CHAPTER 4. MAP PROJECTIONS AND GRID SYSTEMS · CHAPTER 4. MAP PROJECTIONS AND GRID SYSTEMS SECTION...

CHAPTER 4. MAP PROJECTIONS AND GRID SYSTEMS

SECTION I. MAP PROJECTIONS

A map projection is a method of representing a portionof the Earth’s round surface on a flat surface. Becausethis procedure causes distortions of different types,many different projections have been developed.Each projection is dictated by the size of the areabeing mapped, the map scale, and the intended use ofthe maps. See table 4-2 at the end of this section.

Each projection preserves certain properties anddistorts others. Most projections are cylindrical,conical or azimuthal, and project an ellipsoid ontocylinders, cones or plane surfaces. These surfaces maybe tangent to the ellipsoid or they may be secant. Aprojection is tangent to the ellipsoid when only onepoint or line of the projection surface touches theellipsoid. It is secant when two points or lines touchthe ellipsoid. See figure 4-1.

One common characteristic applies to all United Statesmilitary maps: they are all based on a conformalprojection. A conformal map projection is one that atany point, the scale is the same in any direction and theangle between any two lines on the ellipsoid is thesame when projected onto a plane.

Prescribed Projections

The Transverse Mercator (TM) Projection is thepreferred projection for all military mapping, though itis not necessarily used on all military maps. Thefollowing projections are prescribed for U.S. militarytopographic maps and charts that display a militarygrid on a standard scale. Military maps of non-U.S.

Figure 4-1. Projection Types: Tangent and Secant.

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areas produced by other nations may not alwaysconform to the following standards. U.S. maps offoreign areas may be based on other projections due totreaty agreements.

Topographic maps at scales of 1: 500,000 or largerthat lie between 80°S latitude and 84°N latitude arebased on the TM Projection.

Topographic maps at scales of 1: 1,000,000 that liebetween 80°S latitude and 84°N latitude are based onthe Lambert Conformal Conic Projection.

Maps at scales of 1: 1,000,000 or larger covering thepolar regions (south of 80°S latitude and north of 84°Nlatitude) are based on the Polar Stereographic Projection.

Maps at scales smaller than 1: 1,000,000 are based on theprojection best suited for the intended use of the map.

Scale Factor

For most military applications, map distance andground distance are considered the same. However, forsome geodetic and artillery operations (especially whenlong distances or high accuracies are involved), it isnecessary to correct between map and ground distances.

A scale factor is necessary to compensate fordistortions created when projecting an ellipsoidalsurface onto a cylinder, cone or plane depending onthe projection type. The scale factor of a projection isthe ratio of arc length along a differentially small linein the plane of the projection to the arc length on theellipsoid. This number depends on both the location ofthe point and on the direction of the line along whicharc length is being measured. For conformalprojections, the scale factor is independent of thedirection of the line and depends only on the locationof the point. The scale factor is labeled “k”.

The scale factor is considered exact (unity) when it hasa value of 1. Unity occurs at the points of tangency orsecancy between the ellipsoid and the projectedsurface. In a projection where the projected surface istangent to an ellipsoid, the scale factor increases away

from the point of tangency. In a projection where theprojected surface is secant to an ellipsoid, the scalefactor decreases toward the central meridian or originand increases away from the points of secancy.

True ground distance can be converted to a mapdistance by multiplying the ground distance by thescale factor.

Map Scale

A map scale is a representative ratio of map distancesto ground distances. These ratios vary from map tomap. The scale of a map is customarily chosen tocorrespond to the ratio at a given point or along agiven line (if constant along that line) multiplied by asuitable scale factor (usually close to unity). It isusually expressed as a common fraction having one asa numerator and the integer closest to the actual ratioas a denominator.

Maps used by the military vary from small-scaleplanimetric maps showing all of the continents tolarge-scale topographic maps suitable for tacticaloperations of small units and fire control. Militarymaps are classified according to their scale.

