Flight paths look curved on a map because the map is flat and the Earth isn't. The shortest route between two points on a sphere is a great circle, a line that, if you kept going, would wrap all the way round the globe through its centre. Drawn on a flat map, great circles bend toward the poles, so a flight from New York to Tokyo swings up over Alaska rather than heading straight west.
The straight line that isn't
Most world maps use the Mercator projection or something like it, which stretches the far north and south to keep shapes right locally. On a Mercator map a straight line is a route of constant compass heading, called a rhumb line. It's easy to steer, which is why sailors loved it, but it isn't the shortest path. The great circle is, and the difference can be enormous:
| Route | Great circle | Straight on the map | Extra | Furthest point from the equator |
|---|---|---|---|---|
| New York – London | 5,540 km | 5,758 km | +4% | 54° N |
| London – Los Angeles | 8,760 km | 9,732 km | +11% | 62° N |
| New York – Tokyo | 10,875 km | 12,817 km | +18% | 70° N |
| Frankfurt – San Francisco | 9,149 km | 10,536 km | +15% | 67° N |
| Dubai – Los Angeles | 13,400 km | 16,803 km | +25% | 85° N |
| Sydney – Santiago | 11,340 km | 12,774 km | +13% | 62° S |
Worked out from each airport's coordinates. The great circle from New York to Tokyo reaches 70° N, well north of both cities.
See it with a string and a globe
Take a globe and stretch a piece of string tight between London and Los Angeles. The string, the shortest path, runs up over Greenland and Canada's north. Now flatten the globe into a map in your head: the string's path becomes an arc bulging north. Nothing about the flight curves; the map does.
Why real routes aren't perfect great circles
- Winds. Flying with a jet stream can be faster than flying the shortest path against it. Transatlantic tracks are re-planned every day to ride the winds; see why flying east is faster.
- Airspace. Some countries' airspace is closed, restricted or expensive, which forces detours.
- Twin-engine rules. Long over-water routes must stay within a certain flying time of a diversion airport, which can bend tracks toward land.
- Air traffic control, weather systems and airport approach routes add the rest.
That's why the UK government's emission factors, for instance, assume real flights are a little longer than the great circle.
Measure any route
The flight distance calculator gives the great-circle distance between any two airports, with the initial heading, the midpoint and a map of the arc. To see everywhere within a few hours along those arcs, try Where can I fly?. In Flight, your plane flies the great circle too, from your nearest airport to wherever you choose, for as long as you focus.