The Early History of Great Circle Sailing

Abstract

The least spherical distance between two points on the surface of a sphere is that along the minor arc of the great circle on which the two points lie. It is an easy matter to demonstrate this using a cord stretched between two points on a small globe; noting that the circle whose plane coincides with that of the cord contains the centre of the sphere and that it is, therefore, a great circle. It is a little more difficult to prove the fact analytically. The practice of sailing along the shortest route on an ocean passage—sometimes known as ‘orthodromic’ as opposed to rhumbline or ‘loxodromic’ sailing—would require the course to be continually changed (except, of course, in cases in which the rhumb-line and great circle arc coincide). This would clearly be impossible; the term ‘approximate great circle sailing’ is sometimes used to describe the techniques of following a great circle route as closely as practicable.