# Australian National Grid

Prior to 1966, 'the rectangular grid coordinate system', used in conjunction with this [Clarke 1858] spheroid, was called the Australian National Grid (ANG).

Coordinates were quoted in yards, and were derived from a Transverse Mercator projection of latitudes and longitudes, determined in relation to the relevant state or local coordinate origin (National Mapping Council, NMC 1986). The various parameters used with the ANG were:

Central scale factor : 1.0 exactly 400 000 yards 4 915 813.467 yards 5 degrees 116 degrees East longitude.

* The true origin is the intersection of the central Meridian and the Equator, but in Tasmania, to prevent negative coordinates, the origin for ANG coordinates was adopted as the intersection of S34 degrees latitude and E146 degrees longitude, with the False Origin 400 000 yards west and 1 800 000 yards south of this point. This is equivalent to adding 1 000 000 yards to the False Northing shown above for the "standard" ANG.

## Converting from Clarke 1858/ANG to AGD/AMG

Because of the non-homogeneous nature of the pre-1966 ANG coordinates, it is not possible to automatically convert the ANG coordinates to Australian Map Grid (AMG) - an empirical approach has to be used.

The accuracy obtained depends on the area in question and the method used, but at best will generally be in the order of several metres.

Several methods are possible, all but the first depend on having sites whose latitudes and longitudes are known in terms of both Clarke 1858 and Australian Geodetic Datum, AGD (common points).

### Methods

#### Method 1

• Obtain the original survey observations (angles, distances etc), and compute the AGD coordinates, based on the latest AGD coordinates for the fixed control. This is generally not practical because of the work involved and the difficulty in recovering the original observations. It may also be that the control used for the original survey was never computed in terms of the AGD

#### Method 2

• If necessary, convert the existing Clarke 1858 latitudes and longitudes to ANG grid coordinates using Redfearn's formulae (Redfearn, 1948)
• Interpolate AMG coordinates mathematically for the ANG values, based on at least four common points which have both ANG and AMG coordinates and which surround the area of interest. A common method for doing this is to use Lauf's conformal transformation (Lauf, 1961)
• If necessary, convert the AMG grid coordinates to AGD latitudes and longitudes using Redfearn's formulae (Redfearn, 1948)

#### Method 3

• If necessary, convert the existing ANG grid coordinates to Clarke 1858 latitudes and longitudes using Redfearn's formulae, (Redfearn 1948)
• Convert the Clarke 1858 latitudes and longitudes to AGD latitudes and longitudes using one of the following methods:
• Apply a latitude and longitude block shift, based on the comparison of one or more common points. This assumes that if there is more than one common point, the comparisons similar at all of them and an average can be used
• Apply a latitude and longitude block shift, interpolated from differences of Clarke 1858 and AGD latitude and longitude, generated from a number of common points. This may be a linear, planar or polynomial interpolation, depending on the number and configuration of common points; or contours of difference may be drawn to assist visual interpolation
• If required, convert the AGD latitudes and longitudes to AMG grid coordinates, again using Redfearn's formulae

### References

Allman, JS and Veenstra, C. 1984. Geodetic Model of Australia. Division of National Mapping Technical Report 33.

Bomford, AG 1965. Notes on the Australian Spheroids and origins. Division of National Mapping Internal Correspondence.

Jones, MAB 1990. Bear Essentials or Geodesy facts you always wanted to know about but didn't know where to find them. Personal compilation.

Lauf, GB 1961. 'Conformal Transformation from one map projection to another, using divided difference interpolation'. Bulletin Geodesic no.61.

National Mapping Council of Australia, 1978. Mapping 1:250 000: Accuracy of AMG overprinted on R502 Series. (Report presented to 29th Technical Subcommittee Bendigo, 1978).

National Mapping Council of Australia, 1986, 'The Australian Geodetic Datum', Technical Manual. Special Publication 10.

Redfearn, JCB 1948. 'Transverse Mercator Formulae', Empire Survey Review no.69, 1948.

Steed, JB 1990. 'A practical approach to transformation between commonly used reference systems'. The Australian Surveyor, September 1990, vol.35 no.3.