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.
- 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/