GIS Tips - December 1999

State Plane Coordinate Systems

So, I offer: 1) my apologies to Ms. Dempsey for my inappropriate criticism, and 2) my take on State Plane Coordinate Systems. Given that this simplification will also have some inaccuracies, I humbly await the criticism as properly deserved by my action with regard to About.com and Ms. Dempsey.

One could trace the origins of surveying back to ancient Egyptian times. The problem at that time was the annual flood of the Nile. While this annual inundation provided the Egyptian culture its basic sustenance, it also had the undesirable affect of wiping out all the markers that determined whose land was where. Thus, some rudimentary surveying techniques were devised to replace the property boundary markers every year after the waters receded.

Marking property boundaries is still one of the major functions of surveying. Technology has improved over time. However, for several centuries, the basic technique was to start at a known point, and origin, and measure the earth as if its surface was the flat plane tangent to the surface of the earth at the origin point. This approximation worked fine as long as the amount of real estate being surveyed was rather small. The approximation did, however, enable surveyors to use normal two dimensional geometry and trigonometry in their calculations; greatly simplifying their work, and keeping their services practical and affordable.

However, this implies that different surveys used different origin points. Since the earth is not really flat, each different origin point produced a different tangent plane. It follows, therefore, that different surveys of adjacent (or even the same) real estate would be slightly different if different origins (i.e. tangent planes) were used.

To address this problem, someone got the bright idea that everyone in our state should use the same origin point. That is, the same tangent plane. In this manner, all surveys would be consistent with each other. Not only would we all be on the same plane, but we could all reference our coordinates to the same origin point and the actual numerical coordinates of each survey would be consistent.

Over time, this idea caught on, and the legislatures of all states eventually passed laws that said the surveyors could now file legal property descriptions at the county courthouse using these coordinates; and that the descriptions would be considered legal in a court of law should there be some dispute. Thus, we have the evolution of State Plane Coordinate Systems. Of interest here is that the adoption of State Plane Coordinate Systems in all 50 states took decades; it did not just happen in conjunction with the 1927 adjustment of the North American datum.

Since property ownership is a state function, each state can have their own system without a problem; a national system is not required. Since the basic idea behind all of this is to establish a single tangent plane for all surveying, the name for these things is, naturally enough, State Planes. In devising the imaginary plane, and the mathematics to convert latitude and longitude to Cartesian State Plane coordinates, a coordinate system (as defined last month) was developed. So, we have several State Plane Coordinate Systems, or SPCS.

Defining property boundaries is one of the principal functions of surveying. As a result of the surveying process, the amount of land one owns is determined. The precise amount of land may, or may not be, important to the owner until tax time comes. At that time, the land owner may become very concerned if the county assessor suggests that the landowner owns more than he really does. Landowners may also be concerned as oil and other mineral royalties are often prorated by the amount of land owned. Thus, there are many good reasons why the land records maintained at the county courthouse should be as accurate as possible.

Now, recall that the basic premise underlying State Plane Coordinate Systems is that a suitable plane be chosen for the entire state; and that this plane be so chosen as to approximate the earth over the entire region covered by the state. It should not be a surprise to the Casual Cartographer that the single plane approximation is going to work fine for Rhode Island, but maybe not so well for Texas, or Alaska. What’s a surveyor to do? This idea is too good to give up on.

Monday night quarterbacking this issue, it appears pretty obvious that the solution to the problem is that the larger states needed more than one standard origin, i.e. more than one tangent plane. Perusing this solution, it was decided that for the principal purpose of surveying, i.e. property ownership boundaries, an accuracy of one part in ten thousand would be sufficient. This is essentially equivalent to what is known as a "Class I Second Order" survey point, the level of accuracy used for ordinary property boundary surveying. Thus, in establishing the additional origins, or tangent planes, for the larger states, it was determined to do so such that the scale distortion introduced by use of the tangent plane approximation did not exceed one part in ten thousand. (This same standard was used to determine which states were so large as to need more than one tangent plane.) In meeting this criteria, Texas ended up with five different tangent planes, Wyoming with four, Florida with three, and so on.

Now, if Texas has five different tangent planes, how does one know which plane to use for a particular surveying project. For much of Texas, the choice is obvious. But also obvious is that a significant portion of Texas real estate is sort of on the crack between two zones. That is, in many cases either one of two different tangent planes could be used to achieve the desired level of accuracy. Does this not defeat the whole purpose of the "single origin" idea? The solution to this problem again stems from the principal function of surveying.

