Symbolical Expressions of Rhumb Line's Forward and Inverse Solution

In order to solve problems that deal with rhumb lines solution based on different reference ellipsoids in maritime navigation, the rhumb lines basic equations were established. After the symbolical formula of meridian arcs inverse solution being introduced, rhumb lines 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 , which can satisfy practical utilization.