GEODETIC TRIANGULATION-2014-taiko

GEODETIC TRIANGULATION 2014

P.G.C.C.Fonseka

27th

November 2014

Department of Surveying & Geodesy

Faculty of Geomatics

Sabaragamuwa University of Sri Lanka


F A C U L T Y O F G E O M A T I C S

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Geodetic Triangulation – 2014

By

P.G.C.C.Fonseka

FG 447

The report submitted to the Faculty of Geomatics, Sabaragamuwa University of Sri Lanka in

partial fulfillment of the requirements for the BSc. degree in Surveying Sciences.

Coordinator

Dr.Ranmalee Bandara

Supervisor

Dr.M.D.E.K.Gunathilake

FACULTY OF GEOMATICS

SABARAGAMUWA UNIVERSITY OF SRI LANKA

P.O. BOX 02

BELIHULOYA



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DISCLAIMER

This document describes work undertaken as part of a programme 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

This report includes information on project triangulation 2014 which was conducted by the

Faculty of Geomatics, Sbaragamuwa university of Sri lanka cooperated by the 2010/2011 batch

as a necessary practical program in year(III) semester(I) which had to be accomplished within

the given time period. For a geodetic survey the required horizontal control can be established by

triangulation, traversing or by a combination of both. However generally triangulation plays a

major role in establishing control points as it is preferred in hilly and undulated areas and stations

can be established within a comparatively large distance with only the basic requirement of

intervisibility. Triangulation is a rite of ascertaining the location of a point by measuring angles

to it from known points at either end of a fixed baseline, rather than measuring distances to the

point directly. The point can then be fixed as the third point of a triangle with one known side

and two known angles. The length of first line, which is measured precisely, is known as base

line. The other two computed sides are used as new base lines for two other triangles

interconnected with the first triangle. By extending this process, the measurements of further

interconnected triangles are taken. Coordinates of four unknown points were calculated with the

help of spherical coordinate calculation systems, adjustment computations and other relevant

theories, and also computer softwares such as Math Lab using two known points, in this case

Kirioluhena (1st order trig station) and Haawagala(2

nd order trig station).A precise theodolite was

used to measure the angles. Gas lamps were taken as a target for the night observations. However

GPS observations were also taken for the verification of precision. Besides the academic criteria

in organizing such project the practical deprival which had to be conquered, responsibilities and

team efforts were well maneuvered by the participants. Following chapters would explain the

procedure in a more detailed manner.



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ACKNOWLEDGEMENT

This project would not have been possible without the support of many people. The author

wishes to express his gratitude to the dean of Faculty of Geomatics,Sabaragamuwa university of

Sri lanka Dr.K.R.M.U.Bandara and Dr. H.M.I Prasanna, head of the Department of Surveying

and Geodesy for providing necessary facilities and information. Deepest gratitude to the project

coordinator Dr. Ranmalee Bandaara, Senior Lecturer Department of Surveying and Geodesy,

who was abundantly helpful and offered invaluable assistance, support and guidance without

whose knowledge and assistance this study would not have been successful. Special thanks also

to authors supervisor Dr.M.D.E.K Gunathilaka for his guidance and encouragement The author

would also like to convey thanks to Mr.T.I.Munasinghe instructor in Faculty of Geomatics for

consulting as well as strengthening the group members in both physical and mental manner The

author wishes to express his love and gratitude to his beloved batch mates, senior and junior

brothers for their greatest support and help especially to group members for sharing the

literature, practical skills and invaluable assistance throughout hard times. And the author would

like to make this a opportunity to express his regards to all the other academic and non-academic

staff member of the faculty of Geomatics for their help noticed or unnoticed.



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Contents 1. INTRODUCTION ...................................................................................................................... 1

1.1 Commencing of Triangulation ......................................................................................... 1

1.3 Triangulation in Sri lanka ...................................................................................................... 4

1.4 Triangulation in Sabaragamuwa University of Sri lanka ...................................................... 6

1.5 Project Triangulation 2014 .................................................................................................... 6

1.6 Objectives .............................................................................................................................. 8

2. MTHODOLOGY ...................................................................................................................... 10

2.1 Initial Preparations .............................................................................................................. 11

2.2. Preliminary Investigation ................................................................................................... 13

2.3 Inter visibility check in office ............................................................................................. 13

2.4 Reconnaissance Survey ....................................................................................................... 14

2.5 Organization of the program ............................................................................................... 15

2.6 Types of signals ................................................................................................................... 16

2.7 Observation ......................................................................................................................... 18

2.7.1 GPS Observations ......................................................................................................... 18

2.7.2 Angle Observation ........................................................................................................ 19

2.8 Computation Procedure and programming ......................................................................... 21

2.8.1 Computation procedure ................................................................................................ 21

2.8.2 Mean Included Angles and Standard Deviation…………………………………… ...23

2.8.3 Reduce Observed Directions and Distances to ellipsoid……………………………...23

2.8.4 Calculate approximate coordinates……………………………………………………23

2.8.5 Calculate approximate included angles and distances………………………………...25

2.8.6 Computer programming codes ..................................................................................... 25

3. RESULTS AND DISCUSSION ............................................................................................... 26

3.1 Results ................................................................................................................................. 26

1.2 Discussion ...................................................................................................................... 29

4. CONCLUTION AND RECOMMENDATIONS ..................................................................... 34

4.1 Conclusion ........................................................................................................................... 34

4.2 Recommendations ............................................................................................................... 35



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5. REFERENCES AND BIBLIOGRAPHY ................................................................................. 38

