Centre of Mass


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






An essential mechanism to the ability to create a platform under the outside ski to stand and balance on using the same processes used to stand and balance on stable ground, is the Heel to Forefoot Rocker. A slide presentation called Clinical Biomechanics of Gait (1.) by Stephen Robinovitch, Ph.D. (Simon Fraser University – Kin 201) is a good reference for the various aspects of gait.

Slide 19 of the Gait presentation describes the ankle Inversion-Eversion-Inversion sequence of the ankle. The sequence begins with heel strike (HS), followed by forefoot loading (FF), followed by heel off (HO) followed by toe off (TO).

The normal foot is slightly inverted in the swing phase (unloaded) and at heel strike. It is everted through most of the stance phase. The ankle begins to invert in late stance. The kinetic flow of pressure is from the heel to the ball of the foot and big toe. This is what should happen in the transition phase of a turn sequence when a skier begins to transfer more weight to the inside foot and ski from the outside foot and ski. Up until the start of the transition, the skier’s center of mass is behind the inside foot with the majority of pressure under the heel on the transverse center of the foot and ski where is exerts an inversion torque that is tending to rotate the ski into contact with the surface of the snow. The skier maintains the edge angle by applying a countering eversion torque with a combination of external rotation-abduction of the inside leg.

When the skier begins to transfer more weight from the outside ski to the inside ski, the leg releases the countering eversion torque and the ski begins to invert in relation to the surface of the snow.

The presentation on the Clinical Biomechanics of Gait did not include important aspects of the stance phase that occurs in late stance. Nor, did it mention Achilles forefoot load transfer.

The Three Rockers

Slide 23 shows the Three Rockers associated with the gait cycle.

First Rocker – occurs at heel strike. It causes the ankle to plantarflex and rock the forefoot downward about the heel into contact with the ground. The rocker movement is controlled by eccentric dorsiflexor torque.

Second Rocker – shifts the center of pressure from the heel to the forefoot. Eccentric plantarflexor torque controls dorsiflexion of the ankle.

Third Rocker – occurs at heel separation from the ground that occurs in terminal phase of stance.

Slide 13 shows how the knee shifts gears and transitions from flexion in early stance to extension in late stance. In late stance, the Achilles goes into isometric traction. At this point, further dorsiflexion of the ankle passively tensions the plantar ligaments to intiate forefoot load transfer. Load transfer is accentuated when the knee shifts gears and goes into extension moving COM closer to the ball of the foot increasing the length of the lever arm.

Two Phase Second Rocker

Classic descriptions of stance and the associated rockers do not include a lateral-medial forefoot rocker component that occurs across the balls of the feet from the little toe side to the big toe side in conjunction with the heel to forefoot rocker creating what amounts to a Two Phase Second Rocker.

In his comment to my post, OUTSIDE SKI BALANCE BASICS: STEP-BY-STEP (2.), Robert Colborne said:

….… regardless of where the centre of mass is located relative to the centre of pressure in the above-described mechanism, when you go into a stable monopedal stance, as you would when you are in a turn, the ankle is dorsiflexed forward and as this occurs the tibia rotates internally several degrees.

COMMENT: The tibia rotates internally (i.e. into the turn) as a consequence of ankle dorsiflexion. It does not require conscious action by the skier.

This means that the main muscle forces acting across the ankle (the plantarflexors) are no longer acting along the long axis of the foot, but rather partly across it, medially toward the big toe.

So, the beneficial effect of that muscle force is to force the base of the big toe into the ground, and that becomes the centre of the turn (centre of pressure).

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 photo below shows a skier in bipedal stance with weight distributed equally between the two feet standing on a plush carpet with foam underlay. Black hash marks show the positions in space of key aspects of the right foot and leg.

The photo below shows the same skier in monopedal stance with all the weight on the right foot. Forefoot loading from the Two Phase Second Rocker has pushed the toes down into the carpet by compressing the underlay.

The video below shows the dynamic action of the Two Phase Second Rocker.

The Two Phase Second Rocker results in a heel to ball of foot diagonal rocker action acting towards the centerline of the body; i.e. diagonally across the long axis of the ski with the load acting inside the shovel.

