The Ordnance Survey of Britain and Conversion of latitude and longitude to/from OS references. Why these notes? There are frequently articles in the satellite-nav news group asking about the Ordnance Survey national grid in Britain. Questions like : What is the OS reference system? How do I convert references to and from latitude and longitude? How do I set my GPS receiver? Can someone give waypoint information for cities in Britain? Where can I buy UTM maps for Britain? These notes and the accompanying program are an attempt to give background information which will either answer those questions directly or show an alternative way of working which is more helpful in Britain. They have been compiled as a special thanks to all those newsgroup contributors out there who have been so helpful to me in the past. The Ordnance Survey of Britain Britain is covered by a series of maps produced by an organisation called the Ordnance Survey (OS). As the name suggests, the organisation has military origins but it is now an independent company. These maps are the natural choice for all sorts of activity from walking and motoring to land surveying. They are so well established that OS references are given in publications describing the location of campsites, youth hostels and features on walks etc rather than longitude and latitude. They are readily available in bookshops and newsagents across Britain. They cover mainland England, Scotland, Wales, the Isle of Man, the Orkney and Shetland Islands but do not cover Ireland, Northern Ireland or the Channel Islands. The scales published include 4cm/25km for route planning, 2cm/km for motoring or walking and 4cm/km for walking. More detailed maps for surveying and land ownership matters are also available. The OS web site is http://www.ordsvy.gov.uk Road atlases published by organisations such as the AA (Automobile Association) are also based on the Ordnance Survey grid, though you can find atlases which are not. The visitor to Britain will find that maps based on other grids such as longitude and latitude or UTM are difficult or impossible to obtain (I have never seen them!). Whilst longitude and latitude are shown on OS maps, they are only shown on the margins of the map and are very clumsy to use compared with the OS reference with its regular 1km grid lines which I would encourage the visitor to use. The OS System The Ordnance Survey of Great Britain is a transverse Mercator projection. This is a particularly ideal choice for a tall thin area like Britain (or Chile!) in that distances, areas and angles are well mapped with minimal error. Whilst TM is also used in USA and USSR and for UTM it has limitations when used for areas with long east/west distances which force the cartographer to segment the area with discontinuities which are quite absent in Britain. The OS projection is based on a true origin at 49 degrees North, 2 degrees west which is down near the Channel Islands. >From this origin, a square grid is imposed on top of the converging lines of longitude and the curved lines of latitude and points are located by measuring distances in metres east and north from this true origin. Since this process will introduce distortion as you move away from the central longitude of 2 degrees west, a scale factor of 0.9996 is introduced which reduces this distortion - two lines of longitude with zero distortion are thus created. Incidentally, the same factor is used for UTM. Furthermore, to eliminate the inconvenience of negative values of easting, the concept of a false origin is introduced. A value of 500 km is added to eastings and 100km subtracted from northings so placing this false origin near the Isles of Scilly off Lands End in the south west. The model uses the Airy ellipse of 1836. Readers wishing to delve very deeply into the topic of map projections are referred to a publication by a former colleague here in Swansea: Coordinate Systems and Map Projections, D H Maling, Pergamon Press, ISBN 0-08-037234-1. Map References A full reference which is unique across Britain will consist of two letters followed by (usually) six digits giving accuracy to 100 metres eg (SS 599 939). Eight digits are needed for 10 metre accuracy and 10 for one metre. The two letters indicate the 100km square in which the point lies and are invariably omitted since this is usually unambiguous in the context of a walk! The first letter gives the 500km square. 