List of Figures

Fig 1.1 The sketch of the Belgian triangulation

Of Gemma Frisius from the 16th century 1

Fig 1.2 Simple triangles 3

Fig 1.3 Braced quadrilaterals 3

Fig 1.4 Centered triangles and polygons 3

Fig 1.5 Triangulation Network of Sri Lanka 5

Fig 1.6 Network of Trig stations – 2014 7

Fig 2.1 Triangulation Figure 2014 12

Fig 2.2 Cross-sections from contours 14

Fig 2.3 Observation tower 17

Fig 2.4 Polythene Cover 17

Fig 2.5 GPS Instrument Locations 19

Fig 2.6 Angle Observation Order 20

Fig 2.7 Face left and faces right observations. 20

Fig 2.8 Proposed Figure 22

Fig 2.9 Actual Figure 22



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List of Tables

Tbl 1.1 Information about the Stations 8

Tbl 2.1 Included Angles 13

Tbl 3.1 Given Data 23

Tbl 3.2 Known Station Coordinates 26

Tbl 3.3 Probable angles 27

Tbl 3.4 Angle Adjusted coordinates 27

Tbl 3.5 Processed GPS coordinates 28

Tbl 3.6 Comparison of coordinates 29

Tbl 3.7 Difference in coordinates 29

Tbl 3.8 GPS Accuracy 31



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List of Appendices

Appendix A-Corrections 39

Appendix B-B matrix 40

Appendix C-Weight matrix 41

[GEODETIC TRIANGULATION 2014]


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1. INTRODUCTION

1.1 Commencing of Triangulation

Measuring of the distance of two points is possible by making a line between them and by

placing a measuring rod along it – supposed the distance is not too long between our points.

As the distance becomes longer, this procedure starts to be complicated and expensive:

distances of more than a several hundred meters are very hard to measure this way. If the

terrain between our points is rough or impassable, this method cannot be applied at all. A

new method was introduced at the end of the 16th, early 17th centuries. Measuring a longer

distance can be made by measuring a shorter line and some angles. The first triangulation was

proposed by Gemma Frisius (Fig. 11), then in 1615, another Dutchman; Snellius

accomplished a distance measurement by triangulation between the towers of Alkmaar and

Breda (true distance 140 kilometers, throughout the Rhein-Maas delta swamps; Fig. 1.1).

During the campaign, he set up triangles with church towers at the nodes and measured the

angles of all triangles. Having these data, it was needed to measure only one triangle side to

calculate all distances between the nodes.

Fig. 1.1. The sketch of the Belgian triangulation of Gemma Frisius from the 16th century.



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1.2 Concept of Triangulation

In trigonometry and elementary geometry, triangulation is the process of finding a distance to

a point by calculating the length of one side of a triangle, given measurements of angles and

sides of the triangle formed by that point and two other reference points. Some identities

often used (valid only in flat or Euclidean geometry): The sum of the angles of a triangle is

pi rad or 180 degrees. The law of sine’s - The law of cosines - The Pythagorean theorem

Triangulation is used for many purposes, including surveying, navigation, metrology,

astrometry, binocular vision and gun direction of weapons.

Many of these surveying problems involve the solution of large meshes of triangles, with

hundreds or even thousands of observations. Complex triangulation problems involving real-

world observations with errors require the solution of large systems of simultaneous

equations to generate solutions.

The object of the Geodetic Surveying is to determine very precisely the relative or

absolute positions on the earth's surface of a system of widely separated points. The

relative positions are determined in terms of the lengths and azimuths of the lines

joining them. That positions are given in terms of latitude , longitude and elevation

above mean sea level. These geodetic points so, determined furnish the most precise

control to which a more detailed survey of intervening country may be referred. The

geodetic surveying is usually carried out by the Government Agency in Sri Lanka The

Survey Department.

Triangulation systems are classified according to the accuracy required for the horizontal

control. It depends on the type of survey, extent of the survey and purpose of the survey. On

the basis of accuracy and the purpose, the triangulation systems are generally classified as

under.

der triangulation.

.



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Primary triangulation

This is the highest order triangulation and is employed for very large areas. This provides

principal frame work for the national control network for subsidiary triangulations. This

grade triangulation is specially employed for the determination of the shape and size of the

earth surface and also for the small scaling mapping purposes.

Secondary triangulation

This is employed for running a second series of triangles by fixing, points at close intervals

inside the primary series of triangles. It consists of forming small well-conditioned triangles

with less precise instruments.

Tertiary triangulation

This is employed for providing control points between stations of primary and secondary

triangulation system, by running in a third series of triangles to furnish horizontal control for

details on a topographic survey. The triangles are of the smallest size in comparison with the

other two orders of triangulation.

Well - conditioned triangles

The arrangement of triangles in the layout and the magnitude of the angles in individual

triangles, affect the accuracy of a triangulation system.The shape of the triangle in which any

error in angular measurnments, has a minimum effect upon the length of the computed side,

is known as the well condition triangle.

Layout of the Triangulation

The arrangement of the various triangles of a triangulation series is known as the layout of

triangulation. A series of triangulation may consist of the following;

Simple triangles in chain (shown in figure1.2)

Braced quadrilaterals in chain (shown in figure 1.3)

Centred triangles and polygons (shown in figure 1.4)



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Figure 1.2: Simple triangles

Figure1.3: Braced quadrilaterals

Figure1.4: Centred triangles and polygons

1.3 Triangulation in Sri lanka

The triangulation network of Sri Lanka was in 1857 with the measurement of baseline in

Negombo, with a 100-foot chain of iron links under standard tension of 84Ibs. In 1859 a

check base was observed at Batticalo. In 1930 both bases were measured with an invar tape.

The triangles were adjusted and geodetic latitude and longitude were computed on the

Everest ellipsoid plane coordinates using Transverse Mercator projection with Pidurutalagala

as an origin.

Re-computation was done in 1893 and the values obtained were used until 1930.Again it was

modified in 1988 by observing few additional triangles. In 1989 again the authorities decided

to re-compute the whole triangulation network, re-measured the two bases and observing the

angle of one figure for adjusted. In 1935, they published the coordinates and other values of



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about 200 secondary, 510 minor, 1250 intersected, 100 and 110 check points for all future

triangulation or traverse.

