TRIBHUVAN UNIVERSITY Kathmandu Engineering College Kalimati, Kathmandu Report No. 2062/BCE/Survey (EG625) A Report on Survey Camp 2064 at NEATC, Kharipati (For the partial fulfillment of the requirement for the Bachelor’s Degree in Civil Engineering) Submitted By: Submitted to: Group: J The Department of Civil Engineering Rabindra Subedi - 62109/BCE/062 Kathmandu Engineering Subash Thapa Magar - 62115/BCE/062 Kalimati, Kathmandu Nawin Kumar Acharya - 62106/BCE/062 Sukriti Suvedi - 62118/BCE/062 Bhuban Singh - 62084/BCE/062 29 th Jestha 2065
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TRIBHUVAN UNIVERSITY
Kathmandu Engineering College Kalimati, Kathmandu
Report No. 2062/BCE/Survey (EG625)
A Report on Survey Camp 2064 at NEATC, Kharipati
(For the partial fulfillment of the requirement for the Bachelor’s Degree in Civil Engineering)
Submitted By: Submitted to: Group: J The Department of Civil Engineering Rabindra Subedi - 62109/BCE/062 Kathmandu Engineering Subash Thapa Magar - 62115/BCE/062 Kalimati, Kathmandu Nawin Kumar Acharya - 62106/BCE/062 Sukriti Suvedi - 62118/BCE/062 Bhuban Singh - 62084/BCE/062
29th Jestha 2065
ABSTRACT
The main objective of the Survey Camp organized by the civil department is to provide an opportunity to consolidate and update the practical & theoretical knowledge in engineering surveying in the actual field condition and habituate to work in different environment with different people. In this survey camp we are supposed to survey a given plot in all its aspect and work on road and bridge alignment and prepare a topographic maps, maps of road and bridge alignment with proper cross section and profile and its topography fulfilling all technical requirements.
This survey camp helped us to build our confidence to conduct engineering survey on required accuracy and we assume that it would be of great use in our future engineering works.
Group J
PREFACE This survey report is truly based on our knowledge gained from the two weeks field trip organized for the partial fulfillment of the requirement for the Bachelor’s Degree in Civil Engineering encoded as EG625CE as per our syllabus in third year first part. This surveying has been able to impart us the great opportunity to consolidate and review the practical and theoretical knowledge on surveying, which we gained in second year.
We have been able to achieve the true objectives of survey and upgrade the knowledge as handling of the instrument, working procedure, problem solving and field booking precisely. This survey camp gave us the practical knowledge of overcoming the technical difficulties and developing a skill in tackling it. It encouraged us to cope with the team members, as the surveying involved all the members equally during the field procedures, calculations and plotting and report preparations.
Actually this survey camp promoted us in developing the ideas of the major and minor traversing, RL transformation, detailing, detailing by plane tabling, topographical map preparation, road and bridge site surveying, curve setting, orientation etc.
In this way the survey camp was really fruitful and it enhanced to enrich our confidence to carryout engineering survey on required accuracy in near future.
ACKNOWLEDGEMENT
This report is the outcome of our work done in two weeks survey camp in NEATC, Kharipati, and Bhaktapur. This camp was organized by Kathmandu Engineering College, Department of Civil Engineering, for the students of 2062 Batch.
We worked on the various aspects of surveying such as topographical and road surveying in NEATC, Kharipati Area and bridge Site at Punyamata River Panauti, Kavre. Our group consisted of five members whose names are listed on the cover page. We worked together as a group in the survey camp – 2064.
We express our great thanks to our respected teachers Er.Narayan Pd. Subedi, Er.Pawan Gautam, Er. Arjun Pd. Parajuli, Er. Ramesh Subedi, Er.Rajendra Soti, Er. Rangan Bhattrai who were very supportive and played a key role in successively finishing the survey camp. We are also thankful to the Department of Civil Engineering, which gave us such a golden opportunity to gain the knowledge on different aspects of surveying that will definitely prove beneficial in every step of the civil engineering projects in near future. We would like to convey our sincere thanks to the management of our college for choosing such a healthy and creative environment for teaching and learning practice for such a long period of fifteen days.
We also would like to thank to the survey camp staffs Mr. Dipendra Shrestha, Mr. Deepak Upreti, Mr. Santosh and Mr. Ram Krishna for their great help during the camp.
Our heartily thanks goes to all other seniors and individuals who helped and guided us with the experiences they had, for the preparation of the Survey Report.
We are also grateful to the very friendly Kharipati natives and the staffs of the NEATC who indirectly helped us for the completion of the project.
Last but not the least we must thank Ar. Chand S. Rana, the principal of KEC for encouraging us during our camping and also the KEC teachers’ team for participating in the DOHORI and Pop Song singing program and on the last evening of our camp for happy ending of our tiresome but very memorable camping.
And at last we would like to thank the readers for their concern in our report. This report is the outcome of our huge and continuous efforts for about 4 months including the survey period.
