MODULE I
CLOSED TRAVERSEA closed traverse is a series of connected lines whose lengths and bearings are measured off these lines (or sides), which enclose an area. A closed traverse can be used to show the shape of the perimeter of a fire or burn area. If you were to pace continuously along the sides of a closed traverse, the finishing point would be the same as the starting location.
Note in the following sketch how the traverse is followed clockwise. If the direction was followed counterclockwise at any point, the bearing letters would change to their opposites but the numbers would not, as shown in the first sketch (1) below. The second sketch (2) is a closed traverse. Here, the series of lines completes a distance area, and the starting and ending points are the same.
Example 1- Jeff paced the perimeter of the Zavala fire. His pace is 13 paces/chain. The declination for his current location is 14.5°E. The direction, distance, and travel for Jeff is as follows: Jeff begins at point 1 and goes N42°W for 27 paces; from point 2 he goes N75°W for 16-1/2 paces; from point 3 he goes N31°W for 24-1/2 paces; from point 4 he goes N36°E for 29-1/2 paces; from point 5 he goes S65°E for 22 paces; from point 6 he goes S13°E for 52-1/2 paces; from point 7 he goes S21°W for 10-1/4 paces back to the starting point, point 1.
Convert the bearings to magnetic readings. Adjust the magnetic readings to true north readings. Plot the closed traverse in feet using an engineer's tenth ruler and protractor.
Step 1.Convert paces into feet. Jeff's pace is 13 paces per chain. Set up the cancellation table (Section 2.1) and solve for distance in feet.
Repeat this step for each distance.
Step 2.Convert the bearings to magnetic readings. See Section 6.1.
The NW quadrant is between 270° and 360°. 360° - 42° = 318°
The SE quadrant is between 90° and 180°. 180° - 65° = 115°
The NE quadrant is between 0° and 90° so those values are used as recorded.
The SW quadrant is between 180° and 270°. 180° + 21° = 201°
The resulting magnetic reading are listed in the table below.
Step 3.Adjust each magnetic reading to a true reading following the guidelines in Section 6.5.
Step 4.Choose a scale. 1/10 inch = 10 feet
Step 5.Using a protractor (angles measured in degrees) and an engineer's scale or tenth's ruler, plot the plan view of the traverse horizontal distance (feet) and the bearing (degrees) between points.
Step 5a.Set the protractor so the 0°/180°line is up (north) and on a north-south axis.
Step 5b.Put a point in the middle hole. This will be point 1.
Step 5c.Read 318° on the outer scale of the protractor.
Put a dot to mark the point.
Step 5d.Draw a line from point 1 up to the dot that is 13-7/10 marks (each inch has 10 marks).
Step 5e.The end of this line will be point 2. Put the hole of the protractor on point 2. Follow steps 5b and 5c with each of the values.
When plotting the values that are in the southern quadrants with a semicircle protractor, rotate the protractor so the 0°/180°line is down (facing south) and read the numbers on the inner scale. Continue to complete all the points. The end result should be a closed traverse as shown.
Step 5f.Convert the true readings to bearings.
P1 to P2 = 360° - 332.5° = N27.5°W
P2 to P3 = 360° - 299.5° = N60.5°W
P3 to P4 = 360° - 343.5° = N16.5°W
P4 to P5 = 0° + 50.5° = N50.5°E
P5 to P6 = 180° - 129.5° = S50.5°E
P6 to P7 = 181.5° - 180° = S1.5°E
P7 to P1 = 215.5° - 180° = S35.5°W
Label the lines of the traverse with the corresponding bearings.
Traverse Computations
Field operation for traverses yields angles or directions and distance for a set of lines
connecting a series of traverse stations. Angles can be checked for error of closure and
corrected so that preliminary corrected values can be computed. And observed distances can
be reduced to equivalent horizontal distanced. The preliminary directions and reduced
distances are suitable for use in traverse computations, which are performed in a plane
rectangular coordinate system.
Computation with plane coordinates by considering the figure below.
Let the reduced horizontal distance of traverse lines ij and jk be dij and djk respectively, and
Ai and Aj be the azimuths of ij and jk. Let Xij and Yij be the departure & latitude.
Xij= dij sin Ai = departure
Yij = dij cos Ai =latitude
If the coordinates of i are xi and yi
So, the coordinates of j are:
Let the reduced horizontal distance of traverse lines ij and jk be dij and djk respectively, and
Ai and Aj be the azimuths of ij and jk. Let Xij and Yij be the departure & latitude.
Xij= dij sin Ai = departure
Yij = dij cos Ai =latitude
If the coordinates of i are xi and yi
So, the coordinates of j are:
Xj=xi+xij ; yj= yi+yij
Xk=xj+xjk ; yk=yj-yjk
=xi+xij+xik ; =yi+yij-yjk
xjk =djk sin Aj yjk=djk cos Aj
Note: the signs of azimuth functions
If the coordinates for the two ends of a traverse line are given, distance between two ends
can be determined as:
dij =[(xj-xi)2+(yj-yi)2]1/2
The azimuth of line ij from north and south is
Balancing the Traverse:
The term 'balancing' is generally applied to the operations of applying corrections to
latitudes and departures so that ΣL = 0, ΣD=0. This applies only when the survey forms a closed
polygon.
The following are common methods of adjusting a traverse:
1. Bowditch's method
2. Transit method
3. Graphical method
4. Axis method
1) Bowditch's Method: To balance a traverse where linear and angular measurements are
required this rule is used and it is also called as compass rule. The total error in latitude
and departure is distributed in proportion to the lengths of the sides.
The Bowditch's rule is:
Correction to latitude (or departure) of any side = Total error in latitude (or departure) * length of
that side /perimeter of traverse
Thus if, CL = Correction of latitude of any side CD= correction to departure of any side
ΣL = Total error in latitude
ΣD = total error in
departure
Σl = length of the perimeter
l = length of any side
CL = ΣL*(l/Σl) and CD=ΣD*(l/Σl)
2) Transit Method: It is employed when angular measurements are more precise than
linear measurements.
The Transit rule is:
Correction to latitude (or departure) of any side = [Total error in latitude (or departure) * latitude
L (or departure D) of that line Arithmetic sum of latitude LT (or departure DT)]
CL=ΣL*(L/LT) and CD=ΣD*(D/DT
MODULE II
Curve Surveying – Elements of simple and compound curves – Method of setting out– Elements of Reverse curve (Introduction only)– Transition curve – length of curve – Elements of transition curve - Vertical curve (introduction only)