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Geodetic Triangulation – 2011

H.M Liyanage28/05/2012

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Geodetic Triangulation – 2011

ByH.M Liyanage

The report is submitted to the Faculty of Geomatics, Sabaragamuwa University of Sri Lanka in partial fulfillment of the requirements for the BSc. degree in Surveying Sciences.

Supervisors

Mr. N.M.P.M Piyasena

Signature of the Dean

Date

FACULTY OF GEOMATICSSABARAGAMUWA UNIVERSITY OF SRI LANKA

P.O. BOX 02BELIHULOYA 70140

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DisclaimerThis document describes work undertaken as part of a program of study at the Faculty of Geomatics, Sabaragamuwa University of Sri Lanka. All views and opinions expressed therein remain the sole responsibility of the author, and do not necessarily represent those of the university.

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Abstract

As the third year project work of the Faculty of Geomatics, triangulation 2011 task was launched and the geodetic spherical coordinates of selected stations were calculated. The triangulation project was involved with the establishment of the horizontal control point network in Southern province. This task was implemented to get knowledge about theories and practical applications which were under the triangulation.

The horizontal control point network was established by using Kadurupokuna, Karambagala, Hambantota tower, Gonadeniya, Kataragama peak and Haburugala. Kadurupokuna and Haburugala were pre-known stations by using Jackson report. They were situated as baseline. Other four stations were unknown. Precise theodolite was used to measure horizontal angles but we were unable to do the angle observation task because of large distances of stations. So the conventional method was unsuccessful. Therefore GPS observation method was conducted within a schedule. In conventional method angle observations were done by using precise theodolite. The least square adjustment theory was used to adjust the network of triangles. C++ programming language was used to write programs for calculating geodetic coordinates of the unknown stations.

Finally included angles were calculated with the co-ordinates of stations which were taken by using GPS observations. Then the co-ordinates were calculated again by using mid latitude formula. Theoretical knowledge, practical applications, working as a group, planning, organizing and leadership skills were greatly improved within this project. The whole procedure of the task will be described at the appropriate chapter. The suggestions and the conclusions are entered under the recommendation section. Therefore it can be followed for the development of the future triangulation tasks in SUSL.

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Acknowledgement

Firstly, my greatest thanks for Mr. K. R.M. U. Bandara, the dean of the Faculty of Geomatics of Sabaragamuwa University of Sri Lanka and Mr. N.M.P.M Piyasena who was head of the Department of Surveying and Geodesy, for providing the instructions and making the necessary arrangement to this dissertation. Secondly, my special thanks to Mr. P.G.V Abeyrathne, head of the Department of Surveying and Geodesy for giving initial guidance in the preparation of this dissertation and giving courage to finish this project. I wish to offer my sincerely thanks to the instructors of our group Mr. G.P Gunasinghe, academic staff of Faculty of Geomatics who gave us good practical knowledge, helped us to provide the apparatus at right time. Then, I would thank to all academic staffs and all non-academic staffs of the Faculty of Geomatics who helped us to success this practical session. Finally, I extend my grateful thank to my group members, for helping me so many ways by sharing their ideas and knowledge. Also I would like to thank to our junior brothers and sisters, who helped to do the triangulation 2011.

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Table of Content

01. Introduction……………………………………………………………………………………………1

1.1. Triangulation...............................................................................................................................1

1.2. History of Triangulation..............................................................................................................1

1.2.1. World History of Triangulation...........................................................................................1

1.2.2. History of the Sri Lanka Triangulation................................................................................1

1.3. Purpose of Triangulation.............................................................................................................2

1.4. Classification of Triangulations...................................................................................................2

1.5. Triangulation Program of Sabaragamuwa University..................................................................3

1.5.1. Triangulation History of Sabaragamuwa University of Sri Lanka.......................................3

1.5.2. Triangulation in 2010...........................................................................................................3

Unknown Station.................................................................................................................................5

1.5.3. Objectives............................................................................................................................6

1.6. Limitation of Triangulation..........................................................................................................6

1.6.1. General Limitation...............................................................................................................6

1.6.2. Practical Limitation..............................................................................................................6

1.7. Report Structure...........................................................................................................................7

02. Theoretical Background……………………………………………………………………………...8

2.1. Lay out of Triangulation..............................................................................................................8

2.2. Strength of figure.........................................................................................................................9

2.3. Field Observations.......................................................................................................................9

2.3.1. Angle Observations..............................................................................................................9

2.3.2. GPS Observations..............................................................................................................11

2.4. Least Square Adjustment...........................................................................................................13

2.5. Computation Procedure.............................................................................................................14

2.5.1. Calculation of Mean Included Angles................................................................................14

2.5.2. Calculation of Standard Deviation.....................................................................................14

2.5.3. Calculation of Weight Matrix............................................................................................15

2.5.4. Mid Latitude Formula........................................................................................................15

2.5.5. Calculation of length of side by using Sine formula..........................................................17

2.5.6. F Matrix.............................................................................................................................18

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2.5.7. Jacobian Matrix.................................................................................................................19

03. Methodology………………………………………………………………………………………….21

3.1. Initial Preparation......................................................................................................................21

3.1.1. Preliminary investigation...................................................................................................21

3.2. Organization of the program......................................................................................................22

3.3. Type of Signals..........................................................................................................................23

3.3.1. Signal Tower......................................................................................................................23

3.3.2. Identification Signal at night..............................................................................................24

3.4. Angle Observation & GPS Observations...................................................................................24

3.4.1. Angle Observation.............................................................................................................24

3.4.2. GPS Observations..............................................................................................................24

04. Results and Discussion………………………………………………………………………………26

4.1. Results.......................................................................................................................................26

4.2. Discussion..................................................................................................................................27

05. Conclusions and Recommendations……………………………………………………………… 29

5.1. Conclusions...............................................................................................................................29

5.2. Recommendations......................................................................................................................29

06. References & Bibliography…………………………………………………………………………32

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01. Introduction

In the introduction part of the report, there is a brief explanation about the background of the triangulation, situation of group practices and trig stations.

