Site Surveying Report 2 Traversing

Site Surveying (QSB 60103) Mr. Chai Voon Chiet

Wong De­ Vin (0319814)

Chin Khang Wei (0320728)

Tan You Liang (0320215)

Teh Qing Da (0318590)

Sim Chia Ting (0320932)

CONTENT PAGE

NO. DESCRIPTION PAGE

1 1.0 OBJECTIVE 3

2 2.0 INTRODUCTION

2.1 CLOSE TRAVERSE

2.2 OPEN TRAVERSE

2.3 OUTLINE OF APPARATUS

2.4 SETTING UP A THEODOLITE

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3 3.0 FIELD DATA (LOOP TRAVERSE)

3.1 ANGULAR ERROR AND ADJUSTMENTS

3.2 COURSE BEARINGS AND AZIMUTHS

3.3 COURSE LATITUDE AND DEPARTURE

3.4 STATION COORDINATES

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4 4.0 SUMMARY

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1.0 OBJECTIVES

The objective of traversing: ­

To determine the actual position of the boundary.

To authorize the position of the boundary line.

To determine the area encircled within a boundary.

To establish ground control for photographic mapping.

2.0 INTRODUCTION

Traversing is that type of survey in which a number of connected

survey lines form the framework and the directions and lengths of the

survey lines are measured with the help of an angle measuring

instrument and a tape or chain respectively.

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2.1 CLOSED TRAVERSE

Figure 1.1: Closed Traverse

When the lines form a circuit which ends at the starting point, it is known as

closed traverse. The closed traverse is suitable for locating the boundaries of

lakes, woods, etc and for survey of large areas.

2.2 OPEN TRANSVERSE

Figure 1.2: Open Traverse

An open traverse originates at a starting station, proceeds to its

destination, and ends at a station whose relative position is not

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previously known. The open traverse is suitable for surveying a long

narrow strip of land as required for a road of canal or the coast line.

2.3 OUTLINE OF APPARATUS

(a) Theodolite

Figure 1.3: Theodolite

A theodolite is an optical surveying instrument used to measure angles and

directions. The theodolite gives more precise readings; angles can be read to

fractions of a degree

(b) Tripod

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Figure 1.4: Tripod

The tripod is a device used to support any one of a number of surveying

instruments. The head of the tripod supports the instrument while the feet are

spiked to anchor the tripod to the ground.

(c) Tubular and Bull’s Eye Spirit Level

The spirit level is used to indicate the horizontal level. They have slightly

curved glass, which is incompletely filled with either spirit or alcohol.

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(d) Plumb bob

Figure 1.6: Plumb bob

A plumb bob is a weight with a pointed tip on the bottom and suspended from

a string, used as a vertical reference line. It is used to transcribe positions

onto the ground for placing a marker.

(e) Ranging rod

Figure 1.7: Raging rod

A 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.

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2.4 SETTING UP A THEODOLITE

Figure 1.8: Carrying out a traversing

STEP 1: Drive a surveyor's nail into the ground at the point where you want to

set up the theodolite. Angles will be measured from this point, as will

distances.

STEP 2: Set up the tripod legs with a length is approximately above the chest

level. Be certain to check that the hole in the center of the mounting plate is

located over the nail. Drive in the tripod leg into the ground by stepping on it.

STEP 3: Place the instrument on the mounting plate and screw in the

mounting knob beneath the instrument.

STEP 4: Adjust the theodolite to level by moving the tripod legs, using the

bull's­eye level. Fine­tune the adjustment with the leveling knobs on the

instrument.

STEP 5: Adjust the small sight, called the vertical plummet, at the bottom of

the theodolite. This sight allows you to make certain the instrument is

centered directly over the nail. Fine­tune the vertical plummet by adjusting the

knobs on the bottom of the theodolite.

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STEP 6: Look through the main scope and aim the crosshairs at the point to

be measured. Twist the locking knobs to hold the theodolite in position on the

exact point. View the horizontal and vertical angles in the viewing scope on

the side of the instrument.