Fig 1.5 Triangulation Network of Sri Lanka

The above triangulation system was not accurate enough to provide the required control for

surveys carried out by accurate instruments, such as electromagnetic distance measuring

equipment and total stations. The increasing demand to establish a national land information

system also paved the path to establish more precise geodetic control network.

Accordingly country's first high accurate Global Positioning System was procured in 1994.

By using the above Global Positioning System distance were measured between base stations

accurately in order to establish precise control network. The longest line measured was from

Jaffna to Matara with a distance of 417.26674 km to an accuracy of 3 centimeters.



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Finally the coordinates of all control points were computed and published in 1999 and the

average linear accuracy of the system was 1:790,000. This system was known as Sri Lanka

Datum 1999 (SLD 99) [3].

1.4 Triangulation in Sabaragamuwa University of Sri lanka

It was first initialized in 2001 as the 'Triangulation Program 2001'by the students of

Department of Surveying Sciences. The chosen station points were Kirimaduhela,New-

Kopiawatta,Kirioluhena,Kirimaduhela,Paraviyangala and Hawagala. As to fix the azimuth for

each line star observation sequences were also done. Hawagala and Kirioluhena were the

known coordinate control stations, which was used as the base line for the whole

triangulation process. These two points are included in the national triangulation network as

primary and secondary respectively. To perform a well-shaped triangulation network

additional stations suchas New-Paraviyangala, Kirimaduhela, Hawagala, Bogandeniyahena,

Wikiliya, Welihinna, Hatarabage, Mannanhinna etc. were taken. Since 2001 it was

continuously done up to the present 2014.

1.5 Project Triangulation 2014

The 2014 triangulation project was inaugurated by the batch of 2010/2011 starting on the 1st

of June 2014 and ending it successfully on the 10th of June 2014.The batch was sorted in to

six groups while six triangulation stations were chosen out of eight by considering the shape

of the network (the best figure was taken), intervisibility, participants, weather and

geographical conditions. The final trig points were Hawagala, New Paraviyangala,

Bogandeniyahena, Hatarabage, Kirimaduhela and Kirioluhena. Kirioluhena is a first order

and Hawagala is a second order trig point comprehended in the national triangulation

network which is maintained by the survey department of Sri Lanka .Hence the coordinates

are known the line between them was taken as the base line. The other station coordinates

had to be calculated through angle observations.



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Fig 1.6 Network of Trig stations - 2014

Our group contained 10 members and the given trig station was Hawagala.

Task : Geodetic Triangulation 2013

Our group no : 03

Number of members : 10

Coordinator and Supervisor : Dr.Ranmalee Bandara

Instructor : Dr.M.D.E.K Gunathilaka

Assistants : Two assistants

Duration : From 01/06/2014 to 10/06/2014



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Station Information Table

Name Order Height(m) Province District D.S. Division

Kirimaduhela 3st 635 Sabaragamuwa Ratnapura Imbulpe

Hawagala 2rd

1380 Sabaragamuwa Ratnapura Imbulpe

Kirioluhena 1rd

728 Sabaragamuwa Ratnapura Molamure

Bogandeniyahena 3rd

581.8 Uva Badulla Marangahawela

Hatharabage 3rd

749m Sabaragamuwa Ratnapura Imbulpe

New Paraviyangala 2nd

1638m Sabaragamuwa Ratnapura Imbulpe

Tbl 1.1 Information about the Stations

Hawagala Peak

Height : 1320m(MSL)

Temperature : 20°C

Province : Sabaragamuwa

District : Ratnapura

D.S. Division : Imbulpe

Gramasewa Division : Marathanna

1.6 Objectives

1.6.1 Major Objective

To find out the coordinates of unknown trig stations by using the triangulation concept.



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1.6.2 Minor Objectives

To practice real world GPS observation.

Comparison of GPS system coordinates and triangulation coordinates of same control

points.

To build up the collaboration with various fields and societies.

To manage the entire project according to the given time frame.

To develop a computer program for practical and calculation necessities.

1.6.3 General uses of a triangulation project are as follows

Establishing accurate and precise ground control points for photogrammetric and

large scale surveys.

To determine the size and the shape of the earth by observing latitudes and longitudes

gravity and etc.

To take measurements of disfigurement of structures such as dams

Precise horizontal control network can be established for different types of surveying

tasks such as large engineering projects. Also some as follows,

Horizontal control for topographic surveys,

To fix the centerline, terminal points and shaft points for long

tunnel

To fix centerlines for long line highways, tunnels bridges, etc.

To fix centerlines, piers and abutments of long bridges.

For construction of buildings and public works of large extent

To transfer control points across large bodies of water in hydrographical

surveys.

For finding the direction of the movement of clouds.

For the Detection of crustal movements etc.



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2. MTHODOLOGY

The whole process can be summarized into the following figure.

Primary Investigation

Field Observation Organizing of the Task

Triangulation

Budgets Field Assistants

Schedules Equipment Medical Needs

Smoke

Mirror

Inter visibility and selection

figure

Calculation

Angles GPS Star Observation

Informing legal

authorities

Preparing Office Field

Find azimuth Face Right

Face Left



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2.1 Initial Preparations

Precursory preparations consists selecting and confirming the most suitable figure of

triangulation stations to continue with the triangulation project. With the help of 1:50000

topographic map of Sri Lanka regarding the maps of Haputale and Blangoda area, six trig

stations were chosen out of eight by considering the following facts.

Triangulation stations should be inter-visible to each other. Therefore these stations

are selected on the top of high rise mountains.

The triangles which consist in the triangulation network should be well conditioned.

The arrangement of triangulation stations should be easy for the further triangulation

works. (ex : 1st order -----------> 2

nd order)

The access to the triangulation stations should be easy with the instruments &

equipments.

Stations should be useful for providing intersected points & also for subsequent detail

survey.

The line of sights among the triangulation stations should not be passing through the

industrial areas to avoid the irregular atmospheric refractions.

In a wooded area, the stations should be selected such that the cost of clearing &

cutting & building towers are lowest.

Triangulation stations should not be located in the urban areas.

