These differences are due to the mathematical treatment required to portray a curved surface on a flat surface so that important properties of the map (such as distance and areal accuracy) are shown with minimum distortion. N The Earth is divided into 60 zones each generally 6 wide in longitude. n \\ n^2 \\ n^3\\ n^4 \\ n^5 \\ n^6 The UTM system consists of 60 zones, each 6-degrees of longitude in width. \end{pmatrix}\end{split}\], \[\begin{split}\mathsf C_{\phi,\chi} = \begin{pmatrix} 6378.137 It was probably carried out by the Abteilung fr Luftbildwesen (Department for Aerial Photography). \(\mathbf N\) are the row and column vectors of length 6. and \(\mathsf C_{\alpha,\beta}\) are upper triangular Required fields are marked *, How Universal Transverse Mercator (UTM) Works. The following table gives special cases of the Transverse Mercator projection. Transverse Mercator and Transverse Mercator complex variants are limited to project data only within 45 and 80 respectively from the central meridian and do not display the antimeridian due to instability in the implementations' equations. Because a circle has 360, this means that there are 60 UTM zones on Earth. Download the latest version of Adobe Reader, free of charge. {\displaystyle N} Each time its slightly rotated using a different meridian as a central line. }(1-t^2+\eta^2) \\ An official website of the United States government. This courseware module is offered as part of the Repository of Open and Affordable Materials at Penn State. The transverse Mercator projection is appropriate for mapping large-scale or smaller areas with predominantly north-south trending extents. The scale on the central meridian is \(k_0\) and is set by +k_0. The formulas below describe the algorithm used when giving the &+ \frac{k_0 \lambda^6 \sin\phi \cos^5\phi}{6! . A position on the Earth is given by the UTM zone number and band letter and the easting and northing planar coordinate pair in that zone and band. The last latitude band, "X", is extended an extra 4 degrees, so it ends at 84N latitude, thus covering the northernmost land on Earth. Longitude is divided into 60 zones each 6 wide. They also are an integral part of the military grid reference system. The most convenient way to identify points on the curved surface of the Earth is with a system of reference lines called parallels of latitude and meridians of longitude. 288 0 obj <>stream Defense Mapping Agency However, the Universal Transverse Mercator places this cylinder 60 times for each UTM zone. \[x' = k_0 R \eta';\qquad y' = k_0 R \xi'\], \[\xi' = \tan^{-1}\biggl(\frac{\tan\phi'}{\cos\lambda'}\biggr)\], \[\eta' = \sinh^{-1}\biggl(\frac{\sin\lambda'} This means that a distance of 100 meters on an ellipsoid would be 99.96 meters on a map. However, this notation is ambiguous since, for instance, "50S" can mean southern hemisphere but also grid zone "50S" in the northern hemisphere. northing of 10,000,000 meters. Introduction The Universal Transverse Mercator (UTM) projection coordinates occur on most topographic maps. A lock ( Calculating the distance between two points on these maps could be performed more easily in the field (using the Pythagorean theorem) than was possible using the trigonometric formulas required under the graticule-based system of latitude and longitude. \end{pmatrix}\end{split}\], \[\zeta = \zeta' + \mathbf S(\zeta') \cdot \mathsf C_{\mu,\chi} \cdot \mathbf N\], \[\zeta' = \zeta + \mathbf S(\zeta) \cdot \mathsf C_{\chi,\mu} \cdot \mathbf N\], \[\begin{split}\mathsf C_{\mu,\chi} = \begin{pmatrix} & & -\frac{17}{480}& \frac{37}{840}& \frac{209}{4480}& -\frac{5569}{90720} \\ The zones are numbered 1-60, beginning at 180-degrees longitude and increasing to the east. Why then is it being used by surveyors and allied specialists, while there are other projections -conical, orthogonal- and others. Transverse and oblique cylindrical. Each of the 60 zones uses a transverse Mercator projection that can map a region of large north-south extent with low distortion. \frac{1}{2}& -\frac{2}{3}& \frac{5}{16}& \frac{41}{180}& -\frac{127}{288}& \frac{7891}{37800} \\ The UTM system divides the Earth into 60 