# North Carolina Property Mappers Association. Advanced Mapping. Section 4 NORTH AMERICAN DATUMS

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1 North Carolina Property Mappers Association Advanced Mapping Section 4 NORTH AMERICAN DATUMS 4-1

2 4.1 Datums A datum is a set of quantities used as a basis to calculate other quantities. In mapping, it is a system or set of monuments referred to a reference surface. Both horizontal and vertical datums are used in surveying and mapping. The horizontal control monuments are referenced to an ellipsoid and are assigned geodetic coordinates. The vertical control monuments are referred to the geoid and assigned heights (elevations) above this reference surface. The earliest horizontal reference system in the United States was called the U.S. Standard Datum, adopted in This became known as the North American Datum in 1913, to reflect adoption by Canada and Mexico. This datum was based on the Clarke Spheroid of The earth is actually a spheroid because it bulges slightly at the equator due to centrifugal force caused by the earth's rotation on its axis. The shape of the earth is best described as an oblate ellipsoid. The equatorial diameter of the earth is approximately 27 miles greater than the polar diameter. Datums were established as a means to relate positions over wide regions and the entire world. Surveyors performing localized plane surveys do not take into consideration the curvature of the earth, whereas, surveyors performing geodetic surveys must allow for curvature. 4.2 Reference Datums Horizontal and vertical datums consist of a network of control monuments and benchmarks whose horizontal position and elevations have been determined by precise geodetic control surveys. These monuments serve as reference points for originating subordinate surveys of all types. The simplest form of horizontal control is the traverse, which consists of a series of marked stations connected by measured courses and the measured angles between them. When such a series of distances and angles returns to its point of beginning or begins and ends at stations of superior (more accurate) control, it can be checked and the small errors of measurement adjusted for mathematical consistency. By assuming or measuring a direction of one of the courses and rectangular coordinates of one of the stations, the rectangular coordinates of all the stations can be computed. A system of triangles usually affords superior horizontal control. All of the angles and at least one side (the base) of the triangulation system are measured. Though several arrangements can be used, one of the best is the quadrangle or a chain of quadrangles. Each quadrangle, with its four sides and two diagonals, provides eight angles that are measured. To be geometrically consistent, the angles must satisfy three so-called angle equations and one side equation. That is to say the three angles of each triangle, which add to 180 must be of such sizes that computation through any set of adjacent triangle within the quadrangles will give the same values for any side. Ideally, the quadrangles should be parallelograms. If the system is connected with previously determined stations, the new system must fit the 4-2

3 established measurements. 4.3 The North American Datum of 1927 As the triangulation schemes eventually crossed the country between the Atlantic and Pacific Oceans, and new arcs of triangulation began to fill the areas between, discrepancies in the closures between loops became evident. With the certainty that additional filling of the triangulation framework would be on going, it was felt that an adjustment of the primary control was needed. This adjustment was made by holding a fixed position called Meades Ranch in the State of Kansas. It is referred to as the North American Datum of 1927 (NAD 27). This project yielded adjusted latitudes and longitudes for some 25,000 monuments existing at the time. Figure 4-1 illustrates the U.S. horizontal control network in Figure 4-1 Status of horizontal control in the United States 4-3

5 Figure 4-2 North American Datum of

6 Figure 4-3 Approximate changes in latitude and longitude (in meters) in the conterminous United States from NAD 27 to NAD 83. (Upper figure) Latitude. (Lower figure) Longitude. (Adopted from National Geodetic Survey maps.) 4.6 Vertical Datums A vertical datum is defined by the system of monumentation used to define "sea level" (the geoid). This geoid is established in a practical sense by the numerical values of recognized benchmarks. The most common datum used in the United States has been the National Geodetic Vertical Datum of 1929 (NGVD 29), formerly called the "Sea Level Datum of 1929". A few hundred thousand miles of leveling lines were executed after 1929, including 4-6

