A rhumb line is a line which crosses all meridians at the same angle. Such a route is of constant true heading. This property is the reason rhumb line navigation was invented, and Mercator maps created.
On a Mercator map you just draw the straight line between the two points. This means you can always draw a route between two arbitrary places. E.g. let's connect:
- Rio de Janeiro
- Nome, a small city in Alaska
- An abitrary point at coordinates lat = 85°, lon = 0°.
Dotted lines show how the route completes pole-to-pole (full rhumb lines)
On most projections, rhumb lines appear as curves spiraling between poles, e.g. on this orthographic projection:
Why rhumb line navigation in the first place?
16th century navigators knew perfectly the shortest route was a great circle. But following a great circle requires constant and precise heading adjustments.
To simplify navigation, they split a great circle route into segments, and navigated each segment as a rhumb line, that is a route within the same rhumb, a rhumb being 1/32th of compass rose (a 32-point rose was often part of the map). They adjusted the heading only at the beginning of the next segment, possibly after they confirmed their position using a sextant.
They used maps just invented by Gerardus Mercator for the purpose of facilitating drawing rhumb lines and determining headings.
Aircraft with computerized navigation systems and autopilots are able to adjust the heading as required. They restored the interest in pure great circle navigation.