Group - J
TABLE OF CONTENT ABSTRACT PREFACE ACKNOWLEDGEMENT LIST OF TABLES ……………………………………………………………………………… 1
I. INTRODUCTION……………………………………………………………………… 2 1.1. Background…………………………………………………………………....... 2 1.2. Objectives………………………………………………………………………. 3 1.3. Project Area……………………………………………………………………. 4 1.4. Norms………………………………………………………………………….. 5 1.5. Working Schedule……………………………………………………………… 7
II. TRAVERSING………………………………………………………………………… 9
2.1. Introduction ………………………………………………………………. …… 9 2.2. Principle of theodolite survey ……………………………………………… 9 2.3. Methods of theodolite traversing…………………………………………… 9 2.4. Latitude, Departure and closing error……………………………………… 10 2.5. Balancing of consecutive co-ordinates ……………………………………. 11 2.6. Objective ………………………………………………………………..….. … 11 2.7. Major Traverse ………………………………………………………………… 11
2.7.2.1. Reconnaissance……………………………………………….. 11 2.7.2.2. Pegging………………………………………………………….12 2.7.2.3. Linear measurement…………………………………………… 12 2.7.2.4. Angular measurement………………………………………… 12 2.7.2.5. Correction of internal angles……………………………………12 2.7.3.6. Bearing Computation of Traverse legs………………………… 12 2.7.3.7. Coordinate Computation of Traverse Stations………………… 13 2.7.3.8. Plotting of Major Traverse Stations…………………………… 14 2.7.3.9. Sample Calculation…………………………………………… 14 2.7.3.10. Final Co-ordinate sheet……………………………………… 14
2.8. MINOR TRAVERSE………………………………………………………… 14
2.8.1. Introduction…………………………………………………………. 14 2.8.2. Methodology………………………………………………………… 14 2.8.2.1. Reconnaissance………………………………………………… 14 2.8.2.2. Marking and fixing control points…………………………… 14 2.8.2.3. Measurement of Traverse Legs………………………………… 14 2.8.2.4. Measurement of Interior Angles……………………………… 14 2.8.2.5. Bearing Computation of the Traverse Legs…………………… 15 2.8.2.6. Coordinates Computation of Minor control points……………… 15 2.8.2.7. Plotting of Minor Traverse Stations…………………………… 15 2.8.3. Instruments used………………………………………………… 15 2.8.4. Final Co-ordinate Sheet………………………………………… 15 2.8.5. Other Observation and calculation Sheet……………………… 16
3.4. Two Peg Test…………………………………………………………………17 3.4.1. Introduction………………………………………………………………17 3.4.2. Observation……………………………………………………………… 17 3.4.3. Level Transfer from B.M. to T.B.M………………………………………18
3.4.3.1. Observation and calculation……………………………………19 3.4.4. Level transfer from T.B.M. to Major Traverse ………………………… 19
3.4.4.1. Observation and Calculation………………………………… 19 3.4.5. Level transfer from Major to Minor Traverse……………………………..19
3.4.5.1. Observation and calculation……………………………………19 3.5. Reciprocal Leveling……………………………………………………………19
IV. TACHEOMETRIC DETAILING…………………………………………………….20 4.1. Introduction……………………………………………………………………20 4.2. Objective……………………………………………………………………….20 4.3. General theory & Methodology…………………………………………… 21
4.3.1. Measurement and Data……………………………………………………21 4.3.2. Field procedure ………………………………………………………… 21 4.3.3. Calculation ………………………………………………………………. 21 4.3.4. Accuracy and Precision……………………………………………………21 4.3.5. Instrument…………………………………………………………………22
4.4. Contouring……………………………………………………………………..22 4.4.1. Methods of Locating Contour…………………………………………….22 4.4.2. Interpolation of Contours…………………………………………………23
4.5. Conclusion…………………………………………………………………… 24 4.6. Observation and calculation…………………………………………………. 24
V. ORIENTATION……………………………………………………………………. 25 5.1. To determine the position of unknown point by the method of Intersection…25
5.2. To determine the unknown position of Instrument ………………………….31 5.2.1. Instruments Required……………………………………………………31 5.2.2. Objectives……………………………………………………………….31 5.2.3. Theory…………………………………………………………………...34 5.2.4. Observations And Calculations…………………………………………32 5.2.5. Result…………………………………………………………………... 38
8.7.7.1. Observation and Calculation………………………… 58 8.8. Observations and Calculations……………………………………… 59 8.9. Computation And Plotting………………………………………… 59 8.10. Comments And Conclusion………………………………………… 59
IX. CONCLUSION AND RECOMMENDATIONS…………………………… 61 9.1. Conclusion…………………………………………………………… 61 9.2. Recommendations…………………………………………………… 61
X. BIBLIOGRAPHY………………………………………………………… 62 XI. ANNEX…………………………………………………………………… 63
Appendix A Data and Calculation Appendix A1: Topographic Survey Appendix A2: Bridge Site Survey Appendix A3: Road Site Survey
Appendix B Map and Drawing Appendix B1: Major Traverse Appendix B2: Tachometric Detailing of Minor Traverse Appendix B3: Bridge Site (Triangulation and Tachometric) Appendix B4: Road Site Graph No. 1(A) – Bridge (Longitudinal Section) Graph No. 1(B) - Bridge (Cross Section) Graph No. 2(A) - Road (Longitudinal Section) Graph No. 2(B) - Road (Cross Section)
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LIST OF TABLES TOPOGRAPHY SURVEY
Final Major Co‐Ordinate Sheet: Table No: 2.2
Final Minor Co‐Ordinate Sheet: Table No 2.2
Linear Measurement: Table No 2.3
Angular Calculation Major Traverse: Table No 2.4
Horizontal Angular Obs. Sheet Minor Traverse: Table No 2.5
Detailing Field book: Table No 2.6
FLY LEVELLING From permanent BM to TBM: Table No 3.1
Level Transfer To Major Traverse: Table No 3.2
Level Transfer To Minor Stations: Table No 3.3
ROAD SURVEY
Road Gales Table: Table No 7.1 Chainage And IP Calculation Sheet: Table No 7.2 Level Transfer To IP’s: Table No 7.3 Detailing Sheet: Table No 7.4
BRIDGE SITE SURVEY Co‐Ordinate Sheet (Gales Table): Table No 8.1 Angular Correction And Calculation sheet: Table No 8.2 Distance Calculation Sheet: Table No 8.3 RL. Transfer And Calculation Sheet: Table No 8.4 Angular Observation Sheet: Table No 8.5 Detailing: Table No 8.6
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I. INTRODUCTION
1.1. BACKGROUND:
Surveying in the simplest form is the measure of relative position of points or absolute measurement of any feature on or beneath the earth surface by using distance, angle, and elevation measuring instruments. Land‐ area surveys are made to determine the relative horizontal and vertical position of topographic features and to establish reference marks to guide construction or to indicate land boundaries. Reconnaissance of the area is followed by a preliminary survey; a map and then a plan are prepared based on the plan. Survey is used to establish property boundaries involving a through knowledge of real‐estate laws as well as skills in survey techniques.
Topographic maps are graphical representations of natural and man‐made features of parts of the Earth’s surface plotted to scale. They provide the bases for specialized maps and data for compilation of generalized maps of smaller scale. It is impossible to start railways, roads, canals, tunnels, transmission power line, dams, and bridge site location, even building without preliminary survey. Before starting any structure or launching the ambitious projects on the earth surface or below the ground, the role of survey is critical. Survey never means measuring and drawing the ground feature to the corresponding scale and portraying, these vertical relationships with others nearly. It encloses the wide area and the system of surveying and the application is increasing day by day. Besides using Theodolite traversing on the land, now remote sensing system and photogrammetric has changed the survey procedure in new format. In true sense the modern scientific methodology is approaching to the true value, which is never defined in terms of survey, with very high precision. Although modern sophisticated instruments such as EDM has introduced new establishment but the basic principle is remains unchanged. However it is true that we are more nearer to their true value with this modern equipment and handling is very easy. For the purpose of water line, sanitary or road also the relative altitude are required, which is ascertain by the levelling. Even the details of the enclosed area and the ground nature can be portrayed in combined form as topographic map. The whole land can be surveyed in different plots and can be united into a single map. The main thing is not to violate the basic survey principles viz. working from whole to part, consistency of work, accuracy required according to scale and independent check.
