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45-639: The Bittell Reservoirs ( grid reference SP017748 ) are located in Worcestershire between Barnt Green to the south and the Birmingham district of Longbridge to the north. They consist of the Upper (Upper Bittell) and Lower (Lower Bittell) reservoir. They were built to feed the Worcester and Birmingham Canal , which was finished in the 1790s, however, the reservoir was not completed until 1837. The 'Upper' reservoir

90-606: A = 6378.137 {\displaystyle a=6378.137} km and an inverse flattening of 1 / f = 298.257 223 563 {\displaystyle 1/f=298.257\,223\,563} . Let's take a point of latitude φ {\displaystyle \,\varphi } and of longitude λ {\displaystyle \,\lambda } and compute its UTM coordinates as well as point scale factor k {\displaystyle k\,\!} and meridian convergence γ {\displaystyle \gamma \,\!} using

135-623: A transverse Mercator projection with an origin (the "true" origin) at 49° N , 2° W (an offshore point in the English Channel which lies between the island of Jersey and the French port of St. Malo ). Over the Airy ellipsoid a straight line grid, the National Grid, is placed with a new false origin to eliminate negative numbers, creating a 700 km by 1300 km grid. This false origin

180-563: A designated central meridian. The scale factor at the central meridian is specified to be 0.9996 of true scale for most UTM systems in use. The National Oceanic and Atmospheric Administration (NOAA) website states that the system was developed by the United States Army Corps of Engineers , starting in the early 1940s. However, a series of aerial photos found in the Bundesarchiv-Militärarchiv (the military section of

225-461: A false Easting of −500 000 meters is added to the central meridian. Thus a point that has an easting of 400 000 meters is about 100 km west of the central meridian. For most such points, the true distance would be slightly more than 100 km as measured on the surface of the Earth because of the distortion of the projection. UTM eastings range from about 166 000 meters to 834 000 meters at

270-496: A grid index where the tens denote the progress from West to East and the units from South to North. In the north of Scotland, the numbering is modified: the 100 km square to the north of 39 is numbered N30; the square to the north of 49 is N40, etc. The grid is based on the OSGB36 datum (Ordnance Survey Great Britain 1936, based on the Airy 1830 ellipsoid ), and was introduced after

315-410: A living. The irony of the reservoir is the length of time it took to build: only 6 years after it was finished the Birmingham & Gloucester railway was built alongside, mitigating the economic reasoning behind the large investment. The reservoirs are quite obscure nowadays, however they are used actively. Today one can fish in several places, especially on the lower reservoirs. The upper reservoir

360-550: A reference meridian of longitude λ 0 {\displaystyle \lambda _{0}} . By convention, in the northern hemisphere N 0 = 0 {\displaystyle N_{0}=0} km and in the southern hemisphere N 0 = 10000 {\displaystyle N_{0}=10000} km. By convention also k 0 = 0.9996 {\displaystyle k_{0}=0.9996} and E 0 = 500 {\displaystyle E_{0}=500} km. In

405-418: A region of large north-south extent with low distortion. By using narrow zones of 6° of longitude (up to 668 km) in width, and reducing the scale factor along the central meridian to 0.9996 (a reduction of 1:2500), the amount of distortion is held below 1 part in 1,000 inside each zone. Distortion of scale increases to 1.0010 at the zone boundaries along the equator . In each zone the scale factor of

450-510: Is a global (or universal) system of grid-based maps. The transverse Mercator projection is a variant of the Mercator projection , which was originally developed by the Flemish geographer and cartographer Gerardus Mercator , in 1570. This projection is conformal , which means it preserves angles and therefore shapes across small regions. However, it distorts distance and area. The UTM system divides

495-464: Is an abbreviated alphanumeric reference where the letters are simply omitted, e.g. 166712 for the summit of Ben Nevis. Unlike the numeric references described above, this abbreviated grid reference is incomplete; it gives the location relative to an OS 100×100 km square, but does not specify which square. It is often used informally when the context identifies the OS 2-letter square. For example, within

