projected "Main Terms of Reference for the State Geodetic Network"; Federal Geodetic Service of Russia; 1994 2002-06-22 true false http://www.opengis.net/def/crs/EPSG/8.5/20027 Pulkovo 1995 / Gauss-Kruger zone 27 Also found with truncated false easting - see Pulkovo 1995 / Gauss-Kruger CM 159E (code 2486). Russian Federation - onshore between 156°E and 162°E. 156 162 50.27 77.2 OGP 2014-05-01 false false http://www.opengis.net/def/area/EPSG/8.5/1786 Russia - 156°E to 162°E onshore Medium scale topographic mapping. conversion OGP 2002-06-22 true false http://www.opengis.net/def/coordinateOperation/EPSG/8.5/16227 6-degree Gauss-Kruger zone 27 Also found with zone truncated from false easting: see 6-degree Gauss-Kruger cm 159E (code 16327). Original transformation by Gauss-Kruger formula. Between 156°E and 162°E, northern hemisphere between equator and 84°N, onshore and offshore. 156 162 0 84 OGP 2011-05-09 false false http://www.opengis.net/def/area/EPSG/8.5/1985 World - N hemisphere - 156°E to 162°E Medium scale topographic mapping. ISO 1000. 1995-06-02 false http://www.opengis.net/def/uom/EPSG/8.5/9001 metre Also known as International metre. SI standard unit. length 0 EPSG guidance note #7-2, http://www.epsg.org 2012-02-13 true false true For Projected Coordinate System OSGB 1936 / British National Grid Parameters: Ellipsoid Airy 1830 a = 6377563.396 m 1/f = 299.32496 then e'^2 = 0.00671534 and e^2 = 0.00667054 Latitude of natural origin (LatO) = 49°00'00"N = 0.85521133 rad Longitude of natural origin (LonO) = 2°00'00"W = -0.03490659 rad Scale factor (ko) = 0.9996013 False Eastings (FE) = 400000.00 m False Northings (FN) = -100000.00 m Forward calculation for: Latitude = 50°30'00.00"N = 0.88139127 rad Longitude = 00°30'00.00"E = 0.00872665 rad Constants of the projection: n = 0.00167322 B = 6366914.609 h1 = 0.0008347452 h2 = 0.0000007554 h3 = 1.18487E-09 h4 = 2.40864E-12 QO = 0.9787671618 ?O0 = 0.8518980373 ?O1 = 0.0008273732 ?O2 = -0.0000001986 ?O3 = -1.0918E-09 ?O4 = 1.2218E-12 Mo = 5429228.602 Q = 1.0191767215 ? = 0.8781064142 ?0 = 0.0278629616 ?0 = 0.8785743280 ?1 = -0.0000086229 ?1 = 0.0008215669 ?2 = -0.0000000786 ?2 = -0.0000002768 ?3 = 1.05551E-10 ?3 = -1.01855E-09 ?4 = 3.97791E-13 ?4 = 1.67447E-12 ? = 0.0278542603 ? = 0.8793956171 Then Easting E = 577274.99 metres Northing N = 69740.50 metres Reverse calculation for same easting and northing first gives: h1' = 0.0008347455 h2' = 0.0000000586 h3' = 1.65563E-10 h4' = 2.13692E-13 Then ?' = 0.87939562 ?' = 0.0278542603 ?1' = 0.0008213109 ?1' = -0.0000086953 ?2' = -0.0000000217 ?2' = -0.0000000061 ?3' = -1.41881E-10 ?3' = 1.486E-11 ?4' = 1.49609E-13 ?4' = 3.50657E-14 ?0' = 0.8785743280 ?0' = 0.0278629616 ?' = 0.8781064142 Q' = 1.0191767215 Q" 1st iteration = 1.0243166838 Q" 2nd iteration = 1.0243306667 Q" 3rd iteration = 1.0243307046 Q" 4th iteration = 1.0243307047 Then Latitude (Lat) = 50°30'00.000"N Longitude (Lon) = 00°30'00.000"E http://www.opengis.net/def/method/EPSG/8.5/9807 Transverse Mercator 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. For the calculation of easting and northing from latitude and longitude, first calculate constants for the projection: n = f / (2-f) B = [a/(1+n)] (1 + n^2/4 + n^4/64) h1 = n/2 ? (2/3)n^2 + (5/16)n^3 + (41/180)n^4 h2 = (13/48)n^2 ? (3/5)n^3 + (557/1440)n^4 h3 = (61/240)n^3 ? (103/140)n^4 h4 = (49561/161280)n^4 Then the meridional arc distance from equator to the projection origin (Mo) is computed from: If LatO = 0 then Mo = 0 else if LatO ? 90°N ? ?/2 radians Mo = B (?/2) else if LatO ? 90°S ? -?/2 radians Mo = B (-?/2) else Qo = asinh(tan LatO) ? [e atanh(e sin LatO)] ?o = atan(sinh Qo) ?O0 = asin (sin ?o) Note: The previous two steps are taken from the generic calculation flow given below for latitude Lat, but here for LatO may be simplified to ?O0 = ?o = atan(sinh Qo). ?O1 = h1 sin(2?Oo) ?O2 = h2 sin(4?Oo) ?O3 = h3 sin(6?Oo) ?O4 = h4 sin(8?Oo) ?O = ?O0+ ?O1+ ?O2+ ?O3+ ?O4 Mo = B ?O end Note: if the projection grid origin is very close to the pole (within 2" or 50m), the tangent function in the equation for Qo is unstable and may fail. Mo may instead be calculated as: Mo = a[(1 ? e^2/4 ? 3e^4/64 ? 