1.1 Triangulation

In this surveying method, we consider about well defined triangles on the earth’s surface. The required area is divided into triangles. Length of one side of triangle and its angles with the other two are measured and other sides can be calculated by trigonometrically. If the coordinates of any trig point, azimuth and length of any side of triangle are known, the coordinates of other triangulation points can be computed.

A number of control points are necessary to prevent accumulation of errors of surveyed area. By using geodetic surveying accurate control points for large area on the earth surface can be established. So the accumulation of error will become small.

The main object of Geodetic Surveying is to determine the relative or absolute positions very precisely on the earth's surface of a system of widely separated points. The relative positions of control points are determined by using the lengths and azimuths of lines by joining them. These points are given in terms of latitudes, longitudes and elevation above the mean sea level.

Base line is the one side of triangle whose length is predetermined and vertices of triangles are known as trig stations. In Sri Lanka, national geodetic surveying task carried out by Survey Department in Sri Lanka.

1.2 History of triangulation

1.2.1 World history of triangulation

At ancient time, European, Greek and other people of Egypt used triangulation concepts and the method of surveying by triangulation was first introduced by the Dutchmen Snell in 1615-17.

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1.2.2 History of the Sri Lanka triangulation

In Sri Lanka, the Triangulation was started in 1857 with the measurement of a base line of a triangle in Negombo. Subsequently angles of a scheme of triangles covering most of the southern half of the Island and connected to the Indian Triangulation by a narrow chain of triangles running roughly by way of Batticaloa - Trincomalee - Mannar - Delft were observed (www.survey.dept-slt.lk). The check was observed in Batticaloa. The triangles were adjusted and the geodetic latitude, longitudes were computed on the Everest ellipsoid plan co-ordinate using the Transverse Mercator projection, taking Piduruthalagala as the origin.During the middle of 19thcentury attempted to prepare a map of Sri Lanka. To fulfil this requirement the concept of triangulation was utilized to establish a systematic mapping. The Triangulation was started on 1857. The triangulation network had been expanded across the entire land area achieved a remarkable level of accuracy under the facilities, technology and instrument availability at that period. To do these task two base lines were measured in western and eastern part of the country. In 1892 triangulation was completed and co-ordinates were published. The triangulation network was recomputed and new values were published at 1930 after the development of surveying technology and modern instruments. The new geodetic net has been established using Tellurometer and Geodimeter during the period of 1850-1960. The spherical co-ordinates were transformed to grid co-ordinates for mapping purposes by using Transverse Mercator Projection.

1.3 Purpose of triangulation project

The Triangulation survey can be used for the various purposes.

Establishing precise and accurate ground control points for photogrammetric and large surveys

To determine the size and shape of the earth by observing latitudes, longitudes gravity and etc.

To take measurements of disfigurement of structures such as dams. To take measurement of deformations of structures such as dams. Precise horizontal control network can be established for different types of surveying tasks

such as large engineering projects. Some of these projects are ,

Horizontal controls for topographic surveys To fixed centerline for long line highways, tunnels, bridges etc. To fix the centre line, terminal points and shaft points for long tunnel. To fix centre line, piers and abutments of long bridges. For construction of building and public works of large extent. Control points can be transferred across large water bodies of hydrographic

surveying.

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1.4 Classification of Triangulation

Generally the triangulation systems are classified under three main types depends on the basis of accuracy and the purpose. They are;

1. Primary triangulation or first order triangulation.2. Secondary triangulation or second order triangulation.3. Tertiary or third order triangulation.

Primary triangulation

This is the highest order triangulation and it’s for very large areas. Primary triangulation provides principal frame work for the national control network for subsidiary triangulations. This type of triangulation is specially employed for the determination of the shape and size of the earth surface and for the small scale mapping purposes.Primary triangulation provides the most precise control points for secondary triangulation. This system generally used to provide the basic framework of horizontal controls for large area such as national network. Every precaution is taken in making linear, angular and astronomical observation. The primary triangulation system embraces the vast area (usually the whole of the country).

Secondary triangulation

This is done for running a second series of triangles by fixing points at close intervals inside the primary series of triangles. It contains of small well-conditioned triangles with less precise instruments. The triangles of secondary triangulation are smaller than the primary triangulation.

Tertiary triangulation

Third order triangulation is done for providing control points between stations of primary and secondary triangulation system. These triangles use to furnish horizontal control for collecting details for topographic or engineering surveys. The triangles are very small in comparison of the other two orders of triangulation and instrument with moderate precision may be used.

