Theodolite report

BQS MARCH INTAKE 2016 │FIELDWORK TWO │TRAVERSING
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SCHOOL OF ARCHITECTURE, BUILDING AND DESIGN
BACHELOR OF QUANTITY SURVEYING (HONOURS)
SITE SURVEYING (QSB60103)
Fieldwork two: Theodolite report
Group member:
Name Student ID
1. Wong Qin Kai 0320024
2. Lee Shze Hwa 0320053
3. Ng Huoy Miin 0319097
4. Hoi Wei Han 0323335
Lecturer: Mr. Chai Voon Chiet
Submission date: 12th July 2016

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TABLE OF CONTENT
TITLE CONTENT Page
No.
1.0 Introduction to Traversing
1.1 Open Traverse
1.2 Close Traverse
1.3 Azimuths and Bearings 3 - 7
1.4 Allowable Misclosure Traverse
1.5 Compass Rule
2.0 Outline ofApparatus
2.1 Theodolite
2.2 Optical Plummet
2.3 Adjusted Leg-Tripod
2.4 Ranging Pole 8 - 10
2.5 Bull’s Eye Level
2.6 Plumb Bob
2.7 Measuring Tape
2.8 Bar-coded Levelling Rod
3.0 Objective 11
4.0 Field Data
4.1 Compute the Angular Angle and Adjust the Angle 12-22
4.2 Calculate the Horizontal and Vertical Distances between the Survey Points and
Theodolite
4.3 Compute the Course Bearing and Azimuth

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4.4 Compute the Coarse Latitude and Departure
4.5 Determine the Error of Closure
4.6 Adjust Course Latitude and Departure
4.7 Compute Station Coordinate 23-25
4.8 Loop Traverse Plotted Using Coordinate (Graph)
5.0 Conclusion 26
6.0 ReferencesList 27
1.0 INTRODUCTION TO TRAVERSING
A traverse is a type of survey which include a series of lines known as traverse legs joined
together to a series of selected points known as traverse stations (TS). The distance and angle of
the survey lines are measured by a surveyor to figure out the relative positions of the traverse
stations by using specialized instruments such as theodolites which used to measure the angles
and measuring tape which used to measure the distance between traverse stations. We can also
use electronic distance-measurement instruments (EDMs) to measure the distance in a more
effectively and efficiently way. The purpose of establish traversing:
 Determine the positions of existing boundary markers.
 Determine the positions of boundary lines.
 Establish ground control of photographic mapping.
 Establish control for gathering data and locating construction work, railroads, highways
and utilities.
The types of traverse use in construction surveying are open traverse and close traverse.

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1.1 OPEN TRAVERSE
Open traverse is a series of lines and angles that starts with known point and terminates with
unknown location. The field measurements cannot be checked because errors are not revealed.
Therefore, the observations for field measurements should be repeated to minimize the errors.
Generally, open traverse use in exploratory purpose like mine surveying.
1.2 CLOSED TRAVERSE
Closed traverse divided into two types which are loop traverse and connecting traverse. Loop
traverse is when the traverse starts and terminates at the same points and form an enclosure
traverse. The location of the point is known and the errors can be minimized by internal check on
the accuracy of field measurements. However, the systematic errors cannot be detected, therefore
loop traverse is recommended for minor project. On another hand, connecting traverse is when
the traverse starts and terminated at different points and both points is known. It is more reliable
compare to loop traverse as the systematic errors can be detected. Hence, connecting traverse is
preferred to all types traverse.
← Loop Traverse

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Connecting Traverse
1.3 AZIMUTHS AND BEARINGS
Azimuths are commonly used for designating the
direction of a line. It defined as the horizontal angles
measured clockwise from any reference meridian.
Normally, azimuths are measured from the north and the
range is from 0° to 360°. Azimuths are used in survey
works such as boundary, topographic, control and
computations.
Bearings also used for designating the direction of a line.
It defined as the acute horizontal angles measured between
reference meridian and the line which means that bearings
will not greater than 90°. Besides, bearings are measured in
relation to the north or south end of the meridian. In order
to indicate which quadrant of the line located, the two
letters N (North) or S (South) and W (West) or E (East) are
used.

