Why flight paths look curved on a map

Draw a line between London and Los Angeles on a wall map and it runs west, across the Atlantic, roughly level with the top of Spain. Track a real flight between them and it goes nowhere near there. It heads north-west, crosses Ireland, Iceland and the southern tip of Greenland, comes down over Hudson Bay, and only turns south somewhere over the Canadian prairies.

The aircraft is not going the long way round. The map is lying.

The map is the problem

Almost every flat world map you have ever seen is some variation of the Mercator projection, which was designed in 1569 for navigation by sea. Its great virtue is that a constant compass bearing is a straight line on the chart. Its great vice is that it must stretch the world horizontally as you move away from the equator — enormously so, near the poles.

Greenland is the famous casualty. On a Mercator map it looks comparable to Africa. In reality Africa is around fourteen times larger. What the projection is doing to Greenland's shape, it is also doing to every route that passes near it: squashing a short path into something that looks like a long detour.

Great circles

On a sphere, the shortest distance between two points lies on a great circle — a circle whose centre is the centre of the Earth. The equator is one. Every line of longitude is one. Lines of latitude, apart from the equator, are not, which is why flying "straight along" a latitude is usually the long way round.

Take a globe and a piece of string, and pull it taut between London and Los Angeles. The string will cross Greenland. That is the real answer, and the curve you see on a flight tracker is that answer drawn on a distorted map.

The effect is strongest for long routes at high latitudes. A flight from London to Rome barely curves at all. A flight from New York to Hong Kong goes almost directly over the North Pole, and looks on a flat map like a wild misjudgement.

What actually bends the route further

Great circles set the ideal. Several things pull real flights away from it.

The jet stream. A band of fast-moving air, generally west to east across the northern hemisphere, often exceeding 150mph. Eastbound flights climb into it to save fuel and time; westbound flights deliberately avoid it. This is why the same route is routinely an hour shorter in one direction, and why the two directions often take visibly different paths.

Airspace. Routes bend around closed or restricted airspace, and around countries an airline cannot overfly. These constraints move with geopolitics, and long-haul maps change with them.

Diversion rules. Twin-engined aircraft crossing oceans must stay within a certified flying time of a suitable airport — the ETOPS rules. This keeps some routes closer to Iceland, the Azores or the Aleutians than pure geometry would.

Why it matters if you are guessing

If you see an aircraft overhead and want to reason about where it is going, the bearing is genuinely informative — but only if you think on a globe rather than a map. An aircraft over Ireland heading north-west is not going to the middle of the Atlantic. It is very likely going to the west coast of North America.

That is the reasoning Where To is built around. The daily puzzle shows you a short section of an aircraft's actual course on a globe, deliberately cut short of both ends, and asks you to work outwards from it.