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1.5 Triangulation Program of Sabaragamuwa University

1.5.1 Triangulation History of Sabaragamuwa University of Sri Lanka

Survey students of Sabaragamuwa University have done the first triangulation task in 2001. It

has been done with minimum instrument capacity by the students in the first batch of the

Department of Surveying Sciences. The line of Hawagala and Kirioluhena used as base line. It is

also one side of triangle of Sri Lanka triangulation network. At the first time, 1st batch used new

Kopiyawatha as base point for triangulation task. From the 1st batch up to 10th batch Hawagala

and Kirioluhena used as base line. At the 2nd time of triangulation task was done in mid of the

year 2002 and Kirimaduhela used as base station. It was used up to triangulation task of 10 th

batch. Paraviyangala, Hawagala, Kirioluhena, new Welibissa, Randakadura and Kirimaduhela

were the triangulation stations. At the 3rd time of triangulation task was done in 2003 and

selected further some triangulation station such as St.Machel and Welihinna. At that time

Paraviyangala triangulation station was shifted down due to the difficulties to reach to the top of

the hill. Triangulation task of 4th batch was done in 2005. 5th and 6th batches were done

triangulation task in year 2006 and used new triangulation stations such as Rye-Wikiliya and

Welibissa. 10th triangulation tasks have been finished at present in 2011.

1.5.2 Triangulation in 2011

Triangulation task 2011 was carried out by the students of 2007/2008 batch in Faculty of Geomatics by dividing into six groups. This was the first triangulation task which has been done out of area in SUSL. Triangulation 2011 was done in Southern province in Sri Lanka. Selected triangulation stations for our task were the first order control points of national triangulation network. Haburugala and Kadurupokuna were selected as base line and the base station was Karabagala. Haburugala, Kadurupokuna, Karabagala, Gonadeniya, Hambantota Tower and Kataragama peak were used as triangulation stations.

Hambantota tower was allocated for our group.Task : Geodetic Triangulation 2011Our group no : 06Number of member : 09Coordinator : Mr. N.M.P.M. PiyasenaInstructors : Mr. G.P Gunasinghe Assistants : Two assistantsDuration : From 22.02.2011 to 03.03.2011

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All details of triangulation Stations should be entered here

The selected figure

Figure 1.2-Selected triangulation station

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Diagram can be added later (all station)

Kataragama Peak

Karambagala

Hambantota Tower

Haburugala

Kadurupokuna

Gonadeniya

Known stations

Unknown stations

Base line

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1.5.3 Objectives

The main objective of this task was to calculate spherical coordinates of four unknown stations using two known stations and angle observation.

The sub objectives are To compare the accuracy between GPS observation values and the calculated values. To get knowledge about the triangulation program. To get the management about various types of fields. To build up collaboration with various fields and societies.

1.6 Limitation of triangulation

1.6.1 General limitation

The distance between each triangulation stations was very large, because considered triangulation stations are the first order control points in national triangulation system.

Instrument sharing (GPS and PTL) and travelling in between trig stations were difficult due to large distances.

Angles between trig stations were unable to be observed because some trig stations could not be identified due to large distances.

This triangulation task was organized out of tract of SUSL Resources were limited Number of instruments such as GPS and Precise theodolite (PTL) was not sufficient for

triangulation task and power of PTL was not sufficient to observe large distances. Electric power for charging batteries, GPS and for other things could not be taken

quickly. Power of binoculars is not sufficient for observed large distance. The limited funds were allocated for the triangulation task from the university.

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In our station we had to face problems of electricity.

1.6.2 Practical limitations GPS instruments should be only used without obstacles from electric field and magnetic

field. The value of PDOP directly depends on the availability of satellite and accuracy is

decreased when PDOP value is increased. When increasing the GPS observation time, accuracy also increases.

1.7 Report structure Anyone who needs to get knowledge about triangulation task can be utilized this report. This report consists with five chapters.

Chapter 1This chapter deals with an introduction part of this report. It provides explanation about triangulation, history of triangulation, purposes and classification of triangulation, triangulation task in SUSL, objectives of triangulation as well as limitations about triangulation task.

Chapter 2The theoretical background of triangulation task including triangulation techniques, observation and computation procedure is given in this chapter.

Chapter 3 In this chapter, the methodology of the whole triangulation task 2011 is illustrated while focusing to initial preparation, organization of task, observation and calculations.

Chapter 4 This chapter deals with the results and analysis part of the geodetic task. All the final results and the decisions that are made by analyzing the results have been included here.

Chapter 5 In this Chapter all the difficulties and future recommendations for the task have been described.

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2.0 Theoretical Background

In this chapter, the theories belong to triangulation task, observations and computations are discussed.

2.1 Layout of triangulation

Arrangement of the series triangles is the layout of the triangulation. There are three basic types of layouts. They have mentioned in below.

Simple triangle in narrow chain

Figure 2.1: Simple triangulation in chain

Braced quadrilateral

Figure 2.2: Braced quadrilaterals in chain

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Centered triangle and polygon

Figure 2.3: Centered triangles and polygons

2.1 Strength of figure

The strength of the figure, thus, may be defined as a figure which gives the least error in the calculated length of the lines in the system due to the shape of triangle and the composition of the figures. The strength of the figure also depends on number of trigonometric condition, number of observation directions and magnitude of distance and angles. The accuracy of a triangulation system depends on not only the methods and precision used in making observations, but shape of the figure in the system. Therefore well-conditioned triangles must be used.

