The Great Ellipse Solution for Distances and Headings to Steer between Waypoints

Author:

Walwyn P. R.

Abstract

The normal Great Circle method of computing the shortest distance between two positions on the Earth – e.g. from an aircraft's present position (PP) to a waypoint (WP) – is not accurate enough to meet present-day requirements for aircraft Nav–Attack systems.On the surface of an Ellipsoid (or Spheroid), the true ‘shortest distance’ is along a geodesic curve between the two points, but the computation of this curve is complex, and as shown by R. Williams at Reference, the difference between the geodesic and Great Ellipse distances between two points is negligible (<0·01 nm).The Great Ellipse through two points on a spheroid is defined as the ellipse that passes through the two points and the centre of the spheroid; it therefore has a major axis equal to the Earth's, and a minor axis that is between the Earth's major axis (for two points on the Equator) and minor axis (for two points on the same, or diametrically opposite, longitudes). Thus the problem of deciding on which Great Ellipse the two points lie is equivalent to determining the magnitude of the minor axis β of the ellipse on which they both lie.

Publisher

Cambridge University Press (CUP)

Subject

Ocean Engineering,Oceanography

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. THE GEOMETRIC ALGORITHM OF INVERSE AND DIRECT PROBLEMS WITH AN AREA SOLUTION FOR THE GREAT ELLIPTIC ARCS;J MAR SCI TECH-TAIW;2015

2. So, What is Actually the Distance from the Equator to the Pole? – Overview of the Meridian Distance Approximations;TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation;2013

3. The vector solutions for the great ellipse on the spheroid;Journal of Applied Geodesy;2012-01-01

4. New Algorithm for Great Elliptic Sailing (GES);Journal of Navigation;2009-06-15

5. Sphere to Spheroid Comparisons;Journal of Navigation;2006-08-23

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