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540-595: Is called the Helmert datum transformation , which results in a typical 7 m error from true. The definitive transformation from ETRS89 that is published by the Ordnance Survey is called the National Grid Transformation OSTN15. This models the detailed distortions in the 1936–1962 retriangulation, and achieves backwards compatibility in grid coordinates to sub-metre accuracy. The difference between

585-477: Is located south-west of the Isles of Scilly. In order to minimize the overall scale error, a factor of 2499/2500 is applied. This creates two lines of longitude about 180 km east and west of the central meridian along which the local scale factor equals 1, i.e. map scale is correct. Inside these lines the local scale factor is less than 1, with a minimum of 0.04% too small at the central meridian. Outside these lines

630-619: Is now the preferred coordinate reference system across Ireland. ITM is based on the Universal Transverse Mercator coordinate system (UTM), used to provide grid references for worldwide locations, and this is the system commonly used for the Channel Islands . European-wide agencies also use UTM when mapping locations, or may use the Military Grid Reference System (MGRS), or variants of it. The first letter of

675-714: Is on the west coast of Scotland and the greatest in Kent . These two datums are not both in general use in any one place, but for a point in the English Channel halfway between Dover and Calais , the ED50 longitude lines are about 20 m east of the OSGB36 equivalents, and the ED50 latitude lines are about 150 m south of the OSGB36 ones. Universal Transverse Mercator coordinate system Most zones in UTM span 6 degrees of longitude , and each has

720-425: Is to ensure that the level of the canal is kept sufficiently high, even in times of drought. The 'Lower' reservoir(s) are compensatory reservoirs to ensure that the local area does not become parched in dry times. The "Upper" reservoir can be seen as a form of insurance . A dried up, i.e. unusable, canal would have been disastrous for the owners of the canal as well as the artisans and tradesmen who relied upon it for

765-495: Is used for sailing and windsurfing , and is the home of the Barnt Green Sailing Club. The reservoir is also used by 1st Kings Norton Sea Scout Troop who occupy a large boathouse on the south east shore. The Upper reservoir is also used for open water swimming in the summer months by the local triathlon club. One bank of the reservoir is inaccessible because it is a Site of Special Scientific Interest (SSSI) . During

810-562: The British Isles : this article describes the system created solely for Great Britain and its outlying islands (including the Isle of Man ). The Irish grid reference system is a similar system created by the Ordnance Survey of Ireland and the Ordnance Survey of Northern Ireland for the island of Ireland. The Irish Transverse Mercator (ITM) coordinate reference system was adopted in 2001 and

855-659: The German Federal Archives ) apparently dating from 1943–1944 bear the inscription UTMREF followed by grid letters and digits, and projected according to the transverse Mercator, a finding that would indicate that something called the UTM Reference system was developed in the 1942–43 time frame by the Wehrmacht . It was probably carried out by the Abteilung für Luftbildwesen (Department for Aerial Photography). From 1947 onward

900-678: The retriangulation of 1936–1962 . It replaced the Cassini Grid which had previously been the standard projection for Ordnance Survey maps. The Airy ellipsoid is a regional best fit for Britain; more modern mapping tends to use the GRS80 ellipsoid used by the Global Positioning System (the Airy ellipsoid assumes the Earth to be about 1 km smaller in diameter than the GRS80 ellipsoid, and to be slightly less flattened). The British maps adopt

945-561: The British National Grid is derived from a larger set of 25 squares of size 500 km by 500 km, labelled A to Z, omitting one letter (I) (refer diagram below), previously used as a military grid. Four of these largest squares contain significant land area within Great Britain: S, T, N and H. The O square contains a tiny area of North Yorkshire , Beast Cliff at OV 0000 , almost all of which lies below mean high tide. For

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990-503: The Earth in the UTM coordinate system, which means current UTM northing at a given point can differ up to 200 meters from the old. For different geographic regions, other datum systems can be used. Prior to the development of the Universal Transverse Mercator coordinate system, several European nations demonstrated the utility of grid-based conformal maps by mapping their territory during the interwar period . Calculating

1035-407: The Earth into 60 zones, each 6° of longitude in width. Zone 1 covers longitude 180° to 174° W; zone numbering increases eastward to zone 60, which covers longitude 174°E to 180°. The polar regions south of 80°S and north of 84°N are excluded, and instead covered by the universal polar stereographic (UPS) coordinate system. Each of the 60 zones uses a transverse Mercator projection that can map

