**Field Manual 3-34.331**
**TOPOGRAPHIC SURVEYING
**16 January 2001**
**

TOC Chap1 2 3 4 5 6 7 8 9 10 11 AppA AppB AppC AppD Gl Bib

**Chapter 4**

The discipline of surveying consists of locating points of interest on the surface of the earth. Points of interest are defined by spherical or planar coordinate values that are referenced to a defined mathematical figure. In surveying, the figure may be an equipotential surface, an ellipsoid of revolution, or a plane.

4-1. The earth is an ellipsoid, not a sphere, flattened slightly at the poles and bulging somewhat at the equator. Datums are reference surfaces that consider the curvature of the earth for the mathematical reduction of geodetic and cartographic data.

4-2. The geoid is the equipotential surface within or around the earth where the plumb line is perpendicular to each point on the surface. The geoid is considered a MSL surface that is extended continuously through the continents. The geoidal surface is irregular due to mass excesses and deficiencies within the earth. The figure of the earth is considered as a sea-level surface that extends continuously through the continents. The geoid (which is obtained from observed deflections of the vertical) is the reference surface for astronomical observations and geodetic leveling. The geoidal surface is the reference system for orthometric heights.

4-3. The WGS is not referenced to a single datum point. It represents an ellipsoid whose placement, orientation, and dimensions "best fit" the earth's equipotential surface that coincides with the geoid. The system was developed from a worldwide distribution of terrestrial gravity measurements and geodetic satellite observations. Several different ellipsoids have been used in conjunction with the WGS ellipsoid. Several ellipsoids are used in US military mapping. The goal is to eventually refer all positions to the WGS, which has a specific set of defining parameters, or to a WGS-compatible ellipsoid. Ellipsoids may be defined by a combination of algebraically related dimensions such as the semimajor and semiminor axes or the semimajor axis and the flattening. Figure 4-1 illustrates the defining parameters of some ellipsoids used by NIMA.

4-4. A map projection is the systematic drawing of lines representing the meridians and parallels (the graticule) on a flat surface. Different projections have unique characteristics and serve differing purposes. Projecting the graticule of the ellipsoid onto a plane depicts the projections. The intersections of the graticule are computed in terms of the ellipsoid.

4-5. US military maps use the sexagesimal system of angular measurement (the division of a full circle into 360�) for designating the values of the graticule. A degree is divided into 60 minutes, and each minute is divided into 60 seconds. Parallels are numbered north and south from 0� at the equator to 90� at the poles. Meridians are numbered east and west from 0� at the prime meridian to a common 180� meridian. The prime meridian used for US military mapping and charting coincides with the Bureau International de I'Heure defined as zero meridian, located near Greenwich, England.

4-6. The projections used as the framework of all US military maps and charts are all conformal. Conformability indicates that small areas retain their true shape; angles closely approximate their true values; and, at any point, the scale is the same in all directions. The following projections, which show military grids, are prescribed for US military topographic mapping and charting:

- Maps at scales larger than 1:500,000 for areas between 80� south and 84� north are based on the Universal Transverse Mercator (UTM) Projection.
- Maps of the polar regions (south of 80� and north of 84�) are based on the Universal Polar Stereographic (UPS) Projection.

4-7. The Mercator projection is not normally used for military topographic maps; however, its description serves as a basis for understanding the transverse Mercator projection. The Mercator projection can be visualized as a spheroid projected onto a cylinder tangent to the equator and parallel to the polar axis (Figure 4-2). When the cylinder is opened and flattened, a distortion appears. The distortion becomes more pronounced as the distance from the equator increases. The Mercator projection is transversed by rotating the cylinder again until the spheroid is parallel to a second axis (the meridian), which is then open and flattened (Figure 4-3). For military purposes and to minimize distortion, the transverse Mercator projection uses 60 longitudinal zones, each 6� wide.

4-8. Most military operations assume that map and ground distances are equivalent. However, in certain geodetic and artillery operations, where long distances are involved and the accuracy of results is essential, it is necessary to correct for the difference between distances on the map and distances on the ground. This is done by using scale factors from prepared tables or formulas. For the transverse Mercator projection, the scale factor is 1.00000 (unity) at the lines between each zone, decreasing inwardly to 0.9996 at the central meridian (CM) and increasing outwardly to about 1.0010 near the zone boundaries at the equator.

4-9. Grids are applied to maps to provide a rectangular system for referencing and making measurements. There is a definite relationship between the grid and the graticule, so that a corresponding geographic position can be determined for each grid position. Military grids consist of parallel lines intersecting at right angles and forming a regular series of squares. The north-south lines are called eastings and the east-west lines are called northings. Each grid line is one of an even-interval selection of measurement units. The interval is selected according to the map scale. The military prefer to use the UTM grid for areas between 80� south and 84� north.

