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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/35582

Title: 應用向量代數求解大圈航法和混合航法
Solving the Great Circle Sailings and the Composite Sailings Based on Vector Algebra
Authors: Pin-Fang Liu
劉繽方
Contributors: NTOU:Department of Merchant Marine
國立臺灣海洋大學:商船學系所
Keywords: 大圈航法;混合航法;向量代數;球面三角學
great circle sailing;composite sailing;vector algebra;spherical trigonometry
Date: 2013
Issue Date: 2013-10-07T02:56:28Z
Abstract: 本研究以向量代數直接且簡單地求解大圈航法和混合航法的轉向點問題。首先,將地球座標系統的參數轉換至正球體的球面座標中,使其座標固定,再納入相對子午線的概念,使球面上各點係相對於起航點而定義的向量表示式。繼而使用向量代數的多重積,由其所隱含的幾何定義與代數運算結果,可直觀地推導球面三角公式。並評選其公式,建構求解大圈航法和混合航法的控制方程,且配合麥氏航法建構出兩航法之計算程序。其計算程序可自起航點直接解算大圈航法和混合航法之轉向點,是一個可涵蓋航海者所給定三種給定條件之完整求解的方法論。最後,採用可直觀操作且具有物件式導向之Visual Basic 6.0成功地開發大圈航法及混合航法等兩套計算程式,分別命名為GCSPro_VA與CSPro_VA。該兩程式在三種給定條件下除可計算航路資訊、轉向點及相鄰的轉向點間之麥氏航向與麥氏距離等航行計畫所需資訊外,亦可提供總麥氏距離與轉向點個數分析圖,供航海者實際使用。論文最後並將兩程式的計算結果與標準實例之結果做比較,證明本法之簡潔性與開發程式之準確性。
To consider the economic and safety in navigation, the navigators usually use the great circle sailing (GCS) and the composite sailing (CS) for voyage plan in the open sea. First of all, we categorized all given conditions into three kinds of conditions. Then, we use the vector algebra with the technique of the fixed coordinates system, the relative longitude concept and the multiple products of the vector algebra to derive spherical triangle formulae, which can be used to yield the governing equations for the GCS and CS. Further, the governing equations and Mercator sailing are combined together to construct the computational procedures. Finally, these computational procedures are to develop the GCSPro_VA and CSPro_VA programs, which are coded in the Visual Basic 6.0 (VB6) with the graphical user interface (GUI). These two programs can solve the waypoints under all given conditions and display the voyage information, waypoints and the diagram of Mercator distance versus numbers of the waypoints for the navigators. Several benchmark examples are conducted to validate the simplicity and effectiveness of the proposed method.
URI: http://ethesys.lib.ntou.edu.tw/cdrfb3/record/#G0010171008
http://ntour.ntou.edu.tw/handle/987654321/35582
Appears in Collections:[商船學系] 博碩士論文

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