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# Geodesic based trajectories in navigation

Jun 2011 | No Comment

## ECDIS APPROACH

In the course of navigation programmes for ECDIS purposes it became apparent that the standard text books of navigation were perpetuating a flawed method of calculating rhumb lines on the Earth considered as an oblate spheroid. On further investigation it became apparent that these incorrect methods were being used in programming a number of calculator/computers and satellite navigation receivers. Although the discrepancies were not large, it was disquieting to compare the results of the same rhumb line calculations from a number of such devices and find variations of a few miles when the output was given, and therefore purported to be accurate, to a tenth of a mile in distance and/or a tenth of a minute of arc in position. This paper presents and recommends the guidelines that should be used for the accurate solutions. Most of these may be found in standard geodetic text books, such as, but also provided are new formulae and schemes of solution which are suitable for use with computers or tables. The paper also takes into account situations when a near-indeterminate solution may arise. The data for these problems do not refer to actual terrestrial situations but have been selected for illustrative purposes.

The references also present the review of different approaches to contact formulae for the computation of the position, the distance, and the azimuth along a great ellipse. The proposed alternative formulae are to be primarily used for accurate sailing calculations on the ellipsoid in a GIS environment as in ECDIS and other ECS. Among the ECDIS requirements is the need for a continuous system with a level of accuracy consistent with the requirements of safe navigation. At present, this requirement is best fulfilled by the Global Positioning System (GPS). The GPS system is referenced to World Geodetic System 1984 Datum. Using the ellipsoid model instead of the spherical model attains more accurate calculation of sailing on the Earth. Therefore, we aim to construct a computational procedure for solving the length of the arc of a geodesic path, the waypoints and azimuths along it. We aspire to provide the straightforward formulae involving the great elliptic sailing based on two scenarios. The first is that the departure point and the destination point are known. The second is that the departure point and the initial azimuth are given (direct and inverse geodetic problems on reference ellipsoids).

As a minimum, an ECDIS system must be able to perform the following calculations and conversions [Weintrit, 2009]:

− geographical coordinates to display coordinates, and display coordinates to geographical coordinates;

− transformation from local datum to WGS-84;

− true distance and azimuth between two geographical positions;

− geographic position from a known position given distance and azimuth (course);

− projection calculations such as great circle and rhumb line courses and distances;

− “RL-GC” difference between the rhumb line and great circle in sailing along the great circle (or great ellipse?).

The ECDIS allows the navigator to create waypoints and routes including setting limits of approach and other cautionary limits. Both rhumb line and great circle routes can be defined. Routes can be freely exchanged between the ECDIS and GPS or ARPA. Route checking facility allows the intended route to be automatically checked for safety against limits of depth and distance as defined by the navigator.

The mariner can calculate and display both a rhumb line and a great circle line and verify that no visible distortion exists between these lines and the chart data. Authors predict the early end of the era of the rhumb line. This line in the natural way will go out of use. Nobody after all will be putting the navigational triangle to the screen of the ECDIS. Our planned route need not be a straight line on the screen. So, why hold this line still in the use? Each ship’s position plotted on the chart can be the starting point of new updated great circle, or saying more closely, great ellipse or geodesic trajectory.

It is an important question whether in the ECDIS time Mercator projection is still essential for marine navigation. Do we really need it? And what about loxodrome? Let start navigation based on geodesics. It is high time to forget the rhumb line navigation and great circle navigation, too. But first we need clear established methods, algorithms and formulae for sailing calculations. But it is already indicating the real revolution in navigation – total revolution. We will be forced to make the revision of such fundamental notions as the course, the heading and the bearing.

And another very important question: do you really know what kind of algorithms and formulae are used in your GPS receiver and your ECS/ECDIS systems for calculations mentioned above? We are almost sure your answer is negative. So, we have got a problem – a serious problem.

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