4-10. Coordinates may be transformed from one grid system to another (for example, between the Lambert grid and the UTM grid or between different grid zones). The preferred method is to transform the grid coordinates from the first grid system to geographic positions. Then transform the geographic positions to the grid coordinates of the second grid system. This method does not change the datum.

4-11. The US Military Grid-Reference System (MGRS) is designed for use with UTM grids. For convenience, the earth is generally divided into 6� by 8� geographic areas, each of which is given a unique grid-zone designation. These areas are covered by a pattern of 100,000-meter squares. Two letters (called the 100,000-meter-square letter identification) identify each square. This identification is unique within the area covered by the grid-zone designation.

4-12. The MGRS is an alphanumeric version of a numerical UTM grid coordinate. Thus, for that portion of the world where the UTM grid is specified (80� south to 84� north), the UTM grid-zone number is the first element of a military grid reference. This number sets the zone longitude limits. The next element is a letter that designates a latitude bond. Beginning at 80� south and proceeding northward, 20 bands are lettered C through X. In the UTM portion of the MGRS, the first three characters designate one of the areas within the zone dimensions.

4-13. A reference that is keyed to a gridded map (of any scale) is made by giving the 100,000-meter-square letter identification together with the numerical location. Numerical references within the 100,000-meter square are given to the desired accuracy in terms of the easting and northing grid coordinates for the point.

4-14. The final MGRS position coordinate consists of a group of letters and numbers that include the following elements:

The reference is written as an entity without spaces, parentheses, dashes, or decimal points. Examples are as follows:

- The grid-zone designation.
- The 100,000-meter-square letter identification.
- The grid coordinates (also referred to as rectangular coordinates) of the numerical portion of the reference, expressed to a desired refinement.

- 18S (locating a point within the grid-zone designation).
- 18SUU (locating a point within a 100,000-meter square).
- 18SUU80 (locating a point within a 10,000-meter square).
- 18SUU8401 (locating a point within a 1,000-meter square).
- 18SUU836014 (locating a point within a 100-meter square).

4-15. To satisfy special needs, a reference can be given to a 10-meter square and a 1-meter square. Examples are as follows:

- 8SUU83630143 (locating a point within a 10-meter square).
- 18SUU8362601432 (locating a point within a 1-meter square).

4-16. There is no zone number in the polar regions. A single letter designates the semicircular area and the hemisphere. The letters A, B, Y, and Z are used only in the polar regions, and their presence in an MGRS (with the omission of a zone number) designates that the coordinates are UPS. An effort is being made to reduce the complexity of grid reference systems by standardizing a single, worldwide grid reference system (for example, WGS).

4-17. The use of geographic coordinates as a system of reference is accepted worldwide. It is based on the expression of position by latitude (parallels) and longitude (meridians) in terms of arc (degrees, minutes, and seconds) referred to the equator (north and south) and a prime meridian (east and west).

4-18. The degree of accuracy of a geographic reference (GEOREF) is influenced by the map scale and the accuracy requirements for plotting and scaling. Examples of GEOREFs are as follows:

- 40� N 132� E (referenced to degrees of latitude and longitude).
- 40�21� N 132�14� (referenced to minutes of latitude and longitude).
- 40�21�12" N 132�14�18" E (referenced to seconds of latitude and longitude).
- 40�21�12.4" N 132�14�17.7" E (referenced to tenths of seconds of latitude and longitude).
- 40�21�12.45" N 132�14�17.73" E (referenced to hundredths of seconds of latitude and longitude).

4-19. US military maps and charts include a graticule (parallels and meridians) for plotting and scaling geographic coordinates. Graticule values are shown in the map margin. On maps and charts at scales of 1:250,000 and larger, the graticule may be indicated in the map interior by lines or ticks at prescribed intervals (for example, scale ticks and interval labeling at the corners of 1:50,000 at 1� [in degrees, minutes, and seconds] and again every 5�).

4-20. The World GEOREF System is used for position reporting. It is not a military grid and, therefore, does not replace existing military grids. It is an area-designation method used for interservice and interallied position reporting for air-defense and strategic air operations. Positions are expressed in a form that is suitable for reporting and plotting on any map or chart (graduated in latitude and longitude) regardless of the map projection.

4-21. The system divides the surface of the earth into quadrangles, the sides of which are specific arc lengths of longitude and latitude. Each quadrangle is identified by a simple systematic letter code giving positive identification with no risk of ambiguity.

4-22. There are 24 longitudinal zones (each 15� wide) extending eastward from the 180� meridian around the globe through 360� of longitude. These zones are lettered from A to Z inclusive. There are 12 bands of latitude (each 15� high) extending northward from the south pole. These bands are lettered from A to M inclusive, northward from the south pole.

4-23. Each 15� quadrangle is subdivided into 15, 1� zones of longitude eastward from the western meridian of the quadrangle. These 1� units are lettered from A to Q inclusive. Each 15� quadrangle is also subdivided into 15, 1� bands of latitude northward from the southern parallel of the quadrangle. These bands are lettered from A to Q inclusive. Four letters may now identify a 1� quadrangle anywhere on the earth's surface.

