Civil Engineering Reference
In-Depth Information
Now, imagine that the gardener didn't notice the error and he sent a handwrit-
ten note to your friend with the four dimensions. He also makes a note that the
garden is a rectangle (in a rectangle all of the interior angles are 90°). If your
friend decided to draw the garden to scale on a piece of graph paper using the
gardener's dimensions, she would soon find that there was a 2 foot gap. She
would also discover that without additional information, there would be no way
to tell which of the two sides contained the error. Remember, she doesn't have a
sketch; she only has a note containing four dimensions. In a rectangle, the oppo-
site sides have to be the same length. So, in our example, the sides containing the
error could either be 78 or 80 feet. She would know the sides must either be 78 or
80 feet, but she would not be able to determine which dimension was correct.
This is the same sort of dilemma that one sometimes runs into when trying to
interpret a deed description that contains errors. The description may have dimen-
sions and directions for each boundary, but when they are plotted, there is a gap
between the beginning and end points. Sometimes, figuring out where the error
was made can be quite difficult or even impossible. Unlike your friend, who could
just send the gardener a note asking him to recheck his measurements, a surveyor
often has no way of knowing where the deed dimensions came from. Of course,
the error in our example is huge, at least by boundary surveying standards, so let
us look at a more realistic example.
Consider Fig.
4.15
which shows the property boundaries of a parcel of land as
established on the ground by a survey. The boundaries shown in the figure are the
same boundaries shown in Fig.
4.8
but the bearing and distance along Main Street
is slightly different because small errors in measurements were made when the
survey was performed.
If you were to start at the property corner labeled “A”, which we will call the
Point of Beginning, and precisely measure counterclockwise around each bound-
ary line using the bearings and distances shown, you would arrive at a point very
near the point of beginning but not exactly at the point of beginning. It is important
to accept the fact that even the most precise survey will always have small errors in
measuring angles and distances, so the end point will rarely correspond exactly to
the beginning point. Even if a survey did close perfectly on paper, there are prob-
ably still measurement errors—the errors have probably cancelled each other out.
The sum of the errors in a survey will give an error of closure. A similar situa-
tion exists when using GPS except that, because there are no angles and distances
measured, the points themselves will contain uncertainties in their locations.
The error of closure is described by a bearing and a distance which represents
the line that would have to connect the end point with the point of beginning in
order for the figure to close perfectly. The error of closure is shown in Fig.
4.15
as
N14° 10′ 20″E, 0.05 feet (about 5/8 of an inch). The error has been exaggerated in
the drawing for purposes of illustration. The reader can see that the error of clo-
sure represents an additional line in the property boundaries.
Although the error of closure consists of a single bearing and distance, it is
important to understand that the error is usually the result of the accumulation of the
errors which exist in each of the bearings and distances comprising the perimeter
