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.

As discussed in section 5.3, ODN is the national height datum used across mainland Great Britain. There are, however, a number of other British height datums that are used on the surrounding islands. The main ones being; Lerwick on the Shetland Islands, Stornoway on the Outer Hebrides, Douglas on the Isle of Man and St. Marys on the Scilly Isles. All of these height datums are incorporated within the National Geoid Model OSGM15.

OSGB36 and ODN will be retained as the basis of OS mapping for the foreseeable future, but OS Net will be used to access both these coordinate systems by GNSS, using coordinate transformations from ETRS89 to OSGB36 and ODN provided by OS. These transformations are currently the National Grid Transformation OSTN15 and the National Geoid Model OSGM15. In this way, OS surveyors and GNSS‑equipped customers will have access to the national horizontal and vertical datums at any point without visiting traditional control points. Using OSTN15 and OSGM15, OSGB36 and ODN coordinates are obtained by 3‑D transformation software that converts ETRS89 GNSS coordinates obtained from OS Net into the equivalent OSGB36/height datum position.

Using this method of access, OSGB36 and the appropriate datum heights will be continuously accessible, rather than being available only at OS monuments. With the release of OSTN15 (and originally OSTN02), the National Grid has become by definition a transformation of the ETRS89 GNSS coordinate system. Because both horizontal and vertical national mapping coordinate systems are defined in terms of ETRS89, which is easily related to ITRS (see section 6.5 below), the geodetic basis of British mapping is implicitly related to all other national datums that have a known relationship to ITRS.

At some point in the future, the drift of the Eurasian tectonic plate (~25mm/year) relative to WGS84 plus the improved accuracy of stand-alone GPS positioning from even simple “consumer level” receivers will mean the offset between ETRS89 and WGS84 becomes apparent to a much wider group of users, even on small scale mapping. At this time either a change to the epoch of ETRS89 (to closely align it with WGS84) may have to be considered, or the introduction of a small transformation to shift WGS84 coordinates back to ETRS89, before then transforming (e.g. with OSTN15) to OSGB36.

The coordinates and other information of the traditional networks are no longer actively maintained by OS. Access to these traditional control archives is made available through online services on the OS website.

GNSS is the standard tool for precise surveying and mapping, used for all OS precise surveying work. Some characteristics of GNSS as a surveying tool are:

• GNSS is a three-dimensional positioning system: a precise GNSS fix yields latitude, longitude and ellipsoid height.

• The highest precision of GNSS positions is at the 2 mm level horizontally relative to a global datum. To achieve this requires networks of permanently-installed GNSS receivers. Typical field GNSS survey gives accuracies of a few centimetres relative to a global datum. Vertical position quality is generally about 2.5 times worse than horizontal.

• GNSS is a purely geometric positioning tool; that is, GNSS coordinates do not give you any information in relation to level surfaces, only in relation to the geometric elements of coordinate system axes and ellipsoid. For this reason, GNSS does not give orthometric height information.

• GNSS does not require intervisibility between ground reference points; neither is the geometric arrangement of the ground network crucial to the results as it is in theodolite triangulation survey.

• With care, GNSS can be used very accurately for terrestrial survey over any distance – even between points on opposite sides of the world. For this reason, global datums are used for GNSS positioning. This feature makes GNSS vastly more powerful than traditional survey techniques.

The datum of OS Net is the European Terrestrial Reference System 1989 (ETRS89), which we looked at in section 4.2.4. Since this datum is realised by many European precise GNSS reference points, OS Net is actually just a TRF enabling easier access to this datum in Great Britain.

Currently OS Net realises ETRS89 with an ETRF97 frame with a “parent” ITRF of ITRF97 at epoch 2009.756. This OS Net realisation is known as “OS Net v2009”. Prior to this the original OS Net also had an ETRF97 frame with a parent ITRF at ITRF97 but the epoch was 2001.553 so this OS Net realisation is now designated “OS Net v2001”. A small transformation between the two realisations is given in section 6.7.

OS Net comprises of a network of over 100 continuously operating permanent GNSS receivers (COGRs). Because precise GNSS positioning is always carried out in relative mode (that is, observing the vector difference in coordinates between two simultaneously recording GNSS stations), a network of COGRs with precisely known coordinates is a very useful infrastructure. Precise positioning can then be carried out by one person with a single geodetic-quality GNSS receiver, using data downloaded from the COGRs.

All OS Net stations are coordinated in three dimensions by GNSS in the ETRS89 terrestrial reference system. Hence the user obtains ETRS89 coordinates for their unknown points, which are suitable for use with the Ordnance Survey transformations to the mapping coordinate systems OSGB36 and ODN (see section 6 below). ETRS89 coordinates can also very easily be transformed to the international ITRS datum (see section 6.5 below) – this is usually only required for international scientific applications.

Let’s now take a look at the coordinate systems used by OS for mapping Great Britain. There are three coordinate systems to consider:

• OS Net, a modern 3-D TRF using the ETRS89 datum (as described in 'European Terrestrial Reference System 1989 (ETRS89)' ). This coordinate system is the basis of modern Ordnance Survey ‘control survey’ (the surveyor’s jargon for adding local points to a TRF for mapping purposes), and is the basis of definition of all Ordnance Survey coordinates. A subset of OS Net (see section 5.1) has been ratified as the official densification of ETRF89 in GB.

