projected 2020-03-30 true false https://www.opengis.net/def/crs/EPSG/9.9.1/25830 ETRS89 / UTM zone 30N Europe between 6°W and 0°W: Faroe Islands offshore; Ireland - offshore; Jan Mayen - offshore; Norway including Svalbard - offshore; Spain - onshore and offshore. -6 0 35.26 80.53 OGP 2020-07-24 false false https://www.opengis.net/def/area/EPSG/9.9.1/2124 Europe - 6°W to 0°W and ETRS89 by country Large and medium scale topographic mapping and engineering survey. conversion 1995-12-02 true false https://www.opengis.net/def/coordinateOperation/EPSG/9.9.1/16030 UTM zone 30N Between 6°W and 0°W, northern hemisphere between equator and 84°N, onshore and offshore. -6 0 0 84 OGP 2011-05-09 false false https://www.opengis.net/def/area/EPSG/9.9.1/1931 World - N hemisphere - 6°W to 0°W Large and medium scale topographic mapping and engineering survey. Bureau International des Poids et Mesures (BIPM), www.bipm.org 2018-05-29 true false https://www.opengis.net/def/uom/EPSG/9.9.1/9001 metre SI base unit for length. 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 ξO0 = 0.8518980373 ξO1 = 0.0008273732 ξO2 = -0.0000001986 ξO3 = -1.0918E-09 ξO4 = 1.2218E-12 Mo = 5429228.602 Q = 1.0191767215 β = 0.8781064142 η0 = 0.0278629616 ξ0 = 0.8785743280 η1 = -0.0000086229 ξ1 = 0.0008215669 η2 = -0.0000000786 ξ2 = -0.0000002768 η3 = 1.05551E-10 ξ3 = -1.01855E-09 η4 = 3.97791E-13 ξ4 = 1.67447E-12 η = 0.0278542603 ξ = 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 ξ' = 0.87939562 η' = 0.0278542603 ξ1' = 0.0008213109 η1' = -0.0000086953 ξ2' = -0.0000000217 η2' = -0.0000000061 ξ3' = -1.41881E-10 η3' = 1.486E-11 ξ4' = 1.49609E-13 η4' = 3.50657E-14 ξ0' = 0.8785743280 η0' = 0.0278629616 β' = 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 https://www.opengis.net/def/method/EPSG/9.9.1/9807 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 ≡ π/2 radians Mo = B (π/2) else if LatO ≡ 90°S ≡ -π/2 radians Mo = B (-π/2) else Qo = asinh(tan LatO) – [e atanh(e sin LatO)] βo = atan(sinh Qo) ξO0 = asin (sin βo) 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 ξO0 = βo = atan(sinh Qo). ξO1 = h1 sin(2ξOo) ξO2 = h2 sin(4ξOo) ξO3 = h3 sin(6ξOo) ξO4 = h4 sin(8ξOo) ξO = ξO0+ ξO1+ ξO2+ ξO3+ ξO4 Mo = B ξO 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)] β = atan(sinh Q) η0 = atanh [cos β sin(Lon – LonO)] ξ0 = asin (sin β cosh η0) ξ1 = h1 sin(2ξ0) cosh(2η0) η1 = h1 cos(2ξ0) sinh(2η0) ξ2 = h2 sin(4ξ0) cosh(4η0) η2 = h2 cos(4ξ0) sinh(4η0) ξ3 = h3 sin(6ξ0) cosh(6η0) η3 = h3 cos(6ξ0) sinh(6η0) ξ4 = h4 sin(8ξ0) cosh(8η0) η4 = h4 cos(8ξ0) sinh(8η0) ξ = ξ0 + ξ1 + ξ2 + ξ3 + ξ4 η = η0 + η1 + η2 + η3 + η4 and Easting, E = FE + ko B η Northing, N = FN + ko (B ξ – 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 η' = (E – FE) / (B ko) ξ' = [(N – FN) + ko Mo] / (B ko) ξ1' = h1' sin(2ξ') cosh(2η') η1' = h1' cos(2ξ') sinh(2η') ξ2' = h2' sin(4ξ') cosh(4η') η2' = h2' cos(4ξ') sinh(4η') ξ3' = h3' sin(6ξ') cosh(6η') η3' = h3' cos(6ξ') sinh(6η') ξ4' = h4' sin(8ξ') cosh(8η') η4' = h4' cos(8ξ') sinh(8η') ξ0' = ξ' – (ξ1' + ξ2' + ξ3' + ξ4') η0' = η' – (η1' + η2' + η3' + η4') β' = asin(sin