Map scales can sometimes be confusing in the sensethat the scale is smaller as the number increases. Thisconfusion can be cleared by viewing the map scale asa fraction (1/100,000 is a smaller number than 1/50,000). The following are standard scales formilitary maps.

Small-scale: 1: 600,000 and smaller

Medium Scale: larger than 1: 600,000;smaller than 1: 75,000

Large Scale: 1: 75,000 and larger

1: 1,000,000 1: 500,000

1: 250,000 1: 100,000

1: 50,000 1: 25,000

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Mercator Projection

The Mercator Projection is a cylindrical projectionwhere the rotational axis of the ellipsoid coincideswith the axis of the cylinder so that the Equator istangent to the cylinder. Points on the surface of theellipsoid are projected onto the cylinder from theorigin located on the equatorial plane and varyaround three-quarters of the way back from theprojected area. The cylinder is then opened andflattened to produce a plane surface. The parallelsof latitude and meridians of longitude both appearas sets of parallel l ines that intersect at rightangles. The meridians are equally spaced, but thedistance between paral lels increases as theirdistance from the Equator increases. The polescannot be shown on this projection (the normallimits are from 80°N latitude to 80°S latitude). Seefigure 4-2 and figure 4-3.

As the distance from the Equator increases, so does theamount of distortion; e.g., the map scale at 60°N or Slatitudes is nearly twice the map scale at the Equator.Maps or charts with this projection will distort the sizeof an area. This is why Alaska appears to be the samesize as the lower 48 states. This projection is notcommonly used for military purposes except when theentire Earth must be displayed and relative positions ofland masses are more important than size and distance.

Figure 4-3. Mercator Projection Flattened onto a Plane.

Figure 4-2. Mercator Projection.

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Transverse Mercator Projection

The TM Projection is a cylindrical conformalprojection. It is based on a modified MercatorProjection in that the cylinder is rotated (transverse)90° so that the rotational axis of the ellipsoid isperpendicular to the axis of the cylinder. Generally,the TM Projection is considered as a cylinder that issecant to an ellipsoid. Only a six-degree wide portionof the ellipsoid is projected onto the cylinder. Thecenterline of the projected area is called the centralmeridian. The ellipsoid is then rotated six degreesinside the cylinder and another six degree portion isprojected. See figure 4-4.

When the TM Projection is used to project a portionof the ellipsoid onto the cylinder, the Equator andthe central meridian will appear as perpendicularstraight lines. A hemisphere will be distortedtowards its outer edges. The shaded areas of figure4-5 show the varying distortion of two equivalentgeographic areas on the same projection. Note thatboth areas encompass a region 20° by 20° and areboth bounded by 20° and 40°N latitude. Therefore,on the ellipsoid they are the same size. But on theprojected surface the area bounded by 60° and 80°longitude is much larger than the area bounded by0° and 20° longitude. To decrease the amount ofdistortion, the ellipsoid is divided into 60 6°-wideprojection zones, each with a meridian of longitudeas its central meridian. Each zone is projectedbetween 84° 30’ N latitude and 80° 30’ S latitude.

The cylinder used as the projection surface for the TMProjection is generally considered to be secant to theellipsoid as shown in figure 4-4. This means that thecylinder intersects the ellipsoid in two places creatinglines of secancy that are parallel to the central meridianof the projection. The lines of secancy are located180,000 meters east and west of the central meridian ofeach projected zone. See figure 4-6.

Figure 4-7 shows a cross section of an ellipsoid and acylinder of projection that is secant to the ellipsoid. Thecross section is made by passing a plane through theellipsoid at the Equator. Line A’M’D’ represents thesurface of the cylinder. Line AMD represents theprojected portion of the ellipsoid surface. M is thecentral meridian; M’ is the projection of the central

meridian onto the cylinder. A and D are the meridianslocated three degrees from the central meridian. A’ andD’ are the projections of those meridians onto thecylinder. B and C are the points where the cylinderintersects the ellipsoid creating the secant condition.Note that line BM’C is shorter than line BMC. Thisshows that any line that lies between the lines ofsecancy is shorter on its projected plane (map) than it ison the ellipsoid surface. Note also that lines A’B andCD’ are longer than lines AB and CD, respectively.This shows that any line that lies between the lines ofsecancy and the edges of the projection are longer onthe projected plane than they are on the ellipsoidsurface.