• The National Grid, a ‘traditional’ horizontal coordinate system, which consists of: a traditional geodetic datum (see 'We need a datum') using the Airy 1830 ellipsoid; a TRF called OSGB36 (Ordnance Survey Great Britain 1936) which was observed by theodolite triangulation of trig pillars; and a Transverse Mercator map projection (see 'Transverse Mercator map projections') allowing the use of easting and northing coordinates. This coordinate system is important because it is used to describe the horizontal positions of features on British maps. However, its historical origins and observation methods are not of interest to most users and will be skipped over in this booklet. National Grid coordinates are nowadays determined by GNSS plus a transformation rather than theodolite triangulation.

• Ordnance Datum Newlyn (ODN), a ‘traditional’ vertical coordinate system, consisting of a tide‑gauge datum with initial point at Newlyn (Cornwall), and a TRF observed by spirit levelling between 200 fundamental bench marks (FBMs) across Britain. The TRF is densified by more than half a million lower-accuracy bench marks. Each bench mark has an orthometric height only (not ellipsoid height or accurate horizontal position). This coordinate system is important because it is used to describe vertical positions of features on British maps (for example, spot heights and contours) in terms of height above ‘mean sea level’. Again, its historical origins and observation methods are not of interest to most users. The word ‘Datum’ in the title refers, strictly speaking, to the tide‑gauge initial point only, not to the national TRF of levelled bench marks.

Because triangulation networks need hilltop stations whereas levelling networks need low‑lying, easily accessible routes, there are hardly any common points between the height bench mark network and the OSGB36 horizontal network. OS Net provides a single 3-D TRF that unifies ODN and OSGB36 via transformation software (see 'Geodetic transformations'). Using transformation techniques, precise positions can be determined by GNSS in ETRS89 using OS Net and then converted to National Grid and ODN coordinates. This is the approach used today by Ordnance Survey.

Before satellite surveying methods became available in the 1970s, ellipsoid height was a rare and specialised coordinate type. The everyday vertical coordinate type was orthometric height, or more exactly mean sea level height relative to the national tide gauge datum, as realised in mainland Britain by the ODN heights of OS bench marks. Even though anybody with a GNSS receiver can now measure ellipsoid heights quite easily, Geoid‑related height coordinates such as ODN heights are much more useful for most applications because they are heights relative to a level surface.

The ODN datum

Like horizontal datums, vertical datums were ‘traditionally’ defined at a single initial point. In the case of horizontal datums, this is an astronomical observatory. In the case of vertical datums it is a coastal tide gauge. Tide gauge-based vertical datums are still used in most countries.

The tide gauge has a height reference benchmark, the height of which on the gauge scale is known. A long series of sea level records from the tide gauge is averaged to give the vertical offset of MSL from the bench mark. This is the MSL height of the bench mark.

In Britain, the MSL of the tide-gauge benchmark at Newlyn near Penzance in Cornwall is used – hence the name Ordnance Datum Newlyn. Its MSL height was established from continuous tide readings between 1915 and 1921. That adopted value has remained unchanged in the ODN system, even though MSL at the Newlyn gauge has slowly changed. Hence the height of a point above mean sea level given by OS is not affected by variations in mean sea level, and the proper description of an OS height is ‘orthometric height relative to Ordnance Datum Newlyn’.

The ODN TRF

A network of about 200 fundamental bench marks for height measurement was constructed across Britain in the first half of the twentieth century. These are underground chambers containing a height reference object, topped by a small pillar on which is another reference point. The idea is that the point on the top is easy to access for normal use, whereas the hidden underground mark is less susceptible to damage.

The orthometric height of each fundamental bench mark relative to Newlyn was determined by a network of precise levelling lines across Britain. You can find descriptions of the precise levelling technique in land surveying textbooks. This technique is capable of transferring orthometric height from one point to another with an error of less than 2 x √d millimetres, where d is the distance levelled in kilometres. Today, the accuracy of the precise levelling technique is rivalled by the combination of GNSS ellipsoid heighting with a precise gravimetric Geoid model that allows the ellipsoid height difference between two points to be easily converted to an orthometric height difference.

The ODN TRF was subsequently densified by less precise levelling to obtain the heights of about three-quarters of a million Ordnance Survey bench marks all over Britain. These lower-order bench marks are often seen cut into stone at the base of a building, church or bridge. About half a million of them are in existence and usable today. An important error source to bear in mind is possible subsidence of Ordnance Survey bench marks, especially in areas where mining has caused collapse of the ground. In these areas, cases of bench mark subsidence of several metres have been reported.

Relative accuracy of ODN bench marks

The following table is a statistical statement of ODN bench mark accuracy relative to other bench marks in the same area. The primary layer of the ODN TRF consists of the fundamental bench marks, which are considered error-free within the ODN coordinate system. The Ordnance Survey National Geoid Model (see section 6.4 below) relates ODN orthometric heights to the GNSS ellipsoid GRS80. Table 3 shows the expected maximum levelling error between bench marks on the same levelling line. This only describes the original measurement error. The Ordnance Survey bench mark network has not been maintained since the 1970s, so beware of possible bench mark subsidence.

Table 3. Accuracy of Ordnance Survey bench mark levelling, where d is distance levelled in km