Transverse Mercator Projection - Ellipsoidal Transverse Mercator

Ellipsoidal Transverse Mercator

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.

The projection, as developed by Gauss and Krüger, was expressed in terms of low order power series which were assumed to diverge in the east-west direction, exactly as in the spherical version. This was proved to be untrue by British cartographer E.H. Thompson, whose unpublished exact (closed form) version of the projection, reported by L.P. Lee in 1976, showed that the ellipsoidal projection is finite (below). This is the most striking difference between the spherical and ellipsoidal versions of the transverse Mercator projection: Gauss-Krüger gives a reasonable projection of the whole ellipsoid to the plane, although its principal application is to accurate large scale mapping "close" to the central meridian.