For the TM Projection, the scale factor at the linesof secancy is unity (1.000 or exact). The scalefactor decreases toward the central meridian to0.9996. The scale factor increases toward the zonelimits to approximately 1.001 at the Equator. Seefigure 4-7 and table 4-1.

Figure 4-5. Distortion within the TM Projection.

Figure 4-4. TM Projection.


Figure 4-6. Secancy in a 6° Zone.

Table 4-1. TM Projection Scale Factor by UTM Easting.Easting of Starting Station Scale Factor (Meters)

500,000 500,000 0.99960 490,000 510,000 0.99961 480,000 520,000 0.99961470,000 530,000 0.99961 460,000 540,000 0.99961 450,000 550,000 0.99963440,000 560,000 0.99963 430,000 570,000 0.99966 420,000 580,000 0.99966 410,000 590,000 0.99970400,000 600,000 0.99972 390,000 610,000 0.99975 380,000 620,000 0.99977 370,000 630,000 0.99982 360,000 640,000 0.99984 350,000 650,000 0.99985 340,000 660,000 0.99991 330,000 670,000 0.99995320,000 680,000 1.00000 310,000 690,000 1.00005 300,000 700,000 1.00009 290,000 710,000 1.00014 280,000 720,000 1.00021 270,000 730,000 1.00025 260,000 740,000 1.00030 250,000 750,000 1.00037 240,000 760,000 1.00044230,000 770,000 1.00051 220,000 780,000 1.00058 210,000 790,000 1.00064 200,000 800,000 1.00071 190,000 810,000 1.00078 180,000 820,000 1.00085 170,000 830,000 1.00094

Figure 4-7. Line Distortion and Scale Factor in the TM Projection.

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Gauss-Kruger Projection

The Gauss-Kruger (GK) Projection can be described asthe TM Projection derived by mapping directly from anellipsoid that is tangent to the cylinder. It is a conformalprojection with many similarities to the TM Projection.The tangent point is the meridian of longitude chosen asthe central meridian for the projection. As with TM, theGK Projection depicts 60 zones. Many geodesistsconsider the GK and TM Projections to be the sameexcept for scale factor. See figure 4-8.

When a meridian is tangent to a cylinder of projection,there is no distortion along that line. Figure 4-9 shows alllines not located on the central meridian are longer on theprojected surface than they are on the ellipsoid. Forexample, line A’M is longer than line AM when Arepresents the meridian located three degrees from thecentral meridian. A’ is the projection of that meridianonto a cylinder. M is the central meridian (tangent point).

For the GK Projection, the scale factor at the central meridianis unity (1.000 or exact). The factor increases outward towardthe zone limits in excess of 1.004 at the Equator.

Polar Stereographic Projection

The Polar Stereographic Projection is used formapping the Earth’s polar regions and identifies thoseregions as north and south zones. The north zoneextends from the North Pole to 83° 30’ N latitude; thesouth zone extends from the South Pole to 79° 30’ Slatitude. It is a conformal azimuthal projection that isdeveloped by projecting a polar region onto a planethat is tangent to an ellipsoid at the pole or secant tothe ellipsoid at a specific latitude. The plane isperpendicular to the polar axis. The origin of theprojection is the opposite pole. Meridians are straightlines and parallels are concentric circles.

Lambert Conformal Conic Projections

Lambert Conformal Conic Projections are the mostwidely used projections for civilian cartographers andsurveyors. Many nations use it for civil and militarypurposes. This projection can be visualized as theprojection of an ellipsoid onto a cone that is eithertangent or secant to the ellipsoid. The apex of the coneis centered in the extension of the polar axis of theellipsoid. A cone that is tangent to an ellipsoid is onethat touches the ellipsoid at one parallel of latitude. Asecant cone intersects the ellipsoid at two parallelscalled standard parallels. This text discusses the secantcondition. See figure 4-10.

