Why do airlines fly in arcs? Great circle vs rhumb line
Why does a flight route look curved on a map? Learn about great circles, rhumb lines and the difference between a shortest spherical path and a real flight.
Why does the map show an arc?
On a Mercator map, the shortest spherical path between Warsaw and New York looks like an arc bending north. That does not mean taking a detour. Its appearance comes from transferring a curved surface to a flat map. It does not, however, tell you which countries a particular flight will pass over.
Great circles and rhumb lines
To compare the routes, let us use a simple model of the Earth as a sphere:
Which is larger in reality: Africa or Greenland?
- Great-circle route: The shortest path between two points on the surface of a sphere follows the shorter arc of a great circle. The centre of that circle is the centre of the sphere. On a standard Mercator map, this route is usually curved. Routes along the equator and meridians are straight exceptions.
- Rhumb line: A route at a constant angle to geographic north. On a Mercator map it is straight. It is no shorter than the great-circle route. Along the equator or a meridian, the two routes can coincide and have the same length.
A great-circle arc remains curved in three-dimensional space. A straight segment between two surface points would pass through the interior of the sphere. Changing the map changes the appearance of the route, but not its actual length.
The shortest path and a real flight
A great-circle route is a useful reference when comparing distances. An actual flight path also depends on winds, weather, available airspace and air traffic control requirements. With favourable winds, a longer path over the Earth can mean a shorter flight time or lower fuel use.
The distance difference between a great-circle route and a rhumb line alone is therefore not enough to calculate fuel or time savings. The result depends on the particular route, aircraft and conditions. A sphere is also an approximation of the shape of the Earth.
See what a projection changes
In the route lab, compare both paths between Warsaw and New York. Then select the gnomonic projection: the displayed great-circle segment becomes straight. In an orthographic view, which resembles a globe, only great circles through the centre of the view appear straight.