Although the best shape of the triangle is isosceles, an equilateral triangle is most suitable due to practical consideration. However the triangles which have an angle smaller than 30º or greater than 120º should not be taken to account.

The accuracy or relative strength of a triangle is expressed as a number which is denoted by R. If this value is small, the strength will increase. Distance angles of a triangle are the angles opposite to known side and the side which is to be computed.

Strength of each figure can be calculated by using following formula.

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D = the number of new directions observed

C = Number of geometric conditions

n' - Number of lines observed in both directions

n - Total number of lines

s' - Number of occupied stations

s - Total number of stations𝛿A, δ B = Difference per second in the sixth place of logarithm of the sine of the distance angles A and B of each triangle in the chain used.

2.3 Field observation

2.3.1 Angle observation

The main part of the triangulation is angle observation and it is used to calculate the included angles between trig stations. Accuracy of the triangulation directly depends on the accuracy of the horizontal angle observations. But, some trig stations could not be identified due to large distances between them and angle observation was unable to be done. Due to this reason, included angles were calculated by using GPS observations. Although angle observation was not done in the field, theoretical background is mentioned.

Horizontal angles are measured by using precise theodolite. When measuring the horizontal angles, various methods can be applied to increase the accuracy. They are,

1. Multiple numbers of observations.It is better to get several angle observations, instead of taking one observation per angle. Adjustment computation can be applied to get more accurate results.

2. Number of zeroSometimes there are some inaccurate graduations of the horizontal circle of the precise theodolite. So it is better to get angle observations for different zeros to eliminate these errors.

3. Face left and Face right observations. This will minimize the eccentric errors in the horizontal plate and vertical plate of the instrument.

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Figure 2.4: face left and face right observation

There are two types of general methods of observing angles in triangulation.

1. The repetition method

Figure 2.5: Repetition method

This method is used when angle is too small and specially for measuring the angle subtended by base at first station for extension. In this method, each angle is measured independently by multiplying it mechanically on the circle. Finally, the mean angle is calculated by dividing the multiple angles by the number of repetition. This method is used to secondary and tertiary work of triangulation.

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A

B

C

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2. The Reiteration method

Figure 2.6: Reiteration method

In this method the signals of the stations are bisected successively and a value is obtained for each direction at each of the several rounds of observations. The direction method is normally used for the primary work.

2.3.2 GPS (Global positioning system) observationGlobal positioning system (GPS) is the best technology in positioning at present. This is a satellite-based navigation system consisting of a network of 24/28 orbiting satellites. It is very fast, convenient and accurate. The accuracy of GPS can be taken up to millimeter level. In triangulation task 2011, only GPS observation was taken.

GPS is possible to determine three-dimensional positions with an accuracy of 5-10 meters worldwide and around the clock using simultaneous observations of 4 four GPS satellites to solve the positioning intersection equation dealing with position and PDOP value. PDOP value should be less than four for accurate readings. When take observations, two GPS were used as master and rover. Master will be permanently and rover will be kinetically. Lastly all observations were downloaded in computer software and compile and eliminate errors from master and rover station observations. Normally mask angle should be greater than 15º.

GPS is very expensive equipment. Especially in developed countries, more expensive and precise receivers are used by land surveyors to locate boundaries, structures, and survey markers and for road construction. Not only that GPS are used in 3D site plans to control automatically blades and buckets of construction equipment. Ground positioning can be determined at any location on earth at any time of the day or night. A minimum of satellites must be available to do the observations to solve the positioning intersection equations dealing with position.

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𝛼𝛽𝛽𝜃

B

C

D

E

F

𝛾𝜆A

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Component of GPS

There are three major segments in GPS system. There are,

1. Space segmentThe Space Segment of the GPS system consists of the GPS satellites. The satellites are placed on six orbital plains. These orbital planes making 55 degrees inclination to the equatorial plane of the earth; the altitude of each orbital plane is 20183Km. So the period of the each satellite is 12 sidereal hours. According to the latest setup, four to twelve satellites can be found above the horizon in any part of the world.

2. Control segmentThe control segment consists of five Ground Control Stations. The exact positions of those stations are known accurately. The master control station is situated in Colorado.

3. User segmentAnyone who used the GPS belongs to user segment. The GPS user segment consists of all civil and military users of the system. Except land surveyors, the number of other civilian users (Navigators, hikers’ scientists, GIS developers) uses GPS. It is capable of dynamic positioning and has applications in hydrographical surveying.

GPS Method for Surveying

1. Static MethodStatic method is the most reliable relative surveying method. In here, two or more

GPS receivers at two or more stations simultaneously receive signals from a minimum of four common satellites. Occupation time depends on the type of GPS receiver, the separation distance between receivers, the ionosphere activity, no of satellites & their geometry. Time duration is 15 min for dual frequency & 30 min for single frequency receivers.

2. Kinematic MethodIt provides to the user a productive and accurate method to establish relative

survey control points. Here, one or more reference receivers (master) remain fixed during the observation period and one or more remote receivers (rovers) are holding on the points in several minutes at each point. During this survey, master and rovers must continuously track a minimum of the same four satellites.

Positional Dilution of Precision (PDOP)

Positional dilution of precision value is used to express how favorable the satellite geometry is.

The more widely distributed the satellites in the sky is better for the accuracy.When visible GPS

satellites are close together in the sky, the geometry is said to be weak and the PDOP value is

high; when far apart, the geometry is strong and the PDOP value is low. Thus a low PDOP value

represents a better GPS positional accuracy due to the wider angular separation between the

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satellites used to calculate a GPS unit's position. Other factors can increase the effective PDOP

are obstructions such as nearby mountains or buildings.

