University of Sharjah

Collage of Engineering

Department of Civil and Environmental Engineering - CEE

Fall - 2016

Course : Surveying Laboratory 0401225

Instructor : Eng. Shaymaa R. Kubaisy

Lab Engineer : Priya Somasekhara Kaimal

Lab Report about :

Measurement of the Internal

Angles of a Loop Traverse
Submitted On : 14th. Dec 2016

Name Student ID
Mohammad Salah U15102551
Almoukdad
Ahmed Sami Bakr U15102527
Ahmed Khalid Salama U14111242
Ahmed Omar U14111006
Ahmed Essam U15104018

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 Table of Contents
Num Content. Page Num.
.
1 Cover Page 1
2 Table of Contents 2
3 Introduction 3
4 Objectives 3
5 Theoretical Background 3
6 Instruments 4
7 Procedure 6
8 Calculations 7
9 Data sheet 10
10 Discussion 11
11 Conclusion 11
12 Sources of Error 12
13 References 13
14 AutoCAD 14
15 Field book 15 – 16

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Introduction :
Introduction Theodolite total station is one of the important devices for our fields. The purpose of this
lab is to introduce to the basic operation of a total station .This instrument can be used to measure
horizontal and vertical angles as well as sloping distance of object to the instrument , and is used to
determine the position and elevation of points (coordinates). The coordinates of these points can then
be used for a variety of purposes, such as determining the area of an irregular object and, also the data
collected and processed may be down-loaded to computers for further processing .

Objectives :
 Learn how to measuring angles by using total station.
 learn how to computation of average measured directions, angles and the sum of the
internal angles of a traverse.
 Learn how to use the total station and to get familiar with its parts.
 to get familiar in finding the elevation by using the total station and the calculations
(without using the level) .

Theoretical Background :
Definitions :

Total station: is a combination of Electromagnetic Distance Measuring Instrument and electronic

theodolite. It is also integrated with microprocessor, electronic data collector and storage system. The
instrument can be used to measure horizontal and vertical angles as well as sloping distance of object to
the instrument.

Departure: the length of the projection, on the east-west reference line, of a survey line.

Zeroing the scale: make the angle zeroing in hour, minute, second 0˚0'0".

Vertical angle: is measure off the horizon with up being positive and down from the horizon being
negative.

Vertical distance: The elevation of a point near the surface of the earth is its vertical distance above or
below an arbitrarily assumed level surface or curved surface every element of which is normal to the
plumb line.

Height of instrument: The height of a levelling instrument above the datum being used in the survey.

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Equations:

Horizontal angle on face left= face left of Z – face left of X

Horizontal angle on face right= face right of Z – face right of X

Mean reduced horizontal angel / Horizontal angle on Y =

Horizontal angle on face¿ Horizontal angle on face¿ ¿

2

Σ𝐼𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑎𝑛𝑔𝑙𝑒𝑠=𝐴+𝐵+𝐶+ = 360⁰

𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙Σ 𝑖𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑎𝑛𝑔𝑙𝑒𝑠= (𝑛−2) ∗180,ℎ𝑒𝑟𝑒 𝑛 𝑖𝑠 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 angles - stations .

𝑀𝑖𝑠𝑐𝑙𝑜𝑠𝑢𝑟𝑒 𝑒𝑟𝑟𝑜𝑟= 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙Σ 𝑖𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑎𝑛𝑔𝑙𝑒𝑠−Σ𝐼𝑛𝑡𝑒𝑟𝑛𝑎𝑙 𝑎𝑛𝑔𝑙𝑒𝑠

𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒𝑠=𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑎𝑛𝑔𝑙𝑒+𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛

𝑑𝑒lt(Δ𝑥)=𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒∗𝑠𝑖𝑛𝜃

𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒 (Δ𝑦) =𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒∗𝑐𝑜𝑠𝜃

n
1 1
Area= ∑ [ x1 ( y i +1− y i−1) ] = ¿
2 i=1 2

RLB=RL A + HI ± ( VD )−HR

V AB=L cos z=L sin α

H B =H A +h i+V AB−hr

Instruments :

Tripod:
Is a portable three-legged frame, used as a platform for
supporting the weight and maintaining the stability of some
other object.

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Total Station:
Total station is a combination of Instrument and electronic
theodolite. It is also integrated with microprocessor, electronic
data collector and storage system. The instrument can be used to
measure horizontal and vertical angles as well as sloping distance
of object to the instrument. 

Reflector:
A reflector TSI uses short pulses of high energy laser light. This
energy is considerably higher than that used by phase shift TSIs
in order to get a return signal off low reflection surfaces. The
instrument measures travel times of the laser pulses and from
that can determine the total instrument-surface-instrument
distance.

Because the laser pulses reflect off different surfaces, care must
be exercised when pointing the instrument. This is especially
critical when there are multiple surfaces at various orientations
near the measurement point. Many instruments feature a built-
in laser pointer which provides the operator a visual indication
of where the measurement will be made.

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Procedure :

Set up the total station :

Tripod Setup :

 Tripod legs should be equally spaced.

 Tripod head should be approximately level.
 Head should be directly over survey point.

