Built in ellipsoids

Tip

Unless you are trying to work with a coordinate reference system that doesn’t exist in the built-in set, you don’t need to worry about these, the correct one will be instantiated for you.

Airy 1830

Ellipsoid::fromSRID(Ellipsoid::EPSG_AIRY_1830)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7001')

Original definition is a=20923713, b=20853810 feet of 1796. 1/f is given to 7 decimal places. For the 1936 retriangulation OSGB defines the relationship of 10 feet of 1796 to the International metre through ([10^0.48401603]/10) exactly = 0.3048007491…

Airy Modified 1849

Ellipsoid::fromSRID(Ellipsoid::EPSG_AIRY_MODIFIED_1849)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7002')

OSGB Airy 1830 figure (ellipsoid code 7001) rescaled by 0.999965 to best fit the scale of the 19th century primary triangulation of Ireland.

Australian National Spheroid

Ellipsoid::fromSRID(Ellipsoid::EPSG_AUSTRALIAN_NATIONAL_SPHEROID)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7003')

Based on the GRS 1967 figure but with 1/f taken to 2 decimal places exactly. The dimensions are also used as the GRS 1967 Modified ellipsoid (see code 7050).

Average Terrestrial System 1977

Ellipsoid::fromSRID(Ellipsoid::EPSG_AVERAGE_TERRESTRIAL_SYSTEM_1977)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7041')

Bessel 1841

Ellipsoid::fromSRID(Ellipsoid::EPSG_BESSEL_1841)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7004')

Original Bessel definition is a=3272077.14 and b=3261139.33 toise. This used a weighted mean of values from several authors but did not account for differences in the length of the various toise: the “Bessel toise” is therefore of uncertain length.

Bessel Modified

Ellipsoid::fromSRID(Ellipsoid::EPSG_BESSEL_MODIFIED)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7005')

Used in Norway and also in Sweden with a 1mm increase in semi-major axis.

Bessel Namibia (GLM)

Ellipsoid::fromSRID(Ellipsoid::EPSG_BESSEL_NAMIBIA_GLM)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7046')

The semi-major axis has the same value as the Bessel 1841 ellipsoid (code 7004) but is in different units - German Legal Metres rather than International metres - hence a different size. a = 6377483.865 International metres. Used in Namibia.

CGCS2000

Ellipsoid::fromSRID(Ellipsoid::EPSG_CGCS2000)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::1024')

Defining parameters semi-major axis, flattening and angular velocity are same as for GRS 1980 (ellipsoid code 7019); GM = 3986004.4e8 m*m*m/s/s (from NASA 1986 Lageos determination).

Clarke 1858

Ellipsoid::fromSRID(Ellipsoid::EPSG_CLARKE_1858)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7007')

Clarke’s 1858/II solution. Derived parameters: a = 6378293.645m using his 1865 ratio of 0.3047972654 feet per metre; 1/f = 294.26068… In Australia and Amoco Trinidad 1/f taken to two decimal places (294.26 exactly); elsewhere a and b used to derive 1/f.

Clarke 1866

Ellipsoid::fromSRID(Ellipsoid::EPSG_CLARKE_1866)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7008')

Original definition a=20926062 and b=20855121 (British) feet. Uses Clarke’s 1865 inch-metre ratio of 39.370432 to obtain metres. (Metric value then converted to US survey feet for use in the US and international feet for use in Cayman Islands).

Clarke 1866 Authalic Sphere

Ellipsoid::fromSRID(Ellipsoid::EPSG_CLARKE_1866_AUTHALIC_SPHERE)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7052')

Authalic sphere derived from Clarke 1866 ellipsoid (code 7008).

Clarke 1880

Ellipsoid::fromSRID(Ellipsoid::EPSG_CLARKE_1880)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7034')

Clarke gave a and b and also 1/f=293.465 (to 3 decimal places exactly). In the 19th century b was normally given as the second defining parameter.

Clarke 1880 (Arc)

Ellipsoid::fromSRID(Ellipsoid::EPSG_CLARKE_1880_ARC)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7013')

Adopts Clarke’s value for a with derived 1/f. Uses his 1865 ratio of 39.370432 inch per metre to convert semi-major axis to metres.

Clarke 1880 (Benoit)

Ellipsoid::fromSRID(Ellipsoid::EPSG_CLARKE_1880_BENOIT)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7010')

Adopts Clarke’s values for a and b. Uses Benoit’s 1895 ratio of 0.9143992 metres per yard to convert to metres.

Clarke 1880 (IGN)

Ellipsoid::fromSRID(Ellipsoid::EPSG_CLARKE_1880_IGN)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7011')

Adopts Clarke’s values for a and b using his 1865 ratio of 39.370432 inches per metre to convert axes to metres.

Clarke 1880 (RGS)

Ellipsoid::fromSRID(Ellipsoid::EPSG_CLARKE_1880_RGS)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7012')

Adopts Clarke’s values for a and 1/f. Adopts his 1865 ratio of 39.370432 inches per metre to convert semi-major axis to metres. Also known as Clarke Modified 1880.

