ALTA/ACSM Land Title Survey: Relative Positional Accuracy

—by Gary Kent

Q: My question is about the proper way to calculate the relative positional accuracy on an ALTA/ACSM Land Title Survey. The formula I found on ACSM’s website is 0.07 feet (or 20mm) + 50 ppm. The parcel that I am performing the Land Title Survey on has a total perimeter dimension of 786.00 feet. Would the correct calculation for the allowable RPA be this?
0.07 feet + (786.00 feet * 50/1,000,000) = 0.07 feet + 0.0393 feet = 0.1093 feet?
Do you use the perimeter distance as above, or do you add in the distance from the Commencing point (a section corner in this case) to the point of beginning of the surveyed tract?
Is it safe to say that the corners most remote from each other will have the greatest RPA?
On my survey I found 4 iron pins that are shown as being in a straight line, but the one near my Northwest corner is actually 0.61 feet East of the line. The other 3 iron pins line up great. This is my greatest uncertainty, so would 0.61 feet be my RPA?

A: The relative positional accuracy (RPA) is between any point that was used to control a land boundary on the survey, relative to any other point that was used to control a land boundary. So the idea of determining the maximum allowable RPA for the survey by calculating it based on, for example, the perimeter of the tract is not correct. The calculation is, by definition, point-to-point specific. The allowable RPA is how much uncertainty, at the 95 percent confidence level, is allowable between the two specific points being checked.
Note, the standards say that this relationship is for any point on the survey relative to any other point on the survey. On a small survey, it’s no big deal to check all of these combinations. On a large survey or network, it would be difficult and time consuming at best to check every possible combination of points. So, you would want to look for the worst cases.
The two points most remote from each other may have the largest RPA, although that is very much dependent on the procedures, equipment and circumstances involved in determining each of those locations. A combination of lower-accuracy equipment or a series of unbalanced or short sites used by necessity to reach some particular point “A” could result in the RPA associated with that point being the worst case, even though the point may not be as remote as some other point on the survey.
The RPA is calculated by a least squares adjustment that must accommodate the various primary elements that contribute to measurement uncertainty. These would include things such as how accurately can you set up the instrument over a point, how accurately can you site a target, and how accurately does your instrument read an angle. A person versed in least squares could make these calculations “by hand” on a simple survey. But as soon as some redundant measurements (or a combination of GPS and traditional measurements) are used, or if the survey includes a large number of points, the calculations will become too complicated for most to do by hand.
There are a number of least squares software programs available that will compute the uncertainty for the points on a survey. What is allowable uncertainty between any two points is 0.07 feet plus 50 ppm? This is based on the direct distance between the two specific points being checked—even if they are not connected by observation and are at opposite ends of the survey.
Whether or not the RPA between those two points passes the allowable RPA “test” is a function of an analysis in which the error ellipses at each point are used to compute a “relative error ellipse” for the relationship between those two points. The length of the semi-major axis of that relative error ellipse at 2 standard deviations is then compared against the 0.07 feet and 50 ppm between the same two points.
Most will want to use a computer program to make these calculations. This seems to annoy or bother many surveyors. However, if they use GPS—and it seems like most do these days—they use software every day to analyze results, propagate errors and create error ellipses. They don’t seem to have a huge problem with that. Calculating RPA using a computer program is no different.