In alpine skiing an athlete's performance or injury mechanisms are strongly influenced by ski vibrations. Ski vibrations are mainly caused by irregularities of the ski-snow interaction (e.g. ripplets and disturbances of the slope, friction between ski and snow). With respect to the ski-snow interaction ski vibrations were not yet considered in computer simulation studies. During this study a planar multibody simulation model of a mono-skier has been developed to investigate transversal vibrations of unedged skis during schussing in the fall line over rough (random) ski slopes. The skis are modelled as dynamic Euler-Bernoulli beams and are incorporated as flexible beams into a multibody skier model. The interaction between skis and snow is modelled by a Kelvin-Voigt constitutive equation for the snow penetration force. The random ripplets and disturbances of the slope are described by random fields, which are generated based on real data obtained from measuring a public ski slope surface with a high resolution laser scanner. By the Monte Carlo simulation method a sequence of runs over random slope surfaces is performed and the ski vibrations of the ski shovel are analysed. The results show that the irregularities on a ski slope contribute considerably to the vibration of a ski and the performance of a skier. Thus, they have to be considered in multibody simulation models of alpine skiing. The developed simulation model will support the understanding of ski vibrations and their causes to improve the run time and to prevent injuries in alpine skiing. The presented simulation model can also be applied to find optimal material parameters to reduce ski vibrations during schussing. This work combines a flexible multibody simulation model and random fields. The implementation of random fields in multibody simulation models admits a more realistic investigation of the mechanical behaviour of complex systems due to random spatial uncertainties in input parameters.

Slalom skiers hit flex poles whereby an impulse is transferred from the skier to the flex pole. Each such impact leads to a speed reduction of the skier, which is clearly greater for relatively lighter skiers than it is for relatively heavier skiers. Additionally, there is an injury risk for the skier caused by the impact and the risk for breakage of the flex pole. For a detailed analysis of causes and consequences of this impact, three-dimensional finite element models were developed for flex poles and a pendulum impactor. The finite element models were validated by comparing data of experiments with the pendulum impactor and simulations. The comparisons included flex-pole motion, flex-pole speed, whiplash measure, pendulum impulse loss and cross-sectional deformed oval shapes. The differences of the comparisons were less than 3% for the first four parameters. The comparison of the cross-sectional deformed oval shapes' behavior agreed well. With the new validated finite element model, the influence of factors such as flex-pole diameter, wall thickness, length and material properties on the transferred impulse and the mechanical loadability of the flex pole can be systematically analyzed. With this knowledge, specifications for flex poles can be adapted to improve fairness at slalom races and reduce the injury risk and the danger of damaging the upright pole.

In skiing the skier-flex pole impact causes a deflection and rotation of the flex pole and a speed loss of the skier. The purpose of the present study was to investigate the effects of skier and pole parameters on time loss, pole deflection, and pole damage speed caused by the skier-pole impact in slalom. Validated finite element models were used for the simulation of the impact. Skier mass, speed and impact height and pole mass, bending stiffness, diameter, and wall thickness were analyzed. Time loss was assessed for seven pole impacts by a simple simulation model of a skier schussing down an inclined plane. From the skier parameters, impact height followed by impact speed showed the highest effect on the skier-pole impulse. The impulse increased with increasing pole mass whereas the effect of bending stiffness was negligible. Time loss could be reduced by lowering the pole mass. However, lowering of pole diameter or wall thickness increased pole deflection enhancing injury risk due to the whiplash effect. Additionally, the reduction of wall thickness decreased pole damage speed with the disadvantage of higher risk of pole fractures. Overall, lowering pole mass for the current impact speeds in World Cup slalom races requires additional investigation. In children and youth races with lower impact speeds than in World Cup races, a pole mass reduction would be possible.