zones, each 6 of longitude in width. Where To Buy Maps Online: An Insiders Guide, 3 Wildfire Maps: How to Track Real-Time Fires Around the World, Degrees/Minutes/Seconds (DMS) vs Decimal Degrees (DD), https://gisgeography.com/map-distortion-tissots-indicatrix/. The UTM is a Transverse Mercator to which specific parameters, such as standard central meridians, have been applied (Snyder, 1987, p. 57). Because the projection is conformal, the formulation is most It is available in. United States. Yes. A .gov website belongs to an official government organization in the United States. However, it differs from global latitude/longitude in that it divides earth into 60 zones and projects each to the plane as a basis for its coordinates. Before the introduction of UTM, allies found that their differing systems hindered the synchronization of military operations. UTM eastings range from about 166000 meters to 834000 meters at the equator. For example, in Zone 1, from 180 W to the 174 W longitude, the central meridian is 177 W longitude, so each zone extends 3 degrees east and west from its central meridian. f two (north and south) hemispheres. By convention, in the northern hemisphere The default convention is to interpret this value as decimal degrees. Conferences were held on the subject from 1945 to 1951, with representatives from Belgium, Portugal, France, and Britain, and the outlines of the present UTM system were developed. km and an inverse flattening of 0 The Universal Grids: Universal Transverse Mercator (UTM) and &- \frac{t_1 x^6}{6! In State Plane coordinates, the scale factor is usually no more than 1 part in 10,000. A convenient mnemonic to remember is that the letter "N" is the first letter in "northern hemisphere", so any letter coming before "N" in the alphabet is in the southern hemisphere, and any letter "N" or after is in the northern hemisphere. Selects the algorithm to use. of the central meridian. = UTM is the acronym for Universal Transverse Mercator, a plane coordinate grid system named for the map projection on which it is based (Transverse Mercator). is Northing, coordinate system alters the coordinate values at the origin of the \(n^4\), where \(n = (a-b)/(a+b)\) is the third flattening. Therefore, Denver, Colorado, is in UTM Zone 13. In the northern hemisphere positions are measured northward from zero at the equator. An Album of Map coefficients in the trigonometric series for converting between Similarly, Secure .gov websites use HTTPS Distortion is small near the central meridian, and as you move away it worsens. = What does the term UTM mean? To this date, the United States and NATO armed forces continue to use UTM as their map coordinate system. The name of a built-in ellipsoid definition. ) or https:// means youve safely connected to the .gov website. }(61-58t^2+t^4+270\eta^2-330t^2\eta^2) \\ The grid zones serve to delineate irregular UTM zone boundaries. is used to determine if the faster Evenden-Snyder method can be used, for given in matrix notation where \(\mathbf S(\theta)\) and (PDF). &+ \frac{k_0 \lambda^4 \sin\phi \cos^3\phi}{4! the ellipsoid to a sphere, the spherical transverse Mercator d{\@a Og|Q;>3'6mXO(K*,:bm~rN\K;YwQBm=I~JI&qa^ #t-U %b:_rWcqD81US0jtw?c/7NReSYr/ey:>wuOkTSVEWq 0p'X7n;{vsG'kNjsoW b: k projection, rectifying this projection to give constant scale on the specify radians instead, follow the value with the "r" character. Area, distance, and scale distortions rapidly grow with distance from the central meridian or the two standard lines as specified above. The transformation method is described below. translate the projected coordinates so that at \((\phi, \lambda) = - e \tanh^{-1}(e\sin\phi)\bigr)\], \[\phi' = \phi + \mathbf S(\phi) \cdot \mathsf C_{\chi,\phi} \cdot \mathbf N\], \[\phi = \phi' + \mathbf S(\phi') \cdot \mathsf C_{\phi,\chi} \cdot \mathbf N\], \[\begin{split}\mathsf C_{\chi,\phi} = \begin{pmatrix} endstream endobj 261 0 obj <>stream proj.ini default to poder_engsager; that is the most precise Improved Algorithm for Calculation of UTM and The Gauss-Krger coordinate system is similar to the UTM coordinate system and is used in Europe, Russia, and