# Scale factors, scale differences and scale adjustment

The following article explains the difference between the various scale factors used in preparing a cadastral survey dataset and situations when a scale adjustment to an existing distance could be justified.

## Projection scale factors

For cadastral survey purposes data is submitted to LINZ in terms of one of the 28 official NZGD2000 Meridional Circuits. Each circuit is a defined projection representing part of the curved surface of the NZGD2000 ellipsoid as a plane surface.

Computed coordinates on a Meridional Circuit plane surface projection are commonly referred to as Grid Coordinates.  A distance computed between grid coordinates is referred to as a ‘projection distance’ or ‘grid distance’.

Distances measured by survey are reduced to an equivalent ellipsoidal distance. Each distance recorded in a CSD must be an ellipsoidal distance (r 74(4)).

To convert an ellipsoidal distance (usually measured or adopted from prior surveys) to an equivalent projection distance, or vice versa, a multiplier or ratio is used and is referred to as the ‘Projection Scale Factor’.

The projection scale factor varies and increases the further east or west a survey is located from the Central Meridian origin for each Meridional circuit.

## Central Meridian Scale Factor

The Central Meridian Scale Factor is a multiplier applied to a Meridional Circuit projection to balance the effects of scale distortion over the coverage area of the projection.

In all NZ meridional circuits the Central Meridional Scale Factor is 1, apart from Mt Eden and North Taieri circuits where it is defined as being 0.9999 and 0.99996 respectively.

## Line Scale Factor

The specific projection scale factor that is used for converting any particular measured or computed distance between two points on a survey is known as the ‘Line Scale Factor’.

In practice most third party surveying software and modern survey controllers will apply the correct projection and line scale factors automatically. However certifying surveyors need to be aware of how their software and survey controllers are applying scale factors and corrections. Care needs to be taken to ensure that all submitted survey data is in terms of the relevant rules for cadastral survey and any required official geodetic datum.

Further detail on Meridional Circuits, scale factors and associated formulas can be found in Standard for New Zealand Geodetic Datum 2000 Projections: Version 2 - LINZS25002.

## Projection scale differences

Distances shown on existing cadastral survey datasets are nominally reduced to a datum ellipsoid, or to mean sea level. Any difference between an ellipsoidal distance reduced to NZGD49, or to Sea Level, and NZGD2000 will equate to only a few parts per million. In practice such differences are considered insignificant for cadastral survey purposes.

## Scale adjustment

In some surveys, evidence may indicate that existing distances on an old survey plan differ from modern survey measurements by a consistent scale factor, sometimes referred to as a local scale factor. Where this is adequately proven, a ‘scale adjustment’ can be applied to the existing distances to bring them into the same terms as the modern measurements.

Any scale adjustment to existing distances must be based on a consistent distance-dependant scale difference being determined over multiple lines of differing lengths located over the extent of the existing survey. Other potential sources of systematic or constant error must also be eliminated.

Where a scale adjustment is applied to existing distances included in a new CSD, the resulting scale adjusted distances must be identified and captured in the CSD Plan with a distance type of ‘calculated’ and not adopted. (r 75(1) & 78(c))

The basis for the scale adjustment should be included in the survey report and preferably supported by accompanying calculation sheets clearly showing how the scale adjustment was determined.

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