EPSG:9808

Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided.

For the mapping of southern Africa a south oriented Transverse Mercator projection is used. Here the coordinate axes are called Westings and Southings and increment to the West and South from the origin respectively.  The standard Transverse Mercator formulas (coordinate operation method code 9807) need to be modified to cope with this arrangement with

Westing, W = FE - k0 nu[A + (1 - T + C)A^3/6 + (5 - 18*T + T^2 + 72*C - 58*e'^2)A^5/120]

Southing, S = FN - k0{M - M0 + nu*tan(lat)*[A^2/2 + (5 - T + 9*C + 4*C^2)A^4/24 + (61 - 58*T + T^2 + 600*C - 330*e'^2)A^6/720]}

In these formulas the terms FE and FN retain their definition, i.e. in the Transverse Mercator (South Orientated) method they increase the Westing and Southing value at the natural origin. In this method they are effectively false westing (FW) and false southing (FS) respectively.

For the reverse formulas, those for the standard Transverse Mercator above apply, with the exception that:

M1 = M0 - (S - FN)/k0
and D = -(W - FE)/(nu1*k0), with nu1 = nu for lat1