Transformation between Cape Datum and Hart94

Although the advantages of adopting a new horizontal datum are evident, many users have huge geographically referenced datasets based on the Cape Datum and need to transform these to the new datum. To do this, one needs to establish the relationship between the two datums as this is not absolutely defined.

Various methods of transformation are available in order to transform current data sets, referenced with respect to the Cape Datum, to the new Hartebeesthoek94 Datum.

Because of computational limitations, there are many distortions in the Cape Datum co-ordinates which have been removed in the computation of Hartebeesthoek94 Datum co-ordinates. For this reason the higher the transformation accuracy required, the more localised the area must be for which transformation parameters are calculated. For high end users, such as Land Surveyors and Engineers, transformation accuracy is of paramount importance. Low accuracy GIS applications may however not require this accuracy and parameters covering larger areas may be acceptable.

In addition to distortions being introduced as a result of computational difficulties, co-ordinates were changed from time to time as and when new observations were added to the triangulation or when local readjustments were made to improve the network. The result was that some beacons have more than one co-ordinate. This has to be taken into consideration when transforming Cape datum co-ordinates to Hartebeesthoek 94 and only Cape datum co-ordinate values as they were at the time of the original survey should be used for transformation purposes

Transformation parameters

When computing transformation parameters one would require co-ordinates of common control points in both datums. The 29 000 trigonometrical beacons and 22 000 Town Survey Marks serve this purpose adequately. In certain parts of the country the density of these control points are far greater than in other areas. The accuracy of the transformation parameter not only depends on the size of the project, but also the proximity to sufficient control points.

At least two points (for 2-D transformations ) or three points (for 3-D transformations), known in both the old and the new Datum must be used to determine the transformation parameters, and must be well distributed throughout the area to be transformed. In order to obtain better parameters, localised transformation parameters must be computed for the area of interest.

2-D Helmert Transformations

At the most elementary level, a 2D Helmert Transformation (which uses 2 translations, a rotation and a scale factor) can be used to define the relationship between the two datums. This mode lis very effective over small areas (up to 40km) and does not take heights into consideration. The mathematical model for the 2-D Helmert transformation is given as:

system 2      system 1
Y2 =         TY + b.X1 + a.Y1
X2 =         TX + a.X1 - b.Y1
The transformation parameters to solve for are therefore:
TX, TY : The translations in each axis.
a, b     : Helmert transformation variables.
The NGI has evaluated 2-D Helmert transformation parameters, derived from the horizontal control survey network data within the two datums, over various sized areas. The averaged residuals obtained are as follows:

An Example

Transforming a co-ordinate (on Lo19º) from Cape Datum to the Hartebeesthoek94 Datum using predetermined parameters.

3-D Transformations
The mathematical model for the 3-D Helmert transformation is given as

   system 2               system 1

An Example

Transforming a co-ordinate (on Lo27º) from the Cape Datum to the Hartebeesthoek94 Datum using predetermined parameters.

Connecting to the Hartebeesthoek94 Datum

In order to reference your data or survey to the Hartebeesthoek94 Datum, the following conditions must be met:

a) The project/survey must be referenced to the WGS84 ellipsoid.
b) The survey and positions of the features must be determined relative to the National Control Survey Network.

*Note: If your positions were determined using GPS in autonomous mode (5-15m accuracy), you can assume that your data is in Hartebeesthoek94 Datum.