National Grid and the OSGB36 TRF

The coordinates of all features shown on OS maps are determined with respect to a TRF called OSGB36 (Ordnance Survey Great Britain 1936). This is what land surveyors would call a ‘traditional triangulation datum’ (as we saw before, this is strictly a misuse of the term ‘datum’ – OSGB36 consists of a datum and a TRF). OSGB36 is usually used with National Grid easting and northing coordinates (see section 7 below) using the formulae given in annex C.

The OSGB36 datum

OSGB36 was not created in quite the logical way specified in traditional surveying textbooks for the establishment of a geodetic coordinate system. Those textbooks say one should first choose an astronomical observatory as the ‘initial point’ at which the datum will be defined. Here one measures the latitude and the direction of north by astronomy, and defines the direction towards the centre of the mapping ellipsoid[7]. By defining an ellipsoidal latitude, longitude and ellipsoid height for the initial point, the mapping ellipsoid and Cartesian axes of the coordinate system is fixed in space relative to that point – that is, the datum is defined. This is the traditional procedure we outlined in section 3.2.

The original triangulation of Britain was carried out between 1783 and 1853 and is known as the ‘Principal Triangulation’. However, when the country was entirely retriangulated between 1936 and 1953 to create OSGB36, the datum definition (the arbitrary position and orientation of the ellipsoid relative to the primary control stations) was adopted from the original triangulation using the average of 11 old primary control station coordinates[8]. Therefore, OSGB36 does not have an initial point – the datum is defined implicitly by the primary control station coordinates. This is an equally acceptable way of defining a datum: the datum being a matter of convenience, it does not matter much how you define it.

The ellipsoid used in the OSGB36 datum is that defined by Sir George Airy in 1830 (later Astronomer Royal). Its defining constants are a = 6377563.396m and b = 6356256.909m (see annex A for a summary of datum constants). Hence the Airy 1830 ellipsoid is a bit smaller than GRS80 and a slightly different shape. Also, it is not geocentric as GRS80 is: it is designed to lie close to the Geoid beneath the British Isles. Hence only a tiny fraction of the surface of the ellipsoid has ever been used – the part lying beneath Britain. The rest is not useful. So, the Airy ellipsoid differs from GRS80 in size, shape, position and orientation, and this is generally true of any pair of geodetic ellipsoids[9].

The OSGB36 TRF

Before the 1950s, coordinate system TRFs contained many angle measurements but very few distance measurements. This is because angles could be measured relatively easily between hilltop primary control stations with a theodolite, but distance measurement was very difficult. A consequence of this was that the shape of the TRF was well known, but its size (scale) was poorly known. The distance between primary control stations was established by measuring just one or two such distances, then propagating these through the network of angles by trigonometry (hence the name ‘trig pillars’).

When the OSGB36 triangulation TRF was established, no new distance measurements were used. Instead, the overall size of the network was made to agree with that of the old 18th century Principal Triangulation using the old coordinates of the 11 control stations mentioned in the previous section. Hence the overall scale of the TRF still used for British mapping came to be derived from the measurement of a single distance between two stations on Hounslow Heath in 1784 using eighteen-foot glass rods! The error thus incurred in OSGB36 is surprisingly low – only about 20 metres in the length of the country (which is approx. 20ppm).

The 326 primary control stations of the OSGB36 TRF cover the whole of Great Britain, including Orkney and Shetland but not the Scilly Isles, Rockall or the Channel Islands. It is also connected to Northern Ireland, the Irish Republic, and France. This primary control network was densified by the addition of 2 695 secondary control stations, 12 236 tertiary control stations and 7 032 fourth order control stations. Hence until recently the ‘official OSGB36’ included more than 22 000 reference points. In continuous survey work over the decades, Ordnance Survey surveyors added many tens of thousands more ‘minor control’ points, which were used in map revision.

OSGB36 coordinates are latitudes and longitudes on the Airy 1830 ellipsoid. Ideally, ellipsoid heights relative to the Airy ellipsoid would be added to give complete three-dimensional information. Unfortunately, no easy method of measuring ellipsoid height was available before the late 1980s, so we only have horizontal information in OSGB36. The coordinates (National Grid eastings and northings) of a large number of OSGB36 trig pillars are available from the Ordnance Survey website.

In 2002 the definition of OSGB36 underwent a fundamental change with the release of the Definitive Transformation OSTN02™. OSTN02 was updated in August 2016 to OSTN15. OSTN15, in combination with the ETRS89 coordinates of the OS Net stations, rather than the fixed triangulation network, now define the National Grid. This is a subtle change in definition only and does not mean that existing OSGB36 coordinates need to be changed in any way.

Relative accuracy of OSGB36 control points

The following table is a statistical statement of the accuracy of OSGB36 control points relative to surrounding control stations of the same type. The primary layer of the OSGB36 TRF consists of the primary triangulation stations, which are considered error-free within the OSGB36 coordinate system. The Ordnance Survey ETRS89–OSGB36 transformation (see section 6.3 below) describes the real distortions in OSGB36 that are not considered here. Table 2 shows the expected accuracy of control station positions in relation to other control stations of the same type within a circular area of the given diameter.

Table 2. Relative accuracy of control stations within the OSGB36 coordinate system.

Type of OSGB36 horizontal control station	Expected accuracy (m) (1 standard error)	Within circular area of diameter (km)
Primary control station	Error free	N/A
Secondary control station	0.06	15
Tertiary control station	0.05	7
Minor control station	0.04	3
Chain survey station	0.08	3
Map detail station	0.06	2