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3.0 FIELD DATA (LOOP TRAVERSE)

Our field traverse is conducted in the staff car park near sports complex in our campus. The field we had is in quadrant. We put a mark for each station on four corner of our selected field. The actual angle and distance is not known at this point.

The following is our readings from the theodolite after the survey,

Point Station Sighted

Stadia Interior Angle Vertical Angle

Top Middle Bottom

A

D L ­ 142.6 L ­ 127.5 L ­ 112.5

86°15’00” L ­ 86°37’40”

R ­ 143.0 R ­ 127.5 R ­ 113.0 R ­ 266°45’40”

B L ­ 138.2 L ­ 127.5 L ­ 116.8

86°14’20” L ­ 86°04’00”

R ­ 138.1 R ­ 127.5 R ­ 116.9 R ­ 266°04’40”

B

C L ­ 143.5 L ­ 131.0 L ­ 118.5

94°33’20” L ­ 92°23’20”

R ­ 143.7 R ­ 131.0 R ­ 118.3 R ­ 272°24’00”

A

L ­ 141.6 L ­131.0 L ­ 120.4 94°33’20”

L ­ 86°03’40”

R ­ 141.7 R ­ 131.0 R ­ 120.3 R ­ 266°04’20”

C

B L ­ 148.1 L ­ 135.5 L ­ 123.0

98°08’20” L ­ 92°06’40”

R ­ 148.0 R ­ 135.5 R ­ 122.5 R ­ 272°05’20”

D

L ­ 146.5 L ­ 135.5 L ­ 124.5 98°01’40”

L ­ 86°35’40”

R ­ 146.5 R ­ 135.5 R ­ 124.5 R ­ 266°37’40”

D

A L ­ 154.5 L ­ 139.5 L ­ 124.5

81°21’20” L ­ 92°59’20”

R ­ 155.0 R ­ 139.5 R ­ 125.0 R ­ 273°00’00”

C

L ­ 150.0 L ­139.5 L ­ 128.5 80°58’40”

L ­ 91°57’40”

R ­ 150.4 R ­ 139.5 R ­ 128.7 R ­ 271°56’20”

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Step 1: Mean the values of Stadia and Angles The value of difference in stadia, vertical angle and interior angle were averaged from the left­hand side readings and right­hand side readings to get a closer accuracy. This table below shows the averaged value of our readings,

Point Station Sighted

Difference in Stadia, S (m) (Top ­ Bottom) Interior Angle Vertical Angle, θ

A D 0.301

86°14’40” 3°18’20”

B 0.213 3°55’40”

B C 0.252

94°29’20” ­ 2°23’40”

A 0.213 3°56’00”

C B 0.253

98°05’00” ­ 2°06’00”

D 0.220 3°23’20”

D A 0.300

81°10’00” ­ 2°59’40”

C 0.216 ­ 1°57’00”

Step 2: Calculate the vertical distance between the four points The vertical distance between each points is calculated with the formula.

, where, K S os²(θ) C cos(θ) D = × × c + × D = horizontal distance between survey point and instrument K = multiplying constant given by manufacturer of the theodolite, (normally = 100) S = difference between top stadia and bottom stadia = vertical angle of telescope from the horizontal line when capturing the θ

stadia readings C = additive factor given by manufacturer of the theodolite, (normally = 0)

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Upon obtaining the horizontal distance, a simple layout diagram was drawn for the traverse site. The distance between the point was averaged to get their mean value. Working Draft, Distance from point A → D = + 000 0.301 cos ² (3°1820") 1 × × ′

= 30.000 m Distance from point A → B = + 000 0.213 cos ² (3°5540") 1 × × ′

= 21.200 m

Distance from point B → C = + 000 0.252 cos² (2°2340") 1 × × ′ = 25.156 m

Distance from point B → A = + 000 0.213 cos² (3°5600") 1 × × ′ = 21.200 m

Distance from point C → B = + 000 0.253 cos² (2°0600") 1 × × ′ = 25.266 m

Distance from point C → D = + 000 0.220 cos² (3°2320") 1 × × ′ = 21.923 m

Distance from point D → A = + 000 0.300 cos² (2°5940") 1 × × ′ = 29.918 m

Distance from point D → C = + 000 0.216 cos ² (1°5700") 1 × × ′ = 21.575 m

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. Step 3: Field Angles Adjustment Compute the angular error and adjust the interior angles.

