Effect of ski boot rear stiffness (SBRS) on maximal ACL force during injury prone landing movements in alpine ski racing: A study with a musculoskeletal simulation model.

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.

A parameter optimization method to determine ski stiffness properties from ski deformation data.

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.

An approximate simulation model for initial luge track design.

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.

Extended method for adiabatic mode reordering.

The task of vibrational mode reordering is very important for reaction valley studies and for the determination of small curvature tunneling effects. An extended algorithm for adiabatic mode reordering is presented. It is based on the method introduced by Konkoli et al. [J Comput Chem 1997, 18, 1282], which is shown to suffer from numerical problems in the region of frequency-crossings and avoided crossings. One improvement is the use of cubic splines for the interpolation of the projected matrix of force constants, which allows larger step sizes between the discrete points along the reaction path, where vibrational analysis is performed. The main improvement is the use of perturbation theory to resolve crossings and avoided crossings. Within this theoretical framework it becomes clear why the method of the maximal overlap between the normal modes cannot work properly, as eigenvectors associated with nearby eigenvalues tend to become "wobbly". Thus a perturbative procedure is designed that is used for all cases where two harmonic frequencies approach each other and the overlap of the associated normal modes is of no practical use. Advantages of the new procedure are the use of larger step sizes along the minimum energy path and the much more reliable resolution of mode-crossings and avoided crossings independent of the systems symmetry. In addition to that it is shown that one should be very cautious in all computational situations when working with eigenvectors associated with nearby eigenvalues.