Clarke 1880 (SGA 1922)

Ellipsoid::fromSRID(Ellipsoid::EPSG_CLARKE_1880_SGA_1922)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7014')

Used in Old French Triangulation (ATF). Uses Clarke’s 1865 inch-metre ratio of 39.370432 to convert axes to metres.

Clarke 1880 (international foot)

Ellipsoid::fromSRID(Ellipsoid::EPSG_CLARKE_1880_INTERNATIONAL_FOOT)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7055')

Clarke’s 1880 definition in feet assumed for the purposes of metric conversion to be international foot. a = 6378306.370…metres. 1/f derived from a and b = 293.4663077… Used in Fiji.

Danish 1876

Ellipsoid::fromSRID(Ellipsoid::EPSG_DANISH_1876)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7051')

Semi-major axis originally given as 3271883.25 toise. Uses toise to French metre ratio of 1.94903631 to two decimal place precision. An alternative ratio with the German legal metre of 1.9490622 giving 6377104m has not been used in Danish work.

Everest (1830 Definition)

Ellipsoid::fromSRID(Ellipsoid::EPSG_EVEREST_1830_DEFINITION)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7042')

Everest gave a and b to 2 decimal places and also 1/f=300.8017 (to 4 decimal places exactly). In the 19th century b was normally given as the second defining parameter.

Everest 1830 (1937 Adjustment)

Ellipsoid::fromSRID(Ellipsoid::EPSG_EVEREST_1830_1937_ADJUSTMENT)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7015')

Used for the 1937 readjustment of Indian triangulation. Clarke’s 1865 Indian-British foot ratio (0.99999566) and Benoit’s 1898 British inch-metre ratio (39.370113) rounded as 0.30479841 exactly and applied to Everest’s 1830 definition taken as a and 1/f

Everest 1830 (1962 Definition)

Ellipsoid::fromSRID(Ellipsoid::EPSG_EVEREST_1830_1962_DEFINITION)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7044')

Used by Pakistan since metrication. Clarke’s 1865 Indian foot-British foot ratio (0.99999566) and his 1865 British inch-metre ratio (39.369971) rounded with slight error as 1 Ind ft = 0.3047995m exactly and applied to Everest’s 1830 definition of a & b.

Everest 1830 (1967 Definition)

Ellipsoid::fromSRID(Ellipsoid::EPSG_EVEREST_1830_1967_DEFINITION)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7016')

Adopted 1967 for use in East Malaysia. Applies Sears 1922 inch-metre ratio of 39.370147 to Everest 1830 original definition of a and 1/f but with a taken to be in British rather than Indian feet.

Everest 1830 (1975 Definition)

Ellipsoid::fromSRID(Ellipsoid::EPSG_EVEREST_1830_1975_DEFINITION)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7045')

Used by India since metrication. Clarke’s 1865 Indian foot-British foot ratio (0.99999566) and his 1865 British inch-metre ratio (39.369971) rounded as 1 Ind ft = 0.3047995m exactly applied to Everest’s 1830 original definition taken as a and b.

Everest 1830 (RSO 1969)

Ellipsoid::fromSRID(Ellipsoid::EPSG_EVEREST_1830_RSO_1969)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7056')

Adopted for 1969 metrication of peninsula Malaysia RSO grid. Uses Sears 1922 yard-metre ratio truncated to 6 significant figures applied to Everest 1830 original definition of a and 1/f but with a taken to be in British rather than Indian feet.

Everest 1830 Modified

Ellipsoid::fromSRID(Ellipsoid::EPSG_EVEREST_1830_MODIFIED)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7018')

Adopted 1967 for use in West Malaysia. Applies Benoit 1898 inch-metre ratio of 39.370113 to Everest 1830 original definition of a and 1/f but with a taken to be in British rather than Indian feet.

GEM 10C

Ellipsoid::fromSRID(Ellipsoid::EPSG_GEM_10C)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7031')

Used for GEM 10C Gravity Potential Model.

GRS 1967

Ellipsoid::fromSRID(Ellipsoid::EPSG_GRS_1967)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7036')

Adopted by IUGG 1967 Lucerne. 1/f given is derived from geocentric gravitational constant (GM)= 398603e9 m*m*m/s/s; dynamic form factor (J2) = 0.0010827 and Earth’s angular velocity w = 7.2921151467e-5 rad/s. See also GRS 1967 Modified (code 7050).

GRS 1967 Modified

Ellipsoid::fromSRID(Ellipsoid::EPSG_GRS_1967_MODIFIED)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7050')

Based on the GRS 1967 figure (code 7036) but with 1/f taken to 2 decimal places exactly. Used with SAD69 and TWD67 datums. The dimensions are also used as the Australian National Spheroid (code 7003).

GRS 1980

Ellipsoid::fromSRID(Ellipsoid::EPSG_GRS_1980)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7019')

Adopted by IUGG 1979 Canberra. Inverse flattening is derived from geocentric gravitational constant GM = 3986005e8 m*m*m/s/s; dynamic form factor J2 = 108263e-8 and Earth’s angular velocity = 7292115e-11 rad/s.