Station Field Angles

A 86°14’40”

B 94°29’20”

C 98°05’00”

D 81°10’00”

Sum of all angles, Σ 359°59’00”

The sum of the interior angles in this loop traverse must equal to,

= ( n ­ 2 ) x 180° , where n = number of sides

= ( 4 – 2 ) x 180°

= 360°

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The total angular error is

= 360° ­ 359°59’00’’

= 1°00’00’’

Therefore, the error per angle is

= 1°00’00” 4÷

= 0°00’15’’ per angle

Errors Correction,

Station Field Angles Correction Adjusted Angles

A 86°14’40” + 0°0’15” 86°14’55”

B 94°29’20” + 0°0’15” 94°29’35”

C 98°05’00” + 0°0’15” 98°05’15”

D 81°10’00” + 0°0’15” 83°10’15”

Sum of all angles, Σ 359°59’00” 360°00’00”

Step 4: Compute Course Azimuths The azimuths is traveling in clockwise direction starting from point A and travel back to the same point A.

Course Azimuths

Assume the line A ­ D is in a 180° straight line, A ­ B,

180°00’00” ­ 86°14’55”

93°45’05”

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B ­ C,

180°00’00” + 93°45’05” ­ 94°29’35”

179°15’30”

C ­ D,

179°15’30” + 180°00’00” ­ 98°05’15”

261°10’15”

The azimuth cycle 360° from the south to point A. D ­ A,

360°00’00”

Step 5: Latitude and Departure

Compute the course latitude and departure with, (a) LATITUDE = LENGTH x COS β (b) DEPARTURE = LENGTH x SIN β

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Working Draft, Path from point A → B,

Latitude = 1.200 cos (93°45’05’’) 2 × = ­ 1.3871

Departure = 1.200 sin (93°45’05’’) 2 ×

= 21.1546 Path from point B → C,

Latitude = 5.211 cos (179°15’30”) 2 × = ­ 25.2089

Departure = 5.211 sin (179°15’30”) 2 ×

= 0.3263 Path from point C → D,

Latitude = 1.749 cos (261°10’15’’) 2 × = ­ 3.3382

Departure = 1.749 sin (261°10’15’’) 2 ×

= ­ 21.4913 Path from point D → A,

Latitude = 9.959 cos (360°00’00”) 2 × = 29.959

Departure = 9.959 sin (360°00’00”) 2 ×

= 0

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The latitude and departure for each station is as followings,

Station Azimuth, β Length, L (m) Cosine β Sine β Latitude Departure A 93°45’05’’ 21.200 ­0.0654 0.9981 ­1.3871 21.1546 B

179°15’30” 25.211 ­0.9999 0.0129 ­25.2089 0.3263 C

261°10’15’’ 21.749 ­0.1535 ­0.9882 ­3.3382 ­21.4913

D

360°00’00” 29.959 1.000 0 29.959 0 A

Σ (Perimeter) 98.119

(∑Δy) 0.0248

(∑Δx) ­0.0104

Step 5: Error of closure and accuracy Determine the error of closure and accuracy; = ∑Δy² ∑Δx² = √ (0.0248)² + (0.0104)² = 0.0269 Hence, the accuracy is

= 1: (P/ Ec)

= 1: (98.119/0.0269)

= 1: 3647.5465 [> 1: 3000]

