最佳滑雪場地設計

Abstract

單板滑雪是一項機具挑戰性的精彩體育賽事，並于1998年正式成為國際冬季奧林匹克運動會的比賽項目。當前，這項比賽主要有三種形式：單板平行大回轉，單板越野競逐，半管滑板。本文主要研究半管滑板場地的設計。 本文從能量的角度對滑雪場地參數及其特性進行分析設計，其中心是根據末端動能來衡量運動員最大騰躍高度，并認為最大騰躍高度是評判運動員表現的重要方面。通過合理的假設，本文建立了動力學模型，用以探究各參數之間的相互關係。基於受力分析與能量分析，建立了運動與能量方程并得到末端能量的表達式。 根據所建立的模型，首先對場地不同組成部分對最大騰躍高度進行研究。藉助Matlab軟體模擬可以發現，平底段與垂直段對其沒有較大影響，而坡度角以及過渡段曲率半徑對其有顯著影響。然後，通過採取不同的曲線對過渡段進行模擬，可以得到理論最佳過渡段曲線為 。通過進一步的模擬仿真，可以得到理論最佳曲線方程中 。最後，本文討論了安全性、建造難度、外界環境等影響因素對場地的影響，并對各因素進行權衡與調整。 最終得到最佳滑雪場地設計方案。平底段長度為18公尺，垂直段高度為1公尺，坡度角為18度，過渡段曲線方程為 ，其頂端夾角為86度。在文章的結尾，對模型之優缺點進行了客觀地分析。

Snowboarding is an adventurous and exciting sport that has been contested at the Winter Olympic Games since 1998. Nowadays, the events are usually held in three specialities: parallel giant slalom, snowboard cross and halfpipe. What we are interested here is the halfpipe, in which athletes perform tricks while going from one side of a ditch to the other. In our paper, we study the design of a snowboard course and its factors from the view of energy. The main idea is to measure the “vertical air” by final energy. By making several assumptions, we build the dynamic model, which reveals essential interactions among different factors. Based on force analysis and energy analysis, we set up energy equations and obtain the general form of final mechanical energy. Based on our model, we firstly study the each part’s influence on the vertical air respectively and change each parameter. We find that the flat-bottom and the height of vert don't have an obvious effect on the change of vertical air, while the slope angle, the curvature radius of transition have obvious effect on the vertical air. Then, by simulating of different type of curves, we find out that when the transition’s geometric function is , snowboarder can reach the maximum vertical air. After further simulation, we obtain that . At last, the adjustments and tradeoffs to develop a practical course are discussed. After taking consideration of construction difficulty, snowboarder's safety and their maximum twist, we adjust the parameters of the halfpipe to make our result more practical. In conclusion, we find a most optimal design of snowboard course, with the length of flat bottom is 0.4m, the height of vert is 1m, the slope angle is 18 degrees, the geometric function of transition is and the edge angle is 86 degrees. At the end of paper, we discuss the strengths and weaknesses of our model.