Surveying Engineering Traversing Practical part 1 Plane and Applied surveying 2 Report number(2) • Report name :Gales Traverse Table(Horizontal angle measurement (FL)of closed traversing • Apparatus • Theodolite Instrument • Tripod • Compass • Pin • Tape • Range pole Object • To conducted survey work in a closed traversing and calculate in depend coordinates and area calculation by coordinate rule. Procedure Traverse; Calculations Traverse .Dada Sheet and Table method work clock wise surveying -Gales Traverse Table. *Traverse Calculations -Traverse Calculation. -Coordinate conversions. -Signs of Departures and Latitudes. *Balancing latitude and departure -Correction for ∆E& ∆N: Bowditch adjustment or compass method -The example… -Vector components (pre-adjustment) *The adjustment components Prepared by: Asst. Prof. Salar K.Hussein Mr. Kamal Y.Abdullah Asst.Lecturer. Dilveen H. Omar Erbil Polytechnic University Technical Engineering College Civil Engineering Department

1. Engineering Surveying
Traversing Practical part
1
Erbil Polytechnic University
Technical Engineering College
Civil Engineering Department
Compass
Plane and Applied surveying 2 3
4
2
B
1
5
2
3
4
B2
L
L23
L34
L4B
A

2. • Report number(2)
• Report name :Gales Traverse Table(Horizontal angle
measurement (FL)of closed traversing
• Apparatus
Theodolite Instrument 1 No.
Tripod 1 No.
Compass 1 No.
Pin 4 Nos.
Tape 1 No.
Range pole 2 Nos.
2

3. Object
• To conduct a survey work in a closed traversing and calculation
of latitude and departure. Also calculate of independent
coordinates, then find the and area by coordinate rule.
3

4. Procedure Traverse:
4
3
4
2
B
1
5
2
3
4
B2
L
L23
L34
L4B
A
Measurements required in the field
for:
1. Compass traverse:
a. Measure all bearing.
b. Measure all Lengths.
2. Theodolite traverse:
a. Measure all the included angles
b. Measure all the lengths.
c. Measure at least one bearing.
W.C.B
CORRCTED
CORRECTION
ANGLE
LENGTH
LINE
STATION

5. Calculations Traverse .Dada Sheet and Table
method work clock wise surveying
5
92 0 0
A
B
C
D
E

6. Gales Traverse Table
The computation for a closed traverse may be made in the following steps
and entered in the tabular form, Which known as Gales Traverse Table.
1. Sum up all the included angles. Their sum should be equal to [(2*N±
4)*90)] or(N ± 2 )*180)Where N is the number of angles (sides) of the
traverse measured.
(+) if the angles are exterior
(-) if the angles are interior.
2. Apply necessary corrections if the above formula does not satisfy.(
divide the error by the no. of angle. Then add or subtract according to
the sign of the error).


6

7. Traverse Calculations
3. Calculate the WCB of the other lines from the observed bearing
of the first line and the corrected included angles.
WCB of AB = Measured (Known).
(BB =WCB±180)
Clockwise Direction (of the survey) Anti clockwise direction
WCB of BC = BB of AB - angle B. =BB of AB + angle B
WCB of CD = BB of BC - angle C. =BB of BC + angle C
WCB of DA = BB of CD - angle D. =BB of CD + angle D
Check WCB of BA = AB=BB of DA - angle A. =BB of DA + angle A
7

8. Traverse Calculation
4. From the WCB of the lines, find the
reduced bearing(RB) of the lines, and determine the quadrants in
which the lines lie.(The equations are depending on which Quadrant
the direction of line lie).
RB of AB= FB of AB (First Quadrant)
RB of DA=180-FB of DA (Second Quadrant)
RB of CD=FB of CD-180 (third Quadrant)
RB of BC=360-FB of BC (Forth Quadrant)
8

9. Traverse Calculation
5. From the measured lengths and the calculated Reduced
Bearing(RB) of the lines, compute the their latitude and
departure(consecutive coordinates).
If angle RB = θ
Latitude = L cos(θ)
Departure = L sin(θ)
6. Add all Northing, and all Southing, and find the difference
between the two sums. Similarly find the difference between the
sum of all easting and sum of all wasting.
9