A common anterior cruciate ligament (ACL) injury situation in alpine ski racing is landing back-weighted after a jump. Simulated back-weighted landing situations showed higher ACL-injury risk for increasing ski boot rear stiffness (SBRS) without considering muscles. It is well known that muscle forces affect ACL tensile forces during landing. The purpose of this study is to investigate the effect of different SBRS on the maximal ACL tensile forces during injury prone landings considering muscle forces by a two-dimensional musculoskeletal simulation model. Injury prone situations for ACL-injuries were generated by the musculoskeletal simulation model using measured kinematics of a non-injury situation and the method of Monte Carlo simulation. Subsequently, the SBRS was varied for injury prone landings. The maximal ACL tensile forces and contributing factors to the ACL forces were compared for the different SBRS. In the injury prone landings the maximal ACL tensile forces increased with increasing SBRS. It was found that the higher maximal ACL force was caused by higher forces acting on the tibia by the boot and by higher quadriceps muscle forces both due to the higher SBRS. Practical experience suggested that the reduction of SBRS is not accepted by ski racers due to performance reasons. Thus, preventive measures may concentrate on the reduction of the quadriceps muscle force during impact.

In the simulation of skiing the force between ski and snow is a decisive factor. We decompose the reaction force into a penetration force normal to the snow surface, a shear force and friction. Two portable measurement devices were developed to study the penetration and shear forces for compacted snow on groomed ski slopes. The penetration force was assessed by measuring the penetration depth of a ski-tool loaded normal to the snow surface. For the shear force the tangential load was measured when the snow began to fail. Overall 236 penetration and 108 shear experiments were conducted on different types of snow. The penetration force was proportional to the volume of snow displaced by the ski-tool. The failure shear force was proportional to the penetration depth multiplied by the length of the tool. The constants of proportionality, H-v and S-f, are material parameters of snow. The snow hardness, H-v, varied between 0.04 and 90 N mm(-3) and the failure shear stress, Sf, between 0.04 and 0.40 N mm(-2). In another investigation, skiing turns were simulated using the presented snow reaction forces. Maximum deviations between computed and real trajectories were <1% of the overall length of the runs.

In Alpine skiing, actions of the skier like edging, angulating, leaning forwards or backwards, and distributing the load between the skis are important factors for the performance of runs. The purpose of this work was to improve our computer simulation model by using a hypoplastic constitutive law for the ski-snow penetration force and to look for feasible driving constraints for the hip, knee, and ankle joints leading to similar runs of the simulation model and the athlete. The model consists of three parts: skier, skis, and ski-snow interaction. The skier is implemented as a seven segment multibody system. The skis are modeled as Euler-Bernoulli beams with given length and side cut. Ski width, thickness, camber, bending and torsional stiffness were obtained from measurements. Applied forces are weight, drag, and ski-snow contact forces. Based on empirical results, the snow shear force is modeled proportional to the penetration depth of the ski. Skisnow friction is implemented with a velocity-dependent friction coefficient. For validation, a video analysis of a field test was used. With input parameters corresponding to the actual situation, the simulated skier performed a run that was quite similar to that of the athlete.

The deformation of skis and the contact pressure between skis and snow are crucial factors for carved turns in alpine skiing. The purpose of the current study was to develop and to evaluate an optimization method to determine the bending and torsional stiffness that lead to a given bending and torsional deflection of the ski. Euler-Bernoulli beam theory and classical torsion theory were applied to model the deformation of the ski. Bending and torsional stiffness were approximated as linear combinations of B-splines. To compute the unknown coefficients, a parameter optimization problem was formulated and successfully solved by multiple shooting and least squares data fitting. The proposed optimization method was evaluated based on ski stiffness data and ski deformation data taken from a recently published simulation study. The ski deformation data were used as input data to the optimization method. The optimization method was capable of successfully reproducing the shape of the original bending and torsional stiffness data of the ski with a root mean square error below 1 N m2. In conclusion, the proposed computational method offers the possibility to calculate ski stiffness properties with respect to a given ski deformation.