∴ ERROR ACCEPTABLE, proceed to adjustment

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Step 6: Adjust Course Latitudes and Departures The correction can be done with “The Compass Rule”:

= OR , where,ΣΔy] P L − [ ÷ × ΣΔx] P L − [ ÷ ×

and = the error in latitude or in departureΔy Σ Δx Σ = the total length or perimeter of traverseP = the length of particular courseL

Station Unadjusted Corrections Adjusted Latitude Departure Latitude Departure Latitude Departure A

­1.3871 21.1546 ­0.0053 0.0022 ­1.3924 21.1568

B ­25.2089 0.3263 ­0.0064 0.0027 ­25.2153 0.3290

C

­3.3382 ­21.4913 ­0.0055 0.0023 ­3.3437 ­21.4890

D

29.959 0 ­0.0076 0.0032 29.9514 0.0032

A

(∑Δy) 0.0248

(∑Δx) 0.0104

Check ­0.0248

0.0104

Check 0.0000

0.0000

Step 7: Station Coordinates Compute the station coordinates with,

N₂ = N₁ + Latitude₁₋₂

E₂ = E₁ + Departure₁₋₂, where, N₂ and E₂ = the Y and X coordinates of station 2

N₁ and E₁ = the Y and X coordinates of station 1

Latitude₁₋₂ = Latitude of course 1­2

Departure₁₋₂ = Departure of course 1­2

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Assuming the point A is on (100,100) coordinates,

Course Adjusted Latitude Adjusted Departure Station N ­ Coordinate

(Latitude ­ y axis) E ­ Coordinate

(Departure ­ x axis)

A 100.0000 100.0000

A ­ B ­1.3924 21.1568

B 98.6076 121.1568

B ­ C ­25.2153 0.3290

C 73.3923 121.4858

C ­ D ­3.3437 ­21.4890

D 70.0486 99.9968

D ­ A 29.9514 0.0032

A 100.0000 (checked)

100.0000 (checked)

A graph was plotted with the coordinates obtained for each station.

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Step 8: Table and Graph of complete traverse (not to scale)

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The complete graph of traversing

Traversing exact location on our field site

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4.0 SUMMARY

Four points A, B, C and D are being laid on the site respectively by

marking with liquid paper on the floor. The theodolite is being placed at the

first point, A. Then from point A, we measure the reading to point B and D

(set at zero degree). The angles of the points are basically taken from

left to right. After that turn over to measure from right to left.

The survey was done proceed to the remaining point B, C, and D. This

form a complete quadrant for the site survey. All the measurement was

recorded in a table. To ensure a correct measurement is obtained and

reducing the error, we do twice on the survey on each points.

Since our area is a four­sided polygon. Henceforth, we can deduce that

the total interior angle is 360° from the formula (n­2) x 180°. However, we

only managed to get a total interior angle of 359°59’00’’ as errors has

occurred while taking the readings.

Therefore, we have to make the adjustments by using distributing the

angular errors. Later, we proceed by getting the latitude and departure of

each point. After we found out that our reading accuracy is acceptable by

using the formula, 1: (P/ Ec) , with a value of 1:3647, we continue to

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closing up the point A and A’ by adjusting the latitude and departure of our

readings by using these two formulae, the compass rule: ­

[∑Δy]/ ∑ l Latitude l x Cumulative Length ( Latitude )

[∑Δx]/ ∑ l Departure l x Cumulative Length ( Departure )

After the adjustment, thus giving a complete quadrant on the site survey.

We are then continue to find the coordinates and plotting them on a graph,

this help us to get a better understanding on our site survey, with all the

detailed dimensions and measurements.

In conclusion, we have learnt how to use a theodolite in proper way and also

able to get a correct measurement. Our groupmates have also been very

helpful as this task cannot be carried out by one less person especially under

the scorching hot sun. Also special thanks to our Site Surveying lecturer, Mr.

Chai to be always there in the field to guide us and make sure that we carry

out the measurement correctly.

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