Above mention things are perquisite while handling the project and for gaining experience such type of survey has to be done and what we do in the survey can is not different from it. In other words it is the combat in field with the theory of survey as tools.
The main objective of the surveying course allocated for Civil Engineering
Students is to promote them the basic knowledge of different surveying techniques relevant to
Civil Engineering works in their professional practice. The surveying is one of the most
important subject matter before and during the civil engineering works like construction of
Highway, Irrigation project, Construction of building etc.
Survey Instruction Committee, Kathmandu Engineering College, organized the
Survey Camp 2064 at Kharipati. The duration of Survey Camp was 15 days, from 2064
Kartik 7 to Kartik 21 NEATC premises at Kharipati V.D.C., Bhaktapur, Nepal.
1.2. Objectives:
The main objective of the camp is to provide a basic knowledge of practical implementation
of different survey works, which is to be encountered in future. It enhances the practical
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knowledge thereby implementing different works and in other side it involves the self‐
confidence eternally. The main objectives of the survey camp can be enlisted as follows:
• To become familiar with the surveying problems that may arise during the field works
in future.
• To became familiar with the instruments, their functions and handling the surveying
instruments for its use in surveying works.
• To become familiar with the spirit and importance of teamwork, as surveying is not a
single person's work.
• To complete the given projects in scheduled time and thus know the value of time.
• To collect required data in the field in systematic ways.
• To compute and manipulate the observed data in the required accuracy and present it in
diagrammatic and tabular form in order to understand by other Engineers and related
personnel easily.
• To tackle the mistakes and incomplete data from the field while in office work.
• To give the good opportunity to use the theoretical background on engineering survey in
the practical life.
• To know the complete methods of report preparation.
Our project was mainly divided into three parts. They were:
I. Topographical Survey of a part of NEATC premises.
II. Bridge Site Survey in Punyamata Khola, Panauti.
III. Road Alignment Survey at NEATC Premises.
a. Topographical Survey:
The first major work during the survey camp was the preparation of
topographical map of NEATC, Kharipati. The topographical map is defined as the map
representing the positions of all the features in x and y‐axis along with the vertical positions
with the help of contour lines. In order to prepare the map, the survey was done in the given
area using the major and minor traverses. Also the elevations (R.L.) were transferred from
the given Benchmark (B.M.) firstly to all the traverse stations and then to all the detailed
points. The contour lines were drawn later by performing the necessary calculations. Finally
the detailed Topographic Map including the major and minor traverse, details and contour
lines of the surveyed area was plotted in the given scale. All the calculations in tabular form
along with the topographical map are presented here with this report.
b. Bridge Site Survey:
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Survey Camp 2064 Group J
The main objective of the bridge site survey is to obtain the preliminary knowledge on
selection and planning of possible bridge site and axis for the future construction of the
bridge. The purpose of the bridge site survey was not only to prepare plan and layout of the
bridge site but also to collect the preliminary data about the site such as normal water flow
level, high flood level, geological features of the ground for planning and designing of the
bridge from the details taken during the surveying. The cross section (upstream and down
stream of the bridge axis), longitudinal section details and detail survey was done using the
principle of triangulation. All the required data and corresponding drawings are attached
here in this report.
c. Road Alignment Survey:
Road construction is an important aspect in the development of transportation network.
The road survey of this camp was carried at NEATC premises, Kharipati. The length of the
road was 781.185 meters. All the cross sections as well as longitudinal section data were
taken at chainage of 20 meter and at each IP and each tangent point. All the calculations and
maps details are presented here in this report.
1.3. Project Area
The description of the project area is as follows:
Nepal Electricity Authority Training Center (NEATC), Kharipati, Bhaktapur is about 18 km
North East of Kathmandu. The area to us for survey is about 200 ropanis of land with
varieties of land (i.e. jungle, vegetation, human settlement etc). The details of the area is as
follows
Country: ‐ Nepal
Region: ‐ Central Development Region
Zone: ‐ Bagmati
District: ‐ Bhaktapur
Location: ‐ NEATC premises for Topographical Survey
Punyamata Khola, Panauti for Bridge Site Survey
NEATC premises for Road Alignment Survey
a. Description of Work
• Traversing:
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Survey Camp 2064 Group J
i) No. of Major Traverse Stations =19
ii) No. of Minor Traverse Stations=6
iii) No. of Link Traverse Stations =6
• Road Alignment:
ii) Length of the road: 781.185m
iii) Cross section: 10m left and 10m right on both sides from central line.
• Bridge Site Survey:
i) Bridge span: 54.915m
iii) Cross section up to 120m on upstream and 60m on downstream at 20m interval.
1.4. Norms (Technical Specifications):
All the students at the camp had to work under some norms provided by survey instruction
committee. The norms are listed as follows:
The given work had to be completed within 15 days keeping 2 days each for road
site and bridge site.
The proper handling and care of the instrument was the responsibility of the entire
group.
The major and minor traverse had to be fixed in such a way that these points were to
be followed:
a) At least two consecutive stations should be visible from a station.
b) Two‐way measurement for one traverse leg should be done. The discrepancy should
be greater than 1:2000
c) The number of traverse stations should be minimum.
d) Two sets of horizontal angle should be taken in major traverse & only one set in
minor traverse. The difference between the mean angles of two set reading should
be within the least count of the theodolite.
e) The leg ratio of the traverse stations should not be less than 1:2 for major traverse
and not less than 1:3 for minor traverse, where ratio stands for the longest side:
shortest side
f) All the available checks should be applied to the traverse and adjusted using
appropriate method.
g) After the completion of the fieldwork, the plotting of the traverse along with details
and the contour lines has to be done thus preparing the topographical map of the
worked area.
h) Plotting should be done by independent co‐ordinate.