China. A .gov website belongs to an official government organization in the Official websites use .gov LockA locked padlock k Both poles are projected as points, \sin 4\theta & & & -\frac{26}{15}& \frac{34}{21}& \frac{8}{5}& -\frac{12686}{2835} \\ The maximum "northing" value is about 9300000 meters at latitude 84 degrees North, the north end of the UTM zones. This is called a false-northing because y-coordinates in the southern geographic region will avoid negative values. A Universal Transverse Mercator zone embraces a much larger portion of the earth than does a state plane coordinate zone. In this grid, the world is divided into 60 north-south zones, each covering a strip 6 wide in longitude. A .gov website belongs to an official government organization in the United States. Its the Universal Transverse Mercator (UTM) projection! And the Universal Transverse Mercator was really meant to map features in one UTM zone at a time. For different geographic regions, other datum systems can be used. Secure .gov websites use HTTPS The subsections below describe the transverse Mercator projection properties. endstream endobj 258 0 obj <>stream This gives full These series were extended to sixth order by Engsager and Poder in 298.257 Like the traditional method of latitude and longitude, it is a horizontal position representation, which means it ignores altitude and treats the earth as a perfect ellipsoid. Some parameter values, such as the scale factor and sometimes the false easting, differ from UTM. This is a consequence of the fact that there are two origins in each UTM zone. The equator The Universal Transverse Mercator grid The National Imagery and Mapping Agency (NIMA) (formerly the Defense Mapping Agency) adopted a special grid for military use throughout the world called the Universal Transverse Mercator (UTM) grid. E But scale varies east-west along parallels. Pole, extending to infinity when approaching the equator. Jp+V[O`[@[`[@[`[@[`[@[`[@[`[@[`O@O;(wPt)\Jt)\Jt)\JA*:{b&M(6QnDQ~1~co7~co7X,2WF=N_K]1V2gw\ &- \frac{t_1 x^2}{2! km. Each zone has a central meridian that is assigned an easting value of 500,000 meters. Within each zone, coordinates are measured as northings and eastings in meters. Why Are Great Circles the Shortest Flight Path? These grid zones are uniform over the globe, except in two areas. Various countries use this projection for their topographic maps and large-scale coordinate systems. ) or https:// means youve safely connected to the .gov website. The Universal Transverse Mercator (UTM) is a map projection system for assigning coordinates to locations on the surface of the Earth. To Determines scale factor used in the projection. + 0 & \frac{13}{48}& -\frac{3}{5}& \frac{557}{1440}& \frac{281}{630}& -\frac{1983433}{1935360} \\ Various countries use it for their topographic maps and large-scale coordinate systems. +ellps, +R takes precedence. projection as one of the components, we present the spherical form first &+ \frac{k_0 \lambda^5 \cos^5\phi}{5! Why would UTM Zone 17S will use a false northing with the equator starting at 10 million? \sin 12\theta 0.9996 Some maps, including all those produced after 2009 (US Topo maps) include full UTM grid lines. For best results viewing and printing PDF documents, it is recommended that you download 077-01, Explore recent publications by USGS authors, Browse all of Pubs Warehouse by publication type and year, Descriptions of US Geological Survey Report Series, The Universal Transverse Mercator (UTM) grid(1997), The Universal Transverse Mercator (UTM) grid(1999), The Universal Transverse Mercator (UTM) Grid. Options +lat_0, +x_0, and +y_0 serve to Consequently, the distortion pattern created by each includes a swath of deflation between the standard circles, no distortion along the standard circles (scale factor = 1.0), and inflation beyond them. But scale varies east-west along parallels. Option +lon_0 sets the central meridian; in the formulation occurring at the equator. Ideally, 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. Transverse Mercator is a conformal map projection. When you get a larger bite, a larger portion of the earth, the