10. Traverse Calculation
7. Apply the necessary correction(Transit Rule) to the latitudes and
departures so that the (sum of the northing is equal to sum of southing
and sum of easting is equal to sum of wasting).
Cl = ∑L * L/Lt where Cl= correction for each latitude.
Cd = ∑D *D/Dt L = Latitude of that line.
∑L = sum of error in latitude.
Lt = total latitude.
Cd = correction for each departure.
D = Departure of that line.
∑D = sum of error in departure. 10

11. Traverse Calculation
8. Find the corrected consecutive coordinates.
9. From the corrected consecutive coordinates, find the
independent coordinates of the so that they are all positive,
the whole of the traverse thus lying in the first quadrant.(NE).
11

12. Coordinate conversions
12
2
2
1
tan
N
E
L
N
E












 



cos
sin
L
N
L
E




Grid to polar Polar to Grid
L

E
N L

E
N

13. Signs of Departures and Latitudes
North
East
West
South
Departure (+)
Latitude (+)
Departure (-)
Latitude (+)
Departure (+)
Latitude (-)
Departure (-)
Latitude (-)
 The latitude of a line is its projection on the north–south meridian
 The departure of a line is its projection on the east– west line
13

14. Step 3
Compute Departure & Latitude (E,N) for each line:
14
• The rectangular components for each line are
computed from the polar coordinates (,L)
Where L= Length of side
 = bearing
• Note that these formula apply regardless of the
quadrant so long as whole circle bearings are used


cos
*
sin
*
L
N
L
E




Departure ( Δ X) = distance (L) sin ß
Latitude ( Δ Y) =distance (L) cos ß

15. The rule states:
“The error in latitude (departure) of a line is to the total error in latitude
(departure) as the length of the line is the perimeter of the traverse”
Correction in Lat. =
𝑬𝒓𝒓𝒐𝒓 𝒊𝒏 𝑳𝒂𝒕. 𝒙 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝒑𝒆𝒓𝒊𝒎𝒆𝒕𝒆𝒓
Correction in Dep. =
𝐸𝑟𝑟𝑜𝑟 𝑖𝑛 𝐷𝑒𝑝. 𝑥 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟
15
Balancing latitude and departure

16. Correction for ∆E& ∆N:
Bowditch adjustment or compass method
• The adjustment to the easting component of
any traverse side is given by :
Eadj = Emisc * side length/total perimeter
• The adjustment to the northing component of
any traverse side is given by :
Nadj = Nmisc * side length/total perimeter
Adding these values for ∆E or ∆N opposite sign of dE ,dN∙
16

17. The example…
• East misclose 0.07 m
• North misclose –0.05 m
• Side AB 77.19 m
• Side BC 99.92 m
• Side CD 60.63 m
• Side DE 129.76 m
• Side EA 32.20 m
• Total perimeter 399.70 m
17

18. Vector components (pre-adjustment)
Side E N dE dN Eadj Nadj
1A 30.16 71.05
AB 79.80 60.13
BC 12.61 -59.31
CD -94.90 -88.50
D1 -27.60 16.58
Misc (0.07) (-0.05)
18

19. The adjustment components
Side E N dE dN Eadj Nadj
1A 30.16 71.05 0.014 -0.010
AB 79.80 60.13 0.016 -0.012
BC 12.61 -59.31 0.011 -0.008
CD -94.90 -88.50 0.023 -0.016
D1 -27.60 16.58 0.006 -0.004
Misc (0.07) (-0.05) (0.070) (-0.050)
19

20. Adjusted vector components
Side E N dE dN Eadj Nadj
1A 30.16 71.05 0.014 -0.010 30.146 71.060
AB 79.80 60.13 0.016 -0.012 79.784 60.142
BC 12.61 -59.31 0.011 -0.008 12.599 -59.302
CD -94.90 -88.50 0.023 -0.016 -94.923 -88.484
D1 -27.60 16.58 0.006 -0.004 -27.606 16.584
Misc (0.07) (-0.05) 0.070 -0.050 (0.000) (0.000)
20

21. Calculation of Independent Coordinates
21
Point
Side
Eadj Nadj X Y Notes Notes
Point A
Side AB 30.146 71.060
500 500 Assumed Assumed
B
BC 79.784 60.142
530.146 571.06
C
CD 12.599 -59.302
609.930 631.202
D
DE -94.923 -88.484
622.529 571.90
E
EA -27.606 16.584
527.606 483.416
A 500 500
+
=
+
=