From following table 2.2 describe about PDOP values and there accuracies.

Table 2.1 : PDOP values and there accuracies

3 Least square

adjustment

A least square adjustment is very important part of the triangulation task. This adjustment computation can be use used for condition equation or observation equation either in terms of azimuths or angles.

There are two methods for adjustment computation.

Method of variation of parameters Method of condition

Variation of parameters method was used in this Triangulation program.

When,n = Number of unknowns m = Number of observation If m > n, adjustment is possible to do.

According to Taylor series;

Where,

= The approximate value for observed quantities.

= The observed quantity.

= The residual of observation

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PDOPAccuracy of the

Measurements

<4 Excellent

4-5 Very good

5-6 Good

6-8 Fair

>8 Poor

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So;

All observation equations can be expressed matrix form as below;

This is the observation equation.Where,

= The Residual matrix

= The Jacobean matrix

= The Correction matrix

= The Error matrix

According to least square adjustment;

Where;

= The N Matrix

= The N Inverse matrix

= The Jacobean matrix

= The Jacobean transpose matrix

= The Weight matrix

= The t Matrix

= The Delta matrix

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The Delta matrix directly gives correction for unknowns. After taking corrections, unknowns and observed quantities can be adjusted.

4 Computation procedure

First of all, included angles and distances between trig stations were calculated by using indirect problem of mid latitude formula due to GPS observation.

Then Haburugala and Kadurupokuna were considered as known stations and other stations were considered as unknown stations.

2.5.1 Mid latitude formula

Mid latitude formula direct problem

Figure 2.7: Figure of mid latitude formula

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A

B

C

D

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Where;

Where;

The coordinates of point

The coordinates of point

a - The semi major axis of the reference ellipsoidb - The semi minor axis of the reference ellipsoide - The eccentricity of the reference ellipsoid

- The Longitude difference between points X and Y

- The Latitude difference between points X and Y

- The Azimuth difference between points X and Y

- The Mean meridian radius of curvature

- The Mean prime vertical radius of curvature

- The Mean Latitude of points X and Y

- The Azimuth from X to Y

- The Azimuth from Y to X

Mid latitude formula indirect problem

Known data:

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G

H

I

E

F

𝛥𝜆YAx’ AxPX

Q

AyS

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The coordinates of point

The coordinates of point

Unknown:

- The Azimuth from X to Y

- The Azimuth from Y to X

S - The length between X and Y

Equation (B)/Equation (A);

From equation (C) and (D);

From equation (A) and equation (B);

The length and azimuth of the line can be calculated by using following procedures.

1. Find from equation (G).

2. Find from equation (F).

3. Find from equation (E).

4. Find from equation (H).

5. Find from equation (I).

6. Find from equation (J).

7. Find from equation (K).

8. When solving above (6) and (7), the can be calculated.

9. From equation (L), S can be found.

2.5.2 Weight matrix

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J

K

L

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Weight of an observation is a measure of its relative worth compared to other measurements. Weights are used to control the size of corrections applied to measurement in an adjustment. Weight is inversely proportional to variance.

In 2011 triangulation task, angle observation was not done. So there are not variances. Therefore equal weights are used.

The weight matrix is;

2.5.3 F matrix

Where;

= The approximate included angles.

= The included angles calculated.

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2.5.4 Jacobian Matrix

Figure 2.8 Jacobian Matrix Figure

Jacobean Matrix for observed angles can be obtained by using above figure.

By simplifying Equation, we can derive following formula

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Fore Station (f)

Back Station (b)

Instrument Station (i)

N

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Where;T - Number of triangles

- Error in include angle- Azimuth from instrument station (i) to fore station (f)- Azimuth from fore station (f) to instrument station (i)- Azimuth from instrument station (i) to back station (b)- Azimuth from back station (b) to instrument station (i)

IF -Distance between instrument station (i) to fore station (f)IB - distance between instrument station (i) to back station (b) - Latitude of selected location

- Correction for latitude - Longitude for selected location

- Correction for longitude

From determined matrixes and simple operations we find the residuals of each coordinates

Find the Jacobean transpose matrix ( JT) ____________(2.7)Multiply Jacobean transposes and Weight matrix (JTW) _____________ (2.8)Find the T matrix (JTWF) ____________ (2.9)

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Find the N matrix (JTWJ) ____________ (3.0)Find the N inverse matrix (N-1) ___________ (3.1)Find the matrix Δ = N-1 T _____________ (3.2)

Find the Residuals matrix v = J Δ−F _______________ (3.3)Find the adjusted included angle = Observed angle+ Residuals matrix _______ (3.4)By using theories and Matrix operations we can find the final adjusted coordinate of the each trig station.

3.0 Methodology

To achieve this goal, it is necessary to follow a proper method for this triangulation task. The accuracy and total cost of the task depend on the methods which used for triangulation task.

3.1 Initial preparation

3.1.1 Computer program for triangulation

The computer program was written using previous triangulation data by using C++ programming language before begun the triangulation task 2011. Two weeks were allocated for this before beginning the field task.

