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Document : The MERCATOR projections,PETER OSBORNE, EDINBURGH, 2008

Radfearn's transformation formulae

TME(Transverse Mercator on the ellipsoid) is derived as a series by a complex transformation from the NME(Normal Mercator on the ellipsoid) projection.

Image

Direct

The direct series for x and y

Image

Image

Inverse

The inverse series for Image and Image

Image

Image

where

Image

Condition

1. Image

where the coefficients are given by

Image

If we use the numerical values for the Airy ellipsoid, then , in meteres,

Image

2. Function Image and Image are defined in

Image

3. Imageis measured on radians from central meridian

4. The subscripted terms in the inverse series are to be evaluated at the footpoint latitude Image such that Image

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ImageImage Image Image

Image Image Image Image Image Image Image

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