EPSG Dataset :: v12.003

Mercator (variant B)

Coordinate Operation Method Details [VALID]

Name:

Mercator (variant B)

Code:

9805

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.

The formulas to derive projected Easting and Northing coordinates are:

ko = cos(latSP1)/(1 - e^2*sin^2(latSP1))^0.5
where latSP1 is the absolute value of the first standard parallel (i.e. positive).

E = FE + a*ko(lon - lonO)
N = FN + a*ko* ln{tan(pi/4 + lat/2)[(1 - esin(lat))/(1 + esin(lat))]^e/2} where logarithms are natural.

The reverse formulas to derive latitude and longitude from E and N values are:

lat = chi + (esq/2 + 5e^4/24 + e^6/12 + 13e^8/360) sin(2chi)
+ (7e^4/48 + 29e^6/240 + 811e^8/11520) sin(4chi)
+ (7e^6/120 + 81e^8/1120) sin(6chi) + (4279e^8/161280) sin(8chi)

where chi = pi/2 - 2 arctan t
t = B^((FN-N)/(a*ko))
B = base of the natural logarithm, 2.7182818...
and ko is calculated as for the forward transformation above.
lon = ((E - FE)/(a*ko)) + lonO

Example:

For Projected Coordinate System Pulkovo 1942 / Caspian Sea Mercator

Parameters:
Ellipsoid Krassowski 1940 a = 6378245.00m 1/f = 298.300
then e = 0.08181333 and e^2 = 0.00669342

Latitude of first SP = 42°00'00"N = 0.73303829 rad
Longitude of natural origin = 51°00'00"E = 0.89011792 rad
False Eastings FE = 0.00 m
False Northings (at equator) FN = 0.00 m
Forward calculation for:
Latitude = 53°00'00.00"N = 0.9250245 rad
Longitude = 53°00'00.00"E = 0.9250245 rad

gives

ko = 0.744260894
Easting E = 165704.29 m
Northing N = 5171848.07 m

Reverse calculation for same easting and northing first gives :
t = 0.336391288
chi = 0.921795958
Latitude = 53°00'00.000"N
Longitude = 53°00'00.000"E

Method
Parameters:

Parameter Name	Parameter Code	Sign reversal	Parameter Description
Latitude of 1st standard parallel	8823	No	For a conic projection with two standard parallels, this is the latitude of one of the parallels of intersection of the cone with the ellipsoid. It is normally but not necessarily that nearest to the pole. Scale is true along this parallel.
Longitude of natural origin	8802	No	The longitude 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 longitude of the point which in the absence of application of false coordinates has grid coordinates of (0,0). Sometimes known as "central meridian (CM)".
False easting	8806	No	Since the natural origin may be at or near the centre of the projection and under normal coordinate circumstances would thus give rise to negative coordinates over parts of the mapped area, this origin is usually given false coordinates which are large enough to avoid this inconvenience. The False Easting, FE, is the value assigned to the abscissa (east or west) axis of the projection grid at the natural origin.
False northing	8807	No	Since the natural origin may be at or near the centre of the projection and under normal coordinate circumstances would thus give rise to negative coordinates over parts of the mapped area, this origin is usually given false coordinates which are large enough to avoid this inconvenience. The False Northing, FN, is the value assigned to the ordinate (north or south) axis of the projection grid at the natural origin.

Meta Data

Remarks:

Used for most nautical charts.

Information Source:

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

Data Source:

EPSG

Revision Date:

May 3, 2019

Change ID:

[2004.32] [2004.43] [2010.058] [2010.098] [2015.021] [2019.018]

Alias:

Alias	Naming System	Remarks
Mercator (2SP)	EPSG alias	This was the method name used prior to October 2010. However it is ambiguous as it is also applicable to variant C (method code 1044).

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.