Coordinate Systems and Triangulation

The rotational motion of the earth spinning on its axis provides two natural points, the poles, upon which to base coordinate systems. These systems are networks of intersecting lines (graticules) inscribed upon the globe to permit the precise location of surface features. They are a method of organizing the concepts of direction and distance so that a comprehensive system of relationships can be established. Two types of systems are in general usage for reference mapping: a geographical coordinate system which uses lines of longitude and latitude to fix positions, and a rectangular coordinate system, such as the Universal Transverse Mercator (UTM) Grid System, which uses eastings and northings as the locational technique. Navigation charts, in contrast to their terrestrial partner, the topographic map, may be overlaid with another geo-referencing system, the Loran-C network lattice.

The principle of triangulation Figure 1

A great and a small circle Figure 2

The terminology associated with coordinate systems includes the following:

i) Great circle: A plane passing through the centre of the earth cutting the surface in a great circle (Figure 4.2), e.g., all meridians and the equator. An arc of a great circle is the shortest distance between two points on the earth's surface;

ii) Small circle: A plane passing through the earth, other than through the centre (Figure 4.2), e.g., parallels of latitude;

iii) Poles: Terminii (north and south) of the earth's axis;

iv) Meridians (lines of longitude): A set of north-south lines connecting the poles. Each meridian is half a circle. Two opposite meridians make a great circle (Figure 4.3);

v) Equator: The only great circle perpendicular to the earth's axis, and dividing the earth into northern and southern hemispheres;

vi) Parallels (lines of latitude): A set of east-west lines running parallel to the equator (Figure 4.3);

vii) Latitude: The angle (north and south) subtended by two imaginary straight lines, one extending from a given place inwards to the earth's centre, and the other from the earth's centre to the equator (Figure 4.4);

viii) Longitude: The angle (east or west of the prime meridian) subtended by two imaginary straight lines, one extending inwards to the earth's axis, and the other from the earth's axis to the prime meridian (PM), i.e. the meridian chosen for 0° which passes through Greenwich, U.K. (Figures 4.4 and 4.5). Going east from the PM, the meridians are numbered up to 180° East (the eastern hemisphere). Going west from the PM, the meridians are numbered up to 180° West (the western hemisphere) (Figure 4.4). Because the meridians converge at the poles, the 1° longitude interval decreases from 111 kilometres at the equator to 56 kilometres at 60° North or South and zero kilometres at the poles (Table 4.1);

ix) Graticule: A network of lines representing parallels and meridians on paper, i.e. geographic coordinates which are defined in degrees, minutes and seconds;

x) Grid: Two sets of parallel lines crossing at right angles to form squares, i.e. grid coordinates.

(a) Meridians; (b) parallels.  FIGURE 3

The geographic grid of parallels and meridians. Point A has a latitude of 50 North and a longitude of 75 West.

TABLE 4.1

THE LENGTH OF 1° INTERVALS OF SELECTED LATITUDES AND LONGITUDES
LENGTH OF 1° OF LATITUDE LENGTH OF 1° F LONGITUDE
Latitude (Degrees) Statute Miles Kilometres Statute Miles Kilometres
0 68.704 110.569 69.172 111.322
5 68.710 110.578 68.911 110.902
10 68.725 110.603 68.129 109.643
15 68.751 110.644 66.830 107.553
20 68.786 110.701 65.026 104.650
25 68.829 110.770 62.729 100.953
30 68.879 110.850 59.956   96.490
35 68.935 110.941 56.725   91.290
40 68.993 111.034 53.063   85.397
45 69.054 111.132 48.995   78.850
50 69.115 111.230 44.552   71.700
55 69.175 111.327 39.766   63.997
60 69.230 111.415 34.674   55.803
65 69.281 111.497 29.315   47.178
70 69.324 111.567 23.729   38.188
75 69.360 111.625 17.960   28.904
80 69.386 111.666 12.051   19.394
85 69.402 111.692   6.049    9.735
90 69.407 111.700   0.000    0.000

Geographical coordinate system

The geographical coordinate system was developed from concepts originated by Greek philosophers before the Christian era. It is the primary system used for basic locational reckoning, such as navigation and surveying. The system is basically one of spherical coordinates, the meridians and parallels being neither straight nor equally spaced. It is useful for mapping large areas and the measurement of distances and directions in angular measure of degrees, minutes and seconds. A rectangular coordinate system which is far simpler in construction and usage may be superimposed on the geographical coordinate system.

Rectangular coordinate system

The Universal Transverse Mercator (UTM) Grid System is an international system which provides rectangular grid zones for the globe between latitude 80° South and 80° North. Poleward of 80°, the Universal Polar Stereographic Grid System is used. These systems are named after the map projections on which they are based. The UTM Grid System consists of 60 grid zones, each 6° of longitude in width (Figure 4.6). The origin (0°) of the grid zone is the intersection of the central meridian and the equator, both straight lines. The grid is a network of 1,000 metre, 10,000 metre or 100,000 metre squares, each identified by the grid coordinates of its lower left hand corner. In stating grid coordinates, the number of metres east or eastings (right) is given first, followed by the number of metres north or northings (up). The procedure for reading UTM grid coordinates is explained in Figure 4.7. In order to have all eastings increase towards the right across the entire zone, the central meridian is given the arbitrary value of 500,000 metres east. The equator is given the value of 0 metres north as the reference line for northings increasing up to the 80th parallel north. For the southern hemisphere, the equator is given the arbitrary northing of 10 million metres north, so that northings begin with their lowest value at 80° South latitude and increase northward to attain that figure at the equator. The Universal Transverse Mercator Grid System has now been widely adopted for topographic maps, referencing of satellite imagery, natural resource data bases and similar applications which require precise positioning.

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