Line of Position

in navigation and geodesy, a line at all points of which a quantity measured by observations to determine the position of the observer on the earth’s surface has the same magnitude as at the observation point. Such quantities may be the distance between the reference point and the unknown point (the line of position is a circle); the elevation of a heavenly body at some point in time (also a circle); the azimuth of the direction from the reference point to the unknown point (a great circle course); or the azimuth of the direction from the unknown point to the reference point (a spherical curve of the fourth order). The intersection of two or more lines of position drawn on a map makes it possible to determine the location of the observer.

in navigation and geodesy, a line at all of whose points some quantity, measured to determine the observer’s position on the earth’s surface, has the same value as at the point of observation. Such quantities may be

(1) the distance r between a known (reference) point and the unknown position, in which case the line of position has the form of a circle of radius r circumscribed about the reference point;

(2) the zenith distance z or altitude h of a celestial body at some instant, in which case the line of position is also a circle circumscribed on the surface of the terrestrial globe with a spherical radius z = 90 — h about the celestial body’s geographical position, that is, the point at whose zenith the body was located at the time of observation;

(3) the azimuth A of the bearing from the reference point to the unknown position, in which case the line of position is an orthodromics, that is, a great circle circumscribed on the surface of the terrestrial globe and passing through the reference point in a direction corresponding to the azimuth A;

(4) the azimuth from the unknown position to the reference point, for example, a radio bearing from a ship or aircraft to a radio beacon, in which case the line of position is a fourth-order spherical curve on the earth’s surface, or an isoazimuth.

Lines of position are constructed on a geographic map from observational data and indicate the observer’s position. For complete determination of a position, it is necessary to construct at least two lines of position, whose intersection corresponds to the unknown location. Here, to ensure a reliable determination, both lines of position must intersect at an angle that is not too acute—at least 30°. If the lines of position have several, usually two, points of intersection, it is not difficult to select the necessary point, since the approximate location of the point of observation is usually known. For the same reason, observers often restrict themselves to constructing only a short segment near the approximate position of the observer rather than an entire line of position. This segment is replaced with the tangent to the line of position.

Lines of position are used extensively in navigation and aviation to determine the position of a ship or aircraft from the observed altitudes of two celestial bodies. This method was first published by the American sailor T. Sumner in 1843. Such celestial lines of position are called Sumner lines. A convenient, simple method of calculating and constructing these curved lines on a map was demonstrated in 1849 by the Russian sailor M. A. Akimov. Since the late 19th century, celestial lines of position have been calculated and constructed by an even more convenient method proposed by the French sailor M. St.-Hilaire in 1875.

A generalization of the line-of-position method was made by the Soviet scientist V. V. Kavraiskii. The application of lines of position to the equalization of geodetic measurements has been worked out in detail by the Soviet scientist N. G. Kell’.