# Geographic Coordinates

Geographic coordinates are usually in angular (latitude/longitude) or projected (easting/northing or x/y) form. Angular coordinates are derived from simplified 3D model of the Earth's surface (sphere or ellipsoid). If projection is applied, 3D surface is further transformed on the flat 2D plane, which involves some distortion.

Angular form is used mostly in a large-scale applications like aviation and marine. Mathematics of angular system uses ellipsoid model of the Earth with appropriate semi-diameters and coordinate origin parameters. As Earth's shape is not strictly regular, each ellipsoid model deviates from the real Earth shape. To minimize this deviation, many countries have developed their own reference ellipsoid with slightly different parameters, which yield best possible accuracy in respective region.

For applications of smaller scope, projected coordinates are often more handy. In many cases the coordinates are expressed in meters or feet units, measured from some reference point. Projection uses number of reference points to allow short coordinate notation and to reduce deformation introduced by projection. Because of the reference point system (grid), projected coordinates are sometimes referred to as grid coordinates. Grid cells are assigned with unique codes that are not only part of coordinate notation but they also simplify searching for required map sheet in case of printed maps. Each projection deforms relations like distance, area or azimuth between the map spots. Therefore, projection methods are designed so that at least one relation is preserved - equal before and after projection (area, for an example), while others are inevitably distorted by 3D to 2D transformation. Preserved relation depends on the application, it can be the azimuth in case of navigation or the area in case of a land management application. Many projection methods preserve distance to allow its easy measurement on the map and its calculation from the 2 points coordinates. Anyway, projected coordinate system (2D) is always based on some angular coordinate system (3D). No projection is ideal for all applications. Therefore, many projection methods are in use.

As mentioned above, there are many angular systems with their parameters (called shortly "datums") and many projected systems (each based on some datum). While working in the GPS mapping field, however, some are encountered more often than others. Global Positioning System uses World Geodetic System (revision 1984, i.e. WGS84) as the reference coordinate system. Map files compatible with Garmin GPS units use WGS84 too. Therefore, Mapwel converts all input data like shape files or calibration point coordinates to WGS84 angular coordinates, which are used in its internal data structures. Among projections, UTM (Universal Transverse Mercator) seems to be used most often. If map data use UTM projection, the projection must be reversed to get coordinates in Latitude/Longitude form. These must be further transformed to WGS84 if other reference ellipsoid was used.

## UTM - Most Common User Errors

Most UTM grid cells are regular. Exceptions are V30, V32, X31, X33, X35, X37 in north-west Europe.
Most common error: wrong use of lat. band letter 'S'. Some sources use 'S' to denote southern hemisphere, not latitude band 'S'. In such a case, conversion will place resulting point north to equator, where S band is located.
Work-around: In such a case, use 'M' band letter instead. M band is on southern hemisphere. Conversion algorithm derives only hemisphere information from the band letter (in case of regular grid cells), because range of the northing (y-axis) coordinate covers whole distance from equator to pole. Band letter allows indexing of paper maps.

## British Grid - Most Common User Errors

British grid uses square cells 100x100 km large. Therefore, coordinates (in meters) must fit into 0.0 ~ 100000.0 meters range. The most common error is wrong interpretation of abbreviated coordinates (from a printed map) and as a consequence, placing the floating point on a wrong position. If your map is shifted after conversion, most probably the coordinates coding must be revised.