# 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

1. TheSkiingMarine says:

Would an interlocking segmented boot sole tensioned by a steel cable be doomed to failure because of inability to fight torsional forces being acted upon the sole of the boot. I have been working on a novel ski walk mechanism that relies on the above posited mechanism, but according to your post it would become compromised while turning and lead to injury. Is the sole completly of limits for modification in an Alpine Tourimg boot? Can the ski walk truly only be the free movement of the cuff down to the ankle?

1. This an area where there needs to be significant research. The Italian engineers officially opened the door to this issue by conducting and publishing research. But as far as I am aware, the ski industry has yet to be respond to the findings of the Italian paper.

When I designed the Birdcage research vehicle in 1991 with the biomedical engineer MACPOD had retained to work on our project, I had suspected since 1980 that the sole of conventional ski deformed significantly under load and had taken steps to address this issue. What I didn’t know was how much and in what manner the sole structure deformed and under what loads.

In 1991, metals were in the order of 10 times stiffer (modulus) than the stiffest plastics available. Since Aesthetic and manufacturing considerations were not issues in designing and fabricating a research vehicle, it was relatively easy to design and incorporate stiffness into the base plate and arms of the Birdcage using engineering principles that was far in excess of the anticipated loads. Designing and manufacturing a consumer product proved to be another matter entirely.

Although I was aware going into the project that new methods were needed, I quickly learned that the existing experts in a field tend to stay with what exists and what in their minds is proven. So the post Birdcage consumer product design exercises defaulted to the existing injection molding processes and this turned out to be the downfall of the attempt to develop a new format ski boot.

Nothing is impossible. But the first step in a solving a problem is to thoroughly understand the nature of the problem. Towards this end, I believe the Italian engineers have taken the first step. But many more steps and studies are needed before your question can be answered.

2. Mike Richardson says:

Dear David
Does altering the flex index of boots with adjustable options to stiffen the attachment of the top of the boot to the bottom of the boot make any difference to the deformation of the lower part of the boot ?

1. Hi Mike, I apologize for the delay in responding.

I believe the concept of boot flex resulting from shell deformation driven by dorsiflexion of the shank is fundamentally flawed. This aspect was discussed in several articles in the book The Shoe in Sport which was first published in German in 1987. So stiffening the attachment of the shaft (upper) of the boot to the shell bottom is a different issue from altering flex index.

As a rule of thumb, I always ski in the stiffest boot shell (durometer) I can get. When I built Lange race boots from raw parts, I had access to shell bottoms and shafts (cuffs) that had much stiffer plastic than the consumer versions. Even with very stiff plastics, I added extra rivets and/or T-nuts to further stiffen the boot shell as a whole. But I also added a carbon fibre structural boot board that was both epoxied to the shell base and mechanically fastened.

I think what you are alluding will help stiffen the shell base. But a lot depends on the durometer of the plastics (flex index) you are working with. In the past, I have warned ski pros and racers that the shell flex index they had chosen was too soft. Eventually moving to a much stiffer shell made my point.

3. Peða Gudac says:

I note that very little of the damping engineered into the ski is effective to suppress rapid transients in this flex mode.

4. JWolter7 says:

Good writing.
I get that one, and agree 100%

5. Cam watson says:

David:
This is very accurate. On warm weather days in winter on hard unforgiving snow it is easy to feel the deformation of the ski boot sole through the middle of a well executed fast GS turn with no skid. In addition, putting a boot on a ski indoors. Anchor the ski to the floor and move laterally you can feel the boot sole deform. This is why we World Cup athletes bury their boots in snow before the start of a race. It stiffens the sole materials and boot. Boot boards have a tremendous effect on performance not to mention the potential for injury.