snow reaction force

THE MECHANICS OF EDGE CHANGE

Comments made by followers of my blog suggest that significant confusion exists 0n the meaning of terms and representations of mechanics, biomechanics and physics used in typical explanations of ski technique and ski mechanics. In particular, there appears to be confusion between pressure and the representation of point forces.

Pressure is a physical force applied to an object that is distributed over the surface of the object.

Center of Pressure or COP is the point center of ground reaction force opposing a corresponding center of applied force acting on a object supported on the ground or a stable surface that acts in the capacity of ground in terms of providing a source of reaction force.

Torque or Moment of Force results from an offset between the centers of opposing physical forces acting on either side of an object.  This offset results in a torque or moment arm that tends ti create rotation about a center. When one force has a greater magnitude than the other force, rotation of the object will occur around the point of rotation.

Why typical balance explanations of skier balance are wrong

Balance in skiing is often depicted as a simple alignment of opposing point forces, usually a resultant force R acting in opposition to a snow reaction force S. The mechanics that make the edges of a ski grip are often shown as a simple alignment of opposing forces acting a single point on the edge. Explanations of this nature are physically impossible. What the authorities in skiing seem to conveniently be ignoring is the fact that pressure is applied by the snow along the entire running surface of the edge in contact with the the snow while an opposing area of pressure applied by the weight of the skier is acting on the body of the ski with an offset between the two centers of pressure. The authorities in skiing also seem to conveniently ignore what is arguably the key even in establishing a platform under the outside ski for the skier to stand and balance on, edge change.

Mikaela Shiffrin’s Get Over It drill on the Burke Mountain YouTube site makes a good segue to an explanation of the Mechanics of Edge change in the my next post – https://youtu.be/Bh7KF49GzOc

Bridget Currier is the model every skier should aspire to. She perfectly executes what I call the skimove. The skimove engages the external forces at ski-flat/edge-change to drive multi-plane torques acting about her outside ski into the turn while setting up a solid platform under her outside foot for her to stand on. Magnificent! This video should have at least a million views.

My comment from 2 years ago

Note carefully Currier’s stance in balance on her new outside ski, in particular, the angle of her torso with the snow. This is key to loading the ball of her outside foot.

Note carefully Shiffrin’s comment to move forward onto her new ski and how she used to think the movement was a lateral (sideways) move.

Most important of all – Patient Initiation. The reason? Shiffrin and Currier, don’t tip their outside ski on edge. They rock it on edge with a rocker impulse loading mechanism. The sequence is Rock, Roll n’ Rotate then Rotate the outside leg.

EDGE MECHANICS/SKI CONTROL

The cornerstone of an effective ski technique is the ability of a skier to apply a force to the outside ski that is perpendicular to the transverse aspect of the base and aligned in opposition to the Snow Reaction Force acting at the inside edge. This configuration of forces is essential to make the edge grip and act as a pivot for rotation of the sidecut of a ski in terms of penetration into the snow surface. The ability of a skier to apply a vertical force to the inside edge must co-exist with the ability to apply and control forces acting across the inside edge. This is fundamental to balance and control of the skis.

The post SKI LEVERS describes how the sidecut of a ski creates what amounts to a dual pivot, offset lever system with the edges underfoot acting as pivots for each of the two lever systems as shown in the graphic below.

Screen Shot 2014-11-18 at 11.10.41 AM

But the sidecut of a ski results in much more than a simple offset lever. As the sidecut increases ski width beyond the minimum width underfoot, the amount of lever offset progressively increases as sidecut approaches the tips and tails of a ski. As sidecut increases the width of a ski, the magnitude of torque acting on ski increases until the maximum offset and torque load is reached at the maximum width.

The graphic below shows how the load from the weight W of COM is transferred from the proximal femur to the distal  tibia by the central load-bearing axis. The default position of the centres of the loads WL and WR is on the proximate anatomical center axis of the foot (the proximate transverse centre of the calcaneus).

