NavList:

George in [NavList 3710] illustrate the problem with good examples.

All is based in differential geometry of the curves of altitude.

A circle of equal altitude on the surface of The Earth, is a curve of altitude on a Mercator chart, and the approximation to this curve near the position of the observer is the osculating circle, which have the radius R specified in the computation of table of offsets in Bowditch

The straight line of position in the altitude – intercept method is tangent to this osculating circle.

For more information about the basis:

http://en.wikipedia.org/wiki/Osculating_circle

radius of curvature

Andrés Ruiz

Navigational Algorithms

http://www.geocities.com/andresruizgonzalez