4-24. Each 1� quadrangle is divided into 60� of longitude (numbered eastward from its western meridian) and 60� of latitude (numbered northward from its southern parallel). This direction of numbering is used wherever the 1� quadrangle is located. It does not vary, even though the location may be west of the prime meridian or south of the equator. A unique reference for defining the position of a point to an accuracy of 1� in latitude and longitude (for example, 2 kilometers or less) is given by quoting four letters and four numerals. The four letters identify the 1� quadrangle. The first two numerals are the number of minutes of longitude. The last two numerals are the number of minutes of latitude. If the number of minutes is less than 10, the first numeral will be a zero (for example, 04).

4-25. Each of the 1� quadrangles may be further divided into decimal parts (tenths or hundreths) eastward and northward. Thus, four letters and six numerals will define a location to 0.1� and four letters and eight numerals will define a location to 0.01�.

4-26. To fully understand GPS and the positional information, it is important to understand the reference system on which it is based. GPS satellites are referenced to the WGS-84 ellipsoid. The absolute positions that are obtained directly from the GPS measurements are based on the 3D, earth-centered WGS-84 ellipsoid. Coordinate outputs are on a Cartesian system (X, Y, and Z) relative to an earth-centered, earth-fixed (ECEF) rectangular coordinate system having the same origin as the WGS-84 ellipsoid (geocentric). WGS-84 Cartesian coordinates are then converted into WGS-84 ellipsoid coordinates (latitude, longitude, and height). The GPS uses the WGS-84 ellipsoid for geodetic survey purposes. The GPS routinely provides differential positional results on the order of 1 part per million (ppm), compared to the accepted results of 1:300,000 for NAD 83 and approximately 1:100,000 for NAD 27.

4-27. One application of DGPS surveying is densifying project control. Densification is usually done relative to an existing datum (NAD 27, NAD 83, or local). Even though GPS measurements are made relative to the WGS-84 ellipsoid coordinate system, coordinate differences (such as baseline vectors) on this system can be used directly on any user datum. Minor variations between these datums will be minimal when GPS data are adjusted to fit between local datum stations. Such assumptions may not be valid when high-order National Geodetic Reference System (NGRS) network densification is being performed.

**NOTE: NIMA provides datum
transformation parameters to many more datums (including local)**.

4-28. NAD 27 is a horizontal datum based on a comprehensive adjustment of the US National Control Network of traverse and triangulation stations. NAD 27 is a best fit for CONUS. The relative precision between initial-point monuments of NAD 27 is by definition 1:100,000, but coordinates on any given monument in the network contain errors of varying degrees. As a result, relative accuracy between points on NAD 27 may be far less than 1:100,000.

4-29. NAD 83 uses many more station observations than NAD 27 to readjust the US National Control Network. NAD 83 has an average precision of 1:300,000. NAD 83 is based on the Geodetic Reference System (GRS) of 1980 (GRS-80), earth-centered reference ellipsoid and, for most practical purposes, is equivalent to WGS 84.

4-30. The nationwide horizontal reference network was redefined in 1983 and readjusted in 1986 by the NGS. Since that time, several states and the NGS have begun developing high-accuracy reference networks (HARNs) for surveying, mapping, and related spatial-database projects. These networks (developed exclusively with a GPS) are accurate to 1 part in 1,000,000.

4-31. Orthometric elevations correspond to the earth's irregular geoidal surface and are based on tidal fluctuations of the MSL at a specific location. Measured DEs, based on spirit leveling, are generally relative to geoidal heights. The DEs between two points are called orthometric differences. Orthometric heights for CONUS are generally referenced to NGVD 29 or NAVD 88.

4-32. GPS-determined heights are referenced to an idealized mathematical ellipsoid. This WGS-84 ellipsoid differs significantly from the geoid; thus, GPS heights are not the same as orthometric heights. Due to significant variations in the geoid (even over small distances), elevations cannot be directly equated to orthometric differences. For small project areas where the geoid remains fairly constant, the relationship between orthometric and ellipsoid heights can be obtained from computer modeling or local geoid modeling. Local geoid modeling requires connecting to a sufficient number of existing orthometric BMs from which the elevations of known points can be best fit by adjustment.

4-33. Numerous mathematical techniques have been developed to convert coordinates between NAD 83 and NAD 27. These techniques include a variety of multiple-parameter and multiple-regression transformation equations. Each technique has advantages and disadvantages in terms of accuracy, consistency, and complexity. To eliminate these inconsistencies, the USACE Topographic Engineering Center (TEC) configured a comprehensive coordinate-conversion software program called Corps Conversion (Corpscon). Corpscon is the standard for topographic survey conversions, but newer programs are available. Additional technical information and authorized software programs can be obtained from TEC or NIMA web sites.