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Azimuths Bearings
 Range from 0° to 360°.  Range from 0° to 90°.
 Require numerical value only.  Require numerical value and two letters.
 Measure in clockwise direction only.  Measure in clockwise and counterclockwise
direction.
 Measure either from north or south
only.
 Measure from north and south.
(The table above has shown the different between azimuths and bearings.)
(Source:http://moodle.najah.edu/pluginfile.php/47169/mod_resource/content/0/Angles_Azimu
ths_Bearings.pdf)
1.4 ALLOWABLE MISCLOSURE TRAVERSE
A formula is given in order to check the accuracy of the traversing data. An accuracy about
1:3000 is the average land surveying.
The formula used:
P = The total distance of measured (Perimeter).
Ec = The total error.
An accuracy of at least 1:5000 are necessary for third-order control traverse surveys.
Accuracy= 1: (P/Ec)

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1.5 COMPASS RULE
In order to adjust the field measurements to get an accurate result and eliminate the errors
misclosure, corrections to the latitudes and departures are required.
The formula used:
∑△y and ∑△x = Error in latitude or departure.
P = Total perimeter of the traverse.
L = Length of a particular course
Correction = - [∑Δy] / P x L or – [∑Δx] / P x L

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2.0 Outline of Apparatus
2.1 Theodolite
Theodolite is a basic surveying instrument of unknown origin
but going back to the 16th-century English mathematician
Leonard Digges, it is used to measure horizontal and vertical
angles. In its modern form it consists of a telescope mounted to
swivel both horizontally and vertically. Leveling is
accomplished with the aid of a spirit level, crosshairs in the
telescope permit accurate alignment with the object sighted.
After the telescope is adjusted precisely, the two accompanying
scales, vertical and horizontal, are read.
2.2 Optical Plummet
Optical Plummet a device used in place of a plumb bob in
surveying to center transits and theodolites over a given point,
preferred for its steadiness in strong winds.
2.3 Adjusted Leg-Tripod
Adjusted Leg-Tripod is a device used to support any one of a
number of surveying instruments, such as theodolites, total stations,
levels or transits.
Figure 2.0 Theodolite
Figure 2.1 Optical
Plummet
Figure 2.3 Adjusted Leg-Tripod

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2.4 Ranging Pole
Ranging rod is a surveying instrument used for marking the
position of stations and for sightings of those stations as well as
for ranging straight lines. Initially these were made of light, thin
and straight bamboo or of well-seasoned wood such as teak,
pine and deodar. They were shod with iron at the bottom and
surmounted with a flag about 25 cm square in size. Nowadays
they are made of metallic materials only. The rods are usually 3
cm in diameter and 2 m or 3 m long, painted alternatively either
red and white or black and white in lengths of 20 cm (i.e. one
link length of metric chain). These colours are used so that the
rod can be properly sited in case of long distance or bad weather.
Ranging rods of greater length, i.e., 4 m to 6 m, are called
ranging poles and are used in case of very long survey lines.
2.5 Bull’s Eye Level
Bull's eye level is a "circular bubble" which is the name used by
surveyors in the United Kingdom. Surveying instruments such as
theodolites (transits) and total stations often have a circular bubble as
well as a tubular level or "plate level". The circular bubble is used to
roughly level the instrument in two dimensions and then the plate level,
being more precise, is used to level the instrument more precisely in
each dimension separately by leveling the plate level, then spinning
the instrument 90 degrees and leveling the plate level again.
Figure 2.4 Ranging Pole
Figure 2.5 Bull’s Eye Level

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2.6 Plumb Bob
Plumb bob or a plummet is a weight, usually with a pointed tip on
the bottom, that is suspended from a string and used as a vertical
reference line, or plumb-line. It is essentially the vertical equivalent
of a "water level".
2.7 Measuring Tape
Tape-Measure Fibre or plastic tape-measures typically come in
lengths of 20, 30, 50 or 100 m and it can be used to measure the
distances from one point to another point.
2.8 Bar-coded Levelling Rod
Bar-coded level rod can determine the relative height of the
different points in the area under survey.
Figure 2.6 Plumb
Bob
Figure 2.7 Measuring Tape
Figure 2.8 Bar-coded Levelling Rod

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3.0 Objective
 To learn the principles of running a closed field traverse.
 To establish ground control for photographic mapping.
 To enable students to get hand-on experience in setting up and working with theodolites
and collect the data of the relevant fieldwork.
 To enable students identify the error and make adjustment to the data
 Determine the error of closure and compute the accuracy of work.