GRS 1980 Authalic Sphere

Ellipsoid::fromSRID(Ellipsoid::EPSG_GRS_1980_AUTHALIC_SPHERE)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7048')

Authalic sphere derived from GRS 1980 ellipsoid (code 7019). (An authalic sphere is one with a surface area equal to the surface area of the ellipsoid). 1/f is infinite.

GSK-2011

Ellipsoid::fromSRID(Ellipsoid::EPSG_GSK_2011)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::1025')

Helmert 1906

Ellipsoid::fromSRID(Ellipsoid::EPSG_HELMERT_1906)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7020')

Helmert 1906/III solution.

Hough 1960

Ellipsoid::fromSRID(Ellipsoid::EPSG_HOUGH_1960)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7053')

Hughes 1980

Ellipsoid::fromSRID(Ellipsoid::EPSG_HUGHES_1980)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7058')

Used in US DMSP SSM/I microwave sensor processing software. Semi-minor axis derived from eccentricity=0.081816153. Semi-major axis (a) sometimes given as 3443.992nm which OGP suspects is a derived approximation. OGP conversion assumes 1nm=1852m exactly.

IAG 1975

Ellipsoid::fromSRID(Ellipsoid::EPSG_IAG_1975)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7049')

Indonesian National Spheroid

Ellipsoid::fromSRID(Ellipsoid::EPSG_INDONESIAN_NATIONAL_SPHEROID)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7021')

Based on the GRS 1967 figure but with 1/f taken to 3 decimal places exactly.

International 1924

Ellipsoid::fromSRID(Ellipsoid::EPSG_INTERNATIONAL_1924)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7022')

Adopted by IUGG 1924 in Madrid. Based on Hayford 1909/1910 figures.

International 1924 Authalic Sphere

Ellipsoid::fromSRID(Ellipsoid::EPSG_INTERNATIONAL_1924_AUTHALIC_SPHERE)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7057')

Authalic sphere derived from International 1924 ellipsoid (code 7022).

Krassowsky 1940

Ellipsoid::fromSRID(Ellipsoid::EPSG_KRASSOWSKY_1940)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7024')

NWL 9D

Ellipsoid::fromSRID(Ellipsoid::EPSG_NWL_9D)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7025')

Used by Transit Precise Ephemeris between October 1971 and January 1987.

OSU86F

Ellipsoid::fromSRID(Ellipsoid::EPSG_OSU86F)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7032')

Used for OSU86 gravity potential (geoidal) model.

OSU91A

Ellipsoid::fromSRID(Ellipsoid::EPSG_OSU91A)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7033')

Used for OSU91 gravity potential (geoidal) model.

PZ-90

Ellipsoid::fromSRID(Ellipsoid::EPSG_PZ_90)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7054')

Earth’s angular velocity ω = 7.292115e-5 rad/sec; gravitational constant GM = 3986004.418e8 m*m*m/s/s.

Plessis 1817

Ellipsoid::fromSRID(Ellipsoid::EPSG_PLESSIS_1817)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7027')

Rescaling of Delambre 1810 figure (a=6376985 m) to make meridional arc from equator to pole equal to 10000000 metres exactly. (Ref: Strasser).

Struve 1860

Ellipsoid::fromSRID(Ellipsoid::EPSG_STRUVE_1860)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7028')

Original definition of semi-major axis given as 3272539 toise. In “Ellipsoidisch Parameter der Erdfigur (1800-1950)” , Strasser suggests a conversion factor of 1.94903631 which gives a=6378297.337 metres.

WGS 72

Ellipsoid::fromSRID(Ellipsoid::EPSG_WGS_72)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7043')

WGS 84

Ellipsoid::fromSRID(Ellipsoid::EPSG_WGS_84)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7030')

1/f derived from four defining parameters semi-major axis; C20 = -484.16685*10e-6; earth’s angular velocity ω = 7292115e-11 rad/sec; gravitational constant GM = 3986005e8 m*m*m/s/s. In 1994 new GM = 3986004.418e8 m*m*m/s/s but a and 1/f retained.

War Office

Ellipsoid::fromSRID(Ellipsoid::EPSG_WAR_OFFICE)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::7029')

In non-metric form, a=20926201 Gold Coast feet. DMA Technical Manual 8358.1 and data derived from this quotes value for semi-major axis as 6378300.58m: OGP recommends use of defined value 6378300m exactly.

Zach 1812

Ellipsoid::fromSRID(Ellipsoid::EPSG_ZACH_1812)
Ellipsoid::fromSRID('urn:ogc:def:ellipsoid:EPSG::1026')

Defined as log a = 6.5266022 Klafter (Austrian fathom, Kl), log b = 6.5251990 Kl. a=10^6.526 6022 = 3362035 Kl. Then using the Austro-Hungarian 1871 KL/m legal ratio of 1.89648384, a = 6376045m