Why Airlines Fly in Arcs? Great circle vs rhumb line

Invisible Arcs in the Sky

If you have ever flown from London to New York and tracked the flight path on the screen in front of your seat, you might have noticed something strange. The plane does not fly in a straight line across the Atlantic Ocean. Instead, it heads northwest, flying over Iceland and southern Greenland, drawing a distinct arc on the map. Why do airlines waste fuel on a longer route? The truth is... they don't. This curved line is the shortest path on Earth.

Spherical Geometry: Great Circle vs Rhumb Line

The key to solving this riddle lies in two geometric concepts:

• Great Circle (Ortodroma): The shortest distance between two points on the surface of a sphere. Its center coincides with the center of the Earth. On a flat Mercator map, a great circle path always appears as a curved arc.
• Rhumb Line (Loksodroma): A line crossing all meridians at the same angle. On a Mercator map, a rhumb line is represented as a straight line. While it makes compass navigation easy, it is a longer path than a great circle.

This difference increases the further you move from the equator. For example, flying in a straight line on a flat map from London to Tokyo would be thousands of kilometers longer than a great circle flight passing over Siberia.

Why Airlines Choose the Great Circle

In commercial aviation, every kilogram of fuel counts. Selecting a great circle route saves thousands of gallons of jet fuel and cuts flight times by dozens of minutes. Although on a flat map this path looks longer (because the Mercator projection stretches northern latitudes, making the arc look huge), in 3D reality, it is a straight line.

To better understand this, view our planet under the Orthographic projection (globe view). On a 3D globe, a great circle is a straight line connecting two cities, while the straight path from a Mercator map (rhumb line) turns out to be distorted. Test it yourself in our sandbox: true size comparison map.