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rhumb line[′rəm ‚līn]
a line on a sphere or other surface of rotation that cuts across all meridians at a constant angle K (see Figure 1). The rhumb line and orthodrome (great circle) on a sphere were introduced and studied in 1624 by W. Snell. On a sphere and oblate ellipsoid of rotation where K = 0° and K = 180°, a rhumb line coincides with a meridian; where K = ±90°, it coincides with a geographic parallel. In other cases it has the shape of a spiral: making an infinite number of convolutions on the surface, it comes infinitely close to the poles. On maps using the Mercator projection all rhumb lines are shown by straight lines.
The rhumb line is used extensively in maritime and air navigation, where the angle K is treated as the true course of the ship or aircraft. The use of a rhumb line instead of a great circle, which is the shortest distance between two points on a sphere, is determined by practical convenience in controlling a ship or aircraft, even though the route is longer in this case. Where K≡ 0° (or 180°) the difference in lengths of a rhumb line and a great circle that connect two given points is proportional to the distance between the points and the distance from the equator. Rhumb lines are sometimes used in spheroidal geodesy. The isogonal trajectories of a given family of curves on random surfaces are a very generalized form of the rhumb line.
REFERENCEKavraiskii, V. V. Izbr. trudy, vol. 2, fasc. 2. [Moscow] 1959.
G. A. MESHCHERIAKOV