3.1.2 Selection of triangulation layout/figure

The layout for triangulation task 2011 was selected including they are Karabagala, Haburugala, Kadurupokuna, Gonadeniya, Kataragama Peak, Hambantota Tower. Karabagala used as base point. Kadurupokuna and Haburugala were used as base line. In this session, triangulation stations were selected in southern area in Sri Lanka. This was the first time that the task had been done outside of the SUSL area.

While selecting the triangulation stations, the following factors were considered.

Inter visibility between stations Formation to well-condition triangles (angle >30degree & angle<120degree) Station should be easily accessible Availability of water resources Meteorological data

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Inter visibility check in office

Checking inter visibility in office is very important to achieve the success of the triangulation task because obstacles triangulation stations can be identified and necessary solution can be identified without going to field investigation. Cross sections were drawn between trig stations of Tangalle and Hambantota topography map sheets in 1:50000 scale. By using this data, inter visibility between trig stations were checked. The following figure explains the geometry of inter visibility by using a contour map.

Figure 3.8: Geometry of checking inter visibility by contour map

3.1.3 Collection of required information

Preliminary investigation is the most important part of the triangulation task to fulfill the task accurately, simply and economically. But it could not be done because of unavoidable circumstances before starting the field work. Therefore preliminary field investigation and field work were done in same time period. Information about new triangulation station was collected because it will be necessary to change trig station due to inter visibility.

3.2 Organization in triangulation task 2011

Triangulation is an important task which conducted by faculty of Geomatics of SUSL. Well organization is essential for this task. This program is not an easy one. The time period, number of instruments and extent of basic needs should be estimated and informed when organizing the task. Otherwise the tasks may get time consuming and more expensive. The funds also should be saved.

Important factors have to considered Duration of the work Total cost of work Basic needs such as water, food, transport, medicine

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Technical matters such as type of the monuments, type of signals, instruments

Before beginning the triangulation task 2011, following various authorities were informed. Divisional Secretariat Office of Sewanagala, Sooriyawewa, Hambantota, Tangalle,

Kataragama, and Weeraketiya. Police Station of Sewanagala, Sooriyawewa, Hambantota, Tangalle, Kataragama, and

Weeraketiya.

Important schedules used for triangulation task. Signal communication schedule Mirror signal communication schedule Precise theodolite schedule GPS observation schedule Schedule of vehicle for transferring instruments Communication schedule

Necessary documents used GPS observation sheet Diary

Important requirements Domestic purpose Necessary foods Medical purposes List of equipments for the practical task

3.3 Reconnaissance survey

3.3.1 Reconnaissance of field

Reconnaissance survey is the first step of any type of surveying task at the field. It was done in triangulation task to achieve following facts.

Availability of the monument of the trig station was checked.

Suitable places for the camp site were selected.

Water source near to the station was found.

A place to get electrical power to charge batteries for GPS was found.

Easy accessibility to each station for transporting instruments was discovered.

Inter visibility between stations was verified.

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3.3.2 Inter visibility check in field

Inter visibility between trig stations was checked in field by using mirror signals. Although mirror signals from Kataragama and Karambagala trig stations could be identified to Hambantota trig station. Kadurupokuna mirror signal could not be identified due to long distances. Mirror signal could not be communicated as the schedule because of unavoidable circumstances such as some monuments of the trig station were unable to be found easily.

3.4 Arrangement of Signal Tower and Camps

3.4.1 Signal tower

A signal with a light illumination was used for angle observation at night time. Therefore signal tower was established very precisely on the trig station and all angle observations were done due to its pressure lamps. The accuracy of the triangulation is mainly depends on the degree of accuracy. So the light signal should be given to the correct position on the trig station. The pressure lamps should be fixed vertically on the station. Signal towers were made using “L” irons and nuts for each trig station. They were made using light sections and it should be portable, because sometimes it should be removed for other tasks like GPS observations. Although one pressure lamp is used in normal triangulation, due to large distances between trig stations three or sometimes four pressure lamps were used in this task to get powerful illumination. Our station was situated on a tower in Hambantota town.

Figure 3.9: Signal tower

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Triangulation point

Plate used for centering and put lampPressure Lamp

Special guard due to heavy windy

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Signal tower must consist following characteristics.

Good height for clear visible to other stations. Keep enough space under the plate for setting the instrument and Surveyor’s work.

An ideal signal should consist following factors.

It should be clearly visible from a distance against any background. It should be provided easy accurate bisection by a telescope. It should be capable of being accurately centered over the station mark. It should be exhibited very little phase error of bisection of the signal.

Arrangement of Camps

Three camps were set for our group. One is for base camp, for stores and other one for the

observation camp.

We cleared the surrounding without destroying the order of the nature.

There are lots of scorpions insects in our camp side area. So we were very careful for that.

Our station was near Hambantota town. So there was no big difficult to fulfill our

facilities.

3.4.2 Identification of signals Mirror signal identification at day time

Mirror signals from Karabagala and Kataragama trig stations could be identified. But mirror signals from Kadurupokuna could not be taken due to large distances.

Signal identification at night

At the night time, signals from Karabagala could be identified using precise theodolite. But signals from Kataragama peak could not be identified. Even red polythene frame and wood frame were used to provide signal at the night.

3.5 Observation in field

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3.5.1 Equipment used Precise Theodolite with tripod GPS with all accessories Necessary items for construction of signal tower Binocular Lamps Mirrors Compass

3.5.2 Angle observation

Angle observations were unable to be measured because only one station (Karambagala) was identified by using precise theodolite.

