EPSG

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

2021-11-04

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 - lonF) M = a ko ln{tan(pi/4 + latF/2)[(1 – e sin(latF))/(1 + e sin(latF))]^(e/2)} N = (NF – M) + a ko ln{tan(pi/4 + lat/2)[(1 – e sin(lat))/(1 + e sin(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 atan(t) t = B^((NF-M-N)/(a*ko)) B = base of the natural logarithm, 2.7182818... and ko is calculated as for the forward transformation above. lon = ((E - EF)/(a*ko)) + lonF

Parameters: Ellipsoid Krassowsky 1940 a = 6378245.00m 1/f = 298.300 then e = 0.08181333 and e^2 = 0.00669342 Latitude first SP = 42°00'00"N = 0.73303829 rad Latitude of false origin = 42°00'00"N = 0.73303829 rad Longitude of false origin = 51°00'00"E = 0.89011792 rad Eastings at false origin EF = 0.00 m Northing at false origin NF = 0.00 m Forward calculation for: Latitude = 53°00'00.00"N = 0.9250245 rad Longitude = 53°00'00.00"E = 0.9250245 rad ko = 0.744260894 M = 3819897.85 Easting E = 165704.29 m Northing N = 1351950.22 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