Competitive and recreational sport on artificial ice tracks has grown in popularity. For track design one needs knowledge of the expected speed and acceleration of the luge on the ice track. The purpose of this study was to develop an approximate simulation model for luge in order to support the initial design of new ice tracks. Forces considered were weight, drag, friction, and surface reaction force. The trajectory of the luge on the ice track was estimated using a quasi-static force balance and a 1d equation of motion was solved along that trajectory. The drag area and the coefficient of friction for two runs were determined by parameter identification using split times of five sections of the Whistler Olympic ice track. The values obtained agreed with experimental data from ice friction and wind tunnel measurements. To validate the ability of the model to predict speed and accelerations normal to the track surface, a luge was equipped with an accelerometer to record the normal acceleration during the entire run. Simulated and measured normal accelerations agreed well. In a parameter study the vertical drop and the individual turn radii turned out to be the main variables that determine speed and acceleration. Thus the safety of a new ice track is mainly ensured in the planning phase, in which the use of a simulation model similar to this is essential.

We computed reaction forces and moments acting on a skier during a carved turn. We performed an inverse and a forward dynamic analysis. For a run of an elite skier, marker positions on skier and skis were obtained as functions of time from a video analysis and smoothed by splines. Linear velocities and accelerations were computed by differentiating the splines, angular velocities, and accelerations via rotation matrices. The forces acting at the right ski were measured with two Kistler force plates. For the inverse dynamics, we used an adapted Hanavan model for a skier consisting of upper body, left and right thighs, shanks, and skis. Applied forces considered were weight and ski-snow friction. Drag was neglected. By prescribing a lateral weight distribution from the outer to the inner ski during the turn, reaction forces and moments at the left and right ankle, knee and hip joints were computed from the Newton–Euler equations of motion for constrained rigid multibody systems. The forward dynamics was performed with a three-segment model of a mono-skier consisting of trunk, thigh, and shank. Rotational joints were assumed in knee and hip. The track and the joint angles were prescribed. The inward lean angle was determined by a balance condition that led to nonholonomic constraints. After formulating the equations of motion in descriptor form, the resulting differential-algebraic system was solved with the numerical code RADAU5. Computed and measured reaction forces and moments agreed well within the accuracy of the measurements. The calculated joint loads are consistent with results from the literature. The forward dynamics model can be used to simulate consecutive ski turns. With parameter studies, the effects of slope, tracks, segment properties, ski-snow friction, and velocity of the skier on joint loads and performance of a run can be investigated. Further, injury mechanisms can be analyzed.

Carved turns with Alpine Skis were investigated using a computer simulation model. Varied input data to the model were snow conditions, edging of the skis, and the velocity of the skier. Results include the pressure distribution along the running surface of the skis and the trajectory of the skier.

A computer model was developed to simulate consecutive ski turns. The model consists of a segment model for two skis and a single body for the skier. It was implemented in the multibody simulation software LMS Virtual.Lab. The interaction of ski and snow leads to a normal and a shearing force. For the normal force a hypoplastic relation between force and penetration depth was used. Hypoplasticity considers the effect that compacted snow is inelastic and deformations remain. For the shearing force orthogonal metal cutting theory was applied. During turns the skier has to keep balance. He leans inward to compensate centrifugal force. Neglecting angulation the complement of the inward lean angle is the mean value of the edge angles of the left and the right ski. With a suitable choice of the edge angles the skier kept the balance. Using this model the trajectory of the skier was simulated over four and a half turns. The first turn was rather carved, but in the last turn strong skidding was present. Due to increasing speed the centrifugal force considerably exceeded the shearing strength of snow. The hypoplastic force-penetration relation led to a reasonable penetration depth, which is a crucial factor for the shearing force. Based on this reference simulation the influence of edge angle and forward/backward lean was assessed by performing parameter studies. An increased edge angle caused smaller turn radii. Surprisingly, forward lean caused larger and backward lean smaller turn radii. This phenomenon could be explained by the turn moment of the skier. Both effects were more dominant when the skis skidded.

Carved turns with Alpine Skis were investigated using a computer simulation model. Varied input data to the model were the bending stiffness of the skis, the edging angle, and the velocity. Results include the turn radius and the force distribution along the running surface of the skis.

Understanding friction and reaction forces involved in Alpine Skiing is of great theoretical importance for sport science. We have developed a method to analyze a skier’s motion during a downhill race from video data taken by a single camera. This may help to compare the technical equipment and the skills of different skiers.