3.5.3 GPS observation

The GPS observation was done mainly for the base line measurement and additionally to check the accuracy of the coordinate of all trig stations, but the angle observation was unable to be done in this triangulation task. So GPS observation was very important. It was done to get coordinates of each trig station. Four GPSs were used in this session. Two GPS were the master and one was the rover. Static method with triangle observation was used for this task. In this task Haburugala and Kadurupokuna was the base line and two GPS receivers were always kept in this stations while other two GPS were moved to other stations. GPS receivers which were kept in Haburugala and Kadurupokuna and any other trig stations were observed simultaneously. According to schedule for GPS observation, Leica GPS kit was used in Hambantota trig station.

4.0 RESULTS AND DISCUSSIONS

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4.1 Results

4.2 Discussion

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CONCLUSIONS AND RECOMMENDATIONS

5.1 CONCLUSION

The triangulation task 2011 was a group practical and started to establish the control points and find out the co-ordinates of the unknown points.

Mainly we had to involve with the initial preparation and organization, working together with group members according to the previously prepared time schedules, conduction of the operational stages and handling and the maintenance of the instruments and equipments carefully.

In this practical task we got experience in camping life, applying theoretical knowledge, night observation, GPS handling. We had to be very careful when reached and took instruments to the point because it was on the top of the tower. The tower was so ruined. Some placed had been broken. A ladder was used to climb on the tower. Water, electricity and other facilities were fulfilled with a quarters which was beside to our camp. There was a vacated building nearby our camp and it was used as our kitchen. We were able to buy our food daily from boutiques because we were near Hambantota town.

It was very important of organizing and work together as a team with collaboration, ability to take the correct decisions by discussing with team members, time management and working with fulfill responsibilities and courage to success the major practical task.

We were able to get a better knowledge about C++ programming language because the computer program to calculate unknown stations was written by using above language.

Triangulation survey is a traditional method in surveying. We followed the Jackson report to find the observed co ordinates of Kadurupokuna and Haburugala stations. In this practical task, first we applied the angle observation method, but signals from Kadurupokuna and Kataragama peak were not visible. Only Karambagala signal could be identified. Sometimes we used four gas lamps on the point to give a powerful illumination to other stations. So angle observation was not successed.

Therefore GPS observation task was launched within a schedule. Leica 5400 GPS kit was used for our observation task. Always reference receivers (Master) were fixed in Kadurupokuna and Haburagala as the base line. Other two GPSs were fixed simultaneously on two stations. Though

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the GPS is a worldwide accurate data collection system, the accuracy is mainly depending on the following factors. Such as, satellite geometry, satellite availability, weather conditions and etc.

5.2 Recommendations

We could unable to reach our goal successfully because we were unable to do angle observation. The reason for that was higher distance between trig stations. The other hand field investigation was not done before went to the field. Observation part and investigation part were done simultaneously. So it was better if field investigation had been done before.

It was good effort that the observation camps had done outside of the university area, but there must be a good pre preparation.

Survey Department has done this triangulation task successfully before. So I think we had to do the task well if we had more powerful instruments. It is better to do this task again for other students by supplying those high performed instruments for angle observations.

It was better if we were able to use a flash light instead to gas lamps or patrol maxes because we had to get a powerful illumination for our stations.

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REFERENCE AND BIBLIOGRAPHY

Websiteshttp://en.wikipedia.org/wiki/Triangulation

Books

Text book of Advanced Surveying.Edited by R. AGORFourth Edition: 1997Referred pages 152-309

Surveying (Civil Engineering Series)Edited by S K DuggalSecond edition: 2004Fourth reprinted: 2006Referred pages 20-68

Appendices

Appendix A: Schedule for communications

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Appendix B: Schedule for mirror signal

Date: - 23/02/2011

Time Signal receiving

01 02 03 04 05 06

Sig

nal

sen

din

g

09.00 am – 09.15 am 05 06 01 02

09.15 am – 09.30 am 02 01 04 03

09.30 am – 09.45 am 03 04 01 02 06 05

09.45 am – 10.00 am 04 05 01 03

10.00 am – 10.15 am 06 01

10.15 am – 10.30 am 05 06 01 02

10.30 am – 10.45 am 02 01 04 03

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Station No Station Name Student Name Contact No

01 Karambagala Bandara B.M 0718446285

02 Kadurupokuna Chathuranga K.A.M 0712155006

03 Haburugala Manuranga K.M.P 0712054224

04 Gonadeniya Prasad A.L.A.A 0719064951

05 Kataragama Peak Rathnayake R.M.P.B 0783149548

06 Hambantota Tower De Silva D.N 0718472386

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10.45 am – 11.00 am 03 04 01 02 06 05

11.00 am – 11.15 am 04 05 01 03

11.15 am – 11.30 am 06 01

Where,

01:- Karambagala02:- Kadurupokuna03:- Haburugala04:- Gonadeniya05:- Kataragama Peak06:- Hambantota tower

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Appendix C: Vehicle schedule for transferring instrument