ξ0' / cosh η0') Q' = asinh(tan β') 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(η0') / cos β') 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). https://www.opengis.net/def/parameter/EPSG/9.9.1/8801 Latitude of natural origin -3 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)". https://www.opengis.net/def/parameter/EPSG/9.9.1/8802 Longitude of natural origin 0.9996 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. https://www.opengis.net/def/parameter/EPSG/9.9.1/8805 Scale factor at natural origin 500000 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. https://www.opengis.net/def/parameter/EPSG/9.9.1/8806 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. https://www.opengis.net/def/parameter/EPSG/9.9.1/8807 False northing geographic 2D EPSG. See 3D CRS for original information source. 2018-02-16 true false https://www.opengis.net/def/crs/EPSG/9.9.1/4258 ETRS89 Has been realized through ETRF89, ETRF90, ETRF91, ETRF92, ETRF93, ETRF94, ETRF96, ETRF97, ETRF2000, ETRF2005 and ETRF2014. This 'ensemble' covers any or all of these realizations without distinction. Europe - onshore and offshore: Albania; Andorra; Austria; Belgium; Bosnia and Herzegovina; Bulgaria; Croatia; Cyprus; Czechia; Denmark; Estonia; Faroe Islands; Finland; France; Germany; Gibraltar; Greece; Hungary; Ireland; Italy; Kosovo; Latvia; Liechtenstein; Lithuania; Luxembourg; Malta; Moldova; Monaco; Montenegro; Netherlands; North Macedonia; Norway including Svalbard and Jan Mayen; Poland; Portugal; Romania; San Marino; Serbia; Slovakia; Slovenia; Spain; Sweden; Switzerland; United Kingdom (UK) including Channel Islands and Isle of Man; Vatican City State. -16.1 40.18 32.88 84.17 OGP 2020-07-24 false false https://www.opengis.net/def/area/EPSG/9.9.1/1298 Europe - ETRF by country Geographic Information. ellipsoidal OGP 2015-05-22 true false https://www.opengis.net/def/cs/EPSG/9.9.1/6422 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. https://www.opengis.net/def/axis/EPSG/9.9.1/106 Lat north https://www.opengis.net/def/axis/EPSG/9.9.1/107 Lon east geodetic EPSG 2018-02-16 true false https://www.opengis.net/def/datum/EPSG/9.9.1/6258 European Terrestrial Reference System 1989 Has been realized through ETRF89, ETRF90, ETRF91, ETRF92, ETRF93, ETRF94, ETRF96, ETRF97, ETRF2000, ETRF2005 and ETRF2014. This 'ensemble' covers any or all of these realizations without distinction. Geographic Information. Fixed to the stable part of the Eurasian continental plate and consistent with ITRS at the epoch 1989.0. 1989-01-01 Cartesian OGP 2001-04-29 false https://www.opengis.net/def/cs/EPSG/9.9.1/4400 Cartesian 2D CS. Axes: easting, northing (E,N). Orientations: east, north. UoM: m. Used in projected and engineering coordinate reference systems. https://www.opengis.net/def/axis/EPSG/9.9.1/1 E east https://www.opengis.net/def/axis/EPSG/9.9.1/2 N north