This article addresses the mathematical foundations of rhumblines or loxodrome curves. These curves are critical to navigation and small-scale charting by virtue of the fact that they provide an efficient routeing from one point on a surface to another by means of a constant ‘course angle‘. This article will develop the necessary mathematical relations for the construction of such a curve, then apply the relations to both spherical and oblate-spheroidal surfaces. The purpose of this article is to produce a superior oblate-spheroidal loxodrome curve, which better models curves or routes of constant course on the actual, approximately oblatespheroidal, Earth.
