Great circle vs rhumb line — why the shortest route looks longer
Two routes between the same two points
Imagine flying from Warsaw to New York. You might think it is enough to draw a straight line on the map and follow it. But on a sphere there are two completely different "straight" routes between any two points — and which one is actually the shortest depends on the map you are looking at.
The first is the great circle (orthodrome), the shortest possible path across the surface of a sphere. The second is the rhumb line (loxodrome), a route along which you always travel at the same angle relative to north. These two lines coincide only in special cases (for example along the equator or a meridian). In every other situation they differ, and the gap can reach hundreds of kilometres.
The rhumb line: convenient for sailors, made for Mercator
For centuries navigators loved the rhumb line because it is trivially easy to use: set a constant compass bearing and hold it all the way to your destination — no constant course corrections required. That is exactly why the Mercator projection was created in 1569 — Gerardus Mercator designed it so that every rhumb line appears as a perfectly straight line on the map. You simply laid a ruler between your port of departure and destination, read the angle and sailed.
That convenience comes at a price. A rhumb line is almost never the shortest route. By holding a constant bearing you trace a spiral that creeps toward the pole (the loxodromic spiral) and cover more distance than you need to. For short trips the difference is negligible, but over intercontinental distances it grows dramatically.
The great circle: shortest, but "curved" on a flat map
A great circle is an arc of a circle whose centre coincides with the centre of the Earth. It defines the genuinely shortest route. The catch is that on the Mercator map the great circle is not straight — it bows into an arc that swings toward the pole. That is why a flight path from Europe to North America looks, on a flat map, as if the plane pointlessly detours north over Greenland. In reality it is flying the shortest possible path — the map is deceiving you.
On the globe (orthographic projection) the roles reverse: there the great circle becomes visually straight and obvious, while the rhumb line looks bent. This is the clearest proof that the "straightness" of a route is not a physical property but an artefact of the chosen projection — exactly as we described in why all maps lie.
How big is the difference, really?
Take the classic example: Warsaw – New York. The great circle is about 6,860 km, while the rhumb line between the same endpoints is several hundred kilometres longer. On transpacific routes (for instance from South America to East Asia) the difference can exceed a thousand kilometres — in practice an extra hour of flight time and tonnes of burned fuel. That is precisely why airlines and shipping plan their journeys along the great circle, adjusting the heading periodically.
Test it yourself
The theory is easiest to grasp by seeing it move. We built an interactive tool: the great circle vs rhumb line comparison. You can pick any two cities (or click your own points on the map) and switch the map projection. You will watch the straight rhumb line contrast with the arcing great circle on Mercator, then see everything flip by 180 degrees once you switch to the globe. The tool also shows by what percentage the rhumb line is longer than the shortest route.
Once these two curves feel familiar, look again at any in-flight route map — those "strange arcs" over the Arctic will stop being a mystery and become proof that the Earth really is a sphere.