Availability of water resources.

Meteorological conditions around the triangulation station located areas.

Safety of the participants in the particular area.

By using the AutoCAD software all possible figures were drawn by joining each station to

the nearest, considering inter-visibility at the office, and the most suitable was taken.



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By considering the factors that the selected figure Triangulation Station are as follows

Kirimaduhela KMH selected

Kirioluhena KOH selected

Hawagala HWG selected

Bogandeniyahena BGH selected

Hatarabage HB selected

New Paraviyangala PVG selected

New Kopiyawaththe NK not selected

Beragala North BN not selected

Fig 2.1 Triangulation Figure 2014



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Triangle Angles(degrees) Condition

1 85 52 43 Well-conditioned





Tbl 2.1 Included Angles

2.2. Preliminary Investigation

It is the process which determines the important decisions in a triangulation. The success of

the project, goals to achieve totally depends on the preliminary investigation which is

described in detail below. It can be categorized into filed and office investigation. Therefore

preliminary investigation is an important stage which one should pay high attention prior to

do a triangulation.

2.3 Inter visibility check in office

Conducting a triangulation project is a time consuming, expensive, and tedious a process. If

two required trigonometric stations are not visible to each other, such trigonometric stations

can’t be used for triangulation procedure. If it’s not checked in the office, that could cause

waste of time & money. Cross sections were drawn between trig stations using 1:50000

Balangoda (75) and Haputhale (76) topographic map sheets. Contours of the required areas

were taken into tracing papers along with spot heights. Using these sketches cross sections

between necessary trig points were drawn so that it could be checked as the topography

would not disturb the inter-visibility. However other obstacles are not possible to check

through this process The Following figure explains the geometry of checking inter visibility

by using a contour map. All the lines were clearly visible without any topographical

obstructions. One day was given for this process.



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Fig 2.2 Cross-sections from contours

2.4 Reconnaissance Survey

The theoretical calculations for inter-visibility had to be proven in the filed hence

circumstances such as tree branches, various constructions, which would intervene with the

line of sight for neighboring mountains, cannot be checked using topographic maps. Vehicle

schedules, food, informing germane authorities, accumulating necessary equipments and all

the other anterior steps were taken before the reconnaissance survey. Assigned six groups

were sent to the relevant trig stations. We were tasked for the Hawagala station .Inter-

visibility was checked using mirror signals using hand mirrors and with the help of sun rays.

It was strictly prohibited to use smoke signals. Magnetic compass and binoculars were used

to identify and confirm the signal. All the other stations were visible to Hawagala without any

obstruction.

In addition a field investigation was done since the place had to be used for 10 days in a

civilized manner. The road to Hawagala mountain trig point was cleared hence an exact road

was not available a root was marked by using white polythene straps so that others may not

get lost while finding the trig point, camping sites. Other facts such as water resources,

camping locations, precautions to avoid animal attacks, easy routs for carry the heavy

materials and also for access, condition of water resources, meteorological condition around



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the site were also take in to account as the successfulness of the whole program depends upon

these facts.

2.5 Organization of the program

The whole triangulation project was limited to a time frame of 10 days. So the task had to be

well prepared to avoid extra expenses and time. They were located far from the university

premises. Second trips could cost more money and time. Essential documents had to been

well prepared. Most of the trig points are located in forest areas far from civilized areas so

precautions had to be taken for the safety of participants and government authorities had to be

informed in case of legal responsibility. Most of the points were not easy to reach so other

available needs such as food and clothing along with tents had to be chosen well. The

available resources such as vehicles and instruments were limited. So to improve efficiency

schedules had to be prepared. Notice, task, direction and other necessary boards were

prepared by group members. Some of the equipment such as lamps, observation tower,

camping tents were provided by the university.

Main facts we focused on,

Duration of the survey.

Total cost for the project.

Water, foods, medicines and other day to day needs.

Necessary equipment for the task.

Transportation facilities in a case of an emergency.

Academic criteria, measurements and methods to observe.

Communication.



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Jurisdictions to be informed,

Divisional Secretariat Office Balangoda, Haldumulla, Imbulpe.

Gramaniladhari of each area.

Police Station of Balangoda, Pambahina, Kalthota.

Schedules to be prepared,

Vehicle for camp arrangement and removing, staff transportation.

Communication.

Transferring of Instruments.

Signaling and GPS, Theodolite observation time periods.

Necessary documents,

Angle observation sheet

GPS observation sheet

GPS transfer notebook

Diary

Important notes on work schedule for each day.

2.6 Types of signals

Signal Tower

Precise theodolites are used in night times to observe other trig stations. Since control points

require high accuracy a signal tower made with L iron bars was used, where a pressure lamp

lies on a wooden board was used so that the light source could be bisected at nights times

using the precise theodolite.



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Iorn Bars

Fig 2.3 Observation tower

Due to various light sources visible during observation period it was hard to hard to identify

the signal lamp. A board covered with red polythene was used to uniquely identify the rest of

the trig stations, by covering and uncovering the light source. Before observations this

procedure was done to roughly identify the location of other points.

Polythene cover

Fig 2.4 Polythene Cover

Plumb

Wooden Plate

used to keep

the lamp

Pressure Lamp



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2.7 Observation

Equipment Used

- Precise theodolite with tripod (SOKKIA YMIA 5650).

- GPS with all accessories (Trimble 5700).

- Binoculars.

- Observation sheets.

2.7.1 GPS Observations

Triangulation was practiced in an era where GPS technology was not born yet. However GPS

observations were done so that the final results from the triangulation process could be

compared with and the precision could be checked.

Four GPS instruments were used which have trademarks as Leica & Trimble. They were used

in the static mode and method of surveying was radial. Since Kirioluhena is a 1st order trig

point the master GPS or the reference GPS was stationed there while Hawagala was used as

the check station because it’s a 2nd order trig point of the national triangulation system.

