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# A: Ellipsoid and projection constants

Shape and size of biaxial ellipsoids used in the UK

 Name Semi-major axis a (m) Semi-minor axis b (m) Associated datums and projections Airy 1830 6 377 563.396 6 356 256.909* OSGB36®, National Grid Airy 1830 modified 6 377 340.189 6 356 034.447 Ireland 65, Irish National Grid International 1924, aka Hayford 1909 6 378 388.000 6 356 911.946 ED50, UTM GRS80 aka WGS84 ellipsoid 6 378 137.000 6 356 752.3141 WGS84, ITRS, ETRS89.

The ellipsoid squared eccentricity constant is computed from a and b by equation (B1).

* For a long time, in previous versions of this publication and other Ordnance Survey publications, the Airy 1830 value for b was quoted as 6,356,256.910.  Research ("Empire Survey Review, Vol. XI, No.84, 1952) shows the correct  rounding is actually .909.

The original dimensions for the Airy 1830 ellipsoid are quoted  as a = 20,923,713 feet and b = 20,853,810 feet.  The conversion of these to metres is derived from the length of a standard bar ("O1").  This bar was the length standard for the Principle Triangulation and the Re-triangulation.  The defined conversion to metric is:

10(log(axis)+9.48401603)

This results in a metric value for the axis given in tenths of a nanometre.  An easier way to express the conversion to metres is to multiply the axis length in feet by [(100.48401603)/10].  Both methods result in the 3-decimal-place values in the table above.  The resulting difference in eastings and northings when using the .909 or .910 values for b is approximately 0.016mm and is therefore insignificant.

Transverse Mercator projections used in the UK

 Projection Scale factor on central meridian F0 True origin, and Map coordinates of true origin (metres),E0 and  N0 Ellipsoid National Grid 0.9996012717 lat 49° N long 2° W E 400 000 N -100 000 Airy 1830 Irish National Grid 1.000035 lat 53° 30' N long 8° W E 200 000 N 250 000 Airy 1830 modified UTM zone 29 0.9996 lat 0° long 9° W E 500 000 N 0 International 1924 UTM zone 30 0.9996 lat 0° long 3° W E 500 000 N 0 International 1924 UTM zone 31 0.9996 lat 0° long 3° E E 500 000 N 0 International 1924

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