Why flight paths curve: great circles on a flat map
The shortest way between two airports is a great circle, which on most maps looks like a bend. Why that is, how much it saves, and why real tracks still leave it.
Published by Overfly ·
Draw New York to London as a straight line on a wall map and it runs almost due east, a little north. The aircraft does not fly it. It sets off north-east, crosses Nova Scotia and Newfoundland, and comes in over Ireland heading east-south-east. On the map that looks like a detour. On the globe it is the shortest way there.
The shortest path between two points on a sphere is an arc of a great circle: a circle whose centre is the centre of the Earth, like the equator or any meridian. Every pair of airports has exactly one great circle through them (two, if they are exactly opposite), and the shorter of its two arcs is the route Overfly draws.
Why it looks bent
A flat map cannot keep both distances and directions true. The familiar Mercator map keeps compass directions straight, so a line of constant bearing, a rhumb line, is drawn straight on it. A great circle crosses each meridian at a different angle, so on Mercator it bows towards the nearer pole.
The difference is real distance. New York JFK to London Heathrow is 2,991 nm on the great circle, with an initial bearing of 051°. Holding one constant bearing the whole way, the rhumb line, is 3,109 nm: 118 nm, about a quarter of an hour, further. The heading also changes along the great circle; leaving Heathrow for New York the initial bearing is 288°, not the reverse of 051°.
The effect grows with distance and latitude. New York to Hong Kong is 7,003 nm on the great circle, which leaves JFK on 352°, nearly due north, and crosses the Arctic. The constant-bearing line would be 8,826 nm, more than 1,800 nm longer. That is why the polar routes exist: on a globe, over the top is the direct way.
Overfly's map can also show a route on an azimuthal equidistant projection (the AZ EQ switch). That projection keeps distances and directions true from its centre point, and every great circle through the centre is drawn as a straight line.
Why real tracks still leave it
The great circle is the shortest route over the ground, not always the quickest through the air. Across the North Atlantic the tracks are drawn each day by the Shanwick and Gander oceanic centres to follow or avoid the jet stream, so an eastbound flight may sit well north or south of the great circle to ride a tailwind. Overfly's wind guide shows how much that wind is worth.
Other reasons are less visible: closed or costly airspace, the need for a twin-engine aircraft to stay within reach of an alternate (see equal-time points and ETOPS), and departure and arrival procedures that add miles at each end. The great circle is the floor, the figure every real route is measured against.
How Overfly measures it
Distances on Overfly are great circles on a sphere of mean Earth radius (3,440 nm), between airport coordinates from OurAirports. The sphere is within about half a percent of the true ellipsoid for any airline distance, and it lets every figure be worked the same way on the server and in your browser. Bearings are true, not magnetic, and the one given is the initial bearing: on a great circle the heading changes the whole way.