Carved turns with alpine skis are investigated. During the movement of a ski, snow is loaded and unloaded. Compacted snow is not elastic, i.e. deformations remain. Such effects are modeled by a hypoplastic constitutive equation. During a turn the shovel digs into the snow and the tail maintains nearly the same penetration depth as the part under maximum load. This results in a higher resistance against shearing for the afterbody of the ski. In the present work we investigated the benefits of the hypoplastic against the elastic forcepenetration relationship. Simulation results for a sledge on two skis are compared to experimental track data.

INTRODUCTION: The performance of ski turns mainly depends on skier actions, material properties, snow conditions, and speed of the skier. In this work we focus on effects due to ski material properties among which bending and torsional stiffness are important ones. METHOD: A computer model was developed to simulate a sequence of ski turns. The model consists of a segment model for the two skis and a single body for the skier. The interaction of the ski with the snow was modeled by a hypoplastic force-penetration relation normal to the snow surface and by orthogonal metal cutting transversal to the ski movement. The model was validated in case of a single turn with constant edge angle (Mossner et al., 2006a). To complete a sequence of ski turns the skier had to edge the skis according to the position in the turn and to lean inward to compensate the centrifugal force. With this choice the trajectory of the skier for four turns was simulated. For evaluating the effect of bending and torsional stiffness on the trajectory of the skier a reference simulation was computed using measured stiffness data of two real carving skis. Next the stiffness data of the two skis were varied and the effect on the trajectory and the turn radius was determined. RESULTS: The trajectories of the skier for two types of carving skis and varied stiffness data were computed for a sequence of turns. At the start the skier carved but due to increasing speed he skidded more and more. Increased bending or increased torsional stiffness caused larger turn radii. In all cases the influence of increased bending stiffness was larger than the influence of increased torsional stiffness but in one case the effect due to torsional stiffness even was as large as the effect due to bending stiffness. Torsional stiffness mainly effected the movement of the skier during the phase of edge change. Variation of both bending and torsional stiffness caused less change of the turn radius then variation of bending or torsional stiffness, only. Effects were small in carved turns and large in skidded turns. DISCUSSION: The importance of bending and torsional stiffness in a sequence of turns could be outlined. In contrast to prior work (Mossner et al, 2006b), where a single turn with constant edge angle was investigated, the influence of torsional stiffness was observed. Effects occur since in the phase of edge change the skis are rapidly bent and twisted whereas during turn phase the skis are constantly bent and twisted. For small velocities the shear strength of snow is not reached. In this case skis bend and twist till the whole edge has snow contact. The ski moves along the circle given by the ski edge. When speed increases and the contact pressure on the running surface of the ski reaches the shear stress of snow, then the ends of the ski begin to shear and consequently the turn radius gets larger. The higher the stiffness of the skis the larger gets the effect. At still higher speed the shear strength of snow is considerably exceeded and the skis are accelerated in transversal direction. Then the turn radius of the skier mainly depends on the shearing behavior of snow.

In a controlled field study, the turning performance of skis with different flexural and torsional stiffness was investigated. The ski manufacturer Blizzard was asked to produce three pairs of skis with different flexural stiffness and equal torsional stiffness and vice versa. The stiffness of these skis was determined by our measuring device that allows recording both the flexural and the torsional stiffness along the ski. To compare the resulting continuous functions 11 parameters were introduced, e.g. maximum values, minimum values in the front and back part of the ski or twist angles. First, differences between mounted and unmounted skis were studied. The flexural stiffness was affected by the binding, but not the torsional stiffness. Then, five ski testers performed controlled runs in a course of thirteen gates under observation of two coaches. Running time and standardized questionnaires for ski testers and coaches were used to describe the turning performance. The results show a trend that the skis with lower torsional stiffness and the skis with higher flexural stiffness affect the turning performance positively. When comparing the middle of the ski to the front and back of the ski, maximal differences in flexural stiffness and minimal differences in torsional stiffness demonstrated better turning performance.