The SPCS zones in the United States were designed in the 1930s for use on the NAD27. Although other projection options were considered for use on the NAD83, the defining SPCS zone parameters were largely unchanged for implementation on the NAD83. The SPCS on the NAD83 consists of fifty-four transverse Mercator projections, sixty-eight Lambert conic conformal projections, and one oblique Mercator projection. Some states are covered by a single zone, but most states require more than one zone due to the limiting width of 158 miles and due to choosing SPCS zone boundaries to follow county boundaries. Other incidental changes were made during the transition from NAD27 SPCS to NAD83 SPCS and can be gleaned from two important publications. Claire (1968) is the “bible” for working with SPC on the NAD27, and Stem (1989) is the “bible” for working with SPC on the NAD83. Each booklet contains a description of the underlying map projections, a listing of the defining parameters for each zone, and a list of equations that can be used to perform bidirectional transformations between latitude/longitude positions and plane coordinates on the respective datum.
History
The following quote is found in a section entitled “SPCS—UTM and Oscar S. Adams” by Joseph Dracup, former geodesist for the U.S. Coast & Geodetic Survey (USC&GS), now the National Geodetic Survey (NGS), http://www.ngs.noaa. gov/PUBS_LIB/geodetic_survey_1807.html (accessed 12 June 2007).
In 1933-34, Oscar S. Adams ably assisted by Charles N. Claire developed the State Plane Coordinate System (SPCS) at the request of George F. Syme a North Carolina Highway engineer. Syme died shortly after the North Carolina system was developed being succeeded by O.B. Bestor to carry on the cause. Bestor was in charge of the State local control project established in 1933, later identified as the North Carolina Geodetic Survey. Most State and the few county projects involved in this program also were so named. Colonel C. H. Birdseye of the USGS, with a strong interest in Statewide coordinate grids[,] also participated in the several conferences leading to the decision to honor Syme’s request.
The first tables for computing Lambert coordinates were developed for North Carolina and the first tables for the transverse Mercator grid were for New Jersey. Tables were prepared for all States early in 1934. For the first time all horizontal control stations previously defined only by latitudes and longitudes would be available in easy to use plane coordinates.
Features
“Special Publication 235” (Mitchell and Simmons [1945] 1977) is a booklet that describes details of the state plane coordinate system. It is of both practical and significant historical value because it documents surveying policies and practices prior to the electronic revolution. Several important features of the SPCS described in “Special Publication 235” include the following:
• The state plane coordinate system provides a method by which the latitude/ longitude positions of the national triangulation network can be represented by plane coordinates. That meant local surveyors and/or engineers could continue using plane surveying procedures yet realize the benefits of basing their work on the national network of geodetic control points established by the federal agencies. This item is still valid in the 2-D arena (a subset of the 3-D arena). But, spatial data are 3-D and the GSDM does for 3-D data what the SPCS does for 2-D data.
• Normal land-surveying measurements in the 1930s were made with a transit and steel tape. Expected accuracies were often in the range of 1:5,000 to 1:8,000 or better. Under those circumstances, a routine distance distortion of 1:10,000 could be tolerated without making a scale factor correction and without significant detrimental impact on the quality of the survey. With newer technology, this assumption is no longer valid because measurement accuracies today routinely exceed those of eighty years ago. Better accuracy is not a problem because high-quality computational results are obtained by applying the grid scale factor correction. With the corrections applied, the SPCS is fundamentally sound for 2-D applications. Elevation is typically used to handle the third dimension.
• There are two distance “corrections” to be made when working with the SPCS:(1) the grid scale factor is used to correct for the distortion between the ellipsoid and the grid, and (2) the elevation factor is needed to reduce a ground-level horizontal distance to the ellipsoid. These two corrections are often combined into one “combination factor” (the product of the grid scale factor and the elevation factor). The grid distance between the plumb lines through two points is the product of the horizontal ground distance and the combination factor. “Special Publication 235” explains both factors quite well, but, as discussed later, this is the primary disadvantage of using the SPCS. Regretfully, when using the SPCS, a foot on the grid is not necessarily a foot on the ground. In many cases, such as centerline stationing on a highway project, the difference between grid and ground distances becomes intolerable.
• Although the NGS has always performed and computed its geodetic surveys in meter units, the NAD27 state plane coordinates were published in foot units—see the sidebar discussion of the U.S. Survey Foot on page 259.
