Table of Contents
|
POSC Specifications Version 2.2 |
Epicentre Usage Guide Projections and Projected Coordinate Systems |
| | |
Table of Contents |
The Mercator projection is a special case of the Lambert Conic Conformal projection with the equator as the single standard parallel. All other parallels of latitude are straight lines and the meridians are also straight lines at right angles to the equator, equally spaced. It is little used for land mapping purposes but is in universal use for navigation charts and is the basis for the transverse and oblique forms of the Mercator. As well as being conformal, it has the particular property that straight lines drawn on it are lines of constant bearing. Thus navigators may derive their course from the angle the straight course line makes with the meridians.
In the few cases in which the Mercator projection is used for terrestrial applications or land mapping, such as in Indonesia prior to the introduction of the Universal Transverse Mercator, a scale factor may be applied to the projection. This has the same effect as choosing two standard parallels on which the true scale is maintained at equal north and south latitudes either side of the equator.
The formulas to derive projected Easting and Northing coordinates are:
For the two standard parallel case, k0 is first calculated from
where j1 is the absolute value of the first standard parallel (i.e., positive).
Then, for both one and two standard parallel cases,
where symbols are as listed above, and ln represents a natural logarithm.
The reverse formulas to derive latitude and longitude from E and N values are:
where
B = base of the natural logarithm, 2.7182818...
and, for the two standard parallel case, k0 is calculated as for the forward transformation above.
For longitude,
For Projected Coordinate System Pulkovo 1942 / Mercator Caspian Sea
Parameters:
|
Ellipsoid |
Krassowski 1940 |
a = 6378245.00 m |
|||
|
|
|
1/f = 298.300 |
|||
|
|
|
e = 0.08181333 |
|||
|
|
|
e2 = 0.00669342 |
|||
|
Latitude First Standard Parallel |
j 0 |
42°00' 00"N = |
0.73303829 rad |
||
|
Longitude of Natural Origin |
l 0 |
51°00' 00"E = |
0.89011792 rad |
||
|
False Eastings |
FE |
0.00 m |
|
||
|
False Northings |
FN |
0.00 m |
|
||
Then the natural orgin at latitude of 0° N has a scale cactor k0 = 0.74426089
Forward calculation for:
|
Latitude |
j |
53°00' 00.00" N = |
0.9250245 rad |
|
Longitude |
l |
53°00' 00.00" E = |
0.9250245 rad |
gives the following easting and northing:
|
Easting |
E = 165704.29 m |
|
Northing |
N = 5171848.07m |
Reverse the calculations. Use the same parameters and use the E and N values to calculate the latitude and longitude:
t = 0.33639129
c
= 0.92179596Then
|
Latitude |
j = |
53°00' 00.00" N |
|
Longitude |
l = |
53°00' 00.00" E |
For Projected Coordinate System Makassar / NEIEZ
Parameters:
|
Ellipsoid |
Bessel 1841 |
a = 6377397.155 m |
|||
|
|
|
1/f = 299.15281 |
|||
|
|
|
e = 0.08169683 |
|||
|
|
|
e2 = 0.00667437 |
|||
|
Latitude of Natural Origin |
j 0 |
0 00°00' 00"N = |
0.00 rad |
||
|
Longitude of Natural Origin |
l 0 |
0 110°00' 00"E = |
1.91986218 rad |
||
|
Scale Factor |
k0 |
0.997 |
|
||
|
False Eastings |
FE |
3900000.00 m |
|
||
|
False Northings |
FN |
900000.00 m |
|
||
Forward calculation for:
|
Latitude |
j |
3°00' 00.00" S = |
-0.05235988 rad |
|
Longitude |
l |
120°00' 00.00" E = |
= 2.09439510 rad |
gives the following easting and northing:
|
Easting |
E = 5009726.58 m |
|
Northing |
N = 569150.82 m |
Reverse the calculations. Use the same parameters and use the E and N values to calculate the latitude and longitude:
t = 1.0534121
c
= -0.0520110Then
|
Latitude |
j = |
3°00' 00.00" S |
|
Longitude |
l = |
120°00' 00.00" E |
| | |
Table of Contents |