Central Axis 3

Unless it can be conclusively demonstrated that the load W transferred to the outside foot of a turn has been transferred to the proximate centre of the head of the first metatarsal and is applying a force aligned with, and in opposition to, the Snow Reaction Force at the inside edge of the outside ski, the load W should be assumed to have been transferred to the anatomical center axis of the foot and from there to the transverse centre of the base of the outside ski.

The graphic below is a schematic representation of a cross section of the ski as a  dual pivot, offset lever system. The inside edge underfoot P is acting in the capacity of a pivot for rotation of the side cut on the left hand side of the schematic into the snow surface. The ability to apply a force aligned in opposition to the Snow Reaction Force acting on the inside edge is literally the pivotable issue. In the schematic below, the load W is acting on the default load transfer axis and is offset from the Snow Reaction Force P acting at the inside edge which is serving as the pivot for rotation of the ski. The force Fs is the reaction force of the snow that opposes rotation of the sidecut of the ski.

Ski Lever A

The graphic below depicts the consequences of the absence of a force acting in to opposition to W. An unbalanced moment of inversion force will result from the offset of W and P that will rotate the ski until it is in either in compliance with the snow surface or inversion reaches the physiologic limits of the subtalar joint. As the ski rotates in inversion, shear forces will be set up that cause the ski to lose its edge and slip out of the turn.

Ski Lever B

The first consideration should always be to ensure that that on groomed and especially hard pistes, the foot can apply a force (Fe) in opposition to the Snow Reaction Force acting at P. This is essential to edge grip and the role of the inside ski as a pivot.

Ski Lever Fe onlyEnsuring that a skier is able to apply a force to the inside edge of the outside ski that is perpendicular to the transverse aspect of the base and aligned in opposition to the Snow Reaction Force acting at the inside edge in concert with the ability to apply and control forces acting across the inside edge should be the highest priority. An inability of a skier to effectively apply force to the inside edge of the outside ski and especially an inability to control forces acting across the edge, will create an unbalanced inversion moment of force about long axis of the ski and foot that can create a state of inversion stress in the affected lower limb. In skis with a Width Profile under foot of 100 mm or greater, a serious condition called Fat Ski Syndrome can result if Fats are used on groomed and especially hard pistes.

 

 

 

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:

REVELATIONS FROM THE FIS GS SKI RULING

The controversy that surfaced in 2011 over the FIS decision to increase turn radius on GS skis revealed a lot about what the various authorities in skiing knew and, especially, what they didn’t know, about the mechanics, biomechanics and physics of skiing. Some critics of the ruling took the position that the reduced sidecuts would actually increase the risk of injury. An article in Ski Racing called, Black Diamond: The Deaf Ears Of The FIS, reviewed the various positions on the matter. And while some critics of the FIS ruling had very strong opinions, no one seemed able to put forth a position based on sound principles of science. In what had to be the height of irony, Guenter Hujara, director of the men’s World Cup was reported to have said, The facts are the facts. If you want safety this is a step you have to take.

Since 1977, I have been stressing the importance of the feet in skiing as the transmission path for forces transferred from the skier’s centre of mass to the snow. Knowledge of the forces acting between the soles of the feet and the snow surface is the arbiter of knowledge as a whole in skiing.  At last, a World Cup official was finally talking about taking a step. But my elation was short-lived. Hujara was talking about new regulations for GS skis, not my long hoped for new regulations for ski boots.

Two statements pertaining to injury mechanisms and ski safety were telling; Scientists at the University of Salzburg determined through a subjective study of 63 experts that the main risk factor was the “system ski, binding, plate, boot,” and By their own (FIS) admission, boots are too complex, and plates are, too. I say, ‘wait a moment’. The common denominator in the ski system/skier interface with the potential to cause injury, especially knee injury, is moments of force (torques). To be more specific, an unbalanced inversion moment of force present across the inside edge of the outside ski and the associated joints of the ankle-complex. By association, an unbalanced external (out of the turn) vertical axial moment of force acting on the tibia that tends to rotate it out of the turn against a well-stabilized femur or, worse, a femur that is being rotated into the turn by the powerful hip rotators. Between the tibia and femur lies the knee; a fragile joint with only ligaments holding the two bones in proximity to each other.

