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I want to know what is the official survey datum, and projection system for Zimbabwe? I think it is ARC1950, UTM Zone36.

Is it better to convert all the old coordinates to WGS LO29 (LO depending on nearest uneven longitude)?

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I am unable to find any official sources, but I believe you are correct about Arc 1950 / UTM Zone 36S (epsg.io page for reference). It's a longshot, but perhaps you could contact someone at the city of Harare, where they are implementing a GIS system, and verify what they are using. It looks like the City of Munich, Germany is assisting them with this.

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I've just found an academic article about the coordinate systems along African regions.

As it's going into a great detail about the different transformations along different countries, it mentions Zimbabwe:

At the time of the establishment of geodetic networks in southern Africa this situation did arise - each country or territory had its own independent datum based upon a particular reference ellipsoid in a particular position. Botswana, Lesotho, South Africa, Swaziland and Zimbabwe nominally use the same datum - known as the Cape or Arc Datum, using the modified Clarke 1880 ellipsoid. In Namibia the Bessel ellipsoid is used, in Mocambique the Clarke 1866 ellipsoid. Only when the different geodetic networks are linked at the border points are the discrepancies (of the order of hundreds of metres) apparent.

Its reference is: J. Rens & C. L. Merry (1990) DATUM TRANSFORMATION PARAMETERS IN SOUTHERN AFRICA, Survey Review, 30:236, 281-293

Its direct link is: http://dx.doi.org/10.1179/003962678791486121

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Arc 1950 datum, Spheroid Clarke 1880 zone 35 and 36

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UTM arc 1950 Zone 35 & 36.

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