Figure 4-8. GK Projection.

Figure 4-9. Line Distortion and Scale Factor in the GK Projection.


When the cone of projection is flattened into a plane,meridians appear as straight lines radiating from a pointbeyond the mapped areas. Parallels appear as arcs ofconcentric circles centered at the point from where themeridians radiate. None of the parallels appears in exactlythe projected positions. They are mathematically adjustedto produce the property of conformality. This projection isalso called the Lambert Conformal OrthomorphicProjection. See figure 4-11.

The parallels of latitude on the ellipsoid that are to besecant to the cone are chosen by the cartographer. Thedistance between the secant lines is based on the purposeand scale of the map. For example, a USGS map showingthe 48 contiguous states uses standard parallels located at33°N and 45°N latitudes (12° between secant lines).Aeronautic charts of Alaska use 55°N and 65°N (10°between secant lines). For the National Atlas of Canada,secant lines are 49°N and 77°N (28° between secants). Thestandard parallels for USGS maps in the 7.5 and 15-minuteseries vary from state to state. Several states are separatedinto two or more zones with two or more sets of standardparallels. See figure 4-12 on page 4-8.

Since this is a conformal projection, distortion iscomparable to that of the TM and Polar StereographicProjections. Distances are true along the standard parallelsand reasonably accurate elsewhere in limited regions.

Directions are fairly accurate over the entire projection.Shapes usually remain relative to scale but the distortionincreases away from the standard parallels. Shapes onlarge-scale maps of small areas are essentially true. Scalefactor is exact (unity or 1.000) at the standard parallels. Itdecreases between and increases away from the standardparallels. The exact number depends on the distancebetween the standard parallels.

Oblique Mercator Projection

The Oblique Mercator Projection is actually manydifferent projections using variations of the TM. All arecylindrical and conformal. But instead of the cylinderbeing transverse 90° from the Mercator Projection, it istransverse at an angle that places the long axis of thecylinder 90° from the long axis of the area being mapped.If the general direction of an area that is to be mapped liesin a northeast/southwest attitude, the cylinder of projectionwould be transverse 45° west of north. The cylinder isusually secant to the ellipsoid to lessen the effects ofdistortion. The location of the lines of secancy variesbetween projections. Many Oblique Mercator Projectionsexist. This publication discusses the Laborde Projectionand the West Malaysia Rectified Skew Orthomorphic(RSO) Projection only.

The Laborde Projection is used to map the island ofMadagascar. It is an Oblique Mercator type projectionwith the long axis of the cylinder oriented at 18° 54’ eastof north. Scale factor at the origin is 0.9995. Thisprojection is used with the International Ellipsoid.

The West Malaysia RSO Projection is used to map theislands of Malaysia. It is an Oblique Mercator typeprojection with the long axis of the cylinder oriented at 36°58’ 27.1542" east of north. Scale factor at the origin is0.99984. This projection is used with the Modified EverestEllipsoid to map the West Malaysia RSO Grid System.

Many other Oblique Mercator Projections are used to mapareas of the world. Most are designed to work with aspecific grid system like the West Malaysia systemdescribed above. Examples of these systems include butare not limited to—l Alaska Zone 1 RSO. l Borneo RSO. l Great Lakes (4 Zones) RSO.

Figure 4-10. Secant Condition of Lambert Conformal Conic Projection.

Figure 4-11. Cone Flattened onto a Plane.

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l Liberia RSO. l Malaya (chain) RSO. l Malaya (yard) RSO. l Switzerland Oblique Mercator.

New Zealand Map Grid Projection

The New Zealand Map Grid (NZMG) Projection isused to map New Zealand. It is a sixth-order complex-algebra polynomial modification of the MercatorProject ion. A cyl inder cannot necessari ly beconsidered in this projection. It is a mathematicalprojection set secant to the International Ellipsoid. TheNZMG has no defined scale factor at the centralmeridian. Scale factor ranges from 1.00023 to 0.00078over the entire projection.