Those two stations created the base line as the coordinates are known. These two instruments

were kept working during observations while other two instruments were shifted between

HB, BH, NP, KH stations. Observations were taken according to the schedule.WGS84 was

used as the reference datum. The cut-off angle was 15° and logging interval was 1s.Erstwhile

conditions were good. At every half an hour required readings (battery level, memory status,

pdop, number of satellites, etc.) were recorded on the observation sheet. The whole process

was completed within a one day.



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Rover

NEW-PARAVIYANGALA

2.5 GPS Instrument Locations

2.7.2 Angle Observation

This is the ultimate mechanism of triangulation. Instrument was handled with great since its

least measurement is 1 seconds, levelling and centering had to be done very precisely.

Different zeros method was used for observations; in this case eight zeros were used.

However it was slightly different from the standard method because after observing the last

station the face of the instrument was changed. Only horizontal angles were taken.NP was the

reference station. An illuminating device was attached hence the observations are taken

during night times. If a point was unable to bisect due to bad environment conditions, next

station was bisected leaving the impossible. However this neglected angle had to be located

from at least one data set in a possible day.

Maste

r

Check BOGANDENIYAHENA

KIRIOLUHENA

HAWAGALA

KIRIMADUHELA

HATHARABAGE

Rover

Rover

Rover



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Fig 2.6 Angle Observation Order

Fig 2.7 Face left and faces right observations.



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2.8 Computation Procedure and programming

2.8.1 Computation procedure

Calculation procedure follows several basic steps which are explained in the report further

with the appropriate details.

Here are the basic steps in order to compute:

Mean Included Angles and Standard Deviation

Reduce Observed Directions and Distances to ellipsoid

Calculate approximate coordinates

Calculate approximate included angles by using computed approximately

coordinate

Form the F-matrix

-Using mean latitude and longitude for the entire area, calculated M and N-

From the B-matrix

-After calculating all the correct observed angles and coordinates of unknown station-



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Before the field observation

Fig 2.8 Proposed Figure

After the observation alter the figure as bellow

Fig 2.9 Actual Figure



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2.8.2 Mean Included Angles and Standard Deviation

All included angles of the triangulation network figure were observed in angle

observations, each angle had been observed eight times and a mean value was calculated.

According to the calculated mean angles, standard deviations were calculated.

2.8.3 Reduce Observed Directions and Distances to ellipsoid

The horizontal angles were observed in field and then all observed angles should be

converted to the ellipsoid by following related equations. The reduced ellipsoid distances

between trig stations were taken from given co-ordinates (latitude and longitude). Directions

were reduced to the ellipsoid and height of target corrections were calculated by using related

equations.

To convert the normal section direction to the corresponding geodetic direction

equation,

𝛿₁ = − (𝑒2

12) (

𝑠

𝑛)

2

𝑐𝑜𝑠𝜑 ͚𝑠𝑖𝑛2𝛼₁₂

Height of target correction equation,

𝛿₂ = (ℎ

2𝑀)𝑒²𝑐𝑜𝑠²�͚�𝑠𝑖𝑛2𝛼₁₂

2.8.4 Calculate approximate coordinates

The following data was given

Station Latitude Longitude

Hawagala 6°43’8.06866” N 80°44’42.38747” E

Kirioluhena 6°37’16.66488” N 80°49’58.27704” E

Tbl 3.1 Given Data



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The geodetic azimuth from Hawagala to Kirioluhena- 138°02’50.2”

Using given two ccordinates azimuth of KOH to HW and distance of KOH to HW

were calculated using indirect problem in Gauss mid latitude Formula

Inderect problem - known(φ1, λ1, φ2, λ2) get (α12, α21, s)

tan (𝛼12 +Δ𝛼

2) = 𝑁𝑚

𝑐𝑜𝑠𝜑𝑚Δ𝜆

𝑀𝑚Δ𝜑𝑐𝑜𝑠Δ𝜆/2

𝑠 ∗ sin (𝛼12 +Δ𝛼

2) = 𝑁𝑚 𝑐𝑜𝑠𝜑𝑚Δ𝜆

𝑠 ∗ cos (𝛼12 +Δ𝛼

2) = 𝑀𝑚Δ𝜑𝑐𝑜𝑠Δ𝜆/2

(All letters have their general meaning)

Azimuths from KOH to other three unknown stations(HA,BH,KMH) were calculated

by using include angles and calculated azimuth

Then using the Spherical Sin formula and considering strength of figure of all sides of

the network was found.

Using, Bowring method latitudes and longitudes of all unknown stations were

calculated (Appendix A).

Direct problem - known (φ1, λ1, s, α12) get (φ2, λ2, α21)

𝜎cos ( α12 +Δα

2)/(aC)

𝜆2 = 𝜆1 +1

𝐴{tan−1(

𝐴 tan 𝜎𝑠𝑖𝑛12

𝐵 cos 𝜑1−tan 𝜎 sin 𝜑1 cos 𝛼1)}

𝐷 =1

2sin−1 [sin 𝜎 (cos 𝛼12 −

1

𝐴sin 𝜑1 sin 𝛼12 tan 𝑤)]

𝜑2 = 𝜑1 + 2𝐷 [𝐵 −3

2𝑒′2𝐷 sin (2𝜑1 +

4

3𝐵𝐷)]

𝛼2 = tan−1 [−𝐵 sin 𝛼12

cos 𝜎(tan 𝜎 tan 𝜑1−𝐵 cos 𝛼1)]

(All letters have their general meaning)



Page 25

2.8.5 Calculate approximate included angles and distances

Using the approximate coordinates, the approximate included angles and distances were

calculated (reverse of Mid Latitude Formula).

The radius of the meridian section (Mm) and prime vertical (Nm) is given by

𝑀𝑚 = 𝑎(1 − 𝑒2)/(1 − 𝑒2𝑠𝑖𝑛2𝜑)³̷₂

𝑁𝑚 = 𝑎/(1 − 𝑒2𝑠𝑖𝑛2𝜑)¹̷₂

The parameters of the WGS84 ellipsoid are given below

a=6378137 m

e²=0.00669437999014

2.8.6 Computer programming codes

The programming codes and the program was burned in the cd,



Page 26

3. RESULTS AND DISCUSSION

3.1 Results

The Triangulation Figure

The known coordinates, which are used to calculate the length of the base line.