1080-569: The OSGB 36 lines in South Cornwall , the difference diminishing to zero in the Scottish Borders , and then increasing to about 50 m north on the north coast of Scotland . (If the lines are further east , then the longitude value of any given point is further west . Similarly, if the lines are further south, the values will give the point a more northerly latitude.) The smallest datum shift

1125-688: The OSGB36 National Grid location for Ben Nevis is at 216600, 771200. Grid references may also be quoted as a pair of numbers: eastings then northings in metres, measured from the southwest corner of the SV square. 13 digits may be required for locations in Orkney and further north. For example, the grid reference for Sullom Voe Oil Terminal in the Shetland islands may be given as HU396753 or 439668,1175316 . Another, distinct, form of all-numeric grid reference

1170-628: The US Army employed a very similar system, but with the now-standard 0.9996 scale factor at the central meridian as opposed to the German 1.0. For areas within the contiguous United States the Clarke Ellipsoid of 1866 was used. For the remaining areas of Earth, including Hawaii , the International Ellipsoid was used. The World Geodetic System WGS84 ellipsoid is now generally used to model

1215-401: The boundaries between the UTM zones are approached. However, it is often convenient or necessary to measure a series of locations on a single grid when some are located in two adjacent zones. Around the boundaries of large scale maps (1:100,000 or larger) coordinates for both adjoining UTM zones are usually printed within a minimum distance of 40 km on either side of a zone boundary. Ideally,

1260-481: The central meridian reduces the diameter of the transverse cylinder to produce a secant projection with two standard lines , or lines of true scale, about 180 km on each side of, and about parallel to, the central meridian (Arc cos 0.9996 = 1.62° at the Equator). The scale is less than 1 inside the standard lines and greater than 1 outside them, but the overall distortion is minimized. The UTM zones are uniform across

1305-433: The context of a location known to be on OS Landranger sheet 41 (which extends from NN000500 in the south-west to NN400900 in the north-east) the abbreviated grid reference 166712 is equivalent to NN166712. If working with more than one Landranger sheet, this may also be given as 41/166712. Alternatively, sometimes numbers instead of the two-letter combinations are used for the 100×100 km squares. The numbering follows

1350-515: The coordinates of each position should be measured on the grid for the zone in which they are located, but because the scale factor is still relatively small near zone boundaries, it is possible to overlap measurements into an adjoining zone for some distance when necessary. Latitude bands are not a part of UTM, but rather a part of the military grid reference system (MGRS). They are however sometimes included in UTM notation. Including latitude bands in UTM notation can lead to ambiguous coordinates—as

1395-560: The coordinates on different datums varies from place to place. The longitude and latitude positions on OSGB 36 are the same as for WGS 84 at a point in the Atlantic Ocean well to the west of Great Britain. In Cornwall , the WGS 84 longitude lines are about 70 metres east of their OSGB 36 equivalents, this value rising gradually to about 120 m east on the east coast of East Anglia . The WGS 84 latitude lines are about 70 m south of

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1440-466: The digits is for the first coordinate and the second half for the other. The most common usage is the six figure grid reference , employing three digits in each coordinate to determine a 100 m square. For example, the grid reference of the 100 m square containing the summit of Ben Nevis is NN 166 712 . (Grid references may be written with or without spaces; e.g., also NN166712.) NN has an easting of 200 km and northing of 700 km, so

1485-559: The distance between two points on these maps could be performed more easily in the field (using the Pythagorean theorem ) than was possible using the trigonometric formulas required under the graticule-based system of latitude and longitude . In the post-war years, these concepts were extended into the Universal Transverse Mercator/ Universal Polar Stereographic (UTM/UPS) coordinate system, which

1530-474: The early 20th century, the bird life of the reservoirs was regularly recorded by the West Midland Bird Club , long before such site-monitoring became commonplace. They were also visited regularly by a young Bill Oddie . The Telegraph (Wednesday 15 November 2017 page 32) reported that during draining of Upper Bittell they found 500 critically endangered European eels. They were rehomed in the canal that