Mount Instrument on Tripod:

 Place Instrument on Tripod
 Secure with centering screw while bracing the
instrument with the other hand.

Focus on Survey Point:

 Focus the optical plummet on the survey point.

Leveling the Instrument:

 Adjust the leveling foot screws to center the survey point in the optical plummet reticle.
 Center the bubble in the circular level by adjusting the tripod legs.

 Loosen the horizontal clamp and turn instrument until

plate level is parallel to 2 of the leveling foot screws.

 Center the bubble using the leveling screws- the

bubble moves toward the screw that is turned
clockwise.

 Rotate the instrument 90 degrees and level using the

3rd leveling screw.

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  Observe the survey point in the optical plummet and center the point by loosening the centering
screw and sliding the entire instrument.

 After re-tightening the centering screw check to make sure the plate level bubble is level in
several directions.

 Draw AutoCAD

Starting with station A angle between (D&B):

 Set the zero angle at point D by using the 0SET button, and it shows in the LCD display.
 Took the distances and vertical angles and recorded in the field book.
 The instrument had been directed towards the point B and it should be centered to the (X) mark
by using the vertical drive and the horizontal drive.
 Took the horizontal and vertical angles and distances and recorded in the field book.

Changed to the right face (F.R.)

 Take the horizontal and vertical angles and distances and recorded in the field book.
 The instrument should be moved by using the horizontal motion clamp and vertical motion
clamp.
 The readings at reflector B&D has been taken and recorded in the field book as what had done
with the left face (F.L.).
 Calculate the angle from field book then corrected by correction formula.

-Repeat the same procedures with the next 3 stations.

Calculations :
Angles measured
A 104⁰ 35’ 6’’
B 60⁰ 24’ 38’’
C 127⁰ 36’ 7.5’’
D 66⁰ 3’ 8’’

Error in interior angles :

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Actual = 360⁰ 0’ 0’’

Measured = 358⁰ 40’ 7’’

Error = 2⁰ 0’ 33’’

2⁰ 0’ 33’ ’
Correction for each angle = = 30’ 8.25’’
4

Angles after correction

A 105⁰ 5’ 14.25’’
B 60⁰ 54’ 46.25’’
C 128⁰ 6’ 15.75’’
D 66⁰ 33’ 16.25’’

Azimuths :

 Bearing AB = 67⁰ (given)

 BB = 67⁰+ 180⁰ = 247⁰
 CWA = 247⁰ + 60⁰ 54’ 46.25’’ = 307⁰ 54’ 46.25’’

 Bearing BC = 307⁰ 54’ 46.25’’( calculated )

 BB = 307⁰ 54’ 46.25’’+ 180⁰ - 360 = 127⁰ 54’ 46.25’’
 CWA = 127⁰ 54’ 46.25’’+ 128⁰ 6’ 15.75’’ = 256⁰ 6’ 12’’

 Bearing CD = 256⁰ 6’ 12’’ (calculated )

 BB = 256⁰ 6’ 12’’- 180⁰ = 76⁰ 6’ 12’’
 CWA = 76⁰ 6’ 12’’+ 66⁰ 33’ 6.25’’ = 142⁰ 39’ 18.25’’

 Bearing DA = 142⁰ 39’ 18.25’’ ( calculated )

 BB = 142⁰ 39’ 18.25’’- 180⁰ = -38⁰ 39’ 18.25’’
 CWA = -38⁰ 39’ 18.25’’+105⁰ 5’ 14.25’’ = 67⁰ 0’ 0’’

B`earing for each line Lengths

AB 67⁰ 0’ 0’’ AB 5.246m
BC 307⁰ 54’ 46.25’’ BC 4.92m
CD 256⁰ 6’ 12’’ CD 4.182m
DA 142⁰ 39’ 18.25’’ DA 5.101m

 ∆X = L(sinɣ)
 ∆Y = L(cosɣ)

∆X ∆Y

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 AB 6.2115 -1.3654
BC 4.299 2.391
CD 3.2907 -2.58
DA 4.679 2.029
Sum 18.4802 0.4746
1
 x correction = * departure, corrected x for each line = x correction+x
p
1
 y correction = * latitude, corrected y for each line = y correction + y
p

P = Sum of lengths = 19.449m

Corrected ∆X Corrected ∆Y
AB 4.984 0.128
BC -4.6798 -0.12
CD -3,973 0.10
DA 4.84 - 0.124
Sum 0 0

Coordinates :

𝑅𝐿 (𝐵) = (𝐴)+𝐻𝐼 ±(𝑉𝐷)−𝐻𝑅

Point X(m) Y(m) Z(m)

A 100 100 25
B 104.984 100.128 24.996
C 100.3042 100.248 24.969
D 96.3312 100.348 24.926

Area by trigonometric method :

A1 = 0.5 * 5.246 * 5.101 = 13.37

A2 = 0.5 * 4.92 * 4.182 = 10.28

A total = A1 + A2 = 23.65 m2

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Data sheet :
Angle Face Left Face Right Mean Reduced
(F.L.) (F.R.) Horizontal Angle

