Civil Engineering Reference
In-Depth Information
4.16 Error of Closure Standards
Some states and governing authorities have rules establishing classes of surveys
or limits on errors of closure or, when using GPS, errors in position. An error of
closure can be represented as a ratio of the magnitude of the error divided into the
sum of the length of all of the boundary lines. For example, in Fig.
4.15
the sum
of the length of the boundaries is 610.13 feet. That is the total distance we would
have to measure if we began at point A and measured each boundary line con-
secutively until we arrived again at point A. If the error of closure were 0.05 feet,
then the ratio would be expressed as 1 foot in 12,203 feet (610.13/0.05) or 1
part in 12,203 parts. Another way of thinking about it is if you were to measure
12,203 feet (about 2 miles) you would be off by 1 foot.
Smaller ratios are indicative of greater errors. For example if the error in
the above example were 0.09 feet the error of closure would be 1 in 6,780
(610.11/0.09). For many boundary surveys an error of closure of 1 in 10,000 to
1 in 15,000 is considered to be the minimum acceptable closure. The American
Congress on Surveying and Mapping (ACSM) standard for measurements which
control land boundaries has a minimum requirement of 1 in 15,000. A closure of
1 in 10,000 corresponds to 0.01 feet in 100 feet, which is the smallest graduation
available on a steel surveyor's tape. When using total stations, errors of closure
of 1 in 50,000 or even 1 in 100,000 are not uncommon. One in 50,000 roughly
equates to a one foot error in 10 miles.
4.17 Understanding the Accuracy of Measurements
In some cases, when we specify a numerical value, the number is exact. For exam-
ple, my dog has two puppies, or 5
+
5
=
10. Clearly, a dog could not have 2.4 or
2.5 puppies. There is no uncertainty in the value. There is also no uncertainty in
the addition of two integers: 5
+
5 cannot equal 10.1. In contrast, when we make
a measurement, there is always some uncertainty in the measurement. Boundary
surveying involves making measurements and the measurements will always con-
tain uncertainties. Surveyors need to understand these uncertainties and know
what level of confidence they have in their measurements. Every measurement
must include an estimate of the confidence in the measurement. For example, sup-
pose we use a steel tape to measure a distance between two points that are exactly
100 feet apart, and we can only read the tape to the nearest hundredth of a foot
(0.01), we might say the distance is 100 feet plus or minus 0.01 feet. The “plus or
minus 0.01 feet” tells us something about the level of confidence we have in the
measurement. We could also use a tape graduated in tenths of a foot (0.1) to make
the same measurement. If we were limited to reading the tape to the nearest tenth,
we would have much less confidence than in the previous example that our meas-
urement was actually 100 feet.
