Civil Engineering Reference
In-Depth Information
two bearings on common lot lines so a person drafting a legal description (usually
an attorney) must be careful to choose the correct quadrants for the bearings.
The above example is a common mistake. In a simple case, such as the one
illustrated, the error would probably be obvious to the person reading the deed
description, particularly if that person had a copy of the plan. However, this type
of error may be much more difficult to locate in a boundary survey having many
boundary lines where there is no plan available to guide the reader.
4.14 Cartesian Coordinates
In boundary surveying, surveys are usually plotted and defined using a Cartesian
coordinate system. A two dimensional Cartesian coordinate system is a rectangu-
lar coordinate system where the axes are 90° apart. Any point can be located using
just two numbers. These numbers are called
Coordinates
. In most rectangular
coordinate systems the axes are labeled X for the horizontal axis and Y for the ver-
tical axis. Values increase up and to the right. In boundary surveying it is custom-
ary to label the axes as
Latitude
and
Departure
. Latitude (Y) is measured north
and south and Departure (X) is measured east and west.
In boundary surveying, surveys are usually plotted and defined using a
Cartesian coordinate system.
Refer to Fig.
4.13
, which shows two points plotted on a coordinate system. If it were
necessary to show elevations, a third or Z coordinate would be shown. In the exam-
ple, the coordinates for point 1 are labeled North 5040.000 and East 4920.000. Once
the coordinates of two points are known, it is possible to calculate the bearing and
distance between them. In our example, the latitude and departure between points 1
and 2 is determined by subtracting one coordinate from the other. For example:
Latitude
=
5140.000
−
5040.000
=
100.000
Departure
=
5020.000
−
4920.000
=
100.000
Once we know the latitude and departure of a line we can use trigonometry to
calculate the bearing of the line and the length of the line. In this case the angular
solution is straightforward. Both the latitude and departure are the same so the line
running from point 1 to 2 must be N45°E. The method of using the coordinates of
two points to calculate the bearing and distance between them is called an
inverse
.
The appendix has examples of using trigonometry to calculate inverses.
Some coordinate systems are arbitrary and some are not. In our example, we
chose an arbitrary coordinate to begin with at the lower left corner: N4,980 and
E4,860. The starting coordinate values do not matter because all calculations are
made using the differences between the coordinates. The coordinates chosen for
our initial point really do not matter. When selecting a starting coordinate, most
