# Transverse Mercator

## Description

Also known as Gauss–Krüger, and similar to the Mercator, except that the cylinder is longitudinal along a meridian instead of the equator. The result is a conformal projection that does not maintain true directions. The central meridian is placed in the center of the region of interest. This centering minimizes distortion of all properties in that region. This projection is best suited for north–south areas.

The State Plane Coordinate System uses this projection for all north–south zones. The UTM and Gauss–Krüger coordinate systems are based on the Transverse Mercator projection.

## Projection method

Cylindrical projection with central meridian placed in a particular region.

## Lines of contact

Any single meridian for the tangent projection. For the secant projection, two almost parallel lines equidistant from the central meridian. For UTM, the lines are about 180 km from the central meridian.

## Linear graticules

The equator and the central meridian.

## Properties

### Shape

Conformal. Small shapes are maintained. Larger shapes are increasingly distorted away from the central meridian.

### Area

Distortion increases with distance from the central meridian.

### Direction

Local angles are accurate everywhere.

### Distance

Accurate scale along the central meridian if the scale factor is 1.0. If it is less than 1.0, there are two straight lines with accurate scale equidistant from and on each side of the central meridian.

## Limitations

Data on a spheroid or an ellipsoid cannot be projected beyond 90° from the central meridian. In fact, the extent on a spheroid or ellipsoid should be limited to 12–15° on both sides of the central meridian. Beyond that range, data projected to the Transverse Mercator projection may not project back to the same position. Data on a sphere does not have these limitations.

A new implementation called Transverse_Mercator_complex has been added to the Projection Engine which is available in ArcGIS desktop. It accurately projects to and from Transverse Mercator up to 80° from the central meridian. Because of the more complex mathematics involved, performance is affected.

## Uses and applications

State Plane Coordinate System, used for zones that are predominantly north–south.

USGS 7-½ minute quad sheets. Most new USGS maps after 1957 use this projection, which replaced the polyconic projection.

North America (USGS, central meridian scale factor is 0.926).

Topographic maps of the Ordnance Survey of Great Britain after 1920.

UTM and Gauss–Krüger coordinate systems. The world is divided into 60 north and south zones six degrees wide. Each zone has a scale factor of 0.9996 and a false easting of 500,000 meters. Zones south of the equator have a false northing of 10,000,000 meters to ensure that all y values are positive. Zone 1 is at 177° W.

The Gauss–Krüger coordinate system is similar to the UTM coordinate system. Europe is divided into zones six degrees wide with the central meridian of zone 1 equal to 3° E. The parameters are the same as UTM except for the scale factor, which is equal to 1.000 rather than 0.9996. Some places also add the zone number times one million to the 500,000 false easting value. GK zone 5 could have false easting values of 500,000 or 5,500,000 meters.

## Parameters

### Desktop

• False Easting
• False Northing
• Central Meridian
• Scale factor
• Latitude of origin

### Workstation

• Scale factor at Central Meridian
• Longitude of Central Meridian
• Latitude of origin
• False Easting (meters)
• False Northing (meters)

## Related Topics

Published 6/7/2010