Cassini Projection

The Cassini Projection can be viewed outwardly as a GKprojection in that the cylinder is transverse 90° from theMercator Projection. It is also tangent to the ellipsoid at the

central meridian of a zone. The Cassini Projection predatesthe GK and TM Projections. It is made by treating allmeridians as planes that extend from the ellipsoid out to thecylinder. This projection causes the Equator and centralmeridian to be perpendicular straight lines. All othermeridians appear as lines that intersect the Equator at rightangles and curve toward the central meridian except forthose meridians that are located 90° from the centralmeridian. Those meridians appear as straight lines that areparallel to the Equator. Scale factor at the central meridianis unity (1.00 or exact). This projection is still used in someareas for civil and local grid systems, but is consideredobsolete for most purposes. In many areas it has beenreplaced by the TM Projection. This projection issometimes called the Cassini-Solder Projection.

Position differences between Cassini grid systems andTM grid systems are slight. For example, northing isthe same in the Palestine Cassini Civil Grid as it is inthe Palestine TM Civil Grid. The easting differencebetween the two is zero at 20 kilometers from thecentral meridian and only 4.1 meters at 100 kilometersfrom the central meridian.

Figure 4-12. Oklahoma Lambert Projection; North and South Zones.


Table 4-2. Projection Features.

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Table 4-2. Projection Features (Continued).

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Table 4-2. Projection Features (Continued).

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SECTION II. GRID SYSTEMS

A grid system is a two-dimensional plane-rectangularcoordinate system that is usually based on andmathematically adjusted to a map projection. Thisallows for the transformation from geodetic positions(latitude and longitude) to plane coordinates (eastingand northing) and for the computations relating tothose coordinates to be made by ordinary methods ofplane surveying.

Many grid systems are in use. Most of the local systemswill eventually be converted to one of the universal gridsystems. Some areas will continue to be mapped in alocal system such as the British National Grid (BNG),the Irish Transverse Mercator Grid (ITMG), and theMadagascar Grid (MG). There are two universal gridsused by the United States military and its allies: UTMand Universal Polar Stereographic (UPS).

Grids consist of a system of evenly spaced parallellines lying perpendicular to another system of evenlyspaced parallel lines forming squares. The grounddistance between the lines depends on the scale of themap and the type of grid system. Most systems usemeters as a basis for grid line spacing. Others useyards or feet. Standard scale military maps generallyadhere to grid lines on—

l Large-scale maps spaced at 1,000 meters. l Medium-scale maps at 1:250,000 spaced at 10,000

meters.

For scales smaller than 1:250,000, the grid lines may ormay not be depicted, depending on the map’s purpose.

North-south lines in a grid system are called eastingsand increase in value from west to east. East-west linesin a grid system are called northings and increase invalues from south to north. (These rules do not applyto grid systems that cover the polar regions such as theUPS.) The numerical value of an easting and northingare referenced to a specific origin. A false value isapplied to the easting or northing grid line that falls ata particular reference line or point. Usually, that lineor point is a meridian of longitude; e.g., centralmeridian of a zone or a parallel of latitude (like theEquator, but it can have other references). The originfor the false easting and false northing are normallydifferent lines or points.

Grid convergence is the angular difference betweentrue north and grid north. The direction and the valueof the angle are computed differently depending on thegrid system. In some systems, grid convergence can bethe same as convergence of the meridians.

Universal Transverse Mercator Grid System

The Universe TM (UTM) Grid System is referenced tothe TM Projection. The ellipsoid is divided into 60grid zones, each 6° wide, extending from 84° Nlatitude to 80° S latitude. Zones are numbered from 1to 60. Zone 1 starts at 180° − 174° west longitude,zone 2 at 174° west − 168° west longitude, continuingeast to zone 60 at 174° E − 180° longitude. The primemeridian (0° longitude) separates zones 30 and 31. Seefigure 4-13.

