GB454654A - A great circle graphic calculator for use in solving problems in navigation and astronomy - Google Patents

Abstract

454,654. Calculating-apparatus. KEEBLE, A. T., and DEE, J., 55, Charles Street, Greenwich, Sydney, Australia. Jan. 3, 1935, Nos. 235 and 16384. [Class 106 (i)] Spherical trigonometry calculators.-A graphic calculating device for use in solving problems in navigation, astronomy, and geology comprises a chart formed of a sheet of material having inscribed thereon a line representing on a known system of projection a selected great circle of reference such as a prime meridian orthogonally cut by a family of curves representing a series of great circles which are rational horizons for selected points on the circle of reference, and another set of curves representing azimuths. The chart is divided into two zones forming equatorial and polar regions and is provided with a radial arm pivoted at a point representing a pole and carrying a latitude or declination scale and a vernier adapted to co-operate with a scale of longitude or hour angle. The device is used in conjunction with other sheets bearing representations of the relative positions of terrestrial and celestial objects. To the points on the chart are assigned values which satisfy the equation tan F=Sec. W tan A where A equals the azimuth angle, F the hour angle or terrestrial longitude and W the latitude. The chart as shown in Fig. 1 is formed by placing a sheet of paper tangent at the pole P to a sphere of reference (radius R) and projecting from the centre a line X to represent the central meridian trace. Distances are marked off along this line equal to R cot W to a point B (say 12‹) representing one zone of the chart. Through these points lines Y are drawn at right angles to the line X representing rational horizons. The lines Y are graduated by projecting from the centre and the central meridian the points at intervals A‹ on the great circles corresponding to the latitudes, thereby forming the azimuthal curves Z. The distances are given by the equation x = R cosec W tan A. To complete the chart for equatorial regions or low latitude a cylindrical wall is dropped from the circle U of radius r = R Cot B. The central or gnomonic projection is made on this wall and the wall is laid over outwards and stretched circumferentially. The radius to the boundary T is equal to R cot B+R and the boundary is subdivided into degrees to form a scale F. Consider any radius the rational horizon traces will intersect this radius from the circle T at distances y=R Cot B Cos F tan W. These traces converge to equatorial nodal points where F = 90‹. The azimuthal extensions Z<1> can be determined from the general equation. The gnomonic chart may be used to construct a chart on any other system of projection, for example the Mercator projection by utilizing the radial arm Q and ascertaining by inspection the latitude and longitude co-ordinates of points at intervals along any number of course traces. A Mercator chart N is shown in Fig. 4 with rational horizon traces forming curves Y and azimuthal lines forming curves Z. Examples of the use of the device are described in the Specification. Specification 414,308 is referred to.