| Name | Lambert Conic Conformal (2SP) |
| EPSG Code | 9802 |
| GeoTIFF Code | CT_LambertConfConic_2SP (9) |
| CT_LambertConfConic (9) | |
| OGC WKT Name | Lambert_Conformal_Conic_2SP |
| Supported By | EPSG, GeoTIFF, PROJ.4, OGC WKT |
| Name | EPSG # | GeoTIFF ID | OGC WKT | Units | Notes |
|---|---|---|---|---|---|
| Latitude of false origin | 1 | FalseOriginLat | latitude_of_origin | Angular | |
| Longitude of false origin | 2 | FalseOriginLong | central_meridian | Angular | |
| Latitude of first standard parallel | 3 | StdParallel1 | standard_parallel_1 | Angular | |
| Latitude of second standard parallel | 4 | StdParallel2 | standard_parallel_2 | Angular | |
| Easting of false origin | 6 | FalseOriginEasting | false_easting | Linear | |
| Northing of false origin | 7 | FalseOriginNorthing | false_northing | Linear |
+proj=lcc +lat_1=Latitude of first standard parallel
+lat_2=Latitude of second standard parallel
+lat_0=Latitude of false origin
+lon_0=Longitude of false origin
+x_0=False Origin Easting
+y_0=False Origin Northing
Sometimes however, although a one standard parallel Lambert is normally considered to have unity scale factor on the standard parallel, a scale factor of slightly less than unity is introduced on this parallel. This is a regular feature of the mapping of some former French territories and has the effect of making the scale factor unity on two other parallels either side of the standard parallel. The projection thus, strictly speaking, becomes a Lambert Conic Conformal projection with two standard parallels. From the one standard parallel and its scale factor it is possible to derive the equivalent two standard parallels and then treat the projection as a two standard parallel Lambert conical conformal, but this procedure is seldom adopted. Since the two parallels obtained in this way will generally not have integer values of degrees or degrees and minutes it is instead usually preferred to select two specific parallels on which the scale factor is to be unity, - as for several State Plane Coordinate systems in the United States.
The choice of the two standard parallels will usually be made according to the latitudinal extent of the area which it is wished to map, the parallels usually being chosen so that they each lie a proportion inboard of the north and south margins of the mapped area. Various schemes and formulas have been developed to make this selection such that the maximum scale distortion within the mapped area is minimised, e.g. Kavraisky in 1934, but whatever two standard parallels are adopted the formulas for the projected coordinates are the same.
For territories with limited latitudinal extent but wide longitudinal width it may sometimes be preferred to use a single projection rather than several bands or zones of a Transverse Mercator. If the latitudinal extent is also large there may still be a need to use two or more zones if the scale distortion at the extremities of the one zone becomes too large to be tolerable.
To derive the projected Easting and Northing coordinates of a point with geographical coordinates (*,*) the formulas for the two standard parallel case are:
Easting, E = EF + r sin *
Northing, N = NF + rF - r cos *
where m = cos*/(1 - e2sin2*)1/2 for m1, *1, and m2, *2 where *1 and *2 are the latitudes
of the standard parallels
t = tan(*/4 - */2)/[(1 - e sin*)/(1 + e sin*)]e/2 for t1, t2, tF and t using *1,*2,*
F and * respectively
n = (loge m1 - loge m2)/(loge t1 - loge t2)
F = m1/(nt1n)
r = a F tn for rF and r, where rF is the radius of the parallel of latitude of the
false origin
* = n(* - *0)
The reverse formulas to derive the latitude and longitude of a point from its Easting and
Northing values are:
* = */2 - 2arctan{t'[(1 - esin*)/(1 + esin*)]e/2}
* = *'/n +*0
where
r' = *[(E - EF)2 + {rF - (N - NF)}2]1/2 , taking the sign of n
t' = (r'/aF)1/n
*' = arctan [(E- EF)/(rF - (N- NF))]
and n, F, and rF are derived as for the forward calculation.
With minor modifications these formulas can be used for the single standard parallel
case. Then
E = FE + r sin*
N = FN + r0 - r cos*, using the natural origin rather than the false origin.
where
n = sin *0
r = aFtn k0 for r0, and r
t is found for t0, *0 and t, * and m, F, and * are found as for the two standard
parallel case
The reverse formulas for * and * are as for the two standard parallel case above,
with n, F and r0 as before and
*' = arctan[(E - FE)/{r0 -(N - FN)}]
r' = *[(E - FE)2 + {r0 - (N - FN)}2]1/2
t' = (r'/ak0F)1/n","For Projected Coordinate System NAD27 / Texas South Central
Parameters:
Ellipsoid Clarke 1866, a = 6378206.400 metres = 20925832.16 US survey feet
1/f = 294.97870
then e = 0.08227185 and e^2 = 0.00676866
First Standard Parallel 28o23'00""N = 0.49538262 rad
Second Standard Parallel 30o17'00""N = 0.52854388 rad
Latitude False Origin 27o50'00""N = 0.48578331 rad
Longitude False Origin 99o00'00""W = -1.72787596 rad
Easting at false origin 2000000.00 US survey feet
Northing at false origin 0.00 US survey feet
Forward calculation for:
Latitude 28o30'00.00""N = 0.49741884 rad
Longitude 96o00'00.00""W = -1.67551608 rad
first gives :
m1 = 0.88046050 m2 = 0.86428642
t = 0.59686306 tF = 0.60475101
t1 = 0.59823957 t2 = 0.57602212
n = 0.48991263 F = 2.31154807
r = 37565039.86 rF = 37807441.20
theta = 0.02565177
Then Easting E = 2963503.91 US survey feet
Northing N = 254759.80 US survey feet
Reverse calculation for same easting and northing first gives:
theta' = 0.025651765 r' = 37565039.86
t' = 0.59686306
Then Latitude = 28o30'00.000""N
Longitude = 96o00'00.000""W