The location of any point in the UTM grid system canbe designated by coordinates by giving its distance east-west (easting) and its distance north-south (northing)from the origin of the grid zone. This origin (for eachUTM grid zone) is the intersection of the Equator andthe central meridian of the zone. Each UTM zone has acentral meridian corresponding to the central meridianof each TM Projection zone. The grid is oriented byplacing the east-west axis of the grid in coincidencewith the Equator and the north-south axis of the grid incoincidence with the central meridian of the zone.

Once the grid is oriented, the origin for easting andnorthing are assigned false values. The centralmeridian (origin for easting) of each zone is assignedan easting value of 500,000 meters. The eastingincreases east of the central meridian and decreaseswest. The Equator (origin for northing) is assigned twofalse values. If operating in the Northern Nemisphere,the northing of the Equator is 0 meters and increasesnorth. If operating in the Southern Hemisphere, thenorthing of the Equator is 10,000,000 meters anddecreases south. Grid lines that run north and south areeasting lines. They are parallel to the central meridianof the grid zone. Grid lines that run east and west arenorthing lines. They are parallel to the Equator. Seefigure 4-14 on page 4-14.

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Grid convergence at a point in the UTM system is theangle measured, east or west, from true north to gridnorth. At any point along the central meridian of aUTM grid zone, true north and grid north are the same.At any point not located on the central meridian, gridnorth departs from true north because of convergenceof the meridians. Grid convergence within the UTMsystem is a function of both latitude and longitude. Itwill rarely exceed 3° (53.333 mils) and is normally

listed in the declination diagram of a map. Gridconvergence should be computed for use in fifth orderor higher surveys because the information on the mapis generally computed for the center of the map sheet.For example, the Lawton map sheet (6353III) lists thegrid convergence at 6 mils, the Cache map sheet(6253II) lists it at 4 mils. There are two mils differencebetween the centers of these two adjoining sheets. Seefigure 4-15.

Figure 4-14. UTM Easting and Northing.


In the Northern Hemisphere, grid convergence isnegative east of the central meridian and positivewest. In the Southern Hemisphere, grid convergenceis positive east of the central meridian and negativewest. The direction (+, −) and the value of the gridconvergence are applied to a true azimuth to obtaina grid azimuth. If a grid azimuth must be convertedto a true azimuth, the value of the grid convergence

is the same. However, the opposite sign (direction)must be used. See figure 4-16.

The standard UTM grid zone is 6° wide. However,portions of several grid zones have been modified toaccommodate southwest Norway and the islands ofSvalbard. These grid zone modifications are notavailable in many survey or fire support systems.User-defined options or work-around methods must beused in these areas. Figure 4-17 on page 4-16 showsthe nonstandard portions of the respective grid zones.

Easting and northing values of a point in the UTMgrid system are called grid coordinates. Eastingconsists of six digits before the decimal point. Theonly exception is positions that are actually locatedin an adjacent grid zone. An easting can be writtenwith the first digit (100,000 meters) separated fromthe next five with a space. Northing generally hasseven digits before the decimal point. The exceptionto this is at locations north of the Equator by less than1,000,000 meters. A northing can be written with thefirst two digits (1,100,000 meters) separated from thenext five digits with a space. The number of digitsafter the decimal point depends on the order ofsurvey and the accuracy needed. An example of aUTM grid coordinate is 6 39127.84 − 38 25411.24.

If at any time you cross the Equator from north tosouth (at which point you would have a negativenorthing), you must algebraically add the northing toten million meters to obtain a northing for theSouthern Hemisphere. If you cross the Equator fromsouth to north (which would produce a northing

Figure 4-15. UTM Grid Convergence.

Figure 4-16. Sign of Grid Convergence.

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greater than ten million meters), you must subtract tenmillion meters from your northing to obtain a northingthat can be used in the Northern Hemisphere.

Military Grid Reference System

UTM, GK, and UPS grid coordinates are not unique.Any UTM grid coordinates can be plotted in each of the60 grid zones. Many UTM and GK coordinates will plotin both the Northern and Southern Hemispheres of thesame grid zone. All UPS grid coordinates between 84°and 90° north and south latitudes will plot in each of thetwo UPS grid zones. To make UTM and UPS gridcoordinates unique, the grid zone and grid zonedesignator should accompany them.

