# Converting grid co-ordinates to GPS co-ordinates

I need to convert grid co-ordinates from an old document to GPS co-ordinates that I can plot into Google Earth and ArcGIS. Here are the instructions:

'It was unfortunately not possible to produce maps using UTM co-ordinates. This problem was overcome by imposing a grid onto the map of Zimbabwe and digitising the site maps. The origin (00.00,00) of the grid was at 25 degrees, 05 minutes, 24 second east and 22 30 00 S. A point (80.00,00) along the X-axis was at 32 50 40 E and 22 25 40 S. One unit of distance on the grid represented 10 kilometres on real ground. The co-ordinates given in the following table represent the positions of the sites within this imposed grid.'

An example of a grid co-ordinate is: Name 2030 BD 1 Grid 60.21 24.78

Can anyone instruct me as to how I would go about doing this?

You can create a custom CRS with these parameters:

``````+proj=omerc +lat_0= -22.5 +lonc=25.09 +alpha=0.910238 +k=0.99977264 +x_0=0 +y_0=0 +gamma=0 +a=6378249.145 +b=6356514.966398753 +towgs84=-143,-90,-294,0,0,0,0 +no_defs +to_meter=10000
``````

And you get the 10km-grid as described: I took the old ARC 1950 datum from EPSG:4209 as base, which was common in Zimbabwe before WGS84.

• Great, thank you so much. This is fantastic. Must I then manually convert grid references to co-ordinates or is it possible to do this in an easier way? – Tim Forssman Jul 6 '15 at 7:00
• I mentioned this to a colleague who said placing it into ArcGIS will allow me to import the grid references as a text file and it should project correctly – Tim Forssman Jul 6 '15 at 9:09
• You can use GDAL cs2cs or ogr2ogr to convert between WGS84 and the grid; or add the data as delimited text with the custom CRS. This can be done in either QGIS and Arcgis. – AndreJ Jul 6 '15 at 9:49
• Would be nice to see how you computed the parameters, especially since the documentation for `alpha` in oblique mercator seems hard to find. – Spacedman Jul 6 '15 at 13:19
• That was just trial and error, to get the second point on the y=0 line (and on x=80.0 with the k factor). If that point had the same latitude as the origin, a simple tmerc would be sufficient. Alpha is the clockwise rotation in degrees between East and the y=0 grid line. See this example for a larger rotation: gis.stackexchange.com/questions/83861/… – AndreJ Jul 6 '15 at 13:25