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A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...
The actual flight length is the length of the track flown across the ground in practice, which is usually longer than the ideal great-circle and is influenced by a number of factors such as the need to avoid bad weather, wind direction and speed, fuel economy, navigational restrictions and other requirements.
Great-circle navigation or orthodromic navigation (related to orthodromic course; from Ancient Greek ορθός (orthós) 'right angle' and δρόμος (drómos) 'path') is the practice of navigating a vessel (a ship or aircraft) along a great circle. Such routes yield the shortest distance between two points on the globe. [1]
The disk bounded by a great circle is called a great disk: it is the intersection of a ball and a plane passing through its center. In higher dimensions, the great circles on the n-sphere are the intersection of the n-sphere with 2-planes that pass through the origin in the Euclidean space R n + 1. Half of a great circle may be called a great ...
(East-west paths form a circle in both disk and spherical geometry.) It is possible in this model to traverse the North Pole, but it would not be possible to perform a circumnavigation that includes the South Pole (which it posits does not exist). The Arctic Circle is roughly 16,000 km (9,900 mi) long, as is the Antarctic Circle. [23]
The most common standard flight length measurement is by great-circle distance, a formula that calculates the shortest distance across the curvature of the earth for two airports' ARPs. [5] It is the only measurement that is constant on a given city-pair route and unaffected by operational variances. [6]
The distance from the center point to another projected point ρ is the arc length along a great circle between them on the globe. By this description, then, the point on the plane specified by ( θ , ρ ) will be projected to Cartesian coordinates:
The shortest distance along the surface of a sphere between two points on the surface is along the great-circle which contains the two points. The great-circle distance article gives the formula for calculating the shortest arch length on a sphere about the size of the Earth. That article includes an example of the calculation.