Dutton

In 1926 AD Commander Benjamin Dutton, U.S. Navy wrote his first edition of Navigation and Nautical Astronomy


In navigation, a rhumb line (or loxodrome) is a line crossing all meridians at the same angle, i.e. a path of constant bearing. It is obviously easier to manually steer than the constantly changing heading of the shorter great circle route.

The idea of a loxodrome was invented by a Portuguese mathematician Pedro Nunes in the 1500s.

If you follow a given (magnetic-deviation compensated) compass-bearing on Earth, you will be following a rhumb line, which spirals from one pole to the other, with the exception of 90 and 270 degrees, lines of constant latitude, e.g. the equator. Near the poles, they are close to being logarithmic spirals (on a stereographic projection they are exactly, see below), so they wind round each pole an infinite number of times but reach the pole in a finite distance.