Distância de Voo (Haversine)

Great circle flight distance: the Haversine formula

A flight tracks the great circle, the shortest geodesic over the sphere, rather than the straight line you'd draw on a flat map. To find the distance between two points on a sphere you reach for the Haversine formula: d = 2R · asin(√(sin²(Δφ/2) + cos φ₁ · cos φ₂ · sin²(Δλ/2))), with R ≈ 6371 km as Earth's mean radius, φ the latitude and λ the longitude. A couple of examples: GRU (São Paulo) to JFK (New York) comes out to ≈ 7,681 km, and GIG (Rio) to LIS (Lisbon) to ≈ 7,700 km. A Boeing 787-9 ranges about 14,000 km, so it covers either one without breaking a sweat.

Applications

It comes in handy for aviation planning (FAA, ANAC, ICAO), estimating frequent flyer miles, weighing flight options between hubs, and quick back-of-the-envelope route checks. Keep in mind that the actual flown distance often runs 3–10% longer: real routes stick to airways, steer clear of conflict zones, route around volcanic ash and bad weather, and play the jet streams, with eastbound flights frequently bending their path to catch a tailwind.

FAQ

Why doesn't the route look straight on a flat map? Mercator projections bend the lines. Spin a globe instead and you'll see the great circle from NY to Tokyo arcing up near the Arctic, which is the whole reason polar routes exist.

How precise is Haversine? For most flights it lands within about 0.5%. Earth is really an ellipsoid rather than a perfect sphere, and Vincenty's formula accounts for that, but it's far more than civil aviation needs.

What's the difference between nautical miles and km? One NM equals 1.852 km. Aviation and maritime stick with NM by international convention.