If only it ended with pin cushions.

Now and then surveyors get into a discussion about corners monumented with so many rods and pipes that it looks like a pin cushion or porcupine. The discussion usually focuses on what the surveyor’s actions should be, and what his or her professional responsibility to society is when their measurements or calculations seem to indicate that the corner is at a point different from, but close to, a previously set monument.

One of the actions a surveyor can take when an apparent discrepancy is discovered is to determine what the meaning of the previously set monument is to adjoiners, the various legal authorities and legal jurisdictions. This is not playing lawyer; this is being a good surveyor, the only person authorized under law to establish the position of land lines and monument them, day in and day out.

Another course of action might be to determine the positional uncertainty of the measured point to see if the new point he or she has determined is statistically unrecognizable from the previously set monument. Yet another action would be to talk with the surveyor who set the previous monument. There are more possibilities, especially if there’s more than one other monument presumably representing the same corner. They are all rational, reasonable things that can be done to ensure that the public, not just the client, is being served with the highest level of professionalism the surveyor can deliver—an implicit requirement placed on all licensed land surveyors. More than likely, more than one course of action will have to be taken.

The above discussion is an easy one to understand because the discrepancy is very concrete: everyone can see those “extra” irons. However, it brings to mind all the discrepancies that are much more abstract, but equally important—such as the matter of areas.

It concerns me that surveyors “see” them, but because they are much less tangible than a pin cushion corner, they don’t get the attention or professional closure that they deserve. Without fail, if one looks at 10 plats done by different surveyors, more than half of them will state area to three or more decimal places regardless of whether the land area is large or small or whether the area is expressed in acres or feet. Especially if the area is in square feet, I wonder if the surveyor has thought about the uncertainty in every measurement and whether the total uncertainty is so small that it is less than 0.001 square feet. If you are wondering what I mean, take the square root of 0.001 to see the size of a square that encompasses this area. But even when it is acres, what is the meaning of that 0.001 acre? If it is a plot of exactly one acre, the implied certainty in the area is much better than 43 square feet; in fact it’s about 21 square feet. If it is 50 acres, the implied certainty is over 2,100 square feet—or to put it another way, uncertainty is only apparent below half that level.

For a rectangular parcel, with dimensions X and Y, and where the uncertainty in each of the measurements is ex and ey respectively, the uncertainty in the rectangle’s area due to uncertainties in the measurements of the two sides is

ea = [(Yex)2 + (Xey)2 ]1/2

Where ea is the uncertainty in the area

of the rectangle.

Thus, for an area 1,000 feet by 100 feet, the nominal area is 100,000 square feet. If the long dimension has an uncertainty of 0.04 feet and the short dimension’s uncertainty is 0.02 feet, the uncertainty in the area is about 20 square feet. This means with only two dimensions measured (remember we surveyors would survey all four sides of the rectangle and the four angles, so the uncertainties are actually much larger), there is doubt in the last two zeroes of the nominal area of 100,000 square feet. It could be 100,001 or it could be 99,980 or a large number of other values. And I haven’t even gotten into a discussion of whether the uncertainty is standard deviation, or 90 percent error or 99.99 percent error. And I haven’t touched the matter of significant figures and the implied certainty in distances and bearings. (How many times do we see bearings expressed in arc seconds, tenths of seconds or even hundredths of seconds?)

Then we have the problem of determining whether this survey is accurate or precise. Many surveyors aren’t sure which of these they are aiming for (the correct answer is both—the first because surveyors need to be correct, the second because surveyors need to be consistent). But take the simplified case of a surveyor working at an elevation of 5,000 feet who uses the barometric pressure given by the local radio station. If he uses that value when he sets the PPM correction on his EDM, all his distances are in error by about 50 PPM. This, by the way, corresponds to 1:20,000. But he closes his traverse with an error of closure that results in a survey precision of 1:100,000. I would state, considering just his barometric pressure error only, that there is no way his survey is better than 1:20,000 and probably far worse. But who’s to know? Only the surveyor…if he or she can or wants to know.

We started with pin cushions and have touched on accuracy and precision, significant figures, most probable values, measurement uncertainties and confidence levels. Next time you get involved in a discussion on pin cushion corners, or are faced with a decision to set or not set an iron, think about the statement you are making regardless of which view you choose to take.