PROJECTION SYSTEMS
5.5. STATE PLANE PROJECTIONS
The rapid increases in land values, the need to mark real property boundaries permanently and precisely, the increasing governmental adaptation of Land Information System (LIS) and Geographical Infor- mation System (GIS) databases,1 and many other factors have led to
the wide use of projection systems that eliminate some of the disad- vantages of the tangent plane system. This need was so prevalent that, late in the 19th century, the federal government of the United States began promoting the use of particular projection systems adapted to each state.
Known as State Plane Coordinates (SPC), the system is based on a rigorous mathematical translation of Geodetic Positions into a Grid Coordinate system. The adoption of SPC in private surveys gradu- ally increased through the 20th century. Modern advances in Geodetic Positioning in the 21st century have made the control required for SPC- based surveys available to every Land Surveyor in every corner of the world. The specific version of SPC control that each state adapted is codified in that state’s law. The projection systems used vary greatly, but the benefits, application, advantages, and use of these systems is the same for every state.
One form of state plane projection is demonstrated in Figure 5.2. Instead of a rigid plane of glass, as in Figure 5.1, imagine that a clear, flexible sheet of plastic is wrapped to form a cylinder around a globe.
5.5. STATE PLANE PROJECTIONS 49
FIGURE 5.2 Transverse Mercator Projection
Then the sheet would touch the globe in a series of points instead of in one place. The features visible through the sheet could be traced onto the plastic, and, when unrolled, the sheet of plastic would form a flat plane on which a map of the globe would appear. The features on the map would become distorted as the distance to the line of contact was increased. The area near the line of contact would form a strip that would closely match the globe.
Let us further visualize that, instead of using a blank sheet of plastic, we begin with a clear sheet of plastic that has a rectangular grid pattern already established on it. This grid could consist of two sets of parallel lines intersecting at right angles, and each line would be defined by its distance from an established origin. The distance east is called the “x” distance. The distance north is called the “y” distance. When this grid sheet is wrapped around the globe, we could also deliberately align one of the grid lines with on of the north lines on the globe along the line of contact. Now, for each and every feature on the globe for which there exists a geodetic latitude and longitude measured in degrees, there can be found a corresponding grid location on the projection denned by the
“x” distance and the “y” distance on the grid and measured in feet or meters, depending on the system.
Because the relationship of the sheet of plastic and the globe was rigorously controlled, then a specific set of such strips could be used to map the entire earth. In actual practice, this is what is done through mathematical manipulation of the geodetic positioning network. This procedure and innovative variations of it (using cones or other adap- tations) have produced mapping systems that cover large portions of every state. Most states are typically served by two or three overlapping projection zones.
Maps and surveys developed in these systems are tied to the world- wide geodetic positioning system of latitudes and longitudes. The pro- jection accounts for the convergence of the meridians, as well as the elevation of the parcel. The system mathematically and rigorously projects a portion of the earth’s surface onto a theoretical flat plane. The portion of the earth mapped is typically a strip, about 150 miles or so wide, wrapped around the earth. Most states are divided into overlapping zones in order to obtain full coverage.
The geodetic monumentation network that supports these projec- tions is maintained by the federal agency known as the National Geode- tic Survey (NGS). This agency is responsible for the development and definition of the mathematical models used to approximate the earth. The foundation of this model has undergone significant renovation in recent years. The consequences and advantages of these modifications will be explored.
The development of the Global Positioning System (GPS)2 using a constellation of satellites has greatly reduced the dependence on surface monumentation for precise positioning. Even greater advances, such as the continually operating receiver station (CORS) and the discoveries associated with that system, will be discussed at length later in this book.
All national mapping is also controlled by this geodetic network. The control network includes both horizontal control (geodetic positions) and vertical control (elevations). Any survey work that is performed as part of this network is automatically tied to any other work in the system, be it private or public surveys.
The procedure for establishing a state plane projection survey requires that the Land Surveyor recover one or more monuments of known geodetic position.3 The latitude and longitude of the
2See Chapter 8.