Symbolical Expressions of Rhumb Line's Forward and Inverse Solution

摘要

In order to solve problems that deal with rhumb line's solution based on different reference ellipsoids in maritime navigation, the rhumb line's basic equations were established. After the symbolical formula of meridian arc's inverse solution being introduced, rhumb line's forward and inverse expressions which are non-iterative were derived. Finally, numerical examples were given to testify the accuracy of the forward and inverse expansions derived in this paper. Theory analysis and numerical results show that these new formulas have compact and symbolical form, and the precision of the inverse formulas is up to 10~(-5), which can satisfy practical utilization.