基于等距圆的极球面投影距离量测方法

研究了极球面投影海图上准确便捷地量测距离的方法。推导了极球面投影下大圆航线和等角航线的方程,形状分析表明极区宜采用大圆航线量测距离;根据极球面投影下直线的几何意义推导了其距离计算公式,距离差值分析表明可用直线代替大圆航线准确量测距离;根据极球面投影上小圆线投影为圆的性质,提出了一种基于等距圆的准确便捷的距离量测方法,以满足极球面投影海图的极区导航应用需要。

A Distance Measuring Method on Polar Stereographic Charts Based on Equidistant Circles

An exact and simple method for measuring distance on polar stereographic nautical charts used for polar navigation is investigated. Equations for thumb lines and great-circle lines were deduced;shape analysis results indicate that great-circle distance is preferable for distance measuring in polar navigation. Formulas for calculating the distance of straight-line segments on polar stereographic charts based on their geometry are given as distance difference analysis results indicate that measuring distance by straight segments is feasible. Moreover, an exact and simple distance measurement method based on equidistance circles is presented based on the fact that small-circles on earth can be projected into circles on polar stereographic charts. The proposed method can satisfy the polar navigation application requirements for polar stereographic charts.