Calculation of lengths, distances and areas

Use of GIS for calculation of distances, lengths, areas and angular sizes allows to receive the most exact results which should be identical in any projections for the same geodetic coordinates of processed points.

Topographic maps have the least distortions of linear and angular sizes in the territory limited on a longitude. Topographical maps have Gauss-Kruger projection, which mathematically are described by the same formulas, as projection of Universal Transverse Mercator (UTM). Formulas of projections are given in GOST Р 51794.

To determine the length and azimuth of the segment having a known geodetic coordinates of extreme points, you must first perform coordinate transformations into the plane rectangular coordinates on a topographical map. Accuracy of calculations is influenced essentially position of the central meridian chosen for conversion. At removal of points from central meridian the error of calculations will increase. At a distance up to three degrees from the central meridian the error will be about 1: 1 500 - 1: 2000.

To minimize the distortion the position of central meridian is chosen in the center of the segment, and the scale on the central meridian (Scale Factor) equals 1. Thus, the length of each segment is defined in its own projection. If the segment has length of several degrees on a longitude, expediently division of the segment into some parts on a line of an orthodrome - a geodetic line of the shortest distance on a surface of rotation.

Thus, calculations of lengths, distances and azimuths can be done. The direction angle has its own value in each projection, as it is calculated concerning a vertical line of a rectangular grid of coordinates in the specified projection.

Calculating the area of the object, having on a longitude the extent within 6 degrees, is carried out by recalculation of coordinates to a topographical map with an axial meridian in the center of dimensions of object.

To obtain corrected values of lengths, distances and areas it is necessary in the Options menu to choose the item Specify area and length. After that the results of calculations in tasks Map Computer, Map Editor, dialog Select Object and others - will give more exact values. If this item is not set, calculations are carried out by available coordinates of objects without additional transformations.

It is necessary to consider, that displayed flat rectangular and geodetic coordinates of objects depend on current parameters of a projection and the chosen system of displaying coordinates, and calculations of lengths and the areas without specification of values are carried out by coordinates of the objects stored according to parameters of the map passport.