COP will revert to its default position under the heel because it is under the mechanical line of the lower limb.

COP 7

When this happens COP becomes a bad COP.


1. You can obtain a copy of David Winter’s paper at the following link:

SHIFFRIN’S SKI MOVE

It is hard to find a movement sequence  in video footage that shows what I call the Ski Move from the optimal angle. In order to clearly see how a skier’s centre of mass rotates about the inside (uphill) edge of the inside ski and changes its position in relation to the inside ski when Shiffrin or Ligety start to step on it, the camera has to be looking at the racer head on. Since this sequence is almost impossible to find, I am going to try and create it in Poser.

The marked up sequence in the photo below shows how Shiffrin’s center of mass starts to rotate about the inside edge of her inside ski and into her new turn as she progressively steps on her new ski during the transition phase. As she does this, a point will be reached where her inside ski flattens on the snow. But it does not stop rotating at this point. Shiffrin’s momentum and the pressure she is applying to the ski cause it to change edges and begin to rotate into the new turn. As this is happening, Shiffrin is extending and moving forward in the hips. This drives the centre of pressure to the ball of her foot. The foot pronates and reinforces the rotation of the ski into the new turn. The circled images show where this happens. As Shiffrin’s foot pronates and the forces she is applying rotate her left ski into the new turn, she applies another layer of in-phase rotation with her hip rotators. These synchronized actions produce an over-centre mechanism that rotates her ski in multiple planes into the new turn.

There is a common perception that racers let their outside ski create all the turning effects. But the pivoting Shiffrin and Ligety apply at this key moment does much more than simply rotate the ski into the turn. It creates powerful forces that engage the external forces to drive the outside ski into the turn while creating a platform to balance on.

 

Shiffrin