Linear Equation for the Intersections of Two Circles of Equal Altitude or a Circle of Equal Altitude and a Great Circle of Pseudo Star

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Project title

Code/計畫編號

NSC98-2410-H019-019

Translated Name/計畫中文名

海上航行天文定位作業中兩等高位置線或一等高位置線及虛擬大圓交點直線方程式之研究

Project Coordinator/計畫主持人

Wei-Kuo Tseng

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Merchant Marine

Website

https://www.grb.gov.tw/search/planDetail?id=1887032

Year

2009

Start date/計畫起

01-08-2009

Expected Completion/計畫迄

31-07-2010

Bugetid/研究經費

455千元

ResearchField/研究領域

經濟學

"本計畫使用固定直角座標系統及配合向量代數，針對航海上天文觀測船位問題，推導出可直接計算之等高圈交點之直線方程式，利用這個參數直線方程式可以建構出一個創新的定位方法，帶入地球的球面方程式可以形成一個一元二次方程式，求解後可以帶回參數直線方程式求出觀測定位點。其最大之優點則是不用圖解即可直接計算出天文觀測船位及推導出來的一元二次方程式解的結構非常適合程式撰寫，相較於目前廣泛所使用的截距法，它不僅準確且因可用於較高高度的情境，所以適用範圍更廣。而針對截距法的缺失，亦發展出利用虛擬天體構成另外一個虛擬等高圈以求解天文位置線不用截距的新計算程序。利用Java script 或ASP 語法撰寫演算的網頁程式，後將成果放置於商船系網頁上可增加新知識的流通性，因為Excel 試算表的軟體取得容易性，本計劃亦利用VBA 撰寫相關的增益集放置網頁上，以供海上從業人員及教育訓練使用，期能改善目前商船教育訓練或海上實務作業上天文航海的現況。""In this document, a logical and concise computation method especially suited for coding computer program by using a fundamental concept of vector algebra is developed to deal with classical problems of celestial navigation. A fix (observed point) with two sights is determined by the intersections of their position circles. The most common methods to determine the relevant intersection are Intercept Method. Using the linear equation of the intersections of two planes containing two circles of equal altitude (or a circle of equal altitude and a great circle passing Dead Reckoning, at true course or Assumed Position and Geographical Position) and the equation of a sphere can obtain position function of known variables including altitudes, declinations and GHAs of the celestial bodies. The proposed methods address the sight reduction problem for the condition of a single or two celestial bodies without graphical works. It can be identified that the proposed approach is not only more straightforward and has universal use in different scenarios than the Spherical Triangle Method but is also easier to coding computer program concisely than those methods proposed by other papers. The improved approach is used to solve the astronomical vessel position efficiently. The approach was intended to appeal to the navigator who are interested in the mathematics of navigation and who, nowadays, solves his problems of navigation with a personal computer."

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Linear Equation for the Intersections of Two Circles of Equal Altitude or a Circle of Equal Altitude and a Great Circle of Pseudo Star

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