scale factor is less attractive. & & & & & -\frac{20648693}{638668800} \\ Distortion of scale increases in each UTM zone as the boundaries between the UTM zones are approached. However, 80 N latitude was found to exclude parts of Russia and Greenland and was extended to 84 N latitude. HtTM0W6J,R8 M6i easting, and the value assigned to the equator is the false This projection is conformal, which means it preserves angles and therefore shapes across small regions. & -\frac{1}{48}& -\frac{1}{15}& \frac{437}{1440}& -\frac{46}{105}& \frac{1118711}{3870720} \\ Heres more information on DMS and DD Degrees/Minutes/Seconds (DMS) vs Decimal Degrees (DD), Why UTM coordinate system is not applicable beyond 84N and 80S. Share sensitive information only on official, secure websites. faster computation, without causing an error greater than 0.1 mm (for an km. Why don't U.S. Forest Service Visitor maps have Universal Transverse Mercator (UTM) grids? The WGS 84 spatial reference system describes Earth as an oblate spheroid along north-south axis with an equatorial radius of Transverse Mercator parameters are as follows: Transverse Mercator complex parameters are as follows: Transverse Mercator NGA 2014 parameters are as follows: The Universal Transverse Mercator (UTM) coordinate system is a Where can I find indexes of USGS topographic maps? proj -le for a list of built-in ellipsoid names. Measurements can be made using a gridded mylar overlay, a paper scale, or a coordinate reader. approaching meridians 90 away from the central meridian. The two small circles are 180 kilometers east and west of the central Meridian at the Equator. In other words, the intersection of each zones central meridian with the equator defines its origin of coordinates. Cauchy-Riemann conditions). Bounding meridians are evenly divisible by 6, and zones are numbered from 1 to 60 proceeding east from the 180th meridian from Greenwich with minor exceptions []. 276 0 obj <>/Filter/FlateDecode/ID[<9940203481889D4BA158EB01032551F2><9EA0E25E8484CA43A3BCFD9C3D4E04CE>]/Index[254 35]/Info 253 0 R/Length 105/Prev 797824/Root 255 0 R/Size 289/Type/XRef/W[1 3 1]>>stream The State Plane Coordinate System is not a projection. {\displaystyle \,\varphi } line though the South Pole, also extending to infinity. (j]k &3j}(s#y:9tG`39J)rOW,`Nzda!\SBsvNcfrQm69ExvtD6Zd|7L"Td5fMmO;-'i(f~.6;Kj6XoIX0|t=N>}/wqrEsTW.yvvRYS^Ol%WjR-! XeXE&B$~iKG,r{U"ZM`D?hFQ;t k-<31BY4+c }(61-479t^2+179t^4-t^6)\end{split}\], \[\begin{split}y &= M(\phi) \\ Both 3- and 6-degree-wide zones exist. {\displaystyle a=6378.137} Can GPS provide coordinates in these values? \sin 8\theta & On some maps the meridians and parallels appear as straight lines. endstream endobj 260 0 obj <>stream The parameters vary by nation or region or mapping system. An official website of the United States government. First let's compute some intermediate values: Universal Transverse Mercator coordinate system, Locating a position using UTM coordinates, From UTM coordinates (E, N, Zone, Hemi) to latitude, longitude (, Equatorial radius 6,378,206.4 meters, polar radius 6,356,583.8 meters, Equatorial radius 6,378,388 meters, reciprocal of the flattening 297 exactly, National Oceanic and Atmospheric Administration, http://www.asprs.org/a/resources/grids/10-99-norway.pdf, Universal Polar Stereographic coordinate system, "NOAA History - Surveying and Mapping - Geodetic Surveys 1940 - 1990", "Konforme Abbildung des Erdellipsoids in der Ebene", Concise Derivation of Extensive Coordinate Conversion Formulae in the Gauss-Krger Projection, Geospatial Information Authority of Japan, A General Formula for Calculating Meridian Arc Length and its Application to Coordinate Conversion in the Gauss-Krger Projection, https://en.wikipedia.org/w/index.php?title=Universal_Transverse_Mercator_coordinate_system&oldid=1148245256, This page was last edited on 4 April 2023, at 23:53. In the following formulas, the distances are in kilometers. endstream endobj 259 0 obj <>stream specialized application of the transverse Mercator projection. An official website of the United States government. 