Analysis of three forms of direct and inverse expressions of meridian arc length
In order to analyze the influence of different expressions on the computational efficiency,three expressions of the meridian arc length are given in this paper.The expansion coefficients are rewritten as the third flattening n.The truncation errors of different forms of meridian arc length are calculated and analyzed,the appropriate terms are selected and the practical formulas of the expansion are given.The results show that the coefficients in the direct and inverse of the meridian arc length based on n have fewer digits in the numerical value,more concise form,and are more convenient for popularization and application.When the accuracy of the direct expression is millimeter,the expansion only needs to keep the first four items.When the inverse solution accuracy is 0.000 1",the expansion only needs to keep the first four items to satisfy the accuracy.For the three expressions,the double-angle form has higher computational efficiency.Therefore,it is recommended to use the double-angle form in the process of the positive and negative solutions of the meridian arc length.
geodetic surveyingmeridian arc lengththe third flatteningtruncation errorthree expressions
国家科技期刊平台
NSTL
万方数据
维普
