Transverse Mercator

The transverse Mercator map projection is an adaptation of the standard Mercator projection. The transverse version is widely used in national and international mapping systems around the world, including the UTM. When paired with a suitable geodetic datum, the transverse Mercator delivers high accuracy in zones less than a few degrees in east-west extent.

The transverse Mercator projection is the transverse aspect of the standard (or Normal) Mercator projection. They share the same underlying mathematical construction and consequently the transverse Mercator inherits many traits from the normal Mercator:

Since the central meridian of the transverse Mercator can be chosen at will, it may be used to construct highly accurate maps (of narrow width) anywhere on the globe. The secant, ellipsoidal form of the transverse Mercator is the most widely applied of all projections for accurate large scale maps.

In constructing a map on any projection, a sphere is normally chosen to model the Earth when the extent of the mapped region exceeds a few hundred kilometers in length in both dimensions. For maps of smaller regions, an ellipsoidal model must be chosen if greater accuracy is required; see next section. The spherical form of the transverse Mercator projection was one of the seven 'new' projections presented, in 1772, by Johann Heinrich Lambert. (The text is also available in a modern English translation.) Lambert did not name his projections; the name transverse Mercator dates from the second half of the nineteenth century. The principal properties of the transverse projection are here presented in comparison with the properties of the normal projection.

The ellipsoidal form of the transverse Mercator projection was developed by Carl Friedrich Gauss in 1825 and further analysed by Johann Heinrich Louis Krüger in 1912. The projection is known by several names: Gauss Conformal or Gauss-Krüger in Europe; the transverse Mercator in the US; or Gauss-Krüger transverse Mercator generally. The projection is conformal with a constant scale on the central meridian. (There are other conformal generalisations of the transverse Mercator from the sphere to the ellipsoid but only Gauss-Krüger has a constant scale on the central meridian.) Throughout the twentieth century the Gauss-Krüger transverse Mercator was adopted, in one form or another, by many nations (and international bodies); in addition it provides the basis for the Universal Transverse Mercator series of projections. The Gauss-Krüger projection is now the most widely used projection in accurate large scale mapping.

...
Wikipedia