截距法決定船位之向量解法

Vector Solutions of the Intercept Method for Determining Astronomical Vessel Positions

為策航行安全，當值航行員應以大部分時間擔任瞭望工作，停留於海圖室內時間愈短愈好。傳統解算及繪製船位之截距法繁複費時，本研究探討以向量解析法並配合應用電腦程式計算船位，較傳統解算及繪圖方法快速便捷。本研究首先說明截距法計算船位之原理，再將傳統載距法之解算及繪圖之過程以向量方法將其數學模式以聯立線性方程式表示，並用電腦程式求解此線性聯立方程式以求取船位。文中說明觀測二天體、三天體與多天體決定船位之計算方法，最後以四個案例將以傳統截距法繪製求取船位之結果及與本研究之電腦程式計算結果相比對，含緯度差、經度差及距離差，並以圖表顯示。研究結果可見傳統截距法繪圖所求取之船位與本研究之向量解法計算所得之結果均在天文航海船位容許誤差範圍內。應用本研究之向量解法及配合電腦計算船位較傳統之解算繪圖方式可節省時間與減少計算錯誤並降低繪圖之人為誤差。

For the safety of navigation, it is better for the duty officer to spend most of the time and effort on watch-keeping on the bridge rather than working in the chart room. The process of determining ship's position via traditional intercept method calculating and plotting has always been considered a complex and time consuming task. The motive of this research is to show that the vector solut ions via computer computation can perform better than the traditional calculating and plotting in determining ship's position. The paper first explained the principle of the intercept method. The mathematics model of the intercept method was implemented by the vector method. Simultaneous equations from the vector method were induced then solved by Gauss elimination method to obtain the ship's position. The mathematics model was then implemented through observations of two and three celestial bodies to determine ship's position. Finally, four cases were discussed to compare the differences in latitudes, longitudes, and distances between the readings obtained via traditional calculating and plotting and the results obtained from tile present study. The comparison shows that there is 110 significant difference between the results obtained from the two methods mentioned above. Conclusion is drawn that the vector solutions via computer computation in determining ship's position performs better than the traditional calculating and plotting with the benefits of saving time and reducing possible personal errors.