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Field angles
Angle A = (88°54′00′′ + 88°51‘40‘’)/2 = 88°52’50’’
Angle B = (92°09’40’’ + 92°08’40’’) /2 = 92°09’10’’
Angel C = (89°54’40’’ + 89°55’20’’) /2 = 89°55’00’’
Angle D = (89°00’00’’+ 89°00’40’’) /2 = 89°00’20’’
Station Field angles Length
A 88°52’50’’ 12.275m
B 92°09’10’’ 12.650m
C 89°55’00’’ 12.500m
D 89°00’20’’ 13.100m
Total 359°57’20’’
B
A
C
D

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Compute the angular error and adjust the angles
The sum of the interior angles in any loop traverse must equal to the (n-2) x 180° for geometric
consistency.
 Sum of the interior = (n-2) x 180°
= (4-2) x 180°
= 360°
 Total angular error = 360° - 359°57’20’’
= 00°02’40’’
 Error per angle = 00°02’40’’ / 4
= 00°00’40’’
Station Field angles Correction Adjusted angles
A 88°52’50’’ +00°00’40’’ 88°53’30’’
B 92°09’10’’ +00°00’40’’ 92°09’50’’
C 89°55’00’’ +00°00’40’’ 89°55’40’’
D 89°00’20’’ +00°00’40’’ 89°01’00’’
Total 359°57’20’’ 360°00’00’’

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Calculate the horizontal and vertical distance between the survey points and the theodolite
The horizontal and vertical distances between the survey points and the theodolite can be
calculated by using the equations as below:
Equation:
Where,
D = Horizontal distance between survey point and instrument
S = Different between top stadia and bottom stadia
θ = Vertical angle of telescope from the horizontal line when capturing the stadia readings
K = Multiplying constant given by the manufacturer of the theodolite. (normally is = 0)
C = Addictive factor given by the manufacturer of the theodolite (normally is = 0)
D = K x s x (𝐜𝐨𝐬 𝜽)2
+ C x 𝐜𝐨𝐬 𝜽

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Distance A - B
Top stadia 1.475, Middle stadia 1.415, Bottom stadia 1.355 (facing left)
Top stadia 1.475, Middle stadia 1.415, Bottom stadia 1.355 (facing right)
Distance A – B = [K x s x (𝐜𝐨𝐬 𝜽)2] + [C x 𝐜𝐨𝐬 𝜽]
= [100 x (1.475-1.355) x (cos1)2] + [0 x (cos1)
=12.00m
Distance A - B = [K x s x (𝐜𝐨𝐬 𝜽)2] + [C x 𝐜𝐨𝐬 𝜽]
= [100 x (1.475-1.355) x (cos1)2] + [0 x (cos1)
= 12.00m
Average reading = (12.00m + 12.00m) / 2
= 12.00m
Distance B - A
Distance B - A = [K x s x (𝐜𝐨𝐬 𝜽)2] + [C x 𝐜𝐨𝐬 𝜽]
= [100 x (1.445-1.325) x (cos1)2] + [0 x (cos1)
= 12.00m
Distance B - A = [K x s x (𝐜𝐨𝐬 𝜽)2] + [C x 𝐜𝐨𝐬 𝜽]
= [100 x (1.453-1.322) x (cos1)2] + [0 x (cos1)
= 13.10m
Average reading = (12.00m + 13.10m) /2
= 12.55m
Average reading for angle A is (12.00m + 12.55m) /2
=12.275m

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Distance B – C
Distance B – C = [K x s x (𝐜𝐨𝐬 𝜽)2] + [C x 𝐜𝐨𝐬 𝜽]
= [100 x (1.450-1.320) x (cos1)2] + [0 x (cos1)
= 13.00m
Distance B – C = [K x s x (𝐜𝐨𝐬 𝜽)2] + [C x 𝐜𝐨𝐬 𝜽]
= [100 x (1.445-1.325) x (cos1)2] + [0 x (cos1)
= 12.00m
Average reading = (12.00m+13.00m) / 2
= 12.50m
Distance C - B
Distance C - B = [K x s x (𝐜𝐨𝐬 𝜽)2] + [C x 𝐜𝐨𝐬 𝜽]
= [100 x (1.450-1.330) x (cos1)2] + [0 x (cos1)
= 12.00m
Distance C - B = [K x s x (𝐜𝐨𝐬 𝜽)2] + [C x 𝐜𝐨𝐬 𝜽]
= [100 x (1.458-1.322) x (cos1)2] + [0 x (cos1)
= 13.60m
= 12.80m
Average reading for angle B is (12.50 +12.80) /2
=12.650 m

