EPSG Dataset :: v12.003

Lambert Conic Conformal (1SP variant B)

Coordinate Operation Method Details [VALID]

Name:

Lambert Conic Conformal (1SP variant B)

Code:

1102

Operation is Reversible:

Yes

Formula:

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.

To derive the projected Easting and Northing coordinates of a point with geographical coordinates (lat,lon):

E = Ef + r sin(theta)
N = Nf + rf - r cos(theta)
where
mO = cos(latO)/(1 – e^2 sin^2(latO))^0.5 where latO is the latitude of natural origin
tO = tan(pi/4 – latO/2)/[(1 – e sin(latO))/(1 + e sin(latO))]^e/2
tf = tan(pi/4 – latF/2)/[(1 – e sin(latF))/(1 + e sin(latF))]^e/2
t = tan(pi/4 – lat/2)/[(1 – e sin(lat))/(1 + e sin(lat))]^e/2
n = sin(latO)
F = mO/(n tO^n)
rf = a F tf^n kO
r = a F t^n kO
lonF = lonO
theta = n(lon – lonO)
As with other conics, a negative n and r result for projections centered in the Southern Hemisphere.

The reverse formulas to derive the latitude and longitude of a point from its Easting and Northing values are:

lat = pi/2 - 2arctan{t'[(1 - e sin(lat))/(1 + e sin(lat))]^(e/2)}
lon = theta'/n +lonO
where
n, F, rf and lonO are derived as for the forward calculation
r' = +/-[(E - Ef)^2 + {rf - (N - Nf)}^2]^0.5 taking the sign of n
t' = (r'/(a k0 F))^(1/n)
If n is positive, theta' = atan2{(E – Ef) , [rf – (N – Nf)]}
but if n is negative the signs of both arguments of the atan2 function must be reversed and theta' = atan2{– (E – Ef) , – [rf – (N – Nf)]}

Note that the formula for lat requires iteration. First calculate t' and then a trial value for lat using
lat = π/2-2atan(t'). Then use the full equation for lat substituting the trial value into the right hand side of the equation. Thus derive a new value for lat. Iterate the process until lat does not change significantly. The solution should quickly converge, in 3 or 4 iterations.

Example:

Parameters:
Ellipsoid: GRS 1980, a = 6378137.000 m., 1/f = 298.2572221
then e = 0.081819191 and e^2 = 0.006694380

Latitude of natural origin LatO 44°22'45"N = 0.774562578 rad
Scale factor at natural origin ko 1.000000
Latitude of false origin LatF 45°11'00"N = 0.788597934 rad
Longitude of false origin LongF 6°49'00"E = 0.118973277 rad
Easting at false origin Ef 150000.00 m
Northing at false origin Nf 50000.00 m

Forward calculation for:
Latitude: 47°00'00.000"N = 0.820304748 rad
Longitude: 7°00'00.000"E = 0.12217304 rad
first gives
mO = 0.715900163 tO = 0.422551185 tf = 0.414305398
n = 0.699403505 F = 1.869760448 rf = 6439208.575
t = 0.395846092 r = 6237180.887 theta = 0.002237931

Then Easting E = 163958.366 m
Northing N = 252043.307 m

Reverse calculation for the same easting and northing first gives

r' = 6237180.887
t' = 0.395846092
theta' = 0.002237931

Then Latitude = 47°00'00.000"N
Longitude = 7°00'00.000"E

Method
Parameters:

Parameter Name	Parameter Code	Sign reversal	Parameter Description
Latitude of natural origin	8801	No	The latitude of the point from which the values of both the geographical coordinates on the ellipsoid and the grid coordinates on the projection are deemed to increment or decrement for computational purposes. Alternatively it may be considered as the latitude of the point which in the absence of application of false coordinates has grid coordinates of (0,0).
Scale factor at natural origin	8805	No	The factor by which the map grid is reduced or enlarged during the projection process, defined by its value at the natural origin.
Latitude of false origin	8821	No	The latitude of the point which is not the natural origin and at which grid coordinate values false easting and false northing are defined.
Longitude of false origin	8822	No	The longitude of the point which is not the natural origin and at which grid coordinate values false easting and false northing are defined.
Easting at false origin	8826	No	The easting value assigned to the false origin.
Northing at false origin	8827	No	The northing value assigned to the false origin.

Meta Data

Information Source:

EPSG guidance note #7-2, https://epsg.org

Data Source:

EPSG

Revision Date:

January 13, 2021

Change ID:

[2020.108]

Wildcard	Example
% or *	Any wildcard characters
? or _	One wildcard character
[ - ]	[ - ] Range e.g. N[a-c] will return all geodetic objects that contains a string starting with the letter 'N' or 'n' followed by any of the letters contained within the range specified within the square bracket, e.g. letters a, b and c.
\|	Or e.g. E[a\|e]M will return all geodetic objects that contains a string starting with the letter E(e), ends with the letter M(m) and also contain either the letter a or letter e.