5e^6/256 ?....)LatO ? (3e^2/8 + 3e^4/32 + 45e^6/1024+....)sin2LatO + (15e^4/256 + 45e^6/1024 +.....)sin4LatO ? (35e^6/3072 + ....)sin6LatO + .....] with LatO in radians. Then Q = asinh(tan Lat) ? [e atanh(e sin Lat)] ? = atan(sinh Q) ?0 = atanh [cos ? sin(Lon ? LonO)] ?0 = asin (sin ? cosh ?0) ?1 = h1 sin(2?0) cosh(2?0) ?1 = h1 cos(2?0) sinh(2?0) ?2 = h2 sin(4?0) cosh(4?0) ?2 = h2 cos(4?0) sinh(4?0) ?3 = h3 sin(6?0) cosh(6?0) ?3 = h3 cos(6?0) sinh(6?0) ?4 = h4 sin(8?0) cosh(8?0) ?4 = h4 cos(8?0) sinh(8?0) ? = ?0 + ?1 + ?2 + ?3 + ?4 ? = ?0 + ?1 + ?2 + ?3 + ?4 and Easting, E = FE + ko B ? Northing, N = FN + ko (B ? ? Mo) For the reverse formulas to convert Easting and Northing projected coordinates to latitude and longitude first calculate constants of the projection where n is as for the forward conversion, as are B and Mo: h1' = n/2 ? (2/3)n^2 + (37/96)n^3 ? (1/360)n^4 h2' = (1/48)n^2 + (1/15)n^3 ? (437/1440)n^4 h3' = (17/480)n^3 ? (37/840)n^4 h4' = (4397/161280)n^4 Then ?' = (E ? FE) / (B ko) ?' = [(N ? FN) + ko Mo] / (B ko) ?1' = h1' sin(2?') cosh(2?') ?1' = h1' cos(2?') sinh(2?') ?2' = h2' sin(4?') cosh(4?') ?2' = h2' cos(4?') sinh(4?') ?3' = h3' sin(6?') cosh(6?') ?3' = h3' cos(6?') sinh(6?') ?4' = h4' sin(8?') cosh(8?') ?4' = h4' cos(8?') sinh(8?') ?0' = ?' ? (?1' + ?2' + ?3' + ?4') ?0' = ?' ? (?1' + ?2' + ?3' + ?4') ?' = asin(sin ?0' / cosh ?0') Q' = asinh(tan ?') Q" = Q' + [e atanh(e tanh Q')] = Q' + [e atanh(e tanh Q")] which should be iterated until the change in Q" is insignificant. Then Lat = atan(sinh Q") Lon = LonO + asin(tanh(?0') / cos ?') 0 EPSG guidance note number 7. 1999-09-09 false 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). http://www.opengis.net/def/parameter/EPSG/8.5/8801 Latitude of natural origin 159 Abbeviated as "CM". Abbreviation for "Central Meridian". EPSG guidance note number 7. 2002-06-22 false 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)". http://www.opengis.net/def/parameter/EPSG/8.5/8802 Longitude of natural origin 1 EPSG guidance note number 7. 1999-09-09 false The factor by which the map grid is reduced or enlarged during the projection process, defined by its value at the natural origin. http://www.opengis.net/def/parameter/EPSG/8.5/8805 Scale factor at natural origin 27500000 This alias applies only in the case of projection methods which have an axis positive west, e.g. Transverse Mercator (South Orientated). EPSG guidance note number 7. 2002-07-31 false 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. http://www.opengis.net/def/parameter/EPSG/8.5/8806 False easting 0 This alias applies only in the case of projection methods which have an axis positive south, e.g. Transverse Mercator (South Orientated). EPSG guidance note number 7. 2002-07-31 false 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. http://www.opengis.net/def/parameter/EPSG/8.5/8807 False northing geographic 2D "Main Terms of Reference for the State Geodetic Network"; Federal Geodetic Service of Russia; 1994 2008-09-24 true false http://www.opengis.net/def/crs/EPSG/8.5/4200 Pulkovo 1995 Russian Federation - onshore and offshore. 18.92 -168.97 39.87 85.2 ISO 3166 Maintenance Agency. ftp://ftp.fu-berlin.de/pub/doc/iso 2014-05-01 false false http://www.opengis.net/def/area/EPSG/8.5/1198 Russia Area crosses 180-degree meridian. RU RUS 643 Geodetic survey. ellipsoidal OGP 2008-06-23 false http://www.opengis.net/def/cs/EPSG/8.5/6422 Ellipsoidal 2D CS. Axes: latitude, longitude. Orientations: north, east. UoM: degree Coordinates referenced to this CS are in degrees. Any degree representation (e.g. DMSH, decimal, etc.) may be used but that used must be declared for the user by the supplier of data. Used in geographic 2D coordinate reference systems. http://www.opengis.net/def/axis/EPSG/8.5/106 Lat north http://www.opengis.net/def/axis/EPSG/8.5/107 Long east geodetic "Main Terms of Reference for the State Geodetic Network"; Federal Geodetic Service of Russia; 1994 2008-06-24 false http://www.opengis.net/def/datum/EPSG/8.5/6200 Pulkovo 1995 Scientific adjustment. Fundamental point: Pulkovo observatory. Latitude: 59°46'15.359"N, longitude: 30°19'28.318"E (of Greenwich). 1995-01-01 Cartesian OGP 2001-04-29 false http://www.opengis.net/def/cs/EPSG/8.5/4530 Cartesian 2D CS. Axes: northing, easting (X,Y). Orientations: north, east. UoM: m. Used in projected and engineering coordinate reference systems. http://www.opengis.net/def/axis/EPSG/8.5/48 X north http://www.opengis.net/def/axis/EPSG/8.5/47 Y east