Why the shortest flight looks curved on a map

A shortest path along a spherical surface

A great circle is a circle on a sphere whose center is the sphere’s center. Except for exactly opposite endpoints, the shorter arc of the great circle through two points gives the shortest surface path on a perfect sphere. NASA’s navigation discussion explains why an aircraft’s heading changes along that path.

A flat line drawn across a world map is a different construction. The projection can bend a great-circle path when it turns geographic coordinates into screen coordinates. A curved-looking line is therefore not enough evidence that the journey is longer.

Izvori: NASA · Basics of Space Flight: reference systems · NASA · Great-circle navigation near the poles

Constant bearing answers another question

A rhumb line keeps a constant compass bearing. Mercator draws it as a straight line, which is one reason the projection is associated with navigation. A great-circle path generally changes bearing, so its line is generally curved on Mercator.

There are special cases, such as travel along the equator or a meridian. Avoid the shortcut “all flights curve north.” The appearance depends on the endpoints and projection. Distinguish the shortest spherical distance from a constant compass bearing.

Izvori: USGS · Map Projections: A Working Manual (Snyder, 1987)

A diagram is not an airline’s flight plan

The illustration is calculated from approximate city coordinates and a spherical model. It does not record an actual flight, predict the next departure or show that a particular airline follows this exact line. Those claims would need operational evidence.

Real routing has additional constraints, including airspace, weather and operational requirements. A great-circle illustration supplies a geometric reference, not a complete explanation of a flight’s duration. Use it to understand the map before using flight-specific data to explain an actual journey.

Izvori: FAA · Great Circle Route distance definition

Tokyo and New York on one curved surface

Find Tokyo and New York in the illustration. A route near the ends of a flat world map can appear split by the map seam. Rotate a globe toward the Pacific and northern regions to see both cities as locations on one continuous curved surface.

The great-circle arc follows that surface. A route that bends upward on Mercator can still be the short arc on the sphere. Compare the illustration’s curve with a straight line on the page, then consider the spherical route rather than measuring the printed lines.

Izvori: NASA · Basics of Space Flight: reference systems · USGS · Map Projections: A Working Manual (Snyder, 1987)

Common questions