What is a rhumb line?

Can anyone explain what a rhumb line is and how it is different from the great circle route?

This what the internet says:

Rhumb lines are tracks with a constant track direction between two points on a sphere and therefore must be a longer distance than a great circle track.

From pprune.org

What does it mean to have a constant track direction?

• Jan 27 '20 at 12:03
• "Must be a longer distance" unless the constant track is 0 or 180, or unless you're on the equator flying 90 or 270. Jan 28 '20 at 2:37

a rhumb line, rhumb, (/rʌm/) or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true or magnetic north

From: Wikipedia

If continued, all rhumb lines except the ones following a track of 90 or 270 degrees end up in either the North or South Pole.

If continued, all great circle lines end up back where they started from.

As for the part of the question about constant track direction: track is defined by ICAO as

The projection on the earth’s surface of the path of an aircraft, the direction of which path at any point is usually expressed in degrees from North (true, magnetic or grid).

So, to maintain a constant track would mean that North would always be in the exact same direction from you as you move on. This would eventually take you to one of the poles, unless of course, you were maintaining a track of 90 or 270 degrees.

The picture above shows a constant track of about 75 degrees.

• Worth pointing out: to keep the track constant, the pilot will maintain a turn! To fly straight-and-level, is a great circle.
– ymb1
Jan 27 '20 at 18:33
• True, but that is pretty much the same thing as in the much debated question of what will happen to the altimeter reading when pressure and/or temperature changes. The track is, as is the altitude, maintained in reference to the reading on the instrument. The turn needed to maintain a track is almost nonexistent untill you are close to the N or S Pole. And anyway, flying straight and level is a very theoretical thing IRL ;) Jan 27 '20 at 18:45
• "The track is maintained in reference to the reading on the instrument" That would be a CDI for example, not simply a heading. Between distant waypoints, say in the North Atlantic, the heading change is noticeable, whereas the plane flies the magenta line and doesn't bank (wind aside for now).
– ymb1
Jan 27 '20 at 18:47
• @ymb1, a CDI will guide you on orthodrome (great circle) whether GPS-based, VOR-based or even INS-based. But imagine crossing the Atlantic in a post-war DC-6, where the radio instruments would not have any signal and all you had was magnetic compass and a drifting gyroscopic one. You could only fly segments of rhumb line (well, not even that as the wind changes), possibly adjusting the heading at some points to stay closer to the great circle. Jan 28 '20 at 7:00

In plain English:

Great Circle:

Tie a string tightly around a globe. It will lie in a perfect circle, known as a "great circle".

This can be done only if the string is stretched tightly around the full circumference; it will fall off if moved slightly in any direction.

The circle can be oriented in any way, but on a globe with markings, obvious positions are along the equator, or along any meridian, passing through both north and south poles.

A great circle passing through any two points represents the shortest distance between them when traveling along the surface.

This is why plane flights from Los Angeles to Hanoi, which is even farther south, pass near the Aleutian Islands in Alaska.

Rhumb Line:

Imagine you are navigating a ship or plane using only a compass. The simplest and least error-prone method would be to maintain a constant heading throughout the entire trip.

From Portugal, if you continuously sail south-west, you will reach Brazil. It won't be the shortest or fastest route, but it will be the easiest.

The Mercator Projection map (the "evil one", that makes Greenland look larger than Africa) was designed specifically for this purpose. Draw a straight line from your start to your destination and that course will have a constant heading all the way. Without any adjustments along the route, your compass will always indicate the same direction to go.

Every straight line on a Mercator Projection map is a rhumb line.

Except when following the equator (which is both a rhumb line and a great circle), any rhumb line will eventually reach either the north or south pole.

• So do pilots follow rhumb line tracks/great circle routes? Both have their own advantage. Jan 27 '20 at 15:43
• @Johnson, generally great circles are the fastest and shortest routes, and navigation aids such as GPS eliminate the advantages of using the simple rhumb-line method. Pilots will deviate from a strict great circle to make use of high altitude wind (e.g. jet stream) to go faster and to save fuel, and for political reasons (e.g. don't fly over N.Korea). Jan 27 '20 at 16:03

Consider the above airway, Q114.

It's blue (RNAV) so we don't have to account for the setting dates of VOR stations and their often out-of-date magnetic north alignments.

Note how from PECKS to LEONG it's 081°, and the opposite direction it's 269° from LEONG.

That's 188° for a reciprocal!

If you maintained exactly 081° (rhumb line), you'll miss LEONG, as illustrated in @Jpe61's answer. So pilots maintaining a course via a course deviation indicator (CDI), are flying a great circle (straight line on a sphere).

With a track mode on a navigation display, the track will keep changing in straight-and-level flight to become 089° at LEONG.

Put in another way, when you fly along a course, the given track value is only valid from where that track starts, else it keeps changing, because of the Earth's curvature.