A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robin Stuart
Date: 2017 Feb 5, 08:01 -0800
The question of classification of the components of the problem as being coordinate-driven or geometry-driven is an interesting one and, I believe reveals itself in the formulas in the paper.
The algebraic expressions for the circles of position or constant altitude curves are exactly the same for the sphere and ellipsoid. I was initially astonished by this when I read Williams’ proof in The Geometry of Navigation but came to realize that it is a simple consequence of the way astronomical coordinates are defined. The circles of position are therefore coordinate-driven and don't distinguish between the sphere and ellipsoid.
The specific properties of the ellipsoid appear in the Mercator sailing formulas which are firmly rooted to the ground. If I understand your classification scheme correctly these would be geometry driven.
Actually I think you have hit on a compelling aesthetic reason for not advancing CoP’s. In doing so you mix coordinate-driven and geometry-driven as aspects of the problem. In my approach they are kept separate,