From: J Giffen <jgiffen@hgo.net>
Newsgroups: sci.satellite.nav,sci.math
Subject: loxodrome
Date: Thu, 16 Apr 1998 23:58:31 -0400

Given the start and end lat/long, find the constant
compass course for a rhumb line between the two points.

Let
(x1,y1)=(start longitude, start latitude)
(x2,y2)=(end longitude, end latitude)
A=constant compass direction

Then
(x2-x1)tan A = gd^-1 y2 - gd^-1 y1,
where gd^-1 is the inverse gudermanian, where
gd^-1 u = ln[tan(pi/4 + u/2)], so
(x2-x1)tan A = ln{[tan(pi/4 + y2/2)]/[tan(pi/4 + y1/2)]}, or

A = arctan{[1/(x2-x1)]ln{[tan(pi/4 + y2/2)]/tan(pi/4 + y1/2)]}}

The distance sailed is (y2-y1)csc A (radii), a radius being
60(180/pi) nautical miles.

If y1 and y2 are different signs, like North and South,
let one of them have a negative value.

From  "Hyperbolic Functions,", McMahon, London: Chapman & Hall, 1906