Why don't planes fly in a straight line?

Most maps we look at flatten the Earth using projections like Mercator's, which exaggerate high latitudes. In that representation, the shortest distance between Madrid and New York looks like a horizontal line, but on the real globe the minimum path is a great-circle arc, the one obtained by cutting the sphere with a plane through its center. That arc bends northward in the northern hemisphere, so a transatlantic flight passes over Newfoundland and skirts Greenland. On a flat map that path is perceived as a curve, even though for the aircraft it's the most direct trajectory possible. The savings aren't trivial: on long routes, the difference between the great circle and the straight line on the map easily exceeds several hundred kilometers.

Even with that geometric correction, almost no commercial flight follows the great circle exactly. Airspace is organized into airways, corridors defined by radio navigation aids and five-letter reporting points, and into departure and arrival procedures that funnel traffic toward airports. The flight plan chains those segments together, and air traffic control can add holds, radar vectors, or level changes to maintain separation. Over the oceans, where there's no continuous radar coverage, organized track systems are published daily, grouping traffic into parallel lanes; the North Atlantic tracks change every day depending on the position of the jet stream.

An airliner cruises at around 900 km/h (485 kn) relative to the air, but what matters is the speed relative to the ground. The jet stream, a band of wind at 9-12 km altitude that can exceed 250 km/h, makes it worthwhile to deviate tens or hundreds of kilometers to ride it eastbound or dodge it westbound. Dispatchers calculate the lowest-cost route every day by combining time, fuel, and overflight fees, and that route rarely matches the geodesic. Areas of forecast turbulence, convective storms, and volcanic ash are also routed around, sometimes with diversions planned hours before takeoff.

Airspace isn't uniform. There are military zones, prohibited areas, and countries whose overflight is closed off due to conflicts or diplomatic decisions, forcing detours that lengthen routes between Europe and Asia. Twin-engine aircraft, which today make up the vast majority of long-haul airliners, must also stay within a maximum flying time to a diversion airport with one engine inoperative, the so-called ETOPS rules. In remote areas of the Pacific or the Arctic, that requirement shifts the route toward islands or coastlines with suitable runways. The result of all these layers, geometry, traffic, wind, and regulation, is a trajectory that looks whimsical on the map but follows the logic of safety and cost per mile flown.