Station Latitude Longitude

Hawagala 6°43’8.06866” N 80°44’42.38747” E

Kirioluhena 6°37’16.66488” N 80°49’58.27704” E

Tbl 3.2 Known Station Coordinates



Page 27

Most probable included angles,

Angle number Included Angle

Degrees Minutes Seconds

1 25 49 24.38

2 26 16 38.39

3 34 38 30.12

4 47 49 6.92

5 23 11 12.05

6 8 20 0.81

7 45 29 26.95

8 53 33 44.17

9 56 44 48.44

10 15 32 3.84

11 19 33 7.99

12 57 34 10.45

13 30 35 42.72

14 30 52 42.38

15 63 50 44.56

16 63 54 11.88

17 97 32 58.49

18 102 59 24

19 34 36 17.78

20 60 57 2.99

Tbl 3.3 Probable angles

Final Adjusted coordinates

This table gives the coordinate from the angular adjusted coordinates

Station Latitude (E) Longitude (N)

° ‘ “ ° ‘ “

New Paraviangala 6 43 46.90 80 45 44.39

Bogandeniyahena 6 43 05.70 80 39 41.04

Kirimaduhela 6 41 40.52 80 48 42.37

Hatarabage 6 38 59.75 80 45 44.39

Tbl. 3.4.Angle Adjusted coordinates



Page 28

Processed GPS coordinates

Tbl 3.5 Processed GPS coordinates

Degree Minute Second

Hatarabage

6 39 0.38732 N

80 45 44.79127 E

Bogandeniyahena

6 43 6.5809 N

80 51 58.46015 E

Kirimaduhela

6 41 40.5144 N

80 48 42.51194 E

New Paraviyangala

6 43 47.63566 N

80 47 13.19744 E



Page 29

1.2 Discussion

Comparison between Angular adjusted and GPS adjusted coordinates.

Station GPS Coordinates

Adjusted Coordinates

Latitude Longitude Latitude

Longitude

D M S D M S D M S D M S

Hatarabage 6 39 0.38732 80 45 44.79127 6 38 59.75 80 45 44.39

Bogandeniyahena 6 43 6.5809 80 51 58.46015 6 43 5.7 80 51 58.1

New-

Paraviyangala 6 43 47.63566 80 47 13.19744 6 43 46.9 80 47 12.44

Kirimaduhela 6 41 40.5144 80 48 42.51194 6 41 40.52 80 48 42.37

Tbl 3.6 Comparison of coordinates

Difference between Angular adjusted and GPS adjusted coordinates.

Tbl 3.7 Difference in coordinates

Station Coordinates Difference

Latitude

Longitude

D M S D M S

Hatarabage 0 0 0.64 0 0 0.4

Bogandeniyahena 0 0 0.88 0 0 0.36

New-

Paraviyangala 0 0 0.74 0 0 0.076

Kirimaduhela 0 0 0.01 0 0 0.14



Page 30

Observation weighting gives greater influence to the most precise measurements during the

network adjustment process. Larger standard deviations mean grater measurement

uncertainty and lower precision for the measurements which are then given less weight in the

adjustment. Less number of iterations also decreases accuracy. When calculating approximate

coordinates, the Bowring method was used in the indirect form, instead of Guess mid latitude

formula to prevent iterations. Strength of figure was calculated before applying spherical sine

rule to find the most appropriate values. When calculating the correct coordinate least square

method was applied hence it refers to the notion that would recommend to minimize the

squared error between the data, which are trying to approximate and some functions or class

of functions that are trying to approximate the data with.

According to the above shown comparison table there is a negligible amount of difference

between them. When considering precision, we can be satisfied about the calculated

coordinates.

Suitable stations were chosen by considering well-conditioned triangles. After the field

investigation it was found that KH and NP were not inter-visible due to some huge forest

trees. So the figure was altered according to those conditions. However because of bad

weather changes KH was not observed from HW trig point. So the final figure was deviated

from the figure that was included in the proposal. Instead of 23 angles only 20 angles were

observed and taken for calculations. Some datasets were rejected due to incompleteness.

Some were not consisted with zeros. All the distances between station were less than 2Km,

though it’s a negligible amount when considering with earths radius, the triangles were

considered as spherical triangles.

When creating cross sections using contour maps to check whether the topography would not

disturb the inter-visibility NP was not in 1:50000 map sheets. So a rough location was

selected and the contours were drawn. However the uncertainty was vanished only after field

verifications were done. Field verification process plays a major role in organizing the

Triangulation program. All the future calculation figures and organization of the practical for

instead vehicle schedules, food and other supplies, reservations, amount of men need for

work, whether to continue with the project or not, and all these facts are pre-planned using

the data observed from the reconnaissance survey. If the total program was organized and



Page 31

was ongoing, some necessary stations are not inter-visible, that would be a total waste of time

and money.

Though the calculated coordinates shows a negligible deviation from the GPS observed

coordinates it’s not a measurement of accuracy, it can be defined as a measurement of

precision because GPS instruments also have errors unique to the, some can be eliminated but

some are impossible to eliminate. Errors such as Satellite position errors, Satellite clock

errors, Multi path of ray, Atmosphere errors, Clock inaccuracies and rounding errors etc.

Before start observing from GPS instruments, the area was cleared from trees and reflective

objects so that multi-path errors would be minimized and to obtain a less cut-off angle. Hence

it was middle of a jungle huge electrical and magnetic fields were not be considered.

