The use of the cosine function in modelling of a ski jumping in-run hill
Authors:
- Renata Filipowska
Abstract
The paper deals with the problem of mathematical modelling a curvilinear segment of a ski jumping in-run hill. The aim of the research was to find the profile which makes the take-off action easier for a ski jumper. The value of the normal reaction acting on the sportsman at the point bordering on the take-off table is smaller than the value of this force at the same point for the existing ski jumping hills. Additionally, a reaction at the point of contact the straight and curvilinear segments should be the same. To obtain such the profile, the simplified model was taken into account and appropriate differential equation with exceeded number of boundary conditions is derived. To solve this non-classical boundary-value problem Kansa method is employed. In the proposed model, sliding down the sought curve, a value of centripetal acceleration increases from zero and reaches a maximum at the end of this curve. Taking into account geometrical parameters of two polish ski jumping hills in Bystra, we can obtain the modified profile without the inflexion point, which fulfills all required conditions. The results obtained were verified taking into account an equation of motion, which contains all the forces acting on the jumper during the descent.
- Record ID
- CUTdd3516dac101480c8fd7c6d8fc6f8c50
- Publication categories
- ; ;
- Author
- Pages
- [1-4]
- Other elements of collation
- rys.; tab.; Bibliografia (na s.) - 4; Bibliografia (liczba pozycji) - 10; Oznaczenie streszczenia - Abstr.
- Book
- Simos Theodore, Theodore Simos Tsitouras Charalambos Charalambos Tsitouras (eds.): International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2018), Rhodes, Greece, 13-18 September 2018, AIP Conference Proceedings, no. 2116, 2019, [Melville], American Institute of Physics, AIP Publishing, 4 p., ISBN 978-0-7354-1854-7
- Keywords in English
- mathematical modeling, ski jumping in-runhill, normal reaction force
- DOI
- DOI:10.1063/1.5114246 Opening in a new tab
- URL
- https://aip.scitation.org/doi/abs/10.1063/1.5114246 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 20
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTdd3516dac101480c8fd7c6d8fc6f8c50/
- URN
urn:pkr-prod:CUTdd3516dac101480c8fd7c6d8fc6f8c50
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.