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Survey Camp 2064 Group J
i) Fly leveling should be done to transfer RL from the BM. The permissible error in the
leveling should not be greater than ±25√k mm, where k is the distance in km. All
three‐hair readings should be taken in this case.
j) Fly leveling should determine the RL of all the major and minor traverse station. In
this case, only central hair reading should be taken.
k) The permissible closing error for closed loop should within ±C√ minute, where N =
no of stations and usually C is taken as 1.
i. AREA ACTIVITIES:
• TOPOGRAPHICAL MAP PREPARATION
Scale: 1:500
Area: 1.5 to 2 Hectares
Paper size for plotting : A1 or A2
Contour interval: 1m (depending upon the site relief)
Major Traverse scale 1:1000 (or adjustable)
ii. CONTROL POINT ESTABLISHMENT:
At least 12 stations (Main control stations)
Two set of horizontal angle
One set of vertical angle
Two‐way length measurement (taping), check or compare with the
Tachometric distance.
Traverse line orientation, check by graphically (Telescopic Alidade).
Vertical control by Levelling, check by trigonometrical levelling.
Fly levelling carry out at least 1 kilometer away.
Special Technique of Surveying:
Tacheometric detailing by Resection and Intersection (Three
points at least in each case)
Plane table for detailing (using Telescopic alidade) as
required.
iii. LINEAR STRUCTURE ACTIVITIES (Road alignment survey)
• At least 500 m stretch
• Scale Plan 1:1000
• L –section scale: Vertical 1:100, Horizontal 1:1000 (H:V =1:100
• Left/right observation: 10 m minimum on either side
iv. Curve Setting :
• Horizontal curve:
Simple Circular: by both linear and angular method
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Survey Camp 2064 Group J
Transition: by both linear and angular
• Lead survey by Abney level.
v. BRIDGE SITE SURVEY:
• Up stream: 60m (at least)
• Down stream : 120m (at least)
• Scale for plotting minimum area of observation or coverage.
• Plan 1:500
• Contour interval: 2 m or depending upon site topography.
• Cross‐section: every 20m interval: Scale: Same for both vertical and horizontal (H=V=1:100)
• Observation should be taken 20m beyond the bank on either side of the river or at least 10m above the HFL (high flood level) cover line (contour line).
vi. Instruments Used:
The instruments required during the survey camp are as follows:
Level Machine
Staffs
Theodolite
Magnetic Compass
Measuring tape (30m, 50m)
Ranging rods
Hammer
Arrow
Pegs
Plane table with telescopic alidade
1.5. WORKING SCHEDULE:
Working Schedules no.
Day Survey field Work
1 7th kartik Reconnaissance
2 8th kartik Major Traverse Survey
3 9th Kartik Major and Minor Traverse Survey
4 10th Kartik Two peg Test and Fly Levelling
5 11th Kartik Major, Minor Traverse & Computation
6 12th Kartik Road Site Survey
7 13th Kartik Road Site Survey
8 14th Kartik Coordinate Computation; Adjustment
& plotting
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Survey Camp 2064 Group J
Project Title: Survey Camp 2064
Location: NEATC, Kharipati, Bhaktapur, Nepal
Duration: Kartik 7th to Kartik 21th
Working time: 07:00a.m. To 6:00 p.m.
Class: 7:00‐8:00 p.m. (daily)
Methodology:
The methodology of the surveying is based on the principle of surveying, which includes:
A traverse may be defined as the course taken measuring a connected series of straight lines, each joining two points on the ground; these points are called traverse stations. The straight line between two consecutive traverse stations is called traverse leg, the angle at any station is called traverse angle. The traverse leg are measured by direct chaining or taping and angles at any station is measured with a Theodolite is called Theodolite traversing. According to the nature of the starting or closing station there are two types of traverse.
• Closed traverse • Open traverse
Closed Traverse:
If the figure formed by the lines closes at a station i.e. if it starts and finishes at the
points of known co‐ordinates then the traverse is called closed traverse. It has the
independent check. Known point
Known point
Open Traverse:
If the initial and final points of a traverse are not in the same point, then it is called the open
traverse. It has no independent check Unknown point
Unknown point 2.2. PRINCIPLE OF THEODOLITE SURVEY:
According to the accuracy aimed and nature of the ground, the length of the traverse leg are measured directly on the ground either by Chaining or taping. The traverse angles are measured with Theodolite by setting up the Theodolite on each station. If the co‐ordinates of the one station and the true bearing of the traverse leg connected to it, are known the co‐ordinates of the other traverse station may be calculated with the following formulae: N
X co‐ordinate of B= X Co‐ordinate of A+Lsinθ B(x, y) Y co‐ordinate of B=Y co‐ordinate of A+lcosθ θ Y
A(X, Y) X E
2.3. METHOD OF THEODOLITE TRAVERSING: On the basis of measuring relative directions of traverse legs, the method of Theodolite traversing may be divided into two groups.
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Survey Camp 2064 Group J
a) By measuring the direct angle between two consecutive traverse leg. b) By measuring the direct bearing of the traverse leg.
THEODOLITE TRAVERSING BY ANGLE MEASUREMENT: This method is generally adopted for long traverse when higher degree of accuracy is required. In this method, bearing of the starting and closing traverse legs are generally determined by making astronomical observations to pole, sun or star. In this method, angle between relative directions of traverse legs, are directly measured with Theodolite. Direct angles measured at different traverse stations may be either included angles or deflected angles. Theodolite traversing by observing included angles: The included angles are those angles which measured on the left side of the direction of traverse. It is customary to run a closed traverse in an anticlockwise direction in which only interior angles are measured. In closed circuits, the accuracy of the angular measurement is easily checked by summing up all the included angles as their total sum should be equal to (2n±4)*90°, where n is no. of traverse legs, the +ve sign is used for exterior angles and negative sign is used for interior angles. Arrows shows the direction of traverse. N F E
A s D B C Fig: ‐ A closed traverse with interior angles. B C 2.4. LATITUDE AND DEPARTURE:‐ The latitude or Northing (N) of a survey line is defined as the co‐ordinate measured parallel to the assumed meridian. The Departure or Easting of a survey line is defined as the co‐ordinate measured at right angle to the assumed meridian. The negative latitude is Southing and Positive Latitude is Northing. Similarly the–ve, Departure is Westing and positive departure is Easting. To calculate the Latitude (L) and Departure (D), the following relation is applied. Latitude (L) =l*Cosθ Departure (D) =l*sinθ Where l & θ are length and reduced bearing of traverse leg. CALCULATION OF CLOSING ERROR: In a complete circuit, the sum of the north Latitudes must be equal to the sum of the south latitudes; the sum of easting must be equal to the sum of westing. If linear as well as angular measurement of the traverse along with their computations is correct. If not the distance between the starting station and position obtained by the calculation is called closing error. The closing error can be expressed as a fraction which is: Closing Error/Perimeter of traverse Where, Closing error= ∆E2 ∆N2
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Survey Camp 2064 Group J
2.5. BALANCING THE CONSECUTIVE COORDINATES: Generally, there are two methods of balancing the consecutive co‐ordinates.
a) BOWDITCH’S METHOD: ‐ This method is employed when linear and angular measurements of the traverse are of equal accuracy.