Tbl 3.8 GPS Accuracy

The precise theodolite had to be handled with great care. It contains much more sensitive

instrument parts. The least measurement is 1 second. So when observing a slight error could

make a great deal. It was kind of hard to do levelling and centering during night times,

without practice. When getting observations from a precise theodolite it also generate some

unique errors such as instrumental errors, human errors, atmospheric effects, Less number of

observations, Reading sets taken by several persons etc. To minimize the errors in theodolite

we practice following precautions, the errors due to the eccentricity of vertical axis are

eliminated by reading all the micrometers. The errors due to imperfect adjustments of the line

of collimation and horizontal axis are eliminated by taking both face observations. The errors

due to graduations are eliminated by reading the values of angles on different points of the

circle. The errors due to manipulation, effect of sun, wind and slip due to defective clamps

Ionosphere effects ± 5 meter

Shifts in the satellite orbits ± 2.5 meter

Clock errors of the satellites' clocks ± 2 meter

Multipath effect ± 1 meter

Troposphere effects ± 0.5 meter

Calculation- und rounding errors ± 1 meter



Page 32

are eliminated by taking half of the observations from left to right and other half from right to

left. The accidental errors due to bisection and reading are eliminated by taking number of

observations. And Errors in the graduated circle eliminated by taking different zeros, and

number of zeros. Imperfect bisections can occur because of several persons taking the same

data set. The eye sight from person to person differs. So only a one person should handle the

instrument at a time.

Some readings were omitted considering its variation from previous values. Completing a

one zero set both faces must be observed at one circle within ±5 seconds. Since the weather

was in an unfriendly manner it was really hard to observe other trig points. During this

weather condition, especially the wind it was very hard to maintain the centering and the

levelling of the precise theodolite. The observation tower and gas lamp were protected by

using covers from side to side. After eight days the observation tower was destroyed and the

reservation tents were torn apart. The gas lamp has to be well protected because it had a

chance of exploding.

Observations are done during night time is because during day times it’s hard to uniquely

identify the target since illuminating light sources are available everywhere. And the position

of the sun, humidity, refraction and other reasons the readings could be erroneous. However

even at night times it was kind of hard to observe the target by uniquely identifying it. So

night time would give more accurate results.



Page 33

Conventional Angular Measurement Method GPS Observation Method

Inter-visibility is essential between

the triangulation stations.

Consumes more time.

Need more laborers.

There are loads of human errors can

occur.

There are loads of advanced

mathematical computations.

Observations can be done only at

night time.

Less accurate then GPS observation

method.

Inter-visibility between triangulation

stations is not necessary.

No need of more laborers.

Very quick observation method.

There are lots of source of errors due

to;

Ephemeris

Satellite clock

Ionosphere

Troposphere

Multipath & receiver.

Much more accurate than

conventional method.

Observations can be done at any time

of the day

Besides from the academic criteria by organizing this project we could grasps number of

various experiences. Briefly, food, equipment, instrument managing and handling, social

skills how to deal with various types of people such as villagers, helpers, authorities, money

handling, time management and so on. Living in an uncivilized area with limited number of

facilities was one in a lifetime experience. Managing day to day work, distributing work

among ourselves and making them happen gave us a vast experience in personalities.

Whatever the circumstances safety was first. If sufficient instruments were provided the task

could have been finished in less time. Altogether the project triangulation 2014 was a

success.



Page 34

4. CONCLUTION AND RECOMMENDATIONS

4.1 Conclusion

Triangulation process is an outdated one. It is still practiced so that the participants could get

an experience on how the program is conducted and for academic purposes such as to ensure

that the learnt theories are used in reality. And also to practice in advanced calculations, to try

new solving methods. Experience in handling instruments during tight situations, tough

environment and social phases. To take responsibility, to handle people and goods etc. At the

end were able to handle both the precise theodolite and the GPS instrument in a much easier

manner.

When comparing the conventional and the modern method results acquired from the

triangulation method is nearly equal to the results obtained from the GPS observations.

Which means high accuracy can be acquired. But what we have to focus here is the

procedure. If the coordinates were to find out using GPS instruments the task would have

been finished in less than two days. The conventional method took ten days It is true that the

GPS instruments are much expensive than a precise theodolite but when considering the

whole task using modern technology is very much easier, less calculations, less expensive,

time consuming. So the final conclusion would be that using modern technology such as GPS

to find coordinates of unknown points is much wiser and most suitable.

The final coordinates of the known points which are NP, BH, KH, and HB were calculated

using observed angles. The project triangulation 2014 was a considerably successful one.



Page 35

4.2 Recommendations

A major drawback for the triangulation 2014 was the season of the year that it was chosen to

practice the program. June was not a suitable time period, most of the equipment was

damaged and some were lost, angles were very hard to observe due to mist and rains. So

before organizing such considerably large practical program the season has to be chosen very

wise using not only statistical data but also information from native villages that lives nearby

field sites. According to them February, March is the most suitable season for conducting

such program where the sky is clearer and the atmosphere is dry.

Provided instruments from the University were not sufficient, both precise theodolites and

GPS instruments. So instruments had to be changed from station to station. Schedules had to

be made. It was time consuming. If sufficient instruments were provided the total practical

program could have been finished in less days than it took. Transportation vehicles would

have been available for more purposes and less fuel cost. The given GPS instrument batteries

have exceeded its charging discharging cycles. So they get drained in less time periods and

needed to be charged accordingly. This is also a waste of time. So these instruments need to

be repaired and upgraded accordingly to the available technology. And also for some trig

stations telephone signals were very poor. And mobile phone call costs too much. So it’s

better if the University can provide a different method of communication such as walky-

talkies.

During field investigation the recommended signaling method was mirror signaling.

However due to bad weather condition and the azimuth of the sun it was hard to identify

signals from other stations. There are instruments that create smoke without igniting fire.

Such instruments could be used. Betwixt the observation process at night time, the

identification method was to cover and uncover the gas lamp using red and black polythene.

But in modern days light sources in such manner are displayed everywhere. It’s hard to

identify uniquely. Instead of this method illuminating rods, luminous devices can be used

even in thick foggy conditions. They are much easy to transport and since the source can be

uniquely identified, it would preserve a huge amount of time.



