Many references define a Rhumb Line as a line that crosses all of the meridians at the same angle. This definition leads to a second characteristic, which is that a Rhumb Line is a line of constant heading.
Historically the radial lines on a compass rose were called Rhumb Lines. So sailing a rhumb line course simply meant sailing a constant heading course.
The meridians are clearly lines of constant heading, (True North or True South), so they satisfy this condition for being rhumb lines.
Now let’s look again at the statement that “A Rhumb Line is a line that crosses all of the meridians at the same angle.”
The first point to note is that a line cannot cross any meridian that is not in its path. So we could refine our definition a little bit to become “A Rhumb Line is a line that crosses all of the meridians in its path at the same angle.”
The meridians of longitude are not circles, but are semi-circles. They start at one pole and end at the other. Where one meridian ends, its anti-meridian begins. And where the anti-meridian ends, its meridian begins. This means that the meridians and anti-meridians meet at the poles, but never actually cross each other. So between the poles the meridians of longitude are rhumb lines, which never cross any other meridians.
For a track which goes directly over one of the poles there will be a constant heading followed by an abrupt reversal of heading at that pole, after which the heading will again be constant. So we could argue that this track is made up of two rhumb lines.
Last edited by keith williams; 2nd Mar 2011 at 22:46.