Comparative Analysis of Ski Jumping In-run Hill Models Profile

Year 2021, Volume: 9 Issue: 3, 300 - 315, 15.09.2021

Ihor Zanevskyy , Lyudmyla Zanevska

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.

Keywords

Ski jumping, In-run hill profile, Mathematical Modeling

References

• 1. Banakh V & Zanevskyy I (2010). The profile of the in-run hill and conditions of take off in ski jumping from a trampoline. Chapter 1. A comparative analysis of the in run hill profiles. Sport Science of Ukraine, 30(1): 10-24 (in Ukrainian, abstract in English).
• 2. Certificate of jumping hill (Bischofshofen) No.5 / AUT 5. (2003). International Ski Federation http://www.skisprungschanzen.com/e_index.htm?/e_profile.htm Retrieved 2 February 2020.
• 3. Eastern Ski Jumping & Nordic Combined Foundation (2011). Facts about Ski Jumping hills. Archived from the original on 17 March 2011. Retrieved 23 February 2020.
• 4. Ettema GJ, Braten S, Bobbert MF (2005). Dynamics of the In-Run in Ski Jumping: A Simulation Study. Journal of Applied Biomechanics, 21 (3): 247-259.
• 5. Filipowska R (2008). Optimization of ski jumping inrun profile. Czasopismo Techniczne. Mechanika. Wydawnictwo Politechniki Krakowskiej, 3-M Z: 57-64 (in Polish, abstract in English).
• 6. Gasser Н (2018). Jumping hills construction norm. Implementing Provisions for Art. 411 of the ICR Ski Jumping. FIS, 11. https://assets.fis-ski.com/image/upload/v1592381507/fis-prod/assets/Construction-Norm_2018-2.pdf. Retrieved February 3, 2020.
• 7. Gasser Н (2008). Skisprungschanzen Bau-Normen (Ausfuhrungsbestimmungen zu Art. 411 der IWO Band) Іnternationaler ski verband http://www.fis-ski.com/data/document/skisprungschanzen_bau-normen2008.pdf Retrieved 23 February, 2020 (in German, abstract in English).
• 8. International ski competition rules (2008). Ski jumping. International Ski Federation. http://www.fis-ski.com/data/document/icr_jp_2008.pdf Retrieved February 9, 2020. 9. Jung A, Muller W, Staat M (2019). Optimization of the flight technique in ski jumping: The influence of wind. Journal of Biomechanics, 88: 190-193. DOI: 10.1016/j.jbiomech.2019.03.023
• 10. Jung A, Staat M, Muller W (2014). Flight style optimization in ski jumping on normal, large, and ski flying hills. Journal of Biomechanics, 71 (11): 716–722. DOI: 10.1016/j.jbiomech.2013.11.021
• 11. Jung A., Mueller W., Staat M (2018). Wind and fairness in ski jumping: A computer modelling analysis. Journal of Biomechanics, 75: 147-153.
• 12. Muller W (2009). Determinants of ski-jump performance and implications for health, safety and fairness. Sports Medicine, 39(2): 85-106.
• 13. Neufert E (2004). Bauentwurfslehre. Berlin: Vieweg Verlag (in German, abstract in English).
• 14. Palej R & Filipowska R (2009). Mathematical modelling of the inrun profile of a ski jumping hill with the controlled track reaction force. Journal of theoretical and applied mechanics, 47(1): 229-242.
• 15. Palej R & Struk R (2004). Optimization of ski jumping inrun profile. Czasopismo Techniczne. Mechanika. Wydawnictwo Politechniki Krakowskiej, Z. 5-M: 363-370 (in Polish, abstract in English).
• 16. Palej R & Struk R (2003). The inrun profile of a ski jumping hill with lowered normal reaction of the track. Czasopismo Techniczne. Mechanika. Wydawnictwo Politechniki Krakowskiej, Z 6-M: 127-136 (in Polish, abstract in English).
• 17. Schwameder H (2008). Biomechanics research in ski jumping, 1991-2006. Sports Biomechanics, 7(1): 114-136.
• 18. The new Olympiaschanze of Garmisch-Partenkirchen at the rising of the inrun tower (2007). www.skisprungschanzen.com/ger/gere_garmisch-s.htm Retrieved February 4, 2020 (in German, abstract in English).
• 19. Zanevskyy I & Banakh V (2010). Dependence of ski jump length on the skier’s body pose at the beginning of take-off. Acta of Bioengineering and Biomechanics, 12(4): 77-85.