大圈航路的求解與逼近

Solving and Approximating the Great Circle Track

謝宗軒(Tsung-Hsuan Hsieh)

指導教授 ： 許添本

國立臺灣大學/工學院/土木工程學研究所/博士(2016年)

https://doi.org/10.6342/NTU201700002

摘要

大圈航路能夠節省航行距離，是航海者關切的重要議題，是否選擇航行大圈航路取決於其能節省的距離是否顯著，否則恆向線是更容易行駛的航線。首先，為評估大圈航路，本論文創立一個簡單的判定準則：當頂點位於起航點與到達點之間時，該大圈航路值得使用。進而，若該大圈航路值得使用，其資訊是航海者所關切的，本研究導入天文航海學中天子午線平面圖的概念，提出旋轉變換及圖解法等兩套方法，以求解大圈航路的各種問題。旋轉變換是一種代數方法，相較於其他已發展的代數方法，使用旋轉變換推導求解公式是更簡易的。圖解法是一種幾何方法，應用電腦軟體繪圖，圖解法不須使用任何公式即可獲得與代數方法一樣精確的答案，且圖解法可透過描繪大圈航路判斷其節省距離。最後，航海者實際航行時，通常使用一連串轉向點逼近大圈航路。不同於現有固定間隔的逼近方法，本研究提出非固定間隔的經度等分法，其可以使用適當的轉向點數量，有效的逼近大圈航路。上述提出的所有準則與方法皆透過實務例題展示之。

關鍵字

大圈航路 ； 天子午線平面圖 ； 旋轉變換 ； 轉向點 ； 頂點

並列摘要

The great circle track (GCT), which can save distance, is an important issue that the navigators concern. Whether a GCT is worth using depends on whether the distance it can save is significant. Otherwise, the rhumb line (RL) is easier to steer. First, in this study, a simple criterion is created to evaluate the GCT. The criterion is that the GCT is worth using when the vertex lies between the departure and destination. In addition, if a GCT is worthy to adopt, the information of the GCT would be necessary to the navigators. The rotation transformation (RT) and the graphical method (GM) are proposed to solve the GCT problems, which one both based on the celestial meridian diagram (CMD) in celestial navigation. The RT, which can derive the solving equations, is simpler than other developed algebraic methods. The GM, which is a geometric method and by applying computer software to draw graphs, does not use any equations but is as accurate as that using the algebraic methods. Besides, the GM can depict the GCT to judge its saved distance. Finally, the navigators usually use a series of waypoints to approximate the GCT. Unlike currently practised methods, the proposed longitude bisection method (LBM), which determines the waypoints with varying intervals, can establish the appropriate number of waypoints to approximate the GCT effectively. The all proposed criteria and methods are demonstrated in the practical examples.

並列關鍵字

great circle track ； celestial meridian diagram ； rotation transformation ； waypoint ； vertex

參考文獻

Chen, C. L., Hsieh, T. H. and Hsu, T. P. (2015). A novel approach to solve the great circle track based on rotation transformation. Journal of Marine Science and Technology. doi:10.6119/JMST-013-1212-1

Chen, C. L. (2003). New computational approaches for solving the great circle sailing and astronomical vessel position (Doctoral dissertation). National Taiwan University, Taipei, Taiwan.

Chen, C. L. (2016). A systematic approach for solving the great circle track problems based on vector algebra. Polish Maritime Research, 23(2), 3-13. doi:10.1515/pomr-2016-0014

Chen, C. L., Hsu T. P. and Chang, J. R. (2004). A novel approach to great circle sailings: The great circle equation. The Journal of Navigation, 57(2), 311-320. doi:10.1017

Chen, C. L., Liu, P. F. and Gong, W. T. (2014). A simple approach to great circle sailing: the COFI method. The Journal of Navigation, 67(3), 403-418. doi:10.1017