It is not true, as some have said, that the state plane coordinate systems distort distances by 1:10,000. It is true to say that, when compared to a distance on the map, the equivalent distance on the ellipsoid may be distorted by up to 1:10,000. On a secant projection, the distortion is zero along the lines of exact scale where the two surfaces intersect and the distance on the map is the same as the distance on the ellipsoid. At the center of the zone, the distance is compressed by 1:10,000 or by whatever distortion value was selected by the zone designer. In some cases, a zone width of 158 miles was not quite sufficient to cover the area required, and the distance distortion at the center of the zone is greater than 1:10,000 (i.e., the grid scale factor at the zone center is less than 0.9999)—see constants for California Zone 1, both Oregon zones, Zone 10 in Alaska, North Carolina, South Carolina, four of the five Texas zones, Utah Central Zone, and the offshore zone for Louisiana.
The grid scale factor is only part of the distortion. The elevation factor also contributes to the difference between a horizontal ground distance and the state plane grid distance. Modern practice looks more closely at the grid-ground distance difference (as a result of using the combination factor), and many resort to using surface coordinates or project datums as a way to avoid the mismatch between grid and ground distances. More recently, the use of “low-distortion projections” has been discussed as being a way to minimize the grid-ground distance distortion. The distance distortion issue is largely moot when using the GSDM.
NAD27 AND NAD83
The NAD27 was the only logical datum choice available when the state plane coordinate zones were developed during the 1930s. The zones were selected by matching the projection type with the state’s general configuration. Lambert conic projections were selected for states long in the east-west dimension, while transverse Mercator projections were selected for states oriented primarily north-south. Some states have only one projection, other states require more than one zone to cover the needed width, and some states have more than one projection type. For example, the State of Florida utilizes two transverse Mercator projections and one conic projection, New York employs three transverse Mercator projections and one conic projection, and the State of Alaska uses nine transverse Mercator projections, one conic projection, and one oblique Mercator projection.
In the 1930s, the USC&GS developed a “model law,” which was promoted by the Council of State Governments for several decades. By 1971 the SPC model law was adopted in one form or another by twenty-six states (Mitchell and Simmons [1945] 1977). However, the Michigan Legislature adopted a different projection than that proposed by the USC&GS. Originally, Michigan was to be covered by three transverse Mercator projections, but when the state plane coordinate law was written, professionals within the state opted instead for three conic conformal projections based upon an elevated reference surface selected to minimize the need for the elevation reduction. The elevated system worked as intended and was deemed very beneficial, but, because it was “nonstandard,” there was confusion both in practice and in the published literature about computing the correct combination factor for a line.The Michigan state plane coordinate law for NAD83 returned the reference surface to the ellipsoid.
Relationship between the Meter, the International Foot, and the U.S. Survey Foot
1. The length of the meter was established in the 1790s as 1/10,000,000 of the distance from the equator to the North Pole as determined by a geodetic survey in France.
2. In the early 1800s, prototype meter bars were made and distributed to the nations of the world.
3. Although the meter has been used as the standard of length for geodetic surveys in the United States since the establishment of the Coast Survey (predecessor to the NGS) in 1807, the meter length unit was declared legal for trade in the United States in 1866. The relationship between the foot and meter was stated in 1866 to be 39.37 feet = 12.00 meters exactly.
4. Leading up to and during World War II, Canada, the United States, and Great Britain each used a slightly different relationship between the foot and meter.
United States: 1.00 meter = 39.37 inches, or 1 inch = 2.540005 cm England: 1 inch = 2.539997 cm Canada: 1 inch = 2.540000 cm
5. Following World War II, machinists and aircraft mechanics, working under the auspices of NATO, discovered that parts of aircraft engines built according to the same blueprints were not interchangeable due to differences in unit definitions. A compromise was reached that adopted the Canadian relationship (1 inch = 2.54 centimeters) as the International Foot (1 foot = 0.3048 meters).
6. However, to avoid recomputing and republishing thousands of existing state plane coordinates, the United States retained use of 12 meters = 39.37 feet and gave that long-standing relationship a name—the U.S. Survey Foot. A 1959 Federal Register notice (“Federal Register Notice” 1959) stated that the U.S. Survey Foot should be used “until such time as it becomes desirable to readjust the basic geodetic networks in the United States, after which the ratio of a yard, equal to 0.9144 meter, shall apply” (emphasis added).
7. In 1960 the Eleventh General Conference of Weights and Measures redefined the meter, but not the length. The redefinition made it possible to duplicate the 1.00 meter distance in terms of wavelengths of Krypton 86 gas instead of relying upon the distance between two marks on a prototype bar.
8. The definition of the length of the meter was changed again in 1983—this time in terms of the distance light would travel in a vacuum in 1/299,792,458 seconds. The new definition is the equivalent to saying that light travels 299,792,458 meters in one second.