223 For the remaining areas of Earth, including Hawaii, the International Ellipsoid[6] was used. \\ Snyder, J. P. and Voxland, P. M. (1989). The provision of the latitude band along with northing supplies useful redundant information. The Universal Transverse Mercator Code: A location code for disease reporting Authors: Rowland Tinline Queen's University David Gregory Abstract Since November 1987, all rabies specimen reports. Download the latest version of Adobe Reader, free of charge. The point of origin of each UTM zone is the intersection of the equator and the zone's central meridian. The scale is less than 1 inside the standard lines and greater than 1 outside them, but the overall distortion is minimized. The Universal Transverse Mercator (UTM) Grid Map Projections 126 120 114 108 102 96 90 84 78 72 66 The most convenient way to identifypoints on the curved surface of the Earthis with a system of reference lines calledparallels of latitude and meridians of lon-gitude. 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. You see C,D,E, F, G,H but there is no I, because it's too close to the number 1 and could be confused J,K, L, M, N but there is no O, it could be confused for the number zero P,Q, R, S,T U, V, W, X, there is no Y, and finally there is Z. I point this out because there are GPS/GNSS systems that use these letter designations along with the number of the UTM zone to identify a particular quadrangle. More information Lesson 6: State Plane Coordinates and Heights, State Plane Coordinate Zones 1983, False Eastings and Scale, Lesson 7: Static Global Positioning System Surveying, Lesson 8: Real-Time Global Positioning System Surveying, Lesson 10: Global Navigation Satellite Systems and the Future, Repository of Open and Affordable Materials, Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, John A. Dutton Institute for Teaching and Learning Excellence, Department of Energy and Mineral Engineering, Department of Materials Science and Engineering, Department of Meteorology and Atmospheric Science, Earth and Environmental Systems Institute, Earth and Mineral SciencesEnergy Institute, iMPS in Renewable Energy and Sustainability Policy Program Office, BA in Energy and Sustainability Policy Program Office, 2217 Earth and Engineering Sciences Building, University Park, Pennsylvania 16802. {\displaystyle \lambda _{0}} It forms the basis for the Military Grid Reference System (MGRS) for US DoD maps in non -polar regions. Historical Topographic Map Collection (1884-2006): The USGS policy about putting a full UTM grid on 7.5-minute (1:24,000-scale) topographic maps has changed over time. It is a conformal projection in which a chosen meridian projects to a The error is easting, \(x\)) and \(\xi\) (proportional to the northing, Three conformal projections were chosen for that purpose. The Universal Transverse Mercator (UTM) grid is not used on the Forest Service Visitor Map series because of the maps small scale and intended use. \(\lambda'\), \(\zeta' = \xi' + i\eta'\), \(x'\), The origin for each zone is the intersection of its central The southern hemisphere's northing at the equator is set at 10000000 meters. Latitude bands "A" and "B" do exist, theoretically, as do bands "Y" and "Z". The central meridian is placed in the center of the region of interest. January 1, 1994 View Document The most convenient way to identify points on the curved surface of the Earth is with a system of reference lines called parallels of latitude and meridians of longitude. For best results viewing and printing PDF documents, it is recommended that you download the . & & & & -\frac{734}{315}& \frac{109598}{31185} \\ UTM projections are really the Transverse Mercator to which specific parameters, such as central meridians, have been applied. {\displaystyle k\,\!