NCPMA
ADVANCED MAPPING
North Carolina Property Mappers Association
Advanced Mapping
Section 4
NORTH AMERICAN DATUMS
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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 1901. 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
1866. 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
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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 1927.
Figure 4-1
Status of horizontal control in the United States
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4.4 The North American Datum of 1983
By the 1970's, as happened prior to the 1927 adjustment, there was a growing awareness that
a new adjustment of the North American Datum was needed. During the 1960's, with
electronic distance measurements becoming more common, accuracy’s of surveys were better
and ties to geodetic control became more common. Thus, in 1974, a new program was
undertaken to perform another general adjustment of the North American horizontal datum.
The project was originally scheduled for completion in 1983, hence its name North American
Datum of 1983 (NAD 83), but it was not actually finished until 1986. The adjustment was a
huge undertaking, incorporating the solution of 928,735 simultaneous equations using
266,000 control stations in the United States, Canada, Mexico and Central America. Not
only were the data readjusted for a better mathematical balance, but also a new ellipsoid was
adopted, more suited to worldwide use than the Clarke Spheroid of 1866. The initial point in
the new adjustment is not a single station such as Meades Ranch in Kansas. Rather, the
earth's mass center, and numerous other points whose latitudes and longitudes had been
precisely established from radio astronomy and satellite observation, were used. The earth's
mass center was employed since it fits the earth, in a global sense, more accurately than the
Clarke ellipsoid of 1866. NAD 83 positions are therefore consistent with satellite location
system (an important consideration with the expanding use of GPS), and with other latitudes
and longitudes established worldwide. Figure 4-2 illustrates the North American Datum of
1983.
4.5 The "Supernet" Programs
No sooner had the NAD 83 adjustment been completed, when GPS began to be used more
widely. In a manner similar to what occurred with Electronic Distance Measuring devices
two decades earlier, GPS measurements proved to be more accurate than the NAD 83
geodetic reference system. And so once again, and sooner than may have been expected, it
was time for refinement of the network.
Most states, the impetus coming mostly from transportation departments, sought to establish
their own GPS networks to resolve these coordinate adjustments. These GPS projects have
been called "supernets" and High Precision Geodetic Surveys (HPGS). The adjusted
networks have been called High Precision Geodetic Networks (HPGN) and High Accuracy
Reference Networks (HARN). Some states have begun to designate their revised datum as
NAD 83/91, the last two digits corresponding to the year of completion of the supernet
readjustment.
The result of the "supernets" is a shift in latitude and longitude values from their NCD 83
adjusted values. Thus, we actually now have three sets of latitudes and longitudes to
consider: NAD 27, NAD 83, and the revised NAD 83.
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Figure 4-2
North American Datum of 1983.
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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
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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
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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.
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The following is a list of the states with their respective systems:
Lambert System (E-W)
Alaska
Arkansas
California
Colorado
Connecticut
Iowa
Kansas
Kentucky
Louisiana
Maryland
Massachusetts
Minnesota
Montana
Nebraska
North Carolina
North Dakota
Ohio
Utah
Oklahoma
Virginia
Oregon
Washington
Pennsylvania
West Virginia
South Carolina
Wisconsin
South Dakota
Tennessee
Texas
Transverse Mercator System (N-S)
Alabama
Arizona
Delaware
Georgia
Hawaii
Idaho
Illinois
Indiana
Maine
Michigan
Mississippi
New Mexico
Missouri
Rhode Island
Nevada
Vermont
New Hampshire
Wyoming
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.
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Section 4
Review Questions
1.
2.
3.
4.
5.
The North American Datum of 1927 holds
________________________________ as its reference point.
The North American Datum of 1983 holds ______________________ as
its reference point.
The last adjustment in elevation is called
__________________________________________________________.
The military grid locational system is known as the
___________________________.
The two predominant projection systems are
__________________________ and the
______________________________________.
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Section 4
Review Solutions
1.
2.
3.
4.
5.
The North American Datum of 1927 holds Meades Ranch, Kansas as its reference point.
The North American Datum of 1983 holds the earth’s mass center as its reference point.
The last adjustment in elevation is called the North American Vertical Datum of 1988.
The military grid locational system is known as the Universal Tranverse Mercator.
The two predominate projection systems are Lambert Conformal Conic and the
Transverse Mercator.
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