Plotting Horizontal Control Computations for horizontal control become greatly clarified when you can see
a plot (that is, a
graphic representation to scale) of the traverse on which you are working. A
glance at the plot of a closed traverse, for instance, tells you whether you
should add or subtract the departure or the latitude of a traverse line in
computing the departure or latitude of an adjacent line or in computing the
coordinates of a station. For linear distances that are given in feet and
decimals of feet, you use the correct scale on an engineer’s scale for laying
off linear distances on a plot. For plotting traverses, there are three common
methods: by protractor and scale, by tangents, and by coordinates.
PLOTTING ANGLES BY PROTRACTOR AND
SCALE.— For the
traverse on which you have been
working, the adjusted bearings and distances are as
follows:
Traverse Line Bearing Distance
AB
N26°09'E
285.14 feet
BC
S75°26'E
610.26 feet
CD
S15°31'W
720.28 feet
DA
N41°31'W
789.96 feet
Figure 735.—Traverse plotted by protractorandscale method.
Figure 735 shows the method of how to plot this traverse
with a scale and protractor. First select a scale that will make the plot fit on
the size of your paper. Select a convenient point on the paper for stations A
and draw a light line NS, representing
the meridian through the station.
AB bears N26°9'E.
Set the protractor with the central
hole on A and
the 00 line
at NS, and
lay off 26°09'E. You
will have to estimate the minutes as best you can. Draw a line in this direction
from A, and on the line measure off the length of AB
(285. 14 feet) to scale.
This locates station B on
the plot. Draw a light line
NS through B parallel
to NS through
A, and representing the meridian through station B.
BC bears S75°26'E. Set
the protractor with the central hole on B and the 00 line on NS,
lay off 75°26' from the
S leg of NS to
the E, and
measure off the length of BC
(610.26 feet) to scale
to
Figure 736.—Plotting traverse lines by parallel method from
a
single meridian.
locate C. Proceed
to locate D in the
same manner. This procedure
leaves you with a number of light meridian lines through stations on the plot. A
procedure that eliminates these lines is shown in figure 736. Here you draw a
single meridian NS, well
clear of the area of the paper on which you intend to plot the traverse. From a
convenient point O, you
layoff each of the traverse lines in the proper direction. You can then transfer
these directions to the plot by one of the methods for drawing parallel lines.
PLOTTING ANGLES FROM TANGENTS.— Sometimes
instead of having bearing angles to plot from, you might want to plot the
traverse from deflection angles turned in the field. The deflection angles for
the traverse you are working on are as follows:
AB to BC
78°25'R
BC to CD
90°57'R
CD to DA
122°58'R
DA to AB
67°40'R
Figure 737.—Plotting by tangentoffset method from deflection
angles
larger than 45°.
You could plot from these angles by protractor. Lay off one of the traverse
lines to scale; then lay off the direction of the next line by turning the
deflection angle to the right of the firt line extension by protractor and soon.
However, the fact that you can read a protractor directly
to only the nearest 30 minutes presents a problem.
When you plot from bearings, your error in estimation
of minutes applies only to a single traverse line. When you plot from deflection
angles, however, the error carries on cumulatively all the way around. For this
reason, you should use the tangent method when you are plotting deflection
angles.
Figure 737 shows the procedure of plotting deflection angles larger than
45°. The direction of the starting line is called the meridian, following a
conventional procedure, that the north side of the figure being plotted is
situated toward the top of the drawing paper. In doing this, you might have to
plot the appropriate traverse to a small scale using a protractor and an
engineer’s scale, just to have a general idea of where to start. Make sure
that the figure will fit proportionately on the paper of the desired size.
Starting at point A, you draw the meridian line lightly. Then you lay off AO,
10 inches (or any convenient roundfigure length) along the
referenced meridian. Now, from O
you draw a line OP perpendicular to AO.
Draw a light line
OP as
shown. In a trigonometric table, look for the natural tangent of the bearing
angle 26°90', which equals to 0.49098. Find the distance OP
as follows:
OP = AO
tan 26°09' = 4.9098, or
4.91 inches.
You know that OP is
equal to 4.91 inches. Draw AP
extended; then you lay off the
distance AB to scale
along AP. Remember
that unless you are plotting a closed traverse, it is always advantageous to
start your offsets from the referenced meridian. The reason is that, after you
have plotted three or more lines, you can always use this referenced meridian
line for checking the bearing of the last line plotted to find any discrepancy.
The bearing angle, used as a check should also be found by the same method
(tangentoffset method).
Now to plot the directions of lines from deflection angles larger than 45°,
you have to use the complementary angle (90° minus the deflection angle). To
plot the direction of line BC
in figure 737, draw a
light perpendicular line towards the right from point B.
Measure off again a convenient roundfigured length, say
10 inches, representing BOBOThe
complement of the deflection angle of BC
is 90° – 78°25' =
11°35'. The natural tangent value of 11°35’ is equal to 0.20497. From O_{1}
draw O_{I}P_{1} perpendicular to BO_{I}
Solving for O_{I}P_{l}, you will have
O_{1}P_{1} = BO_{2} tan 11°35' = 2.0497, or 2.05
inches.
Now lay off the distance O_{1}P_{2} Draw a line from B through
P_{1} extended; lay off the distance BC
to scale along
this line. The remaining sides, CD
and DA, are
plotted the same way. Make sure that the angles used for your computations are
the correct ones. A rough sketch of your next line will always help to avoid
major mistakes.
When the deflection angle is less than 45°, the procedure
of plotting by tangent is as shown in figure 738. Here you measure off a
convenient roundfigure length (say 500.00 feet) on the extension of the initial
traverse line to locate point O,
and from O, draw
OP perpendicular to AO.
The angle between BO
and BC is,
Figure738.—Plotting by tangentoffset method from deflection
angle
smaller than 45°.
Figure 739.—Plotting by coordnates.
in this case, the deflection angle. Assume that 23°21'.
The formula for the length of OP
is this is
OP
= BO
tan 23°21' = 500 x
0.43170= 215.85 feet.
