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Finite element simulation of the ski–snow interaction of an alpine ski in a carved turn

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Abstract

Skiing manufacturers depend on the development of new skis on trial and error cycles and extensive product testing. Simulation tools, such as the finite element method, might be able to reduce the number of required testing cycles. However, computer programs simulating a ski in the situation of a turn so far lack realistic ski–snow interaction models. The aim of this study was to (a) implement a finite element simulation of a ski in a carved turn with an experimentally validated ski–snow interaction model, and (b) comparison of the simulation results with instantaneous turn radii determined for an actual carved turn. A quasi-static approach was chosen in which the ski–snow interaction was implemented as a boundary condition on the running surface of the ski. A stepwise linear function was used to characterise the snow pressure resisting the penetration of the ski. In a carved turn the rear section of the ski interacts with the groove that forms in the snow. Two effects were incorporated in the simulation to model this situation: (a) the plasticity of the snow deformation, (b) the influence of the ski’s side-cut on the formation and shape of this groove. The simulation results agreed well with experiments characterising snow penetration. Implementation of the groove in the ski–snow interaction model allowed calculation of the instantaneous turn radii measured in actual turns, but also caused significant numerical instability. The simulation contributes to the understanding of the mechanical aspects of the ski–snow interaction in carved turns and can be used to evaluate new ski designs.

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Acknowledgments

The study was financially supported by the Swiss Foundation for Innovation KTI and the companies Stöckli Swiss Sports AG and Fritschi Swiss Bindings.

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Authors and Affiliations

  1. Human Performance Laboratory, University of Calgary, Calgary, Canada

    Peter Federolf

  2. Institute of Computational Physics, Zurich University of Applied Sciences, Winterthur, Switzerland

    Markus Roos

  3. WSL Institute for Snow and Avalanche Research SLF, Davos, Switzerland

    Peter Federolf & Anton Lüthi

  4. Institute of Mechanical Systems, Swiss Federal Institute of Technology, Zurich, Switzerland

    Jürg Dual

Authors
  1. Peter Federolf
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  2. Markus Roos
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  3. Anton Lüthi
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  4. Jürg Dual
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Correspondence to Peter Federolf.

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Federolf, P., Roos, M., Lüthi, A. et al. Finite element simulation of the ski–snow interaction of an alpine ski in a carved turn. Sports Eng 12, 123–133 (2010). https://doi.org/10.1007/s12283-010-0038-z

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