A: Ellipsoid and projection constants

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Shape and size of biaxial ellipsoids used in the UK

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 [(10^0.48401603)/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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