The Namibian Map System

The Namibian Map System normally comprises two projections for either a countrywide (1:1million) or sheet wise (1:50k, 1:250k) display:

	Countrywide (1:1mio or bigger)	Sheet wise (1:250k, 1:50k)
Projection Spheroid Central Meridian Latitude of Origin Standard Parallels Central Scale Factor False Easting False Northing	Albers Equal Area Bessel 1841 (Schwarzeck Datum) E 17 S 22 S 19, S 27 1.0 0.0 0.0	LO (Gauss Conformal) Bessel 1841 (Schwarzeck Datum) variable E 13,15,17,19,21 S 22 - 1.0 0.0 0.0

The Schwarzeck Datum consists of the Bessel 1841 Spheroid tied to a point called Schwarzeck located at 22º 45' 35".820 S and 18º 40' 34".549 E. Furthermore it comprises the 'German Legal Meter' instead of the international meter
(1 GLm = 1.0000135965 SIm).

The transformation from the Schwarzeck datum into WGS 84 implies X, Y and Z shifts but no rotation. DMA – NIMA and Prof. Charles Merry from the University of Cape Town do give shift values, from which the latter ones are the more accurate:

Bessel Spheroid:

a = 6377397.1550 &”German legal”; meter
b = 6356078.96325 ”German legal” meter
a = 6377483.865 intern. meter
b = 6356165.383 intern. meter
f = 1/299.1528128 (no changes due to length unit)
= 0.003342773182
X, Y, Z shifts in meter
DMA –; NIMA 616 (± 20) 97 (± 20) -251 (± 20)
C. Merry (UCT) 616.80 103.30 -256.90

On the Maps in the LO system you will find the positive X axis to the south and the positive Y-axis to the west. This is a left-handed Cartesian co-ordinate system, whilst the computer thinks in a right-handed system. For the display of gridded data just use the normal co-ordinate system but be careful with the grids origin. Some software allows taking care of this by giving a negative central scale factor.

There are some topographical map sheets floating around in UTM (Datum not specified) and Lambert Conformal (Clarke 1880) projections.

The Geological Survey of Namibia believes that the research and development undertaken by Prof. C. Merry provide the most accurate parameters. Therefore some original notes:

The datum transformation parameters I have supplied are based upon 13 Doppler points, of which the DMA used a subset of 3. The RMS fit for these 13 points is 3m, which means there may be some parts of the country where the discrepancy is 10m (this is an indication of the accuracy of the original terrestrial survey, carried out some 100 years ago).

The map projection is a modified transverse mercator, with a false origin and units of legal meters. The plane co-ordinates would need to be converted to international meters and the (int. meters) co-ordinates of the false origin added. Then the standard transverse Mercator equations can be used to convert the plane co-ordinates to geographical (int. meter values for the modified Bessel ellipsoid: a=6377483.m).

The geographical co-ordinates would be converted to X, Y, Z Cartesian co-ordinates (using a=6377483..m), and the datum shifts added, with appropriate sign.

These transformed Cartesian co-ordinates are converted to WGS84 geographical co-ordinates, using the WGS84 ellipsoid parameters.

My understanding is that the military UTM maps use the modified Bessel ellipsoid, with international meters, not the WGS84 ellipsoid; but I could be wrong.

The difference between international meters and legal meters is fairly small. As far as I know, all practicing surveyors and engineers use instruments (tapes, EDM, GPS) calibrated in international meters and solve for a scale factor (sometimes not even this, when working in small areas) when tying their surveys to the national control network.