State Plane Coordinates vs. Surface Coordinates, Part 1
The following is quoted from a publication of the U. S. Coast and Geodetic Survey.
In the early 1930s, an engineer from a state highway department approached the U. S. Coast and Geodetic Survey seeking a method of utilizing geodetic data over an entire state which would involve only the formulas of plane surveying. This brought about the establishment, in 1933, of the North Carolina Coordinate System by means of which North Carolina could be transformed into plane-rectangular (x and y) coordinates on a single grid, and surveys in all parts of the state referenced thereto, so that survey stations and landmarks could be accurately described by stating their coordinates referring to the common origin of the grid.
Within a year or so after the establishment of the North Carolina Coordinate System, a similar system had been devised for each of the states of the union. For some of these, a single grid origin and meridian of reference were sufficient. Other states, because of their large sizes, were each divided into several belts or zones, each zone having its own origin and reference meridian.
Each state coordinate system is based on a conformal map projection. By using a conformal map projection as the base for a state coordinate system, and limiting one dimension of the area which is to be covered by a single grid, two things are accomplished:
On a conformal map projection angles are preserved. This means that, at a given point, the difference between geodetic and grid azimuths of very short lines is a constant, and angles on the earth formed by such lines are truly represented on the map. For practical purposes of land surveying, this condition holds for distances up to 10 miles. For longer lines the difference varies, and the correction to be applied to any observed (geodetic) angle to obtain a corresponding grid angle is the difference of the corrections to the azimuths of the lines, separately derived. Deviations of grid lengths from geodetic lengths will be a maximum along the margins of the longest dimension of the grid and midway between these margins. The quantity by which a geodetic length is multiplied to obtain the corresponding grid length is termed a scale factor.
The limitations in the width of the projection or grid permits a control of deviations of grid lengths from geodetic lengths. When the width of an area covered by a single grid is 158 statue miles, the extreme difference between geodetic and grid lengths will be 1/10,000 of the length of a line, which is quite satisfactory for most land surveys.”
The publication quoted is Coast and Geodetic Survey Special Publication No. 235, “The State Coordinate Systems.” There is another publication, Coast and Geodetic Survey Publication 62-4, “State Plane Coordinates By Automatic Data Processing.” These two publications provided the surveying and mapping profession with information on deriving 1927 state plane coordinates based on the North American Datum of 1927, (NAD 27) plus information for traverse and other computations with these coordinates.
Several years ago, I was one of three speakers at a seminar at the New Mexico Professional Surveyors Conference in Albuquerque. The state plane coordinate system was brought up, and I asked everybody using state plane coordinates to raise their hand. Only 10 hands were raised, out of about 150 people in the room. I have asked the same question at seminars around the country and I find more people are using the system, but it’s always less than half the people in the room.
Why do so few surveyors use state plane coordinates, and why do others refuse to use it? Because they don’t understand it. Some surveyors blame the engineering community, and I can understand that. At least 95 percent of all young civil engineering graduates have had no exposure to state plane coordinates, and they are the people in charge of highway projects controlled by state plane coordinates. What do these people do? Insist that all state plane coordinates be converted to surface coordinates so that the scale factor for all measured distances is one. Another problem is that some state plane computer software was written by computer programmers who did not take a practical approach to a surveying job.
Let me finish this column with a disclaimer, this is not a finger-pointing article. There are times when surface distances and surface coordinates are more appropriate than grid distances and state plane coordinates. I will cover this in the next one or two columns.