Abstract:

Background. The aim of this research was done to create calculating methods for virtual replacing of a circle arc segment on the in-run hill. This replacement should not change the angle of the in-run hill inclination, but could change the length of the straight-line segment to such an extent that it can follow geometrical parameters of the in-runs in vogue. Materials and Methods. 38 in-runs hills certificated by International Ski Federation; mechanical and mathematical modelling of the in-run hill profile modelled with cycloid, hyperbola, or inclined quadratic parabola with decreased ratio of vertical to horizontal dimensions. Results and Discussion. The decreased ratio of the vertical to horizontal dimensions was in the range of 2.71–0.73% when cycloid was used, 16.33–8.60% when hyperbola was used, and 4.58–0.90% when inclined quadratic parabola was used. When the circle arc was replaced with a quadratic parabola or an inclined cubic parabola, the ratio of the dimensions increased. If the difference between the angles of inclination of straight-line segments increased, this ratio increased too. For the certificated in-runs, the ratio varied in the range of 2.21–8.61% when a quadratic parabola was used and 14.64–19.04% when inclined cubic parabola was used.

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