transverse

Transverse Mercator
The Transverse Mercator projection in its various forms is the most widely used projected coordinate system for world topographical and offshore mapping. All versions have the same basic characteristics and formulas. The differences which distinguish the different forms of the projection which are applied in different countries arise from variations in the choice of the coordinate transformation parameters, namely the latitude of the origin, the longitude of the origin (central meridian), the scale factor at the origin (on the central meridian), and the values of False Easting and False Northing, which embody the units of measurement, given to the origin. Additionally there are variations in the width of the longitudinal zones for the projections used in different territories.

Table 3-3 below indicates the variations in the projection parameters which distinguish the different forms of the Transverse Mercator projection and are used in the Epicentre Transverse Mercator projection method:

Table 3-3: Transverse Mercator
Name
 Areas used
 Central Meridian(s)
 Latitude of Origin
 CM Scale Factor
 Zone Width
 False Easting at Origin
 False Northing at Origin
 
Transverse
Mercator
 Various, world wide
 Various
 Various
 Various
 Usually less than 6°
 Various
 Various
 
Transverse
Mercator South
Oriented
 Southern Africa
 2° intervals E of 11° E
 0°
 1.000000
 2°
 0 m
 0 m
 
UTM North
hemisphere
 World wide. Equator to 84°N
 6° intervals E & W of 3° E & W
 Always 0°
 Always 0.9996
 Always 6°
 500000 m
 0 m
 
UTM South
hemisphere
 World wide. Equator to 80°S
 6° intervals E & W of 3° E & W
 Always 0°
 Always 0.9996
 Always 6°
 500000 m
 10000000 m
 
Gauss-Kruger
 Former USSR, Yugoslavia, Germany, S. America
 Various, according to area of cover
 Usually 0°
 Usually 1.000000
 Usually less than 6°, often less than 4°
 Various, but often 500000 prefixed by zone number
 Various
 
Gauss Boaga
 Italy
 Various
 Various
 0.9996
 6°
 Various
 0 m
 

 The most familiar and commonly used Transverse Mercator in the oil industry is the Universal Transverse Mercator (UTM) whose natural origin lies on the equator. However, some territories use a Transverse Mercator with a natural origin at a latitude closer to that territory.

In Epicentre the coordinate transformation method is the same for all forms of the Transverse Mercator projection. The formulas to derive the projected Easting and Northing coordinates are in the form of a series as follows:

Easting:



Northing:



where





, with l and l0 in radians



with j in radians and M0 for j0, the latitude of the origin, derived in the same way.