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For example, to find the midpoint of the path, substitute σ = 1 ⁄ 2 (σ 01 + σ 02); alternatively to find the point a distance d from the starting point, take σ = σ 01 + d/R. Likewise, the vertex, the point on the great circle with greatest latitude, is found by substituting σ = + 1 ⁄ 2 π. It may be convenient to parameterize the ...
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.
The slant distance s (chord length) between two points can be reduced to the arc length on the ellipsoid surface S as: [21] = (+) / / where R is evaluated from Earth's azimuthal radius of curvature and h are ellipsoidal heights are each point. The first term on the right-hand side of the equation accounts for the mean elevation and the second ...
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 between the two points on the surface of the sphere. (By comparison, the shortest path passing ...
Navigation that follows the shortest distance between two points, i.e., that which follows a great circle. Such routes yield the shortest distance between two points on the globe. [16] To calculate the bearing and distance between two points it is necessary to solve a spherical triangle whose vertices are the origin, the destination, and the ...
In Euclidean geometry, a straight line represents the shortest distance between two points. This line has only one length. This line has only one length. On the surface of a sphere, this is replaced by the geodesic length (also called the great circle length), which is measured along the surface curve that exists in the plane containing both ...
Over longer distances and/or at higher latitudes the great circle route is significantly shorter than the rhumb line between the same two points. However the inconvenience of having to continuously change bearings while travelling a great circle route makes rhumb line navigation appealing in certain instances.
In seafaring, under keel clearance (UKC) is the height between seabed and the keel or hull of a ship. [ 1 ] [ 2 ] [ 3 ] It is used to ensure sufficient navigable water is available for ships at sea. [ 4 ] [ 5 ] [ 1 ] [ 6 ] It is most commonly defied as Master mariners should ensure there is sufficient minimum UKC for their ships ; ports should ...