25 different letters could be given here though only four actually map to the surveyed land areas: S for south west, T for south east, N for the north and Scotland and H for the Shetland Islands. The second letter gives the 100km square within that and is laid out: ABCDE FGHJK LMNOP QRSTU VWXYZ The digits should be split into two groups - in the above example of SS 599 939 the point is 59.9 km east and 93.9 km north of the south west corner of square SS. The measurement of a reference is made easier by the regular grid of 2cm or 4cm squares representing 1km on the ground and printed on every map. The references of those squares are shown on the margins of the map. To determine a reference: - note the letters square from a description in the margins of the map (eg SS) - read off the two digit eastings number at the bottom or top of the map against the vertical line to the left of the point (eg 59) - estimate the horizontal distance in tenths from the line (eg 9) - read off the two digit northings number against the side of the map (eg 93) - estimate tenths north from this (9) The resulting reference SS 599939 is accurate to 100 metres. The procedure is described on the margin of every OS map. If you wish you can to use a centimetre ruler (there is one on my compass) to help you achieve more accuracy or you could invest a pound and buy a plastic scale called a romer. Note that dividers or special scales are not needed as with some US maps. I can recommend an inexpensive index to the maps which is FREE in good bookshops and which describes the grid, but note the misprint on the back of the 1997 edition - Kingston on Hull is in square TA not in square T. Which North? The north-south grid lines lie to the west of true north for areas west of the true origin, and east for those to the east but this difference is only about 0.75 degrees per degree of longitude. The difference between magnetic and true or grid bearings is called magnetic variation in Britain rather than declination as in the US and it varies uniformly across the country with very small anomalies. Variation is small compared with some parts of the world but not quite small enough to be ignored - it was 4.5 degrees west of grid in Wales in 1992, decreasing by a degree every 8 years. Whittaker's Almanac is a good reference for this variation in Britain and is updated annually. How do I set my GPS receiver? If contemplating use of a GPS system in Britain it is almost essential that OS format is catered for. In the case of the Garmin 38/45/12XL family you should set 'British Grid' for format on the navigation setup page. Datum should be set to 'Ord Srvy GB' to avoid errors of up to hundreds of metres. I choose to set my 38 for metric measurements rather than statute since the maps have a 1km grid. 'Auto magnetic' gives good results and complements my trusty Silva compass. I cannot comment on other makes of GPS systems - would readers care to supply text here? Where can I get a list of Waypoints for Britain? If you buy an inexpensive road atlas with Ordnance Survey references it is easy to read them off directly. And the OS maps are easy to read too without using dividers, complex scales etc. However, Christian Schmadalla has set up a web site with zip files holding waypoints of motorway junctions and major cities. Refer to http://www.geocities.com/TimesSquare/1350/index.html. There is excellent information on walks in the Lake District available at: http://netlink.co.uk/users/Idnet/ The Conversion Program With an OS map and a GPS system with an OS display there should be no need for OS reference to latitude and longitude conversions - simply 'think OS' which is easy to read off the map scales. I can think of only two instances when I personally need the conversion: - when writing a program to handle data from the serial output port of my Garmin and which is in latitude and longitude. I still want to work in OSGB format - when relating the location of points in Britain to those outside (eg Where is Sofia? Where is Sirius?) A working demonstration program to convert latitude and longitude to OS grid references and vice-versa is included with this documentation, both in Qbasic/Quickbasic source form and a DOS executable. It includes routines for: - program setup - converting latitude and longitude to/from eastings and northings - converting eastings and northings to/from grid references. It includes a test harness which is deliberately very simple with little in the way of a sophisticated or elegant user interface in order to demonstrate how to interface to the five routines. It also allowed a quality check to be applied! It is intended that the routines can be simply lifted as needed and/or converted to other computer languages. Note that longitude is negative for west of Greenwich and that eastings and northings in the program are in kilometres and are relative to a point in the Atlantic at the far south west of the letter grid - point VV 000 000. This makes calculation of references easier but is neither the true origin nor the false origin of the OS system. The routines use algorithms published by Derek Maling though I claim credit for any errors in the implementation! The program agrees with the conversion in my Garmin 38 within 2 metres for the points in South Wales I have tried but I don't know how this discrepancy arises. This accuracy is well within the limits of US DOD selective availability and of normal map reading resolution and the error is quite insignificant for normal leisure pursuits. Disclaimer This is the first draft of this document. The information given is believed to be accurate and the opinions are my own. Please report any inaccuracies, alternative views or suggested improvements to this document or the program - I may be reached via email at p.r.brady@swan.ac.uk but no spam or adverts please!! My thanks go to Martin Cock for proof-reading this document and giving useful additional information.