Q: My transmitter site has one set of coordinates for NAD27, another set for NAD83, and different values for UTM coordinates. Which are correct? Why the differences?

A: The basic problem is that the earth is not a globe. A globe is a perfect sphere, and the lines of latitude and longitude are clearly marked. Because of our familiarity with globes, we tend to think of the latitude-longitude (or "geodetic") coordinate system as an absolute system, with simple (?) spherical trigonometry for calculations of distance and bearings.

Two factors are used to describe coordinates on the earth’s (not the globe’s) surface, a coordinate datum and an ellipsoid.

First, the absolute theoretical coordinate system exists only in theory (and on the surface of your globe). All real-life coordinate values (like your transmitter site) are based on surveys or other means of actual measurement. The measurements ultimately refer back to a reference point. Since the lines on the globe are not available as real-life reference points, an artificial reference system (or datum) must be used. Numerous datum definitions have been designed. These reference systems include NAD27 (North American Datum of 1927), NAD83, and the UTM (Universal Transverse Mercator) systems, as well as numerous other systems used in various locations around the world.

In other words, there is no such thing as the absolute coordinates of a transmitter site (or any other spot on the earth’s surface). Every real-life coordinate is based on a datum, or reference system. The coordinates of a location are incomplete unless the datum is specified (although, until recently, the NAD27 datum was almost universally assumed in the US and was not always explicitly stated).

Since coordinates are values based on a reference system, if one set of coordinates is known along with its reference system, and information is available for a second reference system, it is possible to calculate a new set of coordinates relative to the second reference. (A trivial example: Denver is 60 miles from Colorado Springs and 90 miles from Pueblo - same place, different reference points.) This is the significance of different coordinates for your transmitter site. A set of coordinate values for one reference system (such as NAD27) can be converted to a new set of values based on a different reference (such as NAD83). Just like the different distances to Denver for different references, the numerical values of the latitude and longitude for different reference systems will be different. The two sets of coordinates represent the same point on the surface of the earth relative to two different reference systems.

Knowing the datum associated with a set of coordinates is important. Using coordinate values and ignoring the datum leads to confusion and errors. For example, if my transmitter site has the coordinates 38° 44’ 45"N, 104° 51’ 39"W based on the NAD27 datum, I can’t use the same value if I need to describe the coordinates for the same location but based on a different reference, like NAD83 (Denver is 60 miles from Colorado Springs, but not 60 miles from Pueblo). The same location on the surface of the earth is described by the coordinates 38° 44’ 44.96"N, 104° 51’ 40.9"W using the NAD83 reference datum. (The conversion can be accomplished with the NADCON program available from the USGS or from SoftWright’s TeleTAP bulletin board, or with TAP 4.) In this particular example, the difference in the location is about 46 meters, or 150 feet. In other words, if I use the first set of latitude and longitude values (based on NAD27) to locate the site on a map based on NAD83 there will be an error of about 150 feet. However, if I use the converted second set of values on the NAD83 map, the location will be correct. The difference between NAD27 and NAD83 in the coterminous US varies from about 10 meters in the Great Lakes region to about 100 meters on the west coast.

Also unlike the globe, the earth is not a sphere, but rather an ellipsoid, a ball slightly flattened at the poles. In addition to the different reference systems used to determine coordinates by surveys, the actual size and shape of the earth have different representations. These representations or "ellipsoids" (depicting the ellipsoidal shape of the earth, the degree of flattening at the poles, etc.) affect the conversion between different coordinate systems as well as any distance and bearing calculations between two sites.

Both the datums and ellipsoids used to represent real-life coordinates have been dramatically affected by technology. The majority of USGS maps of the coterminous United States (published earlier this century) are based on the NAD27 datum which uses an ellipsoid called Clarke 1866. The accuracy of the datum from 1927 and the ellipsoid calculations from sixty years earlier reflect the best technology of that day, but even so includes some errors. (Even the best surveyors are not as accurate as the lines on the globe.) With the advent of global positioning satellites and other recent technology, the size and shape of the earth has been much more precisely determined. One example of the result of these technologies is the ellipsoid known as Geodetic Reference System of 1980 (or GRS80).

Based on this more accurate ellipsoid, the USGS developed a more accurate reference system for determining real-life coordinates through surveying, the North American Datum of 1983, or NAD83. Because of the improved precision and accuracy of the more recent ellipsoid and the related datum, calculations of distance, bearings, etc., based on NAD83 coordinates will generally yield more accurate results.

Many existing facilities (such as transmitter sites) are defined using NAD27 coordinate values. For the sake of accuracy in distance calculations, aircraft safety, etc., many government agencies are requiring updates to the coordinates to reflect the values relative to NAD83. The coordinate latitude and longitude values change even though the site (for example, your tower) hasn’t moved. In a sense, the values change because the reference point has moved with the use of the new datum and ellipsoid defining NAD83. As mentioned above, you can use NADCON or TAP 4 for converting coordinate values between NAD27 and NAD83 to obtain the coordinates for the correct datum required by a particular government agency.

Finally, a brief note on UTM coordinates. The UTM (Universal Transverse Mercator) coordinates represent another reference system. UTM coordinates are not represented in degrees like latitude and longitude values but rather in meters. The UTM system represents small regions (sixty UTM zones, each 6° of longitude wide, cover the globe) as approximations of plane (or flat) areas. This has the significant advantage of simplifying calculations of distance and bearings, since the calculations between two coordinates are based on plane trigonometry using meters, instead of spherical (or elliptical) trig based on degrees. (The UTM system was developed by the US military to simplify calculations in the field during World War II.) UTM coordinates are typically expressed as a "northing" and an "easting" from the reference for the local zone. Conversion between geodetic coordinates (latitude and longitude) and UTM coordinates depend on the datum and ellipsoid of the geodetic system used. NAD27 coordinates are typically converted to UTM using the Clarke 1866 ellipsoid as one of the parameters, while NAD83 coordinates use the GRS80 ellipsoid. Therefore, UTM coordinates also require information about the datum and ellipsoid to fully define the location represented by the coordinates.

To summarize, the coordinates of your transmitter site start with an ellipsoid that defines the size and shape of the earth (an imperfect globe). A datum or reference system is defined for that ellipsoid (like reference lines on an imperfect globe) to allow real-life surveys. Your coordinates are values that locate your site relative to that coordinate system, with different coordinate values to represent the location relative to different reference systems.

(Thanks to David Doyle, a senior geodesist with the National Geodetic Survey, who provided much of the information used to prepare this article.)

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