Theodolite report

BQS MARCH INTAKE 2016 │FIELDWORK TWO │TRAVERSING

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 of Apparatus

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

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4.2 Calculate the Horizontal and Vertical Distances between the Survey Points and Theodolite

4.3 Compute the Course Bearing and Azimuth

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 References List 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.

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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.

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.

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← Loop Traverse

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

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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.

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_Azimuths_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.

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Accuracy = 1: (P/Ec)

http://moodle.najah.edu/pluginfile.php/47169/mod_resource/content/0/Angles_Azimuths_Bearings.pdf

http://moodle.najah.edu/pluginfile.php/47169/mod_resource/content/0/Angles_Azimuths_Bearings.pdf


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

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Correction = - [∑Δy] / P x L or – [∑Δx] / P x L


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.

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Figure 2.0 Theodolite

Figure 2.1 Optical

Plummet

https://en.wikipedia.org/wiki/Dumpy_level

https://en.wikipedia.org/wiki/Total_station

https://en.wikipedia.org/wiki/Theodolite

https://en.wikipedia.org/wiki/Surveying_instruments

http://www.dictionaryofconstruction.com/definition/theodolite.html

http://www.dictionaryofconstruction.com/definition/transit.html

http://www.dictionaryofconstruction.com/definition/plumb-bob.html

http://www.dictionaryofconstruction.com/definition/device.html


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.

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Figure 2.3 Adjusted Leg-Tripod

Figure 2.4 Ranging Pole

Figure 2.5 Bull’s Eye Level

https://en.wikipedia.org/wiki/Total_station

https://en.wikipedia.org/wiki/Theodolite

https://en.wikipedia.org/wiki/Black

https://en.wikipedia.org/wiki/White

https://en.wikipedia.org/wiki/Red

https://en.wikipedia.org/wiki/Cedrus_deodara

https://en.wikipedia.org/wiki/Pine

https://en.wikipedia.org/wiki/Teak

https://en.wikipedia.org/wiki/Bamboo

https://en.wikipedia.org/wiki/Straight_line

https://en.wikipedia.org/wiki/Surveying


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.

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Figure 2.6 Plumb

Bob

Figure 2.7 Measuring Tape

Figure 2.8 Bar-coded Levelling Rod

https://en.wikipedia.org/wiki/Spirit_level


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’’

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88°52’50’

92°09’10’’

89°55’00’’

89°00’20’

B

A

C

D


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)

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D = K x s x (cosθ)2 + C x cosθ


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 (cosθ)2] + [C x cosθ]

= [100 x (1.475-1.355) x ¿2] + [0 x ¿

=12.00m

Distance A - B = [K x s x (cosθ)2] + [C x cosθ]

= [100 x (1.475-1.355) x ¿2] + [0 x ¿

= 12.00m

Average reading = (12.00m + 12.00m) / 2

= 12.00m

Distance B - A



Distance B - A = [K x s x (cosθ)2] + [C x cosθ]

= [100 x (1.445-1.325) x ¿2] + [0 x ¿

= 12.00m

Distance B - A = [K x s x (cosθ)2] + [C x cosθ]

= [100 x (1.453-1.322) x ¿2] + [0 x ¿

= 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 (co sθ)2] + [C x cosθ]

= [100 x (1.450-1.320) x ¿2] + [0 x ¿

= 13.00m

Distance B – C = [K x s x (cosθ)2] + [C x cosθ]

= [100 x (1.445-1.325) x ¿2] + [0 x ¿

= 12.00m

Average reading = (12.00m+13.00m) / 2

= 12.50m

Distance C - B



Distance C - B = [K x s x (cosθ)2] + [C x cosθ]

= [100 x (1.450-1.330) x ¿2] + [0 x ¿

= 12.00m

Distance C - B = [K x s x (cosθ)2] + [C x cosθ]

= [100 x (1.458-1.322) x ¿2] + [0 x ¿

= 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 (cosθ)2] + [C x cosθ]

= [100 x (1.455-1.325) x ¿2] + [0 x ¿

= 13.00m

Distance C – D= [K x s x (cosθ)2] + [C x cosθ]

= [100 x (1.445-1.330) x ¿2] + [0 x ¿

= 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 (cosθ)2] + [C x cosθ]

= [100 x (1.410-1.280) x ¿2] + [0 x ¿

= 13.00m

Distance D - C = [K x s x (cosθ)2] + [C x cosθ]

= [100 x (1.405-1.280) x ¿2] + [0 x ¿

= 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 (cosθ)2] + [C x cosθ]

= [100 x (1.480-1.355) x ¿2] + [0 x ¿

= 12.50m

Distance A – D= [K x s x (cosθ)2] + [C x cosθ]

= [100 x (1.488-1.350) x ¿2] + [0 x ¿

= 13.80m


= 13.15m

Distance D - A



Distance D - A = [K x s x (cosθ)2] + [C x cosθ]

= [100 x (1.408-1.282) x ¿2] + [0 x ¿

= 12.60m

Distance D - A = [K x s x (cosθ)2] + [C x cosθ]

= [100 x (1.415-1.280) x ¿2] + [0 x ¿

= 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’’

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B

A

C

B

92°09’50’’

A

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’’

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C B

89°55’40’’

D

C

89°01’00’’

D A


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

Determine the error of closure

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Algebraic sign convention to latitude and departure


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.

Adjust courses latitude and departure

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Error in departure = 0.000496

Error in latitude = 0.007896

EC Total error = 0.007911563

A’


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

Latitude correction

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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

Compute station coordinates

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N₂ = N₁ + Latitude₁₋₂E₂ = 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

5.0 Conclusion

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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.

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Accuracy = 1: (P/Ec)


6.0 References List1.0 Introduction"Untitled Document". Nptel.ac.in. N.p., 2016. Web. 5 July 2016. Fromhttp://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.hFundamentals 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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https://engineering.purdue.edu/~asm215/topics/bearings.html

http://nptel.ac.in/courses/105107122/modules/module9/html/28-5.htm

Theodolite report

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