The MGRS is designed for use with the UTM andUPS grid systems. It establishes a unique set ofcoordinates for each specific location on the Earth. AnMGRS grid coordinate consists of a grid zone (UTMonly), a grid zone designator, a 100,000-meter squareidentifier, and the easting/northing coordinate.

A grid zone designator is a one-letter code specifyinga particular portion of a UTM/UPS grid zone. The gridzone designator is usually listed in the marginal dataof a military map. See figure 4-18.

Each of the 60 UTM grid zones is divided into 20 gridzone designators. Each designator represents an 8°portion of the grid zone except the northernmost( represents 12°) . Des ignators a re ident i f iedalphabetically by the letters C to X with the letters Iand O omitted. C is the southernmost designator, X isthe northernmost, and the Equator separates M and N.Thus, a grid zone and grid zone designator togetherspecify a region of the Earth covering a 6° by 8° areaexcept in the northernmost designation X (specifies a6° by 12° area).

Both UPS zones (north and south) are divided into twogrid zone designations separated by the 0° and 180°meridians. In the north, the designator Y covers theWes te rn Hemisphe re ; Z cove r s t he Eas t e rnHemisphere. In the south, designator A covers theWestern Hemisphere; B the Eastern Hemisphere.Since numbers are not used to identify UPS gridzones, a UPS grid MGRS coordinate will begin withthe grid zone designator.

Figure 4-17. Nonstandard UTM Grid Zones.


Figure 4-18. MGRS: 100,000-Meter Square Identification Lettering Convention for the UTM Grid, WGS 84/GRS 80 Ellipsoids.

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100,000-Meter Square Identifier

Each UTM/UPS grid zone is divided into 100,000-meter squares. Squares are identified by two letterscalled a 100,000-meter square identifier. The firstletter is columnar. It is the same for all squares in anorth-south column. The second letter is linear. It isthe same for all squares in an east-west row in a gridzone. This identifier is usually listed as part of themarginal information on a military map. The letteringconvention used depends on the reference ellipsoid.This text discusses the UTM lettering convention usedwith the WGS 84 and GRS 80 ellipsoids and the UPSlettering convention used with the Internationalellipsoid. Other ellipsoid lettering conventions aredetailed in DMA TM 8358.1, Datums, Ellipsoids,Grids, and Grid Reference Systems.

UTM

The first (columnar) letter of the 100,000 meter squareidentification originates at the 180° meridian with theletter A and increases alphabetically eastward alongthe Equator for three grid zones to cover an area of18°. The 100,000-meter columns, including partialcolumns at grid zone junctions, are lettered from A toZ but omit I and O. This alphabet is repeated every 18°eastward around the Earth.

The second (linear) letter of the 100,000 meter squareidentification is lettered from A to V but omit I and O,from south to north covering an area of 2,000,000meters and is then repeated northward. In odd-numbered grid zones, it originates at the Equatorincreasing alphabetically north. In even-numberedgrid zones, the second letter originates 500,000 meterssouth of the Equator increasing alphabetically north.Thererefore, in odd-numbered grid zones the secondletter of the 100,000-meter square identification is Aalong the Equator. In even-numbered grid zones thesecond letter is F along the Equator.

Each 6° by 8° square is broken up into 100,000-metersquares that occur only once. For example, there isonly one square identified by the letters WA inside ofthe 6° x 8° square of grid zone designation 3N. Theonly other square in this figure identified by the lettersWA is in grid zone designation 3Q. It can be seen infigure 4-18 that unique coordinates can be established

for every position within the UTM grid using theMGRS.

UPS

The 100,000-meter square identifiers are the same forboth UPS grid zones. The difference between two UPSgrid MGRS coordinates with the same 100,000-metersquare identifiers is the grid zone designator. A/B inthe south, Y/Z in the north. Designators A and Y(Western Hemisphere) are lettered the same, as aredesignators B and Z (Eastern Hemisphere). The northzone only includes that portion of the letteringconvention that falls inside of 84° latitude.