1575-417: The equator. In the northern hemisphere positions are measured northward from zero at the equator. The maximum "northing" value is about 9 300 000 meters at latitude 84 degrees North, the north end of the UTM zones. The southern hemisphere's northing at the equator is set at 10 000 000 meters. Northings decrease southward from these 10 000 000 meters to about 1 100 000 meters at 80 degrees South,

1620-473: The following formulas, the distances are in kilometers . First, here are some preliminary values: First we compute some intermediate values: The final formulae are: where E {\displaystyle E} is Easting, N {\displaystyle N} is Northing, k {\displaystyle k} is the Scale Factor, and γ {\displaystyle \gamma }

1665-402: The globe, except in two areas. On the southwest coast of Norway , zone 32 is extended 3° further west, and zone 31 is correspondingly shrunk to cover only open water. Also, in the region around Svalbard , the zones 32, 34 and 36 are not used, while zones 31 (9° wide), 33 (12° wide), 35 (12° wide), and 37 (9° wide) are extended to cover the gaps. Distortion of scale increases in each UTM zone as

1710-435: The letter "S" either refers to the southern hemisphere or a latitude band in the northern hemisphere—and should therefore be avoided. A position on the Earth is given by the UTM zone number and hemisphere designator and the easting and northing planar coordinate pair in that zone. The point of origin of each UTM zone is the intersection of the equator and the zone's central meridian. To avoid dealing with negative numbers,

1755-473: The local scale factor is greater than 1, and is about 0.04% too large near the east and west coasts. Grid north and true north are only aligned on the central meridian (400 km easting) of the grid which is 2° W (OSGB36) and approx. 2° 0′ 5″ W ( WGS 84 ). A geodetic transformation between OSGB 36 and other terrestrial reference systems (like ITRF2000 , ETRS89 , or WGS 84 ) can become quite tedious if attempted manually. The most common transformation

1800-607: The northern hemisphere and one in the south; the non-ambiguous format is to specify the full zone and hemisphere designator, that is, "17N 630084 4833438". These formulae are truncated version of Transverse Mercator: flattening series , which were originally derived by Johann Heinrich Louis Krüger in 1912. They are accurate to around a millimeter within 3000 km of the central meridian. Concise commentaries for their derivation have also been given. The WGS 84 spatial reference system describes Earth as an oblate spheroid along north-south axis with an equatorial radius of

1845-568: The origin (0, 0), which lies to the west of the Isles of Scilly . The Ordnance Survey (OS) devised the national grid reference system, and it is heavily used in its survey data, and in maps based on those surveys, whether published by the Ordnance Survey or by commercial map producers. Grid references are also commonly quoted in other publications and data sources, such as guide books and government planning documents. A number of different systems exist that can provide grid references for locations within

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1890-505: The reservoir feeds. 52°22′16″N 1°58′26″W  /  52.371°N 1.974°W  / 52.371; -1.974 Ordnance Survey National Grid The Ordnance Survey National Grid reference system ( OSGB ), also known as British National Grid ( BNG ), is a system of geographic grid references , distinct from latitude and longitude , whereby any location in Great Britain can be described in terms of its distance from

1935-440: The second letter, each 500 km square is subdivided into 25 squares of size 100 km by 100 km, each with a letter code from A to Z (again omitting I) starting with A in the north-west corner to Z in the south-east corner. These squares are outlined in light grey on the "100km squares" map, with those containing land lettered. The central (2° W) meridian is shown in red. Within each square, eastings and northings from

1980-518: The south end of the UTM zones. Therefore, no point has a negative northing value. For example, the CN Tower is at 43°38′33.24″N 79°23′13.7″W  /  43.6425667°N 79.387139°W  / 43.6425667; -79.387139  ( CN Tower ) , which is in UTM zone 17, and the grid position is 630 084  m east, 4 833 438  m north. Two points in Zone 17 have these coordinates, one in

2025-412: The south west corner of the square are given numerically. For example, NH0325 means a 1 km square whose south-west corner is 3 km east and 25 km north from the south-west corner of square NH. A location can be indicated to varying resolutions numerically, usually from two digits in each coordinate (for a 1 km square) through to five (for a 1 m square); in each case the first half of

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