Page 36

To obtain high accuracy results from the triangulation process it requires advanced

mathematical calculations and referencing. It’s much easier if the given time period for office

work and calculations was increased a little bit. For the calculation process it’s much easier

and outpaced using Mat Lab instead of C++, since predefined functions are available. So it

would be much more practical if the university can provide an academic propulsion

regarding Mat Lab, a theoretical background for students. A revision of previous lectures;

regarding Geodesy. This is necessary for calculations.

A large time gap was there between the preliminary survey and the actual triangulation task.

For our task it was like more than two months. So a lot could happen between two months.

Environment conditions could change rapidly. Preliminary precautions, plans could be a total

waste of time if things changed. So the program should be conducted as soon as possible

after the reconnaissance survey is finished.

Getting GPS observation was not a part of triangulation. It was done only so that the

precision could be checked and for more field experience. But hence there is no major

observation task done during day time its better if there observations which are done by the

precise theodolite could also be done using total stations and distances could be measure

using EDMs so that all these readings could be compared with each other and a person could

get more academic knowledge about these type of field work. Furthermore horizontal angles,

distances and coordinates could also be recorded for advanced studies. Triangulation is a

process that’s not practiced in the current world, but it’s done here because students could

gain more experience and knowledge theoretically and practically. For precise results star

observations also have be done in finding azimuths. So it’s better to add star observations

also for the practical task so that a participant could gain more comprehension.

Another problem we faced was that due to strong wind the mantle of the gas lamp gets

damaged. The outer core cracks when water is touched such as in rainy conditions.

Sometimes the available gas is not sufficient. In these conditions there is a possibility for the

lamp to explode which would put all the nearby students in danger. And also this caused

erroneous observations for other trig points. It’s much healthier if the university can provide

light sources which are not affected by wind, rain etc. Such as powerful lamps which works

with battery power.

These trig stations are far from civilized areas. Natural hazards can occur at any time, such as

forest fire, landslides etc. Animal attacks can happen at any moment. So in these tight



Page 37

situations decision making is what makes the whole situation reliable. It’s wiser if the

participants can have a training session on how to face these kinds of hazards. Medical

treatment such as vaccination for infections, diseases should be given to participants for their

protection. When living in such condition cleanliness plays a major role. Much more

powerful cleaning chemicals can be used. And also its better if the university can provide

fumes and creams which would give protection from various insects such as mosquitoes,

leaches etc.

Mostly these calculated coordinates are not used for any other purposes. If these coordinates

can be used for other different kind of field practical programs conducted by the Faculty of

Geomatics, these coordinates would automatically be checked repeatedly and a value will be

added for our final results. The location of the triangulation network should be different from

place to place so that the real time experience could be gain. Or else it would not be fresh and

observations can be copied. Another reference station can be added so that high accuracy can

be obtained. Modern technology has given more advanced instruments, so instead of

practicing outdated methods its more useful if this project can be conducted using those types

of instruments in a much wider range.



Page 38

5. REFERENCES AND BIBLIOGRAPHY

Dr.Punmia,Ashok k. Jain and Arun K. Jain,(2005).SURVEYING VOL

II.(15TH

ed.).JODAPUR RAJASTAN, MUMBAI MAHARASHTRA,

JODAPUR RAJASTAN.

Richard H. Rapp(1991),GEOMETRIC GEODESY PART 1,Columbus Ohio.

TRIANGULATION AND TRILATERATION www.newagepublishers.com/samplechapter/001033

TRIANGULATION en.wikipedia.org/wiki/Triangulation

Adjustment computations statistics and Least Squares in Surveying and

GIS,(1997)

Edited by: Paul R. Wolf and Charles D. Ghilani ,(pages 169-199)

http://www.newagepublishers.com/samplechapter/001033



Page 39

Appendices

Appendix A-Corrections

Correction

Hatharabage -3.33E-06

1.39E-05

Kirimaduhela -4.90E-06

-3.22E-06

bogandeniya 2.81E-06

-7.59E-07

new parawiyangla -1.37E-06

-1.67E-06



Page 40

Appendix B- B matrix

-693.94 0 0 0 -280.368 0 0 0 0 0 0 203.562 0 0 0 716.4298 0 0 181.3799 203.562 0 0 -526.456 716.4298 0 0 -318.337 897.4128 0 0 -142.777 -383.795 0 0 421.8912 897.4128 0 0 -387.041 383.7951 0 470.4052 257.5131 0 0 69.45961 -64.4913 0 0 56.02946 719.993 -775.984 0 974.3011 106.4345 -1080.74

207.7287 -983.802 0 775.9842 -652.656 -428.08 0 -1080.74 -207.729 -1093.4 0 0 652.6559 -313.981 0 0

0 1301.166 -475.564 0 0 -338.557 -3.36269 0 0 0 -475.564 -765.908 0 0 3.362689 -275.389

-189.986 0 0 765.9079 -795.569 0 0 275.3894 -397.715 207.7626 0 0 -142.912 -652.539 0 0 427.9985 159.0479 0 -635.785 88.34703 -652.539 0 564.1514 58.21299 0 0 635.7852 844.6754 0 0 -564.192 635.7271 0 0 -839.347 -564.308 0 0 -152.238 -203.531 0 897.4555 -693.851 0 0 -383.678 1100.224

0 776.0398 897.4555 -1673.4 0 1080.619 -383.678 -696.94 0 -775.984 0 -10.0763 0 1080.619 0 -805.347

-635.727 0 0 -130.123 564.3079 0 0 -839.58



Page 41

Appendix C-weight matrix

052869.87605 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 39497.99786 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 026521.20576 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 36142.54395 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 50977.34053 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 71102.26193 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 32763.61220 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 50921.88515 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 43339.13715 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 7714.071178 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 065880.29314 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 096984.60604 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 028224.84762 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 20196.347030 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 981.8885415 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 55473.87710 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 56315.825040 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 019439.73235 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 039210.77925 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012366.10011 0 0 0

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