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Distance C – D
Distance C – D= [K x s x (𝐜𝐨𝐬 𝜽)2] + [C x 𝐜𝐨𝐬 𝜽]
= [100 x (1.455-1.325) x (cos1)2] + [0 x (cos1)
= 13.00m
Distance C – D= [K x s x (𝐜𝐨𝐬 𝜽)2] + [C x 𝐜𝐨𝐬 𝜽]
= [100 x (1.445-1.330) x (cos1)2] + [0 x (cos1)
= 11.50m
= 12.25m
Distance D - C
Top stadia 1.410, Middle stadia 1.345, Bottom stadia 1.280
Top stadia 1.405, Middle stadia 1.345, Bottom stadia 1.280
Distance D - C = [K x s x (𝐜𝐨𝐬 𝜽)2] + [C x 𝐜𝐨𝐬 𝜽]
= [100 x (1.410-1.280) x (cos1)2] + [0 x (cos1)
= 13.00m
Distance D - C = [K x s x (𝐜𝐨𝐬 𝜽)2] + [C x 𝐜𝐨𝐬 𝜽]
= [100 x (1.405-1.280) x (cos1)2] + [0 x (cos1)
= 12.50m
= 12.75m
Average reading for angle C is (12.25+12.75) /2
=12.50m

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Distance A – D
Distance A – D= [K x s x (𝐜𝐨𝐬 𝜽)2] + [C x 𝐜𝐨𝐬 𝜽]
= [100 x (1.480-1.355) x (cos1)2] + [0 x (cos1)
= 12.50m
Distance A – D= [K x s x (𝐜𝐨𝐬 𝜽)2] + [C x 𝐜𝐨𝐬 𝜽]
= [100 x (1.488-1.350) x (cos1)2] + [0 x (cos1)
= 13.80m
= 13.15m
Distance D - A
Distance D - A = [K x s x (𝐜𝐨𝐬 𝜽)2] + [C x 𝐜𝐨𝐬 𝜽]
= [100 x (1.408-1.282) x (cos1)2] + [0 x (cos1)
= 12.60m
Distance D - A = [K x s x (𝐜𝐨𝐬 𝜽)2] + [C x 𝐜𝐨𝐬 𝜽]
= [100 x (1.415-1.280) x (cos1)2] + [0 x (cos1)
= 13.50m
= 13.05m
Average reading for angle D is (13.15+13.05) /2
=13.10m

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A
Compute course bearing and azimuth
Azimuth Bearing
A – B assumed is 00°00’00’’ N 00°00’00’’
B – C = 180° - 92°09’50’’ N 87°50’10’’W
= 87°50’10’’
B
A
C
B
92°09’50’’
A

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A
Azimuth Bearing
C – D = 89°55’40’’ - 87°50’10’’ S 02°05’30’’ W
= 02°05’30’’
Azimuth C-D = 180° - 02°05’30’’
= 177°54’30’’
D – A =180° - 89°01’00’’- 02°05’30’’ S 88°53’30’’E
= 88°53’30’’
Azimuth D – A = 180° + 88°53’30’’
= 268°53’30’’
C B
89°55’40’’
D
C
89°01’00’’
D A

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Compute Course Latitude and Departure
Station Bearing β Length Cosine Sine Latitude Departure
A N 00°00’00’’ 12.275 1.000 0.000 +12.275 +0.000
B N 87°50’10’’W 12.650 0.03775 0.99928 +0.4775 -12.64089
C S 02°05’30’’ W 12.500 0.9993 0.03649 -12.49125 -0.456125
D S 88°53’30’’E 13.100 0.01934 0.99981 -0.253354 +13.097511
50.525 (∑Δy)
0.007896
(∑Δx)
0.000496
Algebraic sign convention to latitude and departure

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Determine the error of closure
A
Accuracy = 1: (P/ EC)
For the average land surveying an accuracy of about 1:3000 is typical.
EC = [ (sum of latitude)2 + (sum of departure)2]1/2
= [ (0.007896)2 + (0.000496)2]
= 0.007911563
P = 50.525m
Accuracy = 1: (50.525/0.007911563)
= 1:6386.222
Therefore, the traversing is acceptable.
Error in departure = 0.000496
Error in latitude = 0.007896
EC Total error = 0.007911563
A’

Page | 23
Adjust courses latitude and departure
The compass rule:
Correction = - [∑Δy] / P x L or – [∑Δx] / P x L
Where,
∑Δy and ∑Δx = the error in latitude and departure
P = total length of perimeter of the traverse
L = length of a particular course
Station Unadjusted Corrections Adjusted
Latitude Departure Latitude Departure Latitude Departure
A 12.275 0.000 -0.001918325581 -0.0001205 12.27308 -0.0001
B 0.4775 -12.64089 -0.001976930233 -0.0001242 0.47552 -12.6410
C -12.49125 -0.456125 -0.001953488372 -0.0001227 -12.49320 -0.4562
D -0.253354 +13.097511 -0.002047255814 -0.0001286 -0.25540 13.0973
(∑Δy)
0.007896
(∑Δx)
0.000496
-0.007896
Check
-0.000496 0.0000
Check
0.0000