A primary objective of the Birdcage studies was to validate my hypothetical model of the Two Stage Diagonal (heel – forefoot) Second Rocker in creating a balance platform under the outside ski for a skier to stand and balance on.

The graphic below shows the alignment of the Two Stage Diagonal (heel – forefoot) Second Rocker.

In my next post, I will discuss the Two Stage Diagonal (heel – forefoot) Second Rocker Turntable Effect.

  1. http://www.sfu.ca/~stever/kin201/lecture_outlines/lecture_17_clinical_biomechanics_of_gait.pdf
  2. http://wp.me/p3vZhu-29n


The intent of my last post was to create an awareness of the lower limb alignment indicative of stability and how a lack of stability, whether intrinsic or caused by footwear, especially ski boots, will cause a skier to default to the use of knee angulation in what will be a failed attempt to hold the edge of the outside ski.

A skier will be unable to develop the requisite biomechanics to balance on their outside ski if they lack stability in barefoot monopedal stance under the minimal challenges associated with a flat, level unperturbed surface. If they lack lower limb/pelvic stability, there could endless combinations of causes which is why I listed a number of resources to help address this deficiency.

If a skier/racer exhibits good to excellent  stability under this basic test and they become unstable with the addition of any form of footwear, it suggests, but does not unequivocally prove, that the footwear is the cause. In more 4 decades of working with skiers and racers at all levels, I have consistently found that I can turn monopedal stability off and on at will. That I can do this without limitation, is indicative of cause and effect. In the 2 world class racers I am presently working with, even a small change in a liner or the over-tensioning of a shaft buckle or power strap has an immediate and noticeable effect on outside limb/pelvic stability and balance.

A key exercise I like to use with racers and elite skies I am working with is the vertical stacking exercise shown in the graphic below. This exercise is performed by starting from bipedal stance with the feet stacked under the heads of the femurs and the head and torso vertical and then making fluid arcing movement of the COM over the ball of the big toe while keeping the torso and head stacked vertically and the pelvis and shoulders horizontal as indicated by orange vertical and horizontal references in the graphic below. The torso should be aligned with the transverse or frontal plane, square with the foot.

A lack of stability in the biokinetic chain is typically evidenced by a drop of the opposite side of the pelvis and a leaning in the opposite direction of the torso and/or the head or both. While this reduces the load on the pelvis side of the  leg it creates a myriad of issues. Inside hip drop will cause the inside leg of a turn to assume the load as the skier inclines thus creating further instability on the outside leg.

Elite skiers and racers like Shiffrin are able to get over it (find stability on their outside foot and ski) in milliseconds. This enables them to retract the inside foot and ski with knee flexion as they incline into a turn similar to the mechanics cyclists use when they corner; outside leg extends, inside leg retracts.

The vertical stacking exercise is best performed in front of a mirror.


In this post, I will discuss where the source of ground or GRF lies in relation to the forces applied by the outside or stance foot of a skier.

Explanatory diagrams of the forces of skiing typically show a resultant force (R) of the components of gravity (G) and centrifugal force (C) acting on the centre of mass (COM) of a skier. The vector of the resultant force (R) emanating from COM is shown acting at a point in the vicinity of the inside edge of the outside ski. If a force diagram is sophisticated, it might show a ground reaction force (GRF) acting at the inside edge of the outside ski or even the centripetal component of centrifugal force.


The overly simplistic nature of such force diagrams infers that control of the edge angle of the outside ski requires nothing more than an alignment of R with inside edge. In this context, the effect of the width of the ski under foot on the skier as shown in the image below is of no consequence.


The influence of the mechanics of both of the above ski configurations on the skier are inferred to be the same even though they are dramatically different as shown in the overlay below.


The reality of such force diagrams is that they represent a static moment in time; a snapshot that tells nothing of the dynamic nature of the forces at play. In order to accurately represent the dynamic forces, force diagrams must include the load from the weight W of COM and especially how and where the load is transferred to the outside foot of a turn, to the ski and from there to the point that I call Ground Zero. Ground Zero is where the forces of the snow and skier meet. The forces at the skier/ski equipment/snow interface should be the subject of intense discussion and debate. More than simply being important, understanding and managing these forces is fundamental to skier balance and the global control of COM essential to a biomechanically sound technique.