Although the definition used for duplicating the length of the meter has evolved over the years, the fundamental unit of length has not changed. The relationship of 12.00 meters = 39.37 feet has existed in the United States for over one hundred years. The name “U.S. Survey Foot” was developed in 1959 to describe the relationship already in existence. “International Foot” is the name given to the relationship used before 1959 by Canada (1 foot = 0.3048 meters) and adopted for use around the world (except for surveying and mapping in the United States). Neither the U.S. Survey Foot nor the International Foot is part of the International System of Units (SI) adopted by the Eleventh General Conference on Weights and Measures in 1960.
When the NAD27 datum was readjusted and published as the NAD83, the legislative intent was for the International Foot to be used as an alternate to meters. Recognizing that, a number of states included the International Foot in the state plane coordinate legislation written and adopted to accommodate the NAD83. Other states objected and ultimately won. A notice published in the Federal Register on May 16, 1998, closes by saying, “The effect of this notice is to allow the U.S. Survey Foot to be used indefinitely for surveying and mapping in the United States. No other part of the 1959 notice is in any way affected by this notice.” The NGS still uses meter units for all geodetic surveying operations.
The upshot is that NAD83 state plane coordinates in the United States may be meters, U.S. Survey Feet, or International Feet. Although the GSDM is based exclusively on metric units, each user has the option of specifying different linear units when displaying or printing P.O.B. results. That is, provision is made for other derived units in the P.O.B. datum option. However, it is intended that the underlying ECEF coordinates will always be metric when using the GSDM.
Current Status: NAD83 State Plane Coordinate Systems
Although developed for use on the NAD27, design of the SPCS was revisited prior to publication of the readjusted NAD83 in North America. Arguments were advanced for taking advantage of the standardization offered by the UTM system, and using 2° UTM zones on the NAD83 was considered. After many discussions and consideration of various alternatives, the decision was to adopt parameters of a different ellipsoid (the GRS 1980 in place of Clarke 1866) and to move the datum origin from “Meade’s Ranch,” Kansas, to the Earth’s center of mass. But, with exceptions, the existing SPCS projections and zone parameters were retained for use on the NAD83. Notable exceptions include the following:
• The reference surface for Michigan was returned to the ellipsoid instead of being computed at an elevation of 800 feet.
• Zone 7 in California was eliminated. Zone 5 now covers that area.
• The states of Montana, Nebraska, and South Carolina elected to relax the arbitrary 1:10,000 criteria and to cover each state respectively with one zone.
Advantages
The advantages of using the SPCS today are largely the same as when the SPCS was first implemented. A map projection flattens a portion of the Earth and allows one to perform 2-D rectangular surveying computations within a defined zone using plane Euclidean geometry. Standardization and wide acceptance are two huge benefits. An incidental benefit of the SPC is that the back azimuth of a line is the same as the forward azimuth + 180°. This feature could also be called a disadvantage because it belies the fact that meridians are not parallel, but converge at the poles.
Disadvantages
A disadvantage of the SPCS for the GIS community is the absence of uniqueness. For inventory, and other purposes, it is highly desirable for the description of any point location to be globally unique. State plane coordinates are unique within a zone but not globally. In addition to knowing the state plane coordinate values for a point, the spatial data user must also know what zone or map projection is associated with the point. Two points having the same (or nearly so) coordinate values may appear to be the same or very close together although they are, in fact, many kilometers apart. A triplet of ECEF rectangular X/Y/Z metric coordinates used in the GSDM is unique within the “birdcage” of orbiting GPS satellites.
In the surveying, mapping, and engineering communities, the biggest disadvantage of using map projections and the SPCS is that they are strictly 2-D mathematical models and spatial data users work with 3 -D data. The GSDM is a rigorous 3 -D model.
• Lack of accessibility: control points are not easy to visit, permission, and so on.
• Lack of proximity: control points are too far away.
• Lack of quality: the published positions are not of sufficiently high quality.
• Lack of understanding: spatial data users need to learn more about the SPCS.
• Mapping distortion: ground distance may differ too much from grid distance.
With the advent of GPS, continued densification of the control network, higher levels of support from NGS, and greater awareness within the spatial data user community, the first four disadvantages have been significantly mitigated. But, the grid-ground difference is more of a problem than ever because more and more people are using equipment and computational processes in which that systematic difference cannot be tolerated. An argument is that more education and better enforcement of minimum standards could overcome those disadvantages. Without discounting the benefits of more education, it is suggested that using the GSDM is another alternative in which spatial data users can fully exploit the three-dimensional characteristics of their data and in which 2-D applications are still supported as a subset of the 3-D model.