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Latitude correction
 The correction to the latitude of course A-B is
(-0.007896/50.525) x 12.275 = -0.001918325581
 The correction to the latitude of course B-C is
(-0.007896/50.525) x 12.650 = -0.001976930233
 The correction to the latitude of course C-D is
(-0.007896/50.525) x 12.500 = -0.001953488372
 The correction to the latitude of course D-A is
(-0.007896/50.525) x 13.100 = -0.002047255814
Departure correction
 The correction to the departure of course A-B is
(-0.000496/50.525) x 12.275 = -0.0001205
 The correction to the departure of course B-C is
(-0.000496/50.525) x 12.650 = -0.00012418
 The correction to the departure of course C-D is
(-0.000496/50.525) x 12.500 = -0.00012271
 The correction to the departure of course D-A is
(-0.000496/50.525) x 13.100 = -0.00012860

Page | 25
Compute station coordinates
N₂ = N₁ + Latitude₁₋₂
E₂ = E₁ + Departure₁₋₂
Where,
N₂ and E₂ = Y and X coordinates of station 2
N₁ and E₁ = Y and X coordinates of station 1
Latitude₁₋₂ = Latitude of course 1-2
Departure₁₋₂ = Departure of course 1-2
Station N coordinate latitude E coordinate departure
A
B
C
D
A
1000.0000 (assumed)
+12.27308
1012.27308
+0.47552
1012.7486
-12.4932
1000.2554
-0.25540
1000.000
1012.6411
-0.0001
1012.6410
-12.6410
1000.0000 (assumed)
-0.4562
999.5438
13.0973
1012.6411
Start & return here for lat. check
Start & return here for dep. check
(Course lat. and dep.)
*Compass – Adjusted coordinates

Page | 26
5.0 Conclusion
In the fieldwork, we used closed loop traverse survey and laid out point A, B, C, D on the site
respectively. Our site for this survey is located at the car park. Closed loop traverse must start
and ends at same point and formed a closed geometric figure which is the boundary lines of a
tract land.
Theodolite is used for measuring the angle of the 4 point (A, B, C, D). At first. we placed the
theodolite at point A and the angle point A is achieved by reading the theodolite through point D
to B. The angle of the theodolite has been obtained from left to right and then right to left to
make the readings more accurately.
The horizontal angles and vertical angles that shown on the panel of theodolite were recorded
during the field works. The data is recorded for the report used. At the end of the process, the
total recorded angles must be 360. However, our total angle recorded is 359o 57’20”. Thus, the
error has occurred as there is a difference of 00°02’40’’. Therefore, adjustment has to be made
by using the trigonometric levelling technique.
For our first attempt, we used pacing method to measure the length of the point. We have done
the readings but failed to get an accuracy of at least 1:3000. Therefore, we tried to go to the site
and try one more time. For second attempt, we get the point A, B, C, D which the group has used
tape-measure to lay out by the course mates done before. Our error in departure is -0.000496 and
our error in latitude is -0.007896. The total error is using the following formula, we calculated
the accuracy of our traverse survey:
For the adjustment of latitude and departure, we used the formula of compass rule. While, for
average land surveying an accuracy of 1:3000 is typical. We obtained an accuracy of 1:6386.
Therefore, the traverse survey is acceptable.
Accuracy= 1: (P/Ec)

Page | 27
6.0 References List
1.0 Introduction
"Untitled Document". Nptel.ac.in. N.p., 2016. Web. 5 July 2016. From
http://nptel.ac.in/courses/105107122/modules/module9/html/28-5.htm
Pike, J. (2016). FM 6-2 Chapter 5 Traverse. Globalsecurity.org. Retrieved 5 July 2016, from
http://www.globalsecurity.org/military/library/policy/army/fm/6-2/Ch5.htm
Pike, J. (2016). Chapter 6. Globalsecurity.org. Retrieved 5 July 2016, from
http://www.globalsecurity.org/military/library/policy/army/fm/3-34-331/ch6.h
Fundamentals of Mapping. (2016). Icsm.gov.au. Retrieved 8 July 2016, from
http://www.icsm.gov.au/mapping/surveying2.html
Bearings and Azimuths. (2016). Engineering.purdue.edu. Retrieved 8 July 2016, from
https://engineering.purdue.edu/~asm215/topics/bearings.html

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