If, l=length of leg ∑l=perimeter of legs ∑L=Total error in Latitude ∑D=Total error in Departure ∂L=Correction to the Latitude of the leg ∂D=Correction to the Departure of the leg. Then, ∂L= l/∑l *∑L ∂D = l/∑L *∑D b) Transit Rule: ‐ If angular accuracy is more than linear accuracy, then transit rule is
applied. According to this rule, Correction to the latitude of leg=Total error in latitude/Sum of Latitude*Latitude of that leg Correction to the departure of leg = Total error in departure/sum of departure*Departure of that leg The traversing consists the measurement of following
a. Angles between successive lines or bearings of each line
b. The length of each line
2.6. OBJECTIVES:
As the principle of surveying is to work from the whole to the part, precision control
points are fixed by triangulation at distances 5 to 10 Km apart. The theodolite traverse is,
therefore, carried out for the following purposes:
To provide control points for chain surveying, plane tabling and photogrammetric
surveys in flat country.
To fix the alignment of roads, canals, rivers, boundaries, etc. when better accuracy
is required as compared to plane tabling.
To ascertain the co‐ordinates of boundary pillars in numerical terms that can be
preserved for future reference such as forest boundary pillars, international
boundary pillars, etc. In case the pillars get disturbed, their positions can be
relayed with the help of their co‐ordinates.
2.7. MAJOR TRAVERSE:
2.7.1. Introduction: The whole site is enclosed by the framework interconnecting the successive control stations &is known as major traverse. Different works are conducted sequentially and is the brief.
2.7.2. METHODOLOGY:
2.7.2.1. Reconnaissance:
The first step of any survey is reconnaissance. The area given to us at the camp for
detailing was the part of total area of NEATC, Kharipati. As in the case of major traversing,
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Survey Camp 2064 Group J
reconnaissance was done before fixing minor stations. These minor stations were purposed
in such a way that it covers each and every important detail. Generally eye estimation is
used and rough calculation is done for fixing the traverse legs. Rough reference sketch
principal features such as buildings, roads are prepared. Various difficulties that had arisen
must be preplanned on the mind.
2.7.2.2. Pegging:
After the completion of the reconnaissance the next step to be taken is to fix the major
traverse first and then the minor ones if necessary. Before fixing a traverse station the care
should be taken that the two other stations are visible from this station and the leg ratio
should be maintained as per the specification. After taking the decision of fixing the station
at any point, that point should be marked with the paint or the peg and then finally the
referencing of the stations should be done.
2.7.2.3. Linear Measurement:
Legs were measured with a standard tape in both forward and backward direction. Ranging
was done for the longer tape lengths with eye estimation and stepping method for slopping
ground. Possible errors due to sagging tension force, temperature change were eliminated
by taking convenient distance and following the error prone methods. Linear accuracy was
within 1:2000
2.7.2.4. Angular measurement:
Two‐set readings were taken in each station one with 00 set and next with 900 set. The
difference in face‐left & face‐right reading and interior angle obtained from both set were
different by more than the least‐count of theodolite used on the field. It was checked in the
field while observation was taken. If it is not the case the reading should be repeated until
the desired accuracy is gained
2.7.2.5. Correction of internal angles:
The traverse must be closed and it was checked by the formula = (2n – 4) x 90°
Where, n = no of traverse stations.
The sum of the interior angles was not equal to (2n – 4) x 90° and the error was equally
distributed in each internal angle of traverse stations.
Adopted accuracy = ± C N minutes Where, C =1 and N= no. of total traverse stations
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2.7.3.6. Computation of bearing:
Actually the bearing of a common leg has to be determined by the sun observation. But this
was not in our course of survey camp. Two points CP1 and Cp2 is given as common points
(stations) to all groups. The bearing of the line joining these two common points CP1 and
Cp2 is given to be 38˚30’00’’.The bearings of other legs were computed with reference to
this bearing and using the following formula:
F.B of any leg = F.B of previous leg + clock wise angle +180(‐180) or (‐540)
If sum of F.B. of previous leg and clock wise angle is less than 180°, use +180, if more than
180º, use ‐180, and if greater than 540º, use ‐540. All bearings were computed in whole
circle bearing system.
2.7.3.7. Computation of independent coordinates:
The latitude (northing) and departure (easting) of every station were referred as its co‐
ordinates. After determination of bearing of each line, using known distance, latitude and
departure of each point were calculated using the relation:
Difference in latitude between two points CP1 and CP2, (∆N) = L Cosθ
Where, L = length of line CP1 – CP2
θ = Bearing of line CP1‐ CP2
Similarly, difference in departure between these two points CP1 and CP2
(∆E) = L Sinθ
Since we used closed traverse, the algebraic sum of the latitude and departures of all the
lines must be equal to zero.
Closing error of the traverse (e) = 22 )()( DL Σ+Σ
Where, ∑L = algebraic sum of the latitude
∑D = algebraic sum of the departure
And the direction of closing error is given by
Tanθ = ∑D / ∑ L
The relative error of traverse = closing error / perimeter of the traverse.
The required accuracy was 1:2000.
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Since there was some closing error, correction for latitude was necessary to make the
closing error zero i.e. the co‐ordinate must be same while closing the traverse at same point.
The co‐ordinate of succeeding station was calculated as:
Easting = easting of previous point + easting diff.
Northing = northing of previous point + northing diff.
2.7.3.8. Plotting the traverse using the coordinates
After the coordinates were calculated, they were plotted in a grid of 10‐by10 squares in the
scale of 1:1000 for the major traverse and 1:500 for the minor traverse.
Necessity of minor traverse:
When the details to be included in the map cannot be taken from the major traverse
stations then it becomes necessary to establish the control points near the detail so that it
can be observed properly and these stations are called minor stations. The minor traverse
should start from major station and should end at the major station too.