Mechanisms of Anterior Cruciate Ligament Injury in World Cup Alpine Skiing  (The American Journal of Sports Medicine, Vol. XX, No. X DOI: 10.1177/0363546511405147), states, under Background,

There is limited insight into the mechanisms of anterior cruciate ligament injuries in alpine skiing, particularly among professional ski racers.

My US Patent No.  5,459,949 published on or about November 29, 1994, goes into great detail about the importance of positioning the foot within in the ski boot and especially positioning the ball of the foot in relation to the inside edge of the outside ski of a turn so as to facilitate the setting up of moments of force (torques) into the turn with which to oppose externally generated torques out of the turn and the avoidance of mechanical relationships that result in unbalanced torques, It can be debated whether the presence of an unbalanced external vertical axial moment of force causes or contributes to an injury. But there is no debate that an unbalanced external vertical axial moment of force is a predisposing factor to injury.

 

Here are some excerpts from the subject patent that discuss moments of force acting about the inside edge of the ski with my notes and emphasis (bold) added. Due to the relatively short moment arm, aligning applied and ground (snow) reaction forces in opposition to each other or even creating an alignment where the applied force is on the inside turn aspect of the inside edge of the outside ski is not, in itself, sufficient to engage the external forces that drive a ski into a turn. It is merely a prerequisite. The factors that multiply moments of force once an over-centre mechanism is initiated are much complex than a simple misalignment of opposing applied and snow reaction forces.

SOLE ADJUSTMENT

While the adjustment of medial forefoot counter 2201 enables the foot 2001 of the user to be correctly aligned on rigid base 2100 yet another problem has arisen. The alignment of the head of the first metatarsal of the foot 2001 of the user has been altered in relation to the appliance affixed to the sole of the footwear, in this instance, a snow ski, in comparison with the alignment of the appliance in relation to the head of the first metatarsal as shown in FIG. 63.

Alignment of the center of the head of the first metatarsal is an important factor influencing physiological mechanisms which balance pronation/supination moments acting transversely across inside edge of appliances such as snow skis. The contact point of such an appliance with the surface on which it is acting can act as a fulcrum and, in so acting, establish a moment arm pivot in situations where the ground reaction force and the force applied by the user are not acting linearly in opposition to each other. In monopedal stance (pronated) the weight of the body acts substantially through the center of the head of the first metatarsal.

It is important, in activities such as snow skiing, that means be provided to allow the center of the head of the first metatarsal to be positioned so that the force applied by the user can be aligned in opposition to the ground reaction force when the snow ski is placed on its inside edge. If opposing ground reaction and applied forces can not be aligned, a moment arm will be created with the effect that the force applied by the user will tend to rotate the foot in the direction of either supination or pronation.

The location of the inside edge of (the outside ski) a snow ski tends to favour a supination moment arm since the ski edge generally lies medial of the center of the head of the second metatarsal. If the force applied by the user is sufficient in the presence of a moment arm to rotate the foot in the direction of either supination or pronation, the long axis of the tibia will also be caused to rotate through an intrinsic mechanism within the tarsus of the foot.

The means to adjust the transverse position of the foot in relation to the inside edge of a snow ski while maintaining the means to independently adjust the position of the foot on the longitudinal axis of the sole of the footwear is important and advantageous to the user and is thus an object of the present invention. FIG. 70 shows substantially the same view as FIG. 69 except that the ground reaction force FR and the force applied by the user F are shown substantially as they would be when the user is in monopedal stance (pronated) with the foot correctly positioned in relation to the inside edge of a snow ski affixed to sole 2101.

