Great circle vs Rhumb line

The shortest path on the globe (great circle) and a constant-bearing route (rhumb line) look completely different depending on the projection. Pick a route and a projection to see the contrast.

Map projection:

Pick cities:

You can also click any two points on the map to trace your own route.

Example routes:

Great circle (orthodrome — shortest path)

Rhumb line (constant compass bearing)

Great-circle distance6,854 km

Rhumb-line distance7,349 km

The rhumb line is 495 km (7.2%) longer

Why do the routes differ?

On the Mercator map the rhumb line (a line of constant bearing) is perfectly straight — which made it handy for navigation. But the actual shortest path is the great circle, which on Mercator curves in an arc towards the pole. On the globe and azimuthal projections it's the reverse: the great circle becomes the straight one.

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