Cartographic Projection
every map is wrong, and by exactly how much
Concept

Composite method — where it appears

A projection assembled from more than one construction, joined along stated parallels. Goode's homolosine is the standard example, using the sinusoidal near the equator and Mollweide beyond it, and the join is continuous in position and not in derivative.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

London to Tokyo, seen four ways. The same two routes on four projections. The gnomonic projection renders every great circle as an exactly straight line, which is what it is for; Mercator renders every rhumb line straight instead. Neither path changed — only the map did.

The gnomonic companion

One projection turns every great circle into a straight line, and it is the only one that does. It shows less than half the sphere, distorts enormously, and was indispensable for three centuries because of that single exact property.

paths · Paths London to Tokyo in three straight legs. The great circle, and the route a plan of three constant-heading legs actually follows between waypoints on it. The two touch at the waypoints and part between them by up to 456 km, and the flown route is 253 km longer than the direct one. The headings are 50°, 109°, 149°. Two routes. The great circle is 9559 km and is the shortest path on the sphere. The rhumb line holds a single compass bearing the whole way and is 11296 km — 1737 km further, or 18.2 per cent. On Orthographic the rhumb line departs from straight by 2.4e-1 of its own length.

Flying a curve in straight legs

Nobody steers a great circle, because a great circle requires the heading to change continuously. What is actually flown is a handful of constant-heading legs between waypoints on it, and the gap between plan and curve falls as the square of the number of legs.

paths · Paths

Named alongside it

The objects these essays reach for when they reach for this one.

Great circleMercatorNavigationAzimuthalBearingCross-track errorGnomonicGraticuleLoxodromeQuadratic lawRhumb lineRoute planning

All concepts