Map Projection

The best model to describe the Earth is a sphere, slightly flattened along the axis of the poles ( the circumference of the Earth along the Equator is longer than the length of a circle passing on both poles). Such flattened sphere is called a spheroïd. Any territory being a part of the surface of the Earth, is hence a part of this spheroïd and accordingly, it is not flat. Mapping the world on a map globe is relatively easy: the Longitude / Latitude angles of each point are simply reported as angles from the centre of the globe. Unfortunately, drawing maps on a piece of paper is more complicated, because it is impossible to simply transform this curved surface (the Earth) to a flat surface (the paper) in one block. Just try with a orange peel, and you will find that you have to cut the peel in many pieces to get a reasonably flat surface.

Since the invention of maps, cartographers were facing this problem (in fact, mapping was easier before Galileo, when everybody was convinced that the Earth was flat !).

Many (maybe hundreds ?) of mathematical solutions were developed to circumvent this problem. These are know as projections . A projection is a mathematical formula translating geographic coordinates (Longitudes / Latitudes) in plane coordinates.

There are many different types of projections, but there are also many different mathematical definitions of the reference spheroïd. In Namibia , all topographic maps produced by the DSM are based on the Bessel spheroïd.

Plane coordinates are usually defined by two perpendicular measurement axis. The origin of the axis is an arbitrary point.

In most modern projection system, the measurement units along these axes are meters.

**Gauss-Bessel reference system : **

Namibian topographic maps are projected in the Gauss projection system and use the Bessel spheroid. This system is sometimes referred as "Lo" system. Gauss projection is a variant of Transverse Mercator, characterised by the central meridian.

In Namibia, 7 different projections are used, using 13°E, 15°E, ..., 25°E as the central meridian, and latitude 22° S as reference parallel.

These projections are named Lo13, Lo15, etc. The Lo zone is indicated on each topographic map, below the scale bar.

Units in Lo system are meters.

It is very important to notice that, contrary to the international conventions, X is used for longitudes and X values increase southwards and Y is used for Longitude, and increase Westwards.

This is just the opposite to "usual" Transverse Mercator coordinates.

On 1:50'000 maps of Namibia , Lo coordinates are indicated in 10'000m units. "-8Y" means -80'000 m longitude, or 80km East of the central meridian. On the 1:250'000 maps, the LO values are placed each 50'000m, but values are also to be multiplied by 10'000 to read Lo coordinates.

To facilitate the reading of coordinates, small red crosses are placed inside the map at the intersection of major values.

**UTM reference system : **

UTM stands for Universal Transverse Mercator. It's an international reference system based on the Transverse Mercator system. This system was mainly used by the army, but it becomes a standard for many applications.

UTM units are also meters and the axis orientation and names are standard (X for longitudes, increasing Eastwards and Y for Latitude increasing towards North.

To be able to interpret UTM reference, the reader must know to which zone they refer. On the new Namibian topographic maps, this is indicated in the purple text placed below the scale bar.

The value of UTM zone (34K in our example) must be adapted to the Longitude of the map. 3 different UTM zones are used for Namibia ; these are indicated on this map ®

On 50k maps, the UTM reference is represented by solid lines in purple colour

The display of UTM values also follows international conventions.

On the 50k maps of Namibia , we followed the example of the old maps (only special edition of the old maps have UTM grids). According to this model, only the two last digits of the value in kilometres are indicated along the sides.

For instance, the value 791000 m will be written 91 along the sides, and 7 91 000 E for the first value in the bottom left corner:

**Geographical Reference System : **

Geographic co-ordinates (Latitude / Longitude) are traditionally given in sexadecimal angular units (Degrees, Minutes and Seconds).

In Namibia, most topographic maps at scale 1:50'000 cover an area of 15 minutes by 15 minutes ("Quarter of Degree"), and most 1:250'000 maps cover 1° Latitude by 2° Longitude.

The 4 corners of a map sheet indicate the longitude/latitude in degrees and minutes.

A ruler divided in segments of 1 minute is placed outside the map area, with corresponding value for each multiple of 5' .

The Namibian maps are based on Gauss projection. Accordingly, Gauss grids are orthogonal (i.e. Gauss grid define squares), but all other grids (geographical and UTM) are NOT orthogonal. This can be observed in the figure of the previous paragraph. This must be taken into account when you measure position on the map !