In the Western Hemisphere the first letter of the100,000-meter square identifier originates at theintersection of the 80° latitude and 90° W longitudelines. It is lettered alphabetically along the east-westaxis from J to Z. M, N, O, V, and W are omitted.

In the Eastern Hemisphere, the first letter of the100,000 meter square identifier originates at the 0° and180° meridians. It is lettered alphabetically along theeast-west axis from A to R but D, E, I, M, N and O areomitted.

The second letter of the 100,000-meter squareidentifier originates at the intersection of the 80°la t i tude /180° long i tude l ines . I t i s l e t t e redalphabetically from A to Z. I and O are omitted.

MGRS Grid Coordinates

Easting and northing coordinates used are the same asthe grid coordinates used with UTM/UPS with thefollowing modifications.

For UTM MGRS grid coordinates, delete the first digit(100,000 meters) from the easting and the first twodigits (1,100,000 meters) from the northing of theUTM grid coordinates. Add the grid zone number, thezone designator, and the 100,000-meter squareidentifier at the front of the coordinates.

For UPS MGRS grid coordinates delete the first twodigits (1,100,000 meters) from both the easting andnorthing UPS grid coordinates. Add the zonedesignator and the 100,000-meter square identifier atthe front of the coordinates.


The entire MGRS grid coordinate is written as oneentity without parentheses, dashes, or decimals.Examples:

Nonstandard Grids

Many grid systems have been developed by individualnations that cover only that nation or a regionsurrounding that nation. Usually, no direct relationshipexists between local grid systems (the same as nodirect relationship exists between the state plane gridsystems of the U.S.). Nonstandard grids are generallynamed for the nation or region they cover and containthe term grid, zone or belt; i.e., Ceylon Belt, MG, andIndia Zone I.

A grid covers a relatively small area. Its limits consistof combinations of meridians, parallels, rhumb lines,or grid lines. A zone is usually wide in longitude andnarrow in latitude. Its limits consist of meridians andparallels. A belt is usually wide in latitude and narrowin longitude.

World Geodetic Reference System

The World Geodetic Reference System (GEOREF) isan alphanumeric system for reporting positions basedon geodetic coordinates. It is a worldwide position

reference system that can be used with any map orchart graduated in latitude and longitude, regardless ofthe map projection. The primary use of the GEOREFis for inter-service and inter-allied positioning andreporting of aircraft and air targets.

User-Defined Grid Systems

When operating in an area that is mapped in a gridsystem other than UTM and UPS, it may be necessaryto define the grid system. Defining the grid system isbasically orienting a fire support system or surveysystem to measure or establish azimuths, distances,and elevations from a different origin than it isprogrammed for. Most current software versions donot allow this option. If the option is available, thefollowing information is necessary:

l Operational ellipsoid.

l Ellipsoid parameters (a, b, 1/f).

l Scale factor (at the origin) for the projection.

l Latitude of the origin.

l Longitude of the origin.

l Unit (meters, feet, yards, chains or rods).

l False easting of the origin.

l False northing of the origin.

Figure 4-19 lists the needed information for severalcommon nonstandard grids published in DMA TM8358.1, table 6. See page 4-20.

Figure 4-20 lists the needed information for severalcommon nonstandard grids not published in DMA TM8358.1, table 6. See page 4-21.

3Q location within a 6° × 8° square3QXV location to within 100,000 meter3QXV41 location to within 10,000 meters 3QXV4312 location to within 1,000 meters3QXV432123 location to within 100 meters3QXV43211234 location to within 10 meters3QXY4321012345 location to within 1 meter

4-20 _____________________________________________________________________________________________ MCWP 3-16.7

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8.1.

CHAPTER 4. MAP PROJECTIONS AND GRID SYSTEMS · CHAPTER 4. MAP PROJECTIONS AND GRID SYSTEMS SECTION...

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Transcript of CHAPTER 4. MAP PROJECTIONS AND GRID SYSTEMS · CHAPTER 4. MAP PROJECTIONS AND GRID SYSTEMS SECTION...