The Direct and Indirect Problem for Loxodromes

Thomas H. Meyer and Craig Rollins

Peer Reviewed

Abstract: A loxodrome is a curve of constant azimuth. Herein are given formulations for the direct and indirect problems for loxodromes. These formulations depend on an elliptic integral and offer a compact solution readily implementable with modern computational platforms that support elliptic integrals. Solutions are developed on the reference ellipsoid and then shown to simplify for solutions on the sphere. Numerical examples show that the differences between ellipsoidally-based computations and spherically-based computations can differ by nearly 10 arc minutes and by 0.31% (25,319.959 m) of the loxodrome segment’s length.
Published in: NAVIGATION: Journal of the Institute of Navigation, Volume 58, Number 1
Pages: 1 - 6
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