If we keep in mind that the principal function of surveying is to record property boundaries, and that most all property boundaries are recorded in county records at the county clerk’s office, all is fine and well if all surveys with a specific county use the same tangent plane. As a result, each county that is in the tangent plane crack decided (or had it decided for them) which tangent plane they would use. The specific tangent plane that is to be used, then, depends upon which county the survey is in. Or perhaps more importantly, the specific county in which the property boundary is to be filed in. Thus, in a state where more than a single tangent plane is required, the region covered by a specific tangent plane is referred to as a zone; and such zones follow county boundaries. That is the zone boundaries are basically political in nature, rather than geographic.

It is important to note that the choice of the actual "tangent plane" in use, and the actual location of the Cartesian coordinate origin on that plane was, to a point, arbitrary. However, the action of the state legislatures to make State Plane coordinates legal essentially means that it takes an act of the legislature to change them. Thus, for practical purposes, the definitions of these coordinate systems are cast in stone. Right? Well almost.

During the construction of the 1983 adjustment to the North American Datum (NAD83), the powers that be realized that all coordinates would eventually need to be changed to reflect this adjustment. Now changing lots and lots of coordinates is indeed painful, and no one wants to do this more than once if at all. Therefore, it became obvious that the switch to NAD83 was an appropriate time to sneak in a few changes to the State Plane Coordinate Systems. So, along with the changes required by NAD83, the tangent planes associated with several states also changed. Montana switched from three zones to one, California dropped Zone Seven, the exact specification of the tangent plane changed in some states and zones, and the origin of the Cartesian coordinates on the tangent plane changed in many cases. The end result is that for each state, there are NAD27 State Plane Coordinates and NAD83 State Plane Coordinates. While of course there is a difference in datums, I am not aware of a single zone where the datum change is the only difference.

Just to make sure of ample job security for Casual Cartographers, during the 1983 adjustment of the North American Datum, the powers that be tried to slip one more change in on us. They tried and, to a certain degree, most succeed. This period of changing coordinates around, they thought, would also be a good time to switch from the English system of units to the universally used (everywhere else but the US) metric system. Finally, we would do away with that ugly thing called the US Survey Foot. It would, eventually, become a historical artifact. Finally, we would do away with the confusion caused by the International Foot. Right? Well almost.

Based on this idea, all of the new State Plane Coordinate Systems, i.e. those adjusted for NAD83, where originally defined with the meter as the basic unit of measure. Unfortunately, us "yanks" being an independent lot, many Americans simply said "I’ve been working feet for 40 years, I ain’t gonna switch now!" An so, while many (all?) state legislatures have accepted the new metric definition of State Plane Coordinate Systems, many have also passed legislation which makes coordinates based on the North American Datum of 1983 and the US Survey Foot legal as well; and some also officially blessed the International Foot.

So, the end result is that we now have a potpourri of tangent planes, Cartesian origins on those tangent planes, and we have all kinds of units used. Thus, when someone provides us a map based on State Planes, we have a wide range of choices to guess from. Best you get the datum and the unit in addition to the zone before accepting such a State Plane map.

Also, the Casual Cartographer should be aware of the following points:

There is only one version of each NAD27 State Plane Zone, and the unit is always US Survey Foot. I have never encountered someone using any other unit with NAD27 State Planes; but of course anything is possible.

NAD83 state plane zones differ from their NAD27 equivalent by more than just the datum shift. If you’re expecting to see, say, a 40 meter difference (40 meters being the local datum shift) between the NAD27 coordinate and its NAD83 equivalent, you’re going to be greatly disappointed.

NAD83 state plane coordinates are often used in units of US Survey Feet, and occasionally in International Feet. If someone gives you a data set in NAD83 State Planes, be sure to inquire about the unit.

In some states, the changes to NAD83 were significant. That is, entire zones were dropped. I do not know of any new zones being added, however. If you do, please let me know.

As far as I know, the switch to NAD83 did not change the zone in which any specific county considered it a part of. If I’m wrong on this, I would appreciate your help.

If you’re to convert a NAD83 State Plane definition from the semi-official meters to another unit (like US Survey Feet), be sure you convert the false northing and easting values as well.

State Plane Coordinate Systems are the result of a desire to standardize the results of surveying. Since property ownership is a State, rather than a federal, thing each State has its own system. Thus, in many states, a single standard tangent plane was established which could be used by surveyors to determine property boundaries within accuracy standards commonly accepted for this purpose. State legislatures encouraged the use of the standard tangent plane by legislating that a properly surveyed boundary given in coordinates based on this plane would, by statute, be acceptable in a court of law. In order to maintain accuracy consistent with that normally used in property boundary surveying, larger states needed more than a single plane. Since the recordation of property boundaries is largely a county function, each county in the larger states chose, or was assigned, to adopt a specific plane as the official plane for that county. The result, for larger states, is multiple zones that follow county boundaries.

See Also: State Planes Not So Plain

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