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3.4.4.8 Tunisia Mining Grid

Note: It is important that these formulas be used as is with the units as explained. The Epicentre implementation of this formula is with NO parameters. That is, the formula applies strictly to the Tunisia Grid, as defined, and is not to be carried elsewhere.

This grid is used as the basis for mineral leasing in Tunisia. Lease areas are approximately 2 x 2 km or 400 hectares. The corners of these blocks are defined through a six figure grid reference where the first three digits are an easting in kilometres and the last three digits are a northing. The latitudes and longitudes for block corners at 2 km intervals are tabulated in a mining decree dated 1^st January 1953. From this tabulation in which geographical coordinates are given to 5 decimal places it can be seen that:

1. the minimum easting is 94 km, on which the longitude is 5.68989 grads east of Paris.
2. the maximum easting is 490 km, on which the longitude is 10.51515 grads east of Paris.
3. each 2 km grid easting interval equals 0.02437 grads.
4. the minimum northing is 40 km, on which the latitude is 33.39 grads.
5. the maximum northing is 860 km, on which the latitude is 41.6039 grads.
6. between 40 km N and 360 km N, each 2 km grid northing interval equals 0.02004 grads.
7. between 360 km N and 860 km N, each 2 km grid northing interval equals 0.02003 grads.

This grid could be considered to be two equidistant cylindrical projection zones, north and south of the 360 northing line. However this would require the introduction of two sphere of unique dimensions. EPSG has therefore implemented the Tunisia mining grid as transformation method in its own right. Formulas are:

f (grads) = 36.5964 + [(N - 360) * A]

where N is in kilometres and A = 0.010015 if N > 360, else A = 0.01002.

l_Paris (grads) = 7.83445 + [(E - 270) * 0.01285], where E is in kilometres.

The reverse formulas are:

E (km) = 270 + [(l_Paris - 7.83445) / 0.01285] where l is in grads.

N (km) = 360 + [(f - 36.5964) / B]

where f is in grads and B = 0.010015 if N > 36.5964, else B = 0.01002.

Modern practice in Tunisia is to quote latitude and longitude in degrees with longitudes referenced to the Greenwich meridian. The formulas required in addition to the above are:

f (degrees) = (f_g * 0.9) where f_g is in grads.

l_Greenwich (degrees) = [(l_Paris + 2.5969213) * 0.9] where l_Paris is in grads.

f (grads) = (f_d / 0.9) where f_d is in decimal degrees.

l_Paris (grads) = [(l_Greenwich / 0.9) - 2.5969213)] where l_Greenwich is in decimal degrees.

Example:

For grid location 302598,

Latitude f  = 36.5964 + [(598 - 360) * A].  As N > 360, A = 0.01005.
              38.97997 grads = 35.08197 degrees.

Longitude l  = 7.83445 + [(E - 270) * 0.01285, where E = 302.
          l  = 8.22437 grads east of Paris
             = 9.73916 degrees east of Greenwich.

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