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The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes.Important in navigation, it is a special case of a more general formula in spherical trigonometry, the law of haversines, that relates the sides and angles of spherical triangles.
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 ...
Finding the geodesic between two points on the Earth, the so-called inverse geodetic problem, was the focus of many mathematicians and geodesists over the course of the 18th and 19th centuries with major contributions by Clairaut, [5] Legendre, [6] Bessel, [7] and Helmert English translation of Astron. Nachr. 4, 241–254 (1825).
To find the way-points, that is the positions of selected points on the great circle between P 1 and P 2, we first extrapolate the great circle back to its node A, the point at which the great circle crosses the equator in the northward direction: let the longitude of this point be λ 0 — see Fig 1.
Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods that assume a spherical Earth, such ...
Thus, 32 points of 11.25° each makes a circle of 360°. An object at 022.5° relative would be 'two points off the starboard bow', an object at 101.25° relative would be 'one point abaft the starboard beam' and an object at 213.75° relative would be 'three points on the port quarter'. This method is only used for a relative bearing.
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9, 10 - Effects of crosswind and tidal current, causing the vessel's track to differ from its heading. A, B - Vessel's track. TVMDC,AW is a mnemonic for converting from true heading, to magnetic and compass headings. TVMDC is a mnemonic initialism for true heading, variation, magnetic heading, deviation, compass heading, add westerly. The most ...