A D 00 ° 00' 00 179 ° 59 ' 44 104 ° 35' 06

B 104 ° 35' 04 284 ° 34 ' 52
B A 00 ° 00' 00 179 ° 59 ' 47 60 ° 24 ' 38
C 60 ° 24 ' 37 240 ° 24 ' 26
C B 00 ° 00' 00 179 ° 59 ' 54 127 ° 36 ' 7.5
D 127 ° 35 ' 12 307 ° 36' 57
D C 00 ° 00' 00 179 ° 59 ' 40 66 ° 03 ' 08
A 66 ° 03 ' 01 246 ° 02' 55
VA 90 ° 02' 32
HI (A) 1.425 m
AB HR (B) 1.49m
HD 5.246m
VD -0.004m
VA 90 ° 19' 02
HI (B) 1.44m
BC HR (C) 1.445m
HD 4.92m
VD -0.027m
VA 90 ° 35' 12
HI (C) 1.40m
CD HR (D) 1.362m
HD 4.182m
VD -0.043m
VA 90 ° 57' 02
HI (D) 1.435m
DA HR (A) 1.33m
HD 5.101m
VD -0.083m

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Discussion :
After doing the experiment and collecting the data, the required calculations were done and compared
to the theoretical calculations. It is found that the experimental summation of the internal angles of the
polygon was not exactly 360ͦ according to the theoretical law. But he difference was 0 5ͦ 0′21”which is
considered acceptable. After that correction process for the angles were done and the summation of the
experimental was equal to the theoretical summation. Then the coordinates, area, reduced levels and
the bearing were calculated in order to complete the required field features .

Conclusion :
In conclusion To sum up , Total station is sensitive , accurate and important instrument for us as
surveyor . Starting with the optical, then the digital which leads to find our desired measurements and
angles. In this lab we learned how to find the internal angles and vertical angles using the total station,
and how to Determine the elevations of the points and the slope distances. So the total station have
many application to do with .

Sources of error :

a) Circle eccentricity:

Circle eccentricity exists when the theoretical center of the mechanical axis of the theodolite does not
coincide exactly with the center of the measuring circle. The amount of error corresponds to the degree
of eccentricity and the part of the circle being read. When represented graphically circle eccentricity
appears as a sine wave. Circle eccentricity in the horizontal circle can always be compensated for by
measuring in both faces (opposite sides of the circle) and using the mean as a result. Vertical circle
eccentricity cannot be compensated for in this manner since the circle moves with the telescope. More
sophisticated techniques are required.

b) Horizontal collimation error:

Horizontal collimation error exists when the optical axis of the theodolite is not exactly perpendicular to
the telescope axis. To test for horizontal collimation error, point to a target in face one then point back
to the same target in face two; the difference in horizontal circle readings should be 180 degrees.

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Horizontal collimation error can always be corrected for by meaning the face one and face two pointings
of the instrument.

c) Vertical circle error:

It is important to check the vertical circle indexing adjustment on surveying instruments on a routine
basis. When direct and indirect zenith angles are measured to the same point, the sum of the two angles
should equal 360°. Over time, the sum of these two angles may diverge from 360° and consequently
cause errors in vertical angle measurements. While averaging the direct and indirect zenith angles easily
eliminates this error, on many jobs it may not be cost effective to make two readings.

d) Pointing errors:

Pointing errors are due to both human abilities to point the instrument and environmental conditions
limiting clear vision of the observed target. The best way to minimize pointing errors is to repeat the
observation several times and use the average as the result.

e) Uneven heating of the instrument:

Direct sunlight can heat one side of the instrument enough to cause small errors. For the highest
accuracy, utilize an umbrella or pick a shaded spot for the instrument.

f) Vibrations:

Avoid instrument locations that vibrate. Vibrations can cause the compensator to be unstable.

g) Collimation errors:

When sighting points, a single time (e.g., direct position only) for elevations, check the instrument
regularly for collimation errors.

h) Adjustment of prism poles:

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When using prism poles, precautions should be taken to ensure accurate measurements. A common
problem encountered when using prism poles is the adjustment of the leveling bubble. Bubbles can be
examined by establishing a check station under a doorway in the office. First, mark a point on the top of
the doorway. Using a plumb bob, establish a point under the point on the doorway. If possible, use a
center punch to make a dent or hole in both the upper and lower marks. The prism pole can now be
placed into the check station and easily adjusted.

i) Recording errors:

The two most common errors are reading an angle incorrectly and/or entering incorrect information
into the field book. Another common (and potentially disastrous) error is an incorrect instrument or rod
height. Although electronic data collection has all but eliminated these errors, it is still possible for the
surveyor to identify an object incorrectly, make a shot to the wrong spot, or input a bad target height
(HR) or HI.

j) Other errors :

 Also one of the errors in this experiment is that the sum of angles is not exactly 360, and it must
be 360 from the interior angle rule which is (n-2) ×180, and n is the number of sides and in this
experiment there are 4 sides so 2×180=360°
 Reading the tape wrongly in measuring the length from the ground to the total station and the
reflector .

References :
 http://theconstructor.org/surveying/error-sources-in-total-station/6052/
 https://en.wikipedia.org/wiki/Total_station
 Lecture Notes

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