Date Time From To Vehicle Instrument

22/02/2011

23/02/2011 6.00 am Karambagala Kataragama Lorry GPS

24/02/20116.00 am Kataragama Hambantota Double cab GPS

8.00 am Gonadeniya Kadurupokuna Crew cab TL03

25/02/2011

6.00 am Gonadeniya Karambagala Crew cab GPS

6.00 am Karambagala Hambantota Lorry

1.00 pm Hambantota Haburugala Lorry TL04

26/02/20116.00 am Kataragama Hambantota Double cab

10.00 am Hambantota Kataragama Double cab GPS

27/02/2011

6.00 am Gonadeniya Kadurupokuna Crew cab

6.00 am Kataragama Hambantota Double cab TL02

6.00 am Karambagala Hambantota Lorry GPS

1.00 pm Kadurupokuna Gonadeniya Crew cab TL03

28/02/2011

01/03/2011 8.00 am Gonadeniya Kadurupokuna Crew cab TL03

02/03/2011

03/03/2011

Night parking

Crew cab : GonadeniyaDouble cab : KataragamaLorry : Karambagala

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Appendix D: Schedule for GPS

Station Name

February - 2011

22 23 24 25 26 27

01 Karambagala G4 G3 G3

02 Kadurupokuna G1 G1 G1 G1 G1 G1

03 Haburugala G2 G2 G2 G2 G2 G2

04 Gonadeniya G3 G3 G3

05 Kataragama Peak G4 G4 G4

06 Hambantota Tower G4 G4 G3

Where,

G1:- Trimble 5700 Base KitG2:- Trimble5700 Rover kitG3:- Leica AT 502-01G4:- Leica AT 502-02

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Appendix E: Schedule for precise theodolite

Station Name

2011

February March

22 23 24 25 26 27 28 01

01 Karambagala PT01 PT01 PT01 PT01 PT01 PT01 PT01 PT01

02 Kadurupokuna PT03 PT03 PT03 PT03

03 Haburugala PT04 PT04 PT04 PT04

04 Gonadeniya PT03 PT03 PT03 PT03

05 Kataragama Peak PT02 PT02 PT02 PT02 PT02

06Hambantota

TowerPT04 PT04 PT04 PT02 PT02

Where,

PT01:- Precise Theodolite 01PT02:- Precise Theodolite 02PT03:- Precise Theodolite 03PT04:- Precise Theodolite 04

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Appendix F: Figure for computation

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Kataragama Peak (05)

Karambagala (01)

Hambantota Tower (06)

Haburugala (04)

Kadurupokuna (02)

Gonadeniya (03)

{ }

( )

Known stations

Unknown stations

Base line

Station number

Line number

Included angle number[ ]

[01][02]

[03][04]

[05]

[06]

[08][07]

[09]

[10]

[11][12]

[13]

[14]

[15]

[16]

[17]{01}

{02}

{03}

{04}

{05}

{06}

{07}

{08}

{09}

{10}

{11}

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Appendix G: Computer program for computation

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Appendix H: Included angles

Included Angle NoIncluded Angle

D M S

01

02

03

04

05

06

07

08

09

10

11

12

13

14

15

16

17

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Appendix I : Known coordinates

Trig StationLatitude Longitude

D M S D M S

Haburugala

Kadurupokuna

Appendix J: Approximate coordinates

Trig StationLatitude Longitude

D M S D M S

Karambagala

Gonadeniya

Kataragama peak

Hambantota tower

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Appendix K: Distance between trig stations

Line No From To Distance (m)

01 Karambagala Kadurupokuna

02 Karambagala Gonadeniya

03 Karambagala Haburugala

04 Karambagala Kataragama peak

05 Karambagala Hambantota tower

06 Kadurupokuna Gonadeniya

07 Gonadeniya Haburugala

08 Haburugala Kataragama peak

09 Kataragama peak Hambantota tower

10 Hambantota tower Kadurupokuna

11 Kadurupokuna Haburugala

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Appendix L: approximate azimuth of all lines

From ToAzimuth

D M S

Karambagala Kadurupokuna

Karambagala Gonadeniya

Karambagala Haburugala

Karambagala Kataragama Peak

Karambagala Hambantota tower

Kadurupokuna Karambagala

Kadurupokuna Gonadeniya

Kadurupokuna Haburugala

Kadurupokuna Hambantota tower

Gonadeniya Karambagala

Gonadeniya Kadurupokuna

Gonadeniya Haburugala

Haburugala Karambagala

Haburugala Kadurupokuna

Haburugala Gonadeniya

Haburugala Kataragama Peak

Kataragama Peak Karambagala

Kataragama Peak Haburugala

Kataragama Peak Hambantota tower

Hambantota tower Karambagala

Hambantota tower Kadurupokuna

Hambantota tower Kataragama Peak

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I Matrix ([approximate angle - observed angle] at 1st iteration)

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Jacobean matrix (at 1st iteration)

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E matrix (at 1st iteration)

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F matrix (at 1st iteration)

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Appendix M: Corrections for coordinates at the each iteration

Trig Station IterationLatitude Longitude

D M S D M S

Karambagala

01 0 0 -1.415758e-12 0 0 -1.415758e-12

02

03

04

05

Gonadeniya

01

02

03

04

05

Katargama peak

01

02

03

04

05

Hambantota tower

01

02

03

04

05

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Appendix N: Adjusted coordinates of unknown stations

Trig StationsLatitude Longitude

D M S D M S

Karambagala

Gonadeniya

Kataragama peak

Habantota tower

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Appendix O: Adjusted included angle

Included Angle NoIncluded Angle

D M S

01

02

03

04

05

06

07

08

09

10

11

12

13

14

15

16

17

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