Optimizing the Design of the Landing Slope of the Zao Jumping Hill Kazuya Seo 1 , Yuji Nihei 2 , Toshiyuki Shimano 3 , Ryutaro Watanabe 2 and Yuji Ohgi 4 1 Department of Education, Art and Science, Yamagata University, 1-4-12 Kojirakawa, Yamagata, Japan 2 Yamagata City Office, 2-3-25 Hatagomachi, Yamagata, Japan 3 Access Corporation, 2-3-4, Minami-1-jo Higashi, Chuo-ku, Sapporo, Japan 4 Graduate School of Media and Governance, Keio University, 5322 Endo, Fujisawa, Japan Keywords: Optimal Design, Ski Jumping, Landing Slope, Flight Dynamics, Safety Landing, Construction Fee, Variety. Abstract: This paper describes a process for optimizing the design of the landing slope of the Zao jumping hill. The features of the landing slope that we considered were the construction fee, the safety of the jumpers on landing, the length of the flight distance such that it makes it an interesting spectacle, and the difficulty for unskilled jumpers. We regard these features as objective functions. The findings can be summarized as follows: it is possible to control the four objective functions by changing the profile of the landing slope; the safety on landing is almost equivalent to the difficulty for unskilled jumpers; there is a trade-off between the length of the flight distance and the safety on landing and the difficulty for unskilled jumpers; the construction fee is influenced by the horizontal distance between the edge of the take-off table and the K- point; and the safety on landing, the flight distance and the difficulty for unskilled jumpers are influenced by the ratio of the height difference and the horizontal distance between the edge of the take-off table and the K-point. 1 INTRODUCTION Since 2012 the Zao jumping hill in Yamagata city has been host to the annual ladies world cup. A ski jumping hill is composed of the in-run, the take-off table, the landing slope and the out-run. The Zao track was renovated to resemble the ski jump at the Sochi Games in 2013, with a take-off table with an angle of 11 degrees downhill. A further renovation related to the landing slope is being planned for 2015, and this is the subject of this study. It is likely to cost 700,000,000 Japanese yen (5,800,000 USD, or 5,000,000 EUR), so there is a huge responsibility on the shoulders of the authors. 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 land safely, and that it be constructed with the minimum cost. 2 OBJECTIVE FUNCTIONS A long flight ditance provides an exciting spectacle for the spectators. The first objective function for the Zao jumping hill is the flight distance; the longer the flight distance, the more exciting the spectacle. On the other hand, the landing slope in Zao is designed to be a difficult slope for unskilled jumpers, which means it will not produce long flight distances for unskilled jumpers. This is the concept of the second objective function. The construction fee was estimated on the basis of the amount of material that is needed to construct the new slope. Some of this material will be moved from the existing Zao jumping hill, while new material will also have to be brought in. Lower cost is, of course, better. The safety on landing was estimated on the basis of the landing velocity. The landing velocity is the velocity component perpendicular to the landing slope at the instance of landing, and this needs to be small to reduce the impact and make the landing safer. 2.1 Construction Fee The construction fee was estimated on the basis of the amount of material needed to construct the new slope. This is the first objective function, F1. The inertial coordinate system is shown in Figure 208 Seo, K., Nihei, Y., Shimano, T., Watanabe, R. and Ohgi, Y.. Optimizing the Design of the Landing Slope of the Zao Jumping Hill. In Proceedings of the 3rd International Congress on Sport Sciences Research and Technology Support (icSPORTS 2015), pages 208-213 ISBN: 978-989-758-159-5 Copyright c  2015 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved