ABSTRACT: We survey last reports and research results in the field of navigational calculations' methods applied in marine navigation that deserve to be collected together. Some of these results have often been rediscovered as lemmas to other results. We present our approach to the subject and place special emphasis on the geometrical base from a general point of view. The geometry of approximated structures implies the calculus essentially, in particular the mathematical formulae in the algorithms applied in the navigational electronic devices and systems. The question we ask affects the range and point in applying the loxodrome (rhumb line) in case the ECDIS equipped with the great circle (great ellipse) approximation algorithms of given accuracy replaces the traditional nautical charts based on Mercator projection. We also cover the subject on approximating models for navigational purposes. Moreover, the navigation based on geodesic lines and connected software of the ship's devices (electronic chart, positioning and steering systems) gives a strong argument to research and use geodesic-based methods for calculations instead of the loxodromic trajectories in general.

KEYWORDS: Marine Navigation, Geodesy, Rhumb Line (Loxodrome), Great Circle (Orthodrome), Geodesic Line, Route Planning Calculations, Great Elliptic Sailing (GES), ECDIS (Electronic Chart Display and Information System)

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