True direction and constant direction
of direction is complicated by that fact that azimuth, or true direction, is
one thing and constant direction is another. Let's compare these two ideas,
Therefore, as you follow an oblique arc, the angle at which you intercept meridians changes with your latitude. The only great circles of constant azimuth are the equator and the meridians.
graphic below, a line of true direction from
In 1), the azimuth is measured with respect to the prime meridian. In 2), the projection is recentered and the azimuth is measured with respect to the 30°E meridian. In 3), the projection is again recentered, and the azimuth is measured with respect to the 60°E meridian. The arc of true direction doesn't change; all that changes is the angle at which it intercepts each meridian. (The projection used here is the Gnomonic, in which all great circles project as straight lines.)
For navigators, a line of true direction is a headache—it's the shortest way from A to B, but you have to keep changing your compass bearings to stay on course.
A line of constant direction (also called a rhumb line or loxodrome) is an alternative way to get from A to B. It's not a great circle arc, so it's not the shortest route, but it's easier to navigate because it crosses every meridian at the same angle. You just follow a constant compass heading—say, 45 degrees—and eventually you get to your destination.
The most famous constant direction map is the Mercator. On it, every rhumb line is projected as a straight line.
On a Mercator projection, all straight lines, like the blue line
On an azimuthal map, lines of constant direction are projected as curves.
Gnomonic projection. The red line is azimuth; the blue line is constant
direction. The true distance from