2.7.3.10. Final Coordinate Sheet: Reference Table no:2.2
2.8. MINOR TRAVERSE:
2.8.1 Introduction:
The traversed framework within the major traverse is called the minor traverse and was run to
detail the small area inside major traverse. All the vertical and horizontal controls were
transferred from the major traverse. Minor traverse legs were stretched in and out the detailing
area according to the requirement so as to achieve maximum information from that station
while performing plane tabling.
2.8.2 Methodology:
2.8.2.1 . Reconnaissance: The area given to us at the camp for detailing was lower zone of NEATC. As in the
case of major traversing reconnaissance was done before fixing minor stations. These minor stations are established in such a way that it covers each and every important detail.
2.8.2.2. Marking and Fixing Control Points:
After reconnaissance, it was concluded that extra four sub stations for detailing, that included 4 links (containing 16 stations in total) and 8 substations and four links joined to the major station forming a close minor traverse. So, 8 minor stations were fixed at the suitable place in such a way that indivisibility criteria between two stations are met.
2.8.2.3. Measurement of Traverse Legs:
As in the major traverse case, two‐way distance measurement was done. The accuracy required for the linear measurement was 1:1000.
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2.8.2.4. Measurement of Interior Angles: On minor traverse stations, only one set of horizontal angles were taken.
Permissible Error = ±C√N minutes for traverse loop, where N is the no of stations. In the same case, error was distributed equally in all measured minor control points only. To determine the R.L. of minor control points, back sight was taken to the major traverse points. Intermediate sight was taken to the staff held at minor control points, and foresight was taken to the same or other major control points for closure. Accuracy =±25√K mm, where K is distance in k.m. Error found was within permissible limit. The error was distributed in each station according to Bowditch’s rule as discussed earlier. If e = total error in R.L. Then, correction =e*l/∑L where, l = length from initial station up to that station and ∑L = perimeter of traverse.
2.8.2.5. Bearing computation of the Traverse Legs: Bearing of traverse leg were calculated in
the same manner as in the major traversing, using the bearing of the major traverse line as known bearing of the initial line. Since the angular error was distributed previously, error in bearing calculation was checked.
2.8.2.6. Coordinate Computation of Minor Control Points:
Using the co‐ordinates of the major control point as given, co‐ordinates of the minor control points is determined in the same manner as in the major traversing. The traversing in this case was closed in the major traverse station and error was distributed in minor control points according to Bowditch’s Rule as done in major traversing.
2.8.2.7. Plotting of Minor Traverse Stations: As in the major traverse station, a full sheet
drawing was divided into 100 mm*100 mm grid and minor control points were plotted on the drawing sheet as a scale of 1:500.
2.8.3. Instrument Used: Theodolite
Staffs
Ranging rods
Tapes
Arrows
Pegs
Compass
2.8.4. Final Coordinate Sheet:
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Reference: Table no. 2.2 2.8.5. Other observation and calculation Sheet:
Reference:
Linear Measurement: Table No.2.3 Horizontal Angular Obs. Sheet Major Traverse: Table No.2.4
Horizontal Angular Obs. Sheet Minor Traverse: Table No.2.5
Detailing : Table No.2.6
III. LEVELLING
3.1. INTRODUCTION:
Leveling is the branch of surveying, which is used to find the elevation of given points with respect to given, or assumed datum, to establish points at a given elevation or at different elevations with respect to a given or assumed datum. To provide vertical controls in topographic map, the elevations of the relevant points must be known so that complete topography of the area can be explored. Leveling was performed to determine the elevation (relative height) from a given datum.
3.2. Objective:
For the execution of engineering projects, such as railways, highways, canals, dams, water supply and sanitary schemes, it is very necessary to determine elevations of different points along the alignments of the proposed projects. Success of such projects depends upon accurate determination of elevations. Levelling is employed to provide an accurate net work of heights, covering the entire area of the project. Levelling is of prime importance to the engineers, both in acquiring necessary data for the design of the project and also during its execution. 3.3. Fly Leveling: 3.3.1. Introduction: Fly leveling is a leveling, which is done to find out the elevation of different points with respect to the standard benchmark. We performed the fly leveling from the TBM1
established by the survey department at Kharipati (way to Nagarkot) which was about 1500
meter away from NEATC. The R.L. of the TBM1 was 1348.122m and after carrying the fly
leveling the R.L. of TBM was 1336.834m but for the uniformity the survey instruction
committee provided the R.L. of TBM as 1336.864m.
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3.3.2. Procedure:
A level machine was set up approximately midway between the benchmark and the
point, whose elevation was to be found by direct leveling. A back sight was taken on the staff
held at the benchmark.
Then,
H.I. = Elevation of B.M. + B.S.
By turning the telescope, another sight was taken on the staff held at the unknown point. At
that time, Elevation = H.I. – F.S. (or I.S.).
In our case before starting fly levelling we performed by the “Two Peg Test” on our
instrument.
3.3.3. Observation and Calculation:
Reference:
From Permanent BM to TBM: Table No.3.1
Level Transfer to Major Stations: Table No 3.2
Level Transfer to Minor Stations: Table No 3.3
3.3.4. Conclusion:
The R.L. of B.M. is given 1348.122 m (provided by the Survey instruction committee). Finally the R.L. of TBM at NEATC was determined by averaging all the R.L. calculated by each group, which was found to be 1336.864 m
3.4. Two Peg Test: 3.4.1. Introduction:
Two‐peg test is one of the methods of adjustment of the line of collimation,
which is done to compensate the collimation error of the leveling instrument. The line of
collimation of the telescope should be parallel to the axis of bubble tube. Therefore, the
adjustment of line of collimation is very necessary, and is of prime importance, since the
whole function of the level is to provide horizontal line of sight. This test is performed prior
to leveling work to confirm the leveling instrument is in the satisfactory condition fulfilling
the permissible limit.
The observations of the two‐peg test are as follows:
3.4.2. Observation:
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T
T M
M B
B
A 25 m C 25m B
1. First setting: the instrument at mid way of A and B
True level difference between A & B=0.886‐0.393 =0.493 B being at higher elevation
2. Second Setting: the instrument near B
Observed correct reading of B=1.331
Different of R.L. =1.828‐1.331=0.497m (B being higher)
Reading of A=reading of B‐True level difference = 1.331‐ 0.493 =0.497m
Collimation error =0.497‐0.493 =0.004
Precision =0.004/50=1:12500
Hence the above error is within permissible limit and showed that the instrument was all right.