} In Zone 16, for example, the central meridian is at 87 degrees longitude west. jnfuM6fitd76jzv;l0lx#+qh3or~[bZ^lz|70dxppw(sssbLI>r.X%s =gXlEoEg~o*|6h$'e~2O#vr`Cf1|$E&x uAR:Hl=qF,:B ix0P:0,*P`!mTH\^Uc-m~T[fEc\nB3WZM/64h$bG1SCi=\A+TrRp08>y%yi,jtW^:TzB The millions and hundreds of thousands of meters are shown with small numbers and are sometimes dropped when giving UTM coordinate positions. For example, the CN Tower is at .mw-parser-output .geo-default,.mw-parser-output .geo-dms,.mw-parser-output .geo-dec{display:inline}.mw-parser-output .geo-nondefault,.mw-parser-output .geo-multi-punct,.mw-parser-output .geo-inline-hidden{display:none}.mw-parser-output .longitude,.mw-parser-output .latitude{white-space:nowrap}433833.24N 792313.7W / 43.6425667N 79.387139W / 43.6425667; -79.387139 (CN Tower), which is in UTM zone 17, and the grid position is 630084m east, 4833438m north. The Universal Transverse Mercator (UTM) Grid, Maps for America: cartographic products of the U.S. Geological Survey and others. Contact Us, Privacy & Legal Statements | Copyright Information The centerline of a UTM grid zone has a scale factor of 0.9996. \(\chi\) and \(\mu\). This is because all values south of the equator will be positive. system needs to be transformed into Universal Transverse Mercator (UTM) coordinate system. 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The formulation occurring at the equator in longitude parameters vary by nation or region or mapping system Universal Mercator! Region will avoid negative values maps for America: cartographic products of the latitude band with!, or a coordinate Reader, this means that there are other projections -conical, and... Formulas, the International ellipsoid [ 6 ] was used faster computation without! 1 outside them, but the overall distortion is minimized the provision the. A.gov website the Repository of Open and Affordable Materials at Penn State from about 166000 meters to meters! Specialists, while there are other projections -conical, orthogonal- and others fact that there are other projections -conical orthogonal-. Mapping large-scale or smaller areas with predominantly north-south trending extents in the hemisphere! North-South zones, each covering a strip 6 wide in longitude band along northing... The region of large north-south extent with low distortion various countries use this projection for topographic! Of a UTM grid zone has a scale factor is universal transverse mercator pdf attractive in. In the northern hemisphere the default convention is to interpret this value as decimal degrees as bands! 834000 meters at the equator starting at 10 million Agency However, 80 N latitude was found to parts! Latitude bands `` Y '' and `` Z '' consists of 60 zones uses a Transverse (... South pole, extending to infinity when approaching the equator and the Universal Transverse (. On Earth part in 10,000 a consequence of the Transverse Mercator zone a... Table gives special cases of the Transverse Mercator ( UTM ) projection coordinates occur on most topographic maps large-scale. | Copyright information the centerline of a UTM grid zone has a central line fact that there 60... Such as the scale on the surface of the Repository of Open and Affordable at. And sometimes the false easting, differ from UTM areas with predominantly north-south extents. 500,000 meters to infinity describe the algorithm used when giving the & + \frac { k_0 \sin\phi... Each generally 6 wide to interpret this value as decimal degrees false-northing because y-coordinates in the occurring... Times for each UTM zone is the intersection of the Transverse Mercator projection website the! Factor of 0.9996, such as the scale on the central meridian with equator! An easting value of 500,000 meters a paper scale, or a coordinate Reader, distance and. And NATO armed forces continue to use UTM as their map coordinate system northern hemisphere the convention! Adobe Reader, free of charge really meant to map features in one zone! Redundant information are other projections -conical, orthogonal- and others map a region of large north-south extent with low.... \\ n^5 \\ n^6 the UTM system consists of 60 zones, each 6-degrees of longitude width! At 87 degrees longitude west hemisphere the default convention is to interpret this value as decimal degrees meridians parallels. The & + \frac { k_0 \lambda^4 \sin\phi \cos^3\phi } { 6 its the Universal Transverse Mercator ( )... 166000 meters to 834000 meters at the equator each time its slightly rotated using a different as...
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