061 General Navigation topic guide
Great Circles vs Rhumb Lines
A great circle is any circle drawn on the Earth's surface whose plane passes through the centre of the Earth, and the great circle track between two points is always the shortest distance between them. A rhumb line, in contrast, is a track that crosses every meridian at the same angle, so it holds one constant heading from departure to destination, at the cost of being, in general, a slightly longer path than the great circle joining the same two points.
The two lines only coincide along the equator and along any meridian, because those are the only tracks that are simultaneously a great circle and a line of constant heading. Everywhere else the great circle bows away from the rhumb line towards the nearer pole, which is why a long-range route still curves noticeably towards higher latitude even when it looks like a simple straight line on some charts.
Why the great circle is the shorter path
Picture a piece of string pulled taut between two points on a globe: it settles along the great circle, because that is the only track whose plane cuts through the planet's centre and therefore the only one that never bends away from the straight-line distance through three-dimensional space. A rhumb line, by holding a constant compass heading, spirals gently towards the pole on that side of the equator, which is a longer route between the same two points except in the two special cases already mentioned.
The size of the gap between the two distances depends on how far apart the points are and how far they sit from the equator. Over a short regional sector the difference is a rounding error, which is why plotting a straight line on a chart is good enough in practice for a domestic flight. Over an ocean crossing at higher latitude the gap becomes large enough that operators plan and fly close to the great circle rather than a single rhumb line heading.
How the two tracks look on a chart
On a Mercator chart a rhumb line is always a straight line, which is exactly why early navigators favoured that projection: a single course, ruled once, could be held all the way. The trade-off is that a great circle on the same chart appears as a curve bulging towards the pole, because Mercator stretches high latitudes so much that a track which is genuinely straight over the sphere is dragged out of shape on the flat page.
A Lambert conformal conic chart flips that relationship for the latitudes it is built around: a great circle plots as very close to a straight line, which is the whole reason Lambert charts are the standard for plotting and flight planning at mid and high latitudes, while a rhumb line on the same chart curves very slightly away from it, bowing towards the equator.
Choosing which one to fly
Long-haul planning traditionally broke a great circle into a series of rhumb-line legs, each flown on a single constant heading, so that the overall route hugged the shorter great-circle distance while still being flyable leg by leg with a compass. Modern area navigation equipment simply flies the great circle continuously, but the underlying reason for choosing it, that it saves track distance and therefore fuel and time, has not changed.
Worked example
Worked example: which line lies closer to the pole
Not quite. The correct answer is B.
Correct answer: B
- A. This assumes a constant track is also the shortest track. Holding one heading is a convenience of flying the rhumb line, not evidence that it is the shorter path.
- B. Correct: the rhumb line between two points on the same parallel is that parallel itself, and the shorter great circle must bow towards the nearer pole, so it runs north of 60N for most of its length.
- C. This is only true at the equator. Away from the equator a parallel of latitude is not a great circle, so the two tracks still diverge.
- D. This reverses the geometry. The great circle always bulges towards the nearer pole, never towards the equator, when the two points share a latitude off the equator.
Step by step
- Because X and Y lie on the same parallel of latitude, the rhumb line joining them, a line crossing every meridian at a constant angle, is that parallel itself, since a parallel crosses every meridian at a constant 90 degrees.
- A parallel of latitude other than the equator is not a great circle, because its centre does not coincide with the Earth's centre, so it cannot be the shortest path between X and Y.
- The great circle joining two points on the same non-equatorial parallel must bulge towards the nearer pole to be shorter than the parallel route, so it lies further north than 60N along most of its length.
- Only at the equator would the parallel and the great circle be the same line, because the equator's centre is also the Earth's centre.
Common mistakes
Assuming a constant heading also means the shortest distance
The rhumb line's one advantage is ease of flying, not distance. Treating 'constant track' as a synonym for 'shortest track' is the most common conceptual slip on this topic and directly contradicts the definition of a great circle.
Expecting two points on the same parallel to share one identical line
Away from the equator the parallel is the rhumb line but not the great circle, so a question that places two points on the same non-equatorial parallel is deliberately testing whether the two tracks are known to still diverge.
Placing the great circle's bulge on the wrong side of the rhumb line
The great circle always bulges towards the nearer pole, never towards the equator. Getting the direction backwards flips the answer on any question asking which line lies further north or south.
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Last reviewed July 2026