3.4.3. Level Transfer from BM to TBM:
It is one of the most important works on the field as it transfers the level from the known
bench mark to the temporary bench mark near the site and from where further level to major
Instrument at Staff point Top Middle Bottom Mid way (C) A 1.011 0.886 0.761
B 0.517 0.393 0.269
Instrument at Staff point Top Middle Bottom Near to B B 1.338 1.331 1.324
A 2.08 1.828 1.575
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and minor traverse can be done easily. In other words we are establishing the control points
with the level transferred from the national survey department.
In the camp, level is transferred from to B.M. to T.B.M.
• Fore sight distance and backsight distance must be in nearly equal distance so as to
eliminate errors due to focusing, refraction and curvature. For maintaining equal
distance: eye judgment is used when the staff man fixed the fore sight distance with the
pacing.
• Three wire reading is taken. At each attempt mean value of three wire readings should
not differ by 0.002 m with the middle wire reading and was checked on the field.
• Fly levelling was run from T.B.M. to B.M. and back to the starting point so as to form loop.
Further correction was established two T.B.M. at the midway in the fly levelling.
• The permissible error was = ±25√ mm, where K is the distance in Kilometer of a loop.
• The R.L. of each staff station was found from rise and fall method.
• Closing error within the permissible limit was distributed to all staff stations according to their
length (station to staff distance)
3.4.3.1. Observation and Calculation:
Reference: (Table No 3.1)
3.4.4. Level transfer from T.B.M. to Major Traverse Station: The level transferred from B.M. to T.B.M. is now transferred to the Major traverse stations or the establishment of the major traverse stations is done with respect to R.L. of T.B.M...
Three wire reading was taken in each station. Fly levelling is done around the traverse and closed at T.B.M. R.L. is calculated by rise and fall method and error in per4missible limit was distributed.
3.4.4.1. Observation and Calculation: Reference: Table No 3.2
3.4.5. Level transferred from Major to Minor Traverse: It transferred the vertical control from major to the minor stations and from where Level was passed to each and every details point. This help in finding the R.L. of the ground points for contouring. By this means the Level was transferred to the every point on the site/Location where camp was launched. While performing this task, following points must kept in mind:
Three wire reading was taken in each station. Fly levelling could be started from R.L. of the known major station to the minor station and that to the known major station or from any major traverse station and closed that to the same station as it has vertical and horizontal control information.
The permissible error was= ±25√K mm, where K is in Kilometer. Error within the permissible limit was distributed proportionally to their lengths. 3.4.5.1. Observation and Calculation: Reference: Table No. 3.3
3.5. Reciprocal Levelling:
Reference: Chapter 7 bridge site survey (page: 57‐58)
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IV. TACHEOMETRIC DETAILING:
4.1. Introduction: Tacheometry is the branch of surveying in which both horizontal and vertical distance between the staff station and instrument station are determined from instrumental observation.
4.2. Objective: The primary objective of tacheometry was the preparation of plans requiring both the horizontal and vertical control. The main objective of tacheometry is the preparation of contoured plan of NETAC, Bhaktapur. T
T’ 4.3. General Theory: M Θ S
B V α A θ H
Fig. Stadia measurement by a tachometer.
Calculation of distance from the Theodolite centre to the staff position is based on similar triangles. Distance from Theodolite to the position of the staff intersected by middle hair, AM in figure= K(S*Cosθ) +C Where, S Cosθ=T’B’=staff intercept normal to the line of sight. K=multiplying factor of theodolite which depends upon the focal length and length between top and bottom hair in the lens. C= additive constant= f+d Where, f= focal length D= distance from objective lens to centre of theodolite For horizontal sight, Horizontal distance between theodolite centre and staff station is, H=KS+C (where k=100 &C=0) generally For inclined line of sight, H=KS* Cos2θ. Where, θ= angle with horizontal S= staff intercept
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For vertical distance, from centre of theodolite to the middle hair position in staff. V=KS Cosθ*Sinθ= (KS Sin2θ)/2 If horizontal angle is taken, H=KS Sin2θ and V=1/2*KS Sin2θ
4.3. Methodology: 4.3.1. Measurement and Data:
Initially the Theodolite is set on a station and necessary adjustment is done. Detailing of the survey area is carried out by setting horizontal angle to 0˚0’0’’ to the corresponding station.
The object is sighted and staff intercept ( top, middle and bottom wire reading ) is Observed and corresponding vertical angle (VCR) and horizontal angle (HCR) is read.
4.3.2. Field Procedure: 1. Zero angles are set at the back sight to the traverse station. 2. Staff reading is taken i.e., bottom, middle and top at the necessary
position. 3. Staff man is allowed to go to the next position. 4. Vertical and horizontal angles are taken. 5. Height of instrument should be taken initially.
Now, the horizontal and vertical distances are obtained using formulas. Then by use of horizontal angles and distance we can plot the necessary details. The vertical distance is reduced to calculate the RL of staff stations which will serve for rough contouring in the topographic map.
4.3.3. Calculation:
If S = Stadia reading (Top wire – Bottom wire)
Θ = Vertical angle (V.C.R. ‐ 90˚ if V.C.R.>90˚ & 90˚‐V.C.R. if V.C.R. <90˚
H = Horizontal distance then,
H = 100*S*Cos2θ + C *Cosθ
And R.L. of staff point = R.L. of instrument station + height of instrument ±V (HTanθ or 50*S*Sin2θ + C Sinθ+ C Sinθ) – Central wire reading.
Note: C= 0 for our instrument, V is taken positive when vertical angle is angle of elevation ( Less than 90˚) and V is taken as negative when vertical angle is angle of depression.
4.3.4. Accuracy and Precision:
The average of sum of upper wire reading and bottom wire reading should be equal to
the central wire reading for the accurate result.
i.e. (Top+ Bottom)/2 = center
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4.3.4. Instrument:
Theodolite
Staffs
Ranging rods
Tapes
Arrows
Pegs
Compass
4.4. Contouring:
The delineation of any property in map form by constructing lines of equal values of
that property from available data points is known as contour mapping. A topographic map,
for example, reveals the relief of an area by means of contour lines that represent elevation
values; each such line passes through points of the same elevation. The method is not wholly
objective because two investigators may produce somewhat different maps whenever
interpolation between data points is necessary for construction of the contours. The
availability of plotting devices in recent years has permitted mapping by computer, which
reduces the effect of human bias on the final product.
Contour lines are imaginary lines exposing the ground features and joining the points of
equal elevations. The map with contour line relief is a topographic map. The relief interval
between two consecutive contour lines is called the contour interval and is fixed. For the
contour plan, the contour interval is kept constant and the provided contour interval was
1m.
