Vector Solutions for Great Circle Navigation

• Published in: Journal of Navigation
• Main Author: Earle, Michael A.
• Format: Article in Journal/Newspaper
• Language: English
• Published: Cambridge University Press (CUP) 2005
• Subjects: North Pole
• Online Access: http://dx.doi.org/10.1017/s0373463305003358; https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0373463305003358

Traditionally, navigation has been taught with methods employing Napier's rules for spherical triangles while methods derived from vector analysis and calculus appear to have been avoided in the teaching environment. In this document, vector methods are described that allow distance and azimuth at any point on a great circle to be determined. These methods are direct and avoid reliance on the formulae of spherical trigonometry. The vector approach presented here allows waypoints to be established without the need to either ascertain the position of the vertex or select the nearest pole; the method discussed here requires only one spherical triangle having an apex at the North Pole and is also easy to implement on a small computer.