Force diagrams like the one shown below should be the minimal starting point for meaningful dialogues on the forces of skiing.

With Central Axis







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.



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


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.



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.


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.


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.



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.


When this happens COP becomes a bad COP.

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


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.




Before I select a new ski boot I want to know the ramp angle of the ski/binding system of the skis I am skiing on.  The net ramp angle is the angle of the boot board in the base of the ski boot plus any ramp angle created by a difference in the height of the heel and toe plates of the binding. The reason net ramp angle is important is that elevating the heel of the foot in relation to the toes (positive ramp or drop) can have either a positive or negative effect on the function of the feet and legs, in particular, the outside foot and leg of a turn. A small amount of ramp angle can significantly stiffen the ankle torsionally and stiffen the foot in general in a way that enables maximal pronation by allowing the forward lean of the column that supports the centre of mass to increase slightly. But past a certain threshold too much net ramp angle can have the opposite effect. Through subjective experimentation in 1977-78, I arrived at approximately 3 degrees as what seemed to be the optimal net ramp angle.

To calculate net ramp angle I use a micrometer or caliper to measure the height of the toe and heel piece platforms of the bindings of my skis and the toe and heel ends of the boot board. First, I measure the height from the base of the ski to the top of the heel and toe plates of the ski bindings. The photo below shows how I measure the height of the heel and toe piece of the Look Nx Fluid binding. In this situation, the ski base to heel piece platform dimension is 5 mm higher than the ski base to toe piece platform dimension. I prefer to use degrees of ramp angle as opposed to what is called ‘drop’ in mm. Degrees are uniform across different foot size whereas drop is not. The ramp angle for the Look binding in the photo below calculated out at positive 1.5 degrees when set up for a 250-255 ski boot. However ramp angle will vary depending on the space between the heel and toe pieces because the vertical dimensions are fixed. Therefor, the ramp angle will increase as boots get smaller boot and decrease as a boot gets larger. So it is important to calculate the ramp angle with the binding set up for the correct boot.



The photo below compares the Look Nx Fluid binding above to a Look Racing Px4 binding. There is no difference between the ski base to binding platform heights of the heel and toe pieces of the Look Racing Px4. So the ramp angle is net zero degrees whereas the ramp angle of the Look Nx Fluid binding is positive 1.5 degrees when set up for a 250-255 ski boot.

Binding Ramp

Most people probably assume that there is some grand strategy behind binding design and ramp angle. But as far as I have been able to tell there, is no rhyme or reason for variations in heel and toe piece platform heights let alone any consistency. I prefer bindings with zero net ramp angle for several reasons. It eliminates a variable that compounds boot board ramp angle. And it eliminates the problem of binding ramp angle changing with changes in the spacing between the heel and toe pieces.

How critical is net ramp angle? I believe the tolerance is very narrow. A ramp angle of 3 degrees may have a very positive effect whereas a net ramp of 4 degrees may have a negative effect. Too great a net ramp angle can have the effect of plantarflexing (ergo – extending) the ankle. Extending the ankle effectively lengthens the chain of muscles in the back of the leg that exerts what I call the plantar-pelvic pull. The sheet-like ligament that underlies the arch of the foot and runs from the toes to the heel is an extension of the Achilles tendon. The chain of muscles in the back of the leg (soleus-gastrocnemius-hamstring) is the chain of muscles in walking and running that act as the centre of mass moves forward to stiffen the foot in preparation for propulsion. Effectively lengthening the chain of muscles in the back of the leg decreases their contractive force and can significantly reduce the stiffening of the ankle and foot required for good balance and control of the outside ski and especially the amount of pressure that can be exerted on the ball of the foot as it pronates.

As far as I have been able to ascertain, the concept of net ramp angle doesn’t appear to be a consideration in ski equipment setup. Yet, I believe that net ramp angle in combination with correct cuff cant and forward lean can literally make or break a skier and especially a racer.  In watching video of World Cup racers, especially females, the typical stance and movement patterns suggest that the majority have excessive net ramp angle. If you want to ski like Ligety and Shiffrin, you need to be able to extend the way they do. You will not able to do this so as to engage the external forces to drive the outside ski into a turn without the correct net ramp angle and cuff cant and forward lean.

In my next post I will describe what I look for in selecting a ski boot.