2. The rhumb line
For many purposes the most convenient way to set a course from
one point to another is along the rhumb line.
The two points are located on a Mercator projection map, and
a straight line (the rhumb line) is drawn between them. The
angle this line makes
with the meridian through the departure point is the course to
be followed. Traveling on that compass course will lead from
the first point to the second.
The rhumb line between two points on the earth's
surface corresponds to the straight line on a Mercator chart.
Why does this work? The method relies on two properties of the
Mercator projection. The first is well known to everyone:
circles of latitude become horizontal lines on the map, and meridians
become vertical lines. The second is more subtle: the Mercator projection is
conformal. This means that angles on the map are the same
as angles on the earth's surface.
So since the compass course (by definition) always makes the same angle
with the local meridian, it corresponds to the path on the Mercator
map that meets each vertical at that same angle. In other words,
a constant-course path must follow the rhumb line "track."
© copyright 2000, American Mathematical Society.