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On the velocity maximization in downhill skiing

R von Hertzen1, U Holmlund, M A Ranta

  • 1Laboratory of Computational Dynamics, Helsinki University of Technology, Finland.

Journal of Biomechanics
|May 1, 1997
PubMed
Summary

Researchers optimized downhill skier speed by shaping hills. Optimal designs can increase final velocity by 50% compared to straight slopes, aiding speed prediction and ski hill design.

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Area of Science:

  • Physics
  • Biomechanics
  • Sports Science

Background:

  • Downhill skiing involves complex dynamics influenced by physical and physiological factors.
  • Understanding these factors is crucial for optimizing skier performance and safety.

Purpose of the Study:

  • To determine the optimal vertical hill profile for maximizing downhill skier velocity increase.
  • To analyze the influence of key dimensionless parameters on skier dynamics and optimal hill shape.

Main Methods:

  • Derivation of dimensionless equations of motion for a downhill skier.
  • Application of variational calculus to find optimal and minimal velocity-increasing hill shapes.
  • Parametric study of air resistance, friction, and terrain geometry effects.

Main Results:

  • Analytical solutions for straight hill dynamics were obtained.
  • Optimal hill shapes were identified, potentially increasing final velocity by up to 50% over straight slopes.
  • The study identified hill shapes for both maximal and minimal velocity increase.

Conclusions:

  • Hill shape significantly impacts downhill skier speed.
  • The findings provide valuable insights for speed prediction and the design of optimal ski racing courses.
  • The dimensionless parameters identified are critical for understanding skier dynamics.

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