7 4-7 thousands of miles of first-order leveling. Because of the additional data, and the need to correct errors in elevations caused by subsidence and crustal movements, the NGS decided an adjustment of the vertical datum was needed. This adjustment, completed in 1991, has resulted in new elevations. The adjusted reference system is called the North American Vertical Datum of 1988 (NAVD 88). The NAVD 88 adjustment changed elevations by only a few millimeters in the eastern half of the United States. However, in the western half, the shift in the vertical datum is on the order of 1 meter, and exceeds 1.5 meters in some areas. These horizontal and vertical datums set the stage for the State Plane Coordinate System, the system which provides a way to utilize new mapping and surveying technology and the many highly accurate control stations. using plane surveying techniques. The State Plane Coordinate System began in 1933 at the suggestion of the North Carolina Highway Department. Until then, using geodetic coordinates from NAD 27 for land and other surveys caused problems. First, the average land owner or user of surveys associated with the land could not relate to dimensions given in angular units between points or corner positions described by latitude and longitude. Second, there was a problem associated with calculations from spherical coordinates, as compared to plane coordinates. As a result of a need for a system for general surveying, the United States Coast and Geodetic Survey (USC & GS) proceeded to design a rectangular system for each state. The system developed in 1933 is based on NAD 27 geodetic positions. The State Plane Coordinate System simply provided means, through mathematical projections, for precise conversions of latitude and longitudes into X and Y coordinates, as it referred to assigned origins in each state. With the NAD 83 readjustment, a new set of plane coordinates was created, based on the revised latitudes and longitudes. Likewise, the "supernet" programs revised the plane coordinates of points a little more. 4.7 Projection Surfaces Because the earth's surface is curved and irregular, it was necessary to develop a projection to cover the area that would provide a plane surface for surveyors and mappers. A map projection is a projection in which one of the surfaces is a spheroid and the other is a surface that can be developed into a plane. Thus, projections provide a means to "flatten" spherically positioned areas without the full limitations of simply ignoring the roundness of the globe. It was determined to use either or both of the two projection systems for the state plane coordinates. The Lambert Conformal Conic Projection System and the Transverse Mercator Projection System. The Lambert employs a cone projection while the Transverse

8 Mercator System uses a cylindrical projection. Typically, the conical projection is used in states that are long in an east-west direction. The cylindrical projection is used largely in states that are long in a north-south direction. The Transverse Mercator of the state plane coordinate system should not be confused with the Universal Transverse Mercator System (UTM). This system is a military grid, using meters, having 6 wide zones (60 in number), covering the entire globe. It is related to state plane coordinates only in that both systems are related to geodetic positions, mathematically. Figure 4-4 Surfaces used in State Plane Coordinate Systems A rectangular grid is developed that covers an area larger than the zone in order to provide a zero X and Y position outside the zone. This zero is located south and west so that only positive numbers are used. The X value is used to show the number of feet east of zero while the Y is used to show the number of feet north of zero. Figure 4-5 shows the State of North Carolina with the grid superimposed. If a state has two or more zones, there is enough overlap that no county will fail to be entirely covered by at least one zone. 4-8

9 The following is a list of the states with their respective systems: Lambert System (E-W) Alaska Louisiana Ohio Utah Arkansas Maryland Oklahoma Virginia California Massachusetts Oregon Washington Colorado Minnesota Pennsylvania West Virginia Connecticut Montana South Carolina Wisconsin Iowa Nebraska South Dakota Kansas North Carolina Tennessee Kentucky North Dakota Texas Transverse Mercator System (N-S) Alabama Idaho Mississippi New Mexico Arizona Illinois Missouri Rhode Island Delaware Indiana Nevada Vermont Georgia Maine New Hampshire Wyoming Hawaii Michigan New Jersey Both Systems Florida New York Most small states, or narrow and elongated states (such as North Carolina), have only one zone. Larger states have two or three zones, and some have more. For example, Texas has five zones and California has seven. 4-9

10 Section 4 Review Questions 1. The North American Datum of 1927 holds as its reference point. 2. The North American Datum of 1983 holds as its reference point. 3. The last adjustment in elevation is called. 4. The military grid locational system is known as the. 5. The two predominant projection systems are and the. 4-10

11 Section 4 Review Solutions 1. The North American Datum of 1927 holds Meades Ranch, Kansas as its reference point. 2. The North American Datum of 1983 holds the earth s mass center as its reference point. 3. The last adjustment in elevation is called the North American Vertical Datum of The military grid locational system is known as the Universal Tranverse Mercator. 5. The two predominate projection systems are Lambert Conformal Conic and the Transverse Mercator. 4-11

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