FIG. 71 shows substantially the same view as FIG. 70 except that the snow ski shown affixed to sole 2101 is wider on its medial aspect in comparison to the snow ski affixed to sole 2101 as shown in FIG. 70. The position of the inside edge of the snow ski in relation to force F applied by the user is such that the ground reaction force FR and the force F applied by the user are not acting linearly in opposition to each other. The transverse offset between the ground reaction force FR and the force F applied by the user creates a moment arm MA which acts lateral of the ski edge with the result that force F applied by the user acting on the moment arm MA will tend to rotate the foot in the direction of supination when the ski is placed on its inside edge.

Fig 70-72

FIG. 72 shows substantially the same view as FIG. 71 except that sole 2101 has been shifted laterally in relation to rigid base 2100 so that the ground reaction force FR and the force F applied by the user are now acting linearly in opposition to each other with the result that the moment arm MA as shown in FIG. 71 facilitates a countering muscularly generated torque from internal rotation of the leg at the pelvis.


The link to US Patent No.  5,459,949 is:

http://patft.uspto.gov/netacgi/nph-Parser Sect1=PTO1&Sect2=HITOFF&d=PALL&p=1&u=%2Fnetahtml%2FPTO%2Fsrchnum.htm&r=1&f=G&l=50&s1=5,459,949.PN.&OS=PN/5,459,949&RS=PN/5,459,949

LIGETY’S MOMENT OF TRUTH – STEP 4

In order to be able to develop a dynamically stable base of support on the outside ski of a turn, one that supports the processes that use external forces to drive the ski into the turn, the ski must have a waist that is close to the centre-to-centre dimension ‘X’ between the balls of the great and 2nd toes. In addition, the anatomical centreline of skier’s foot must be aligned with the running centre of the ski. The graphic below shows what it looks like when the foot is correctly positioned on a ski with the appropriate width underfoot. In reality, there is a stack of equipment between the sole of the skier’s foot and the snow surface. F.I.S. rules allow up to 100 mm of stack height between the sole of a racer’s foot and the snow surface. So the graphic below does not reflect reality. The reason I am starting with the skier’s foot directly on the ski top plate is to demonstrate that an applied vertical force acting against an opposing snow reaction force (SRF) is insufficient to explain the edging mechanics that skiers like Ligety and Shiffrin are able to develop. There are other factors at play that I will introduce in future posts.

L foot on ski

US Patent No 5,265,350 – MacPhail: November 30, 1993 – “The prior art refers to the importance of a “neutral sub-talar joint”. The sub-talar joint is a joint with rotational capability which underlies and supports the ankle joint. The sub-talar joint is substantially “neutral” in bipedal function. That is to say that the foot is neither rolled inward or rolled outward. If the foot can be substantially maintained in a neutral position with the arch supported and with a broad area of the inner aspect of the foot well padded, there will exist a good degree of comfort. Such a state of comfort exists because the foot is not able to roll inward (pronate) to a degree where significant mechanical forces can be set up which would allow it to bear against the inner surface of the boot shell. In effect, this means that initiation of the transition from a state of bipedal to a state of monopedal function, is prevented. This transition would normally be precipitated by an attempt to balance on one foot. If the foot is contained in a neutral position, traditional supportive footbeds (arch supports) are quite compatible with the mechanisms and philosophies of the prior art.”

Here is what the inside and outside feet of a skier in a turn look like when  the feet are in neutral.

Neut edge

Since there are offsets or moment arm between CoP and SRF on each foot, the sole of the inside foot of the turn will tend to roll away from the centreline between the feet (ergo, it will tend to evert) while the sole of the outside foot of the turn will tend to roll towards the centreline between the feet (ergo, it will tend to invert).  Under specific conditions the external forces acting on the skier will tend to make the outside foot of the turn rotate into the turn (ergo, it will tend to evert). But, for reasons that will be provided in a future post it is not possible to create conditions under which the external forces acting on the skier will tend to make the inside foot of the turn rotate into the turn. For this reason the force applied to the snow by the skier must be directed to the inside edge of the outside ski of the turn. The inside foot and leg are used to help direct the force to the outside ski. This what Ligety and Shiffrin do so well.