Table of Contents
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POSC Specifications Version 2.2 |
Epicentre Usage Guide Projections and Projected Coordinate Systems |
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Table of Contents |
The Lambert Conformal Conic with one standard parallel formulas as published by the Army Map Service (AMS) are still in use in several countries. The AMS uses series expansion formulas for ease of computation, as was normal before the electronic computer made such approximate methods unnecessary. Where the expansion series have been carried to enough terms the results are the same as the above formulas to the centimetre level. However in some countries the expansion formulas were truncated to the third order and the projection is not fully conformal. The full formulas are used in Libya but from 1915 for France, Morocco, Algeria, Tunisia and Syria the truncated formulas were used. In 1943 in Algeria and Tunisia, from 1948 in France, from 1953 in Morocco and from 1973 in Syria the truncated formulas were replaced with the full formulas.
To compute the Lambert Conic Near-Conformal the following formulas are used:
Easting: 
Northing: 
using the natural origin rather than the false origin.
Compute constants for the ellipse:
Then compute the meridional arc from the equator to the parallel.
where, if we truncate this term to the third order by assuming that B = C = D = 0,
The reverse formulas for j and l from E and N with ro and MS as above:
where jo and j are in degrees
where lo and l are in radians
where
and
For Projected Coordinate System Deir ez Zor / Levant Zone
Parameters:
Ellipsoid |
Clarke 1880 (IGN) |
a = 6378249.2 m |
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1/f = 293.46602 |
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then |
b = 6356515.0 m |
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n = 0.001706682563 |
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Latitude Natural Origin |
j o |
34°39'00" N = |
0.604756586 rad |
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Second Standard Parallel |
lo |
37°21'00" E = |
0.651880476 rad |
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Scale factor at origin |
ko |
0.99962560 |
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False Eastings |
FE |
300000.00 m |
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False Northings |
FN |
300000.00 m |
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Forward calculation for:
Latitude |
j |
37°31'17.625" N = |
0.654874806 rad |
Longitude |
l |
34°08'11.291" E = |
0.595793792 rad |
first gives
| A = | 4.1067494*10-15 | A' = | 111131.8633 |
| B' = | 16300.64407 | C' = | 17.38751 |
| D' = | 0.02308 | E' = | 0.000033 |
| so = | 3835482.233 | s = | 4154101.458 |
| m = | 318619.225 | ||
| M = | 318632.72 | MS = | 30.82262319 |
| q = | -0.03188875 | ro = |
9235264.405 |
| r = | 8916631.685 |
Then:
| Easting: | E = 15707.96 m | (cf..E = 15708.00 using full formulas) |
| Northing | N = 623165.96 m | (cf..N = 623167.20 using full formulas) |
Reverse the calculations. Use the same parameters and use the E and N values to calculate the latitude and longitude:
| q' = | -0.03188875 |
| r' = | 8916631.685 |
| M' = | 318632.72 |
Then
| Latitude | j = |
0.654874806 rad | = | 37°31'17.625" N |
| Longitude | l = |
0.595793792 rad | = | 34°08'11.291" E |
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