4.4.1. Methods of locating Contours
The methods of locating contours depend upon the instrument used. In general there are
main two basic field methods of locating contours. They are:
i. The direct method. & ii. The indirect method.
i. The direct method: In the direct method, the contours to be plotted are actually traced
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on the ground. Only those points are surveyed which happen to be plotted. This method is slow and tedious. Here, contour map is prepared on the field.
ii. The indirect method
In the indirect method, some suitable guide points are selected and surveyed. The guide
point need not necessarily be on the contours. These guide points, having been plotted serve
as a basis for the interpolation of contours. This method was used to locate the contours.
4.4.2. Interpolation of Contours:
Contour interpolation is the process of spacing the contours proportionately between the
plotted ground points established by indirect methods. The methods of interpolation are
based on assumption that the slope of ground between the two points is uniform. There are
three methods of interpolation. They are:
i. By estimation:
The method of estimation is not very precise. In this method contours are
interpolated between two known R.L. by eye judgment. So, the accuracy of this method
is low compared to other two methods. The accuracy of this method depends upon the
experience of the surveyor
ii. By arithmetic calculations:
The arithmetic calculation method was used while interpolation of contours. It is
accurate method and the positions of contour points between the guide points are
located by simple arithmetic calculation.
iii. By graphical method:
The graphical method is one of the methods of contour interpolation. The accuracy
of this method is high compared to the estimation method but this method is long and
tedious.
Detailing: In order to plot the topographic map in the given scale, detailing was done by using
tacheometry from minor traverse plotted on the drawing sheet. From the tacheometry the
horizontal and the vertical distance were observed. Those distances can be used to plot any
details on site and the contour can also be drawn by calculating the R.L. of each and every
points.
Here the distances are calculated as follows:
H = KS (Cosθ)²
V = KS (Sin2θ)
Where K = 100
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S= (top reading – bottom reading)
θ = vertical angle
Now the R.L. of the staff station is calculated as follows
R.L. of staff station = R.L. of instrument station + HI +V – Middle wire reading
To know the use of telescopic alidade, few detailing were done using it. The alidade used
was self‐reducing type. It is the direct method of detailing in the field. Here the horizontal
and vertical distances are calculated on the spot and then plotted immediately. The
calculations of telescopic alidade may be summarized as
V= (top – bottom)*100
H= (Middle – bottom)*100*f (factor)
R.L. of staff station = R.L. of instrument station + HI + V – Middle reading
Field Verification After the completion of the calculation of major and minor coordinates and plotting
them in the scale of 1:500 (Minor traverse) and 1:1000 (Major traverse) with the help of
gridlines, it has to be verified in the field with the help of telescopic alidade by plane table
method.
4.5. Comments And Conclusion:
Since NEATC area has a lot of variation in regard to the altitude, type of vegetation and other
details within itself, it is a very ideal place for topographical surveying. We were able to
familiarize ourselves with the different practical approaches applied in the actual field
condition. We experienced the difference between working in a smaller area and a larger
one. Along with gaining the lots of confidence regarding the use of instrument, we also felt
the responsibility of planning, executing and implementing a project. On the whole we
experienced the value of teamwork and mutual coordination in the execution of any project.
4.6. Observation And calculation:
Reference: Table 4.1. (Detailing sheet)
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V. ORIENTATION
5.1. To determine The Position of Unknown Point By The Method Of
Intersection :
5.1.1. Introduction: Intersection is the process of determining the position of an unknown and inaccessible
Position, with the help of known points, by setting instruments at the known points. In this method, the instrument is set only at the known points. The vertical angle and horizontal angle from each station to the known point is noted with the help of which the position of unknown points is determined.
5.1.2. Objective:
The main objective of intersection is to determine the co‐ordinate of the unknown point
which may or may not accessible, with the help of the three known points.
5.1.3. Instruments Required:
Theodolite
Ranging rods
Arrows
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VI. CURVES
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6.1. INTRODUCTION:
Curves are generally used on highways and railways where it is necessary change the
direction of motion. A curve may be circular, parabolic or spiral and is always tangential to
straight directions. The main objective of curve setting in the highway is to allow the
vehicles turn their direction safely and smoothly so that the passenger doesn’t fill any jerk
and difficulty.
6.2. SIMPLE CIRCULAR CURVES
A simple circular curve is the curve, which consists of a singular arc of a circle. It is
Tangential to both the straight lines. Setting out of curves can be done by two methods
depending upon the instrument used.
i. Linear method: ‐ In this method, only a chain or tape is used when a high degree of
accuracy is not required and the curve is short.
ii. Angular method: ‐ In this method, an instrument like theodolite is used with or without
chain or tape. Before a curve is set out, it is essential to locate the tangent points of
intersection, points of curve and points of tangents.
The linear method adopted for setting out curve in field was ordinate from long chord. The
angular method adopted in field was Rankine’s method.
o Ordinate from long chord
Mid ordinate can be determined by the relation:
Oo= R‐2
2
2⎟⎠⎞
⎜⎝⎛+
LR
To set out the curve, the long chord is divided into an even number of equal parts. Offset
are calculated from the relation:
Ox= ( )22 XR − ‐ (R‐ Oo) Here, R=Radius of the curve.
Ox= ordinate at distance x from the mid points of the chord.
T1 and T2=tangents points.
L=length of the long chord actually measured on the ground.
Then the curve set out at each of these points.
o Rankine’s method:
In Rankine’s method, we assume that the length of the curve and the chord length are
equal for small chords. The deflection angle to any points on the curve is an angle at the
points of contact to that point. This method is based on the principle that the deflection
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angle to any points on a circular curve is measured by one half the angles subtended by
the arc on P.C. to that point.
The angle subtended by each chord is given by the formula
δ=1718.9 C/R minutes
If δ1, δ2,………….δn are the tangential angles made by successive chords.
∆1,∆2,……………∆n are the total tangential angles or deflection angles and
C1, C2, C3…Cn are length of the chords.
Then, for the second chord,
And for the second chord,
∆2=δ1+δ2=∆1+δ2
Similarly, ∆n=∆n‐1+δn
FIELD PROCEDURE:
1. The instrument was set at T1 and zero set at P1.
2. Then the theodolite was set to read of ∆1.
3. The tape was swung with one end at T1 and another end towards the right of the
theodolite.
4. The arrow was marked at intersection of the tape with cross hