Abstract
This paper describes a procedure for optimizing the design of the landing slope of the Zao jumping hill. The concept behind the design of the landing slope is that the landing slope should enable the spectators to witness an exciting spectacle, that the jumpers can land safely, and that it can be constructed with minimum cost. We regard these features as objective functions. The findings can be summarized as follows: it is possible to control the objective functions by changing the profile of the landing slope; there is not a unique optimal design solution, but the Pareto optimal solutions; a landing slope that gives safety on landing is almost equivalent to a landing slope that produces differences in the flight distance due to differences the jumpers’ skill levels; there is a trade-off between the length of the flight distance and safety on landing; the construction cost is influenced by the horizontal distance between the edge of the take-off table and the K-point. The developed procedure would be applicable not only to Zao in Yamagata city, but also to all ski jumping hills in the world.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsAbbreviations
- b :
-
Width of the landing slope
- D :
-
Drag
- FD i :
-
Flight distance around the local longest flight distance, FD L
- FD L :
-
The local longest flight distance
- F1 :
-
The first objective function, construction cost
- F2 :
-
The second objective function, landing velocity
- F3 :
-
The third objective function, flight distance multiplied by –1
- F4 :
-
The forth objective function, standard deviation in flight distance due to differences in the jumpers’ skill levels
- g :
-
Gravitational acceleration
- H :
-
Height difference between the old Zao and the new Zao
- h :
-
Height difference between the edge of the take-off table and the K-point of the landing slope
- I yy :
-
Moment of inertia of the body–ski combination on its y b –axis
- L :
-
Lift
- M :
-
Pitching moment
- m :
-
Mass of the body–ski combination
- N :
-
Number of Monte-Carlo simulations
- n :
-
Horizontal distance between the edge of the take-off table and the K-point of the landing slope
- Q :
-
Y b component of the angular velocity vector
- r L :
-
Radius of the landing area curve
- r 2L :
-
Radius of the transition curve from L to U at L
- r 2 :
-
Radius of the transition curve from L to U at U
- t f :
-
Flight time
- (U,W) :
-
(x b , z b ) components of the velocity vector
- V :
-
Amplitude of the velocity vector of the ski jumper
- \( v_{ \bot } \) :
-
Landing velocity, velocity component of the ski jumper perpendicular to the landing slope at the point of landing
- (X a , Z a ) :
-
(x b , z b ) components of the aerodynamic force
- (x b , z b ) :
-
Body-fixed coordinate system
- (X E , Z E ) :
-
Inertial coordinate system
- Z N :
-
Vertical position of the new Zao at X E
- Z O :
-
Vertical position of the old Zao at X E
- Z U :
-
Bottom of the landing slope of the old Zao
- α :
-
Angle of attack
- β :
-
Forward leaning angle
- β k :
-
Slope of the landing hill at the K-point
- β H :
-
Slope of the landing hill at the landing position
- γ :
-
Flight path angle
- λ :
-
Ski-opening angle
- Θ :
-
Pitch angle
References
Seo, K., Watanabe, I., Murakami, M.: Aerodynamic force data for a V-style ski jumping flight. Sports Eng. 7, 31–39 (2004)
McNeil, A.J., Hubbard, M., Swedberg, A.D.: Designing tomorrow’s snow park jump. Sports Eng. 15, 1–20 (2012)
Kobayakawa, M., Kondo, Y.: The flight mechanics of ski jumping (in Japanese). Science (Japanese edition) 55–3, 185–190 (1985)
Gasser, H.: Standards for the construction of jumping hills - 2012, Application to Rule 411 of ICR, vol. 3, FIS (International Ski Federation) (2012)
Seo, K., Kobayashi, O., Murakami, M.: Multi-optimisation of the screw kick in rugby by using a genetic algorithm. Sports Eng. 9, 87–96 (2006)
Kohonen, T.: Self-organizing Maps. Springer, Heidelberg (1995)
Acknowledgements
This work is supported by a Grant-in-Aid for Scientific Research (A), No. 15H01824, Japan Society for the Promotion of Science.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Seo, K., Nihei, Y., Shimano, T., Ohgi, Y. (2016). Design Optimization of the Landing Slope of a Ski Jumping Hill. In: Cabri, J., Pezarat Correia, P. (eds) Sports Science Research and Technology Support. icSPORTS 2015. Communications in Computer and Information Science, vol 632. Springer, Cham. https://doi.org/10.1007/978-3-319-52770-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-52770-3_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-52769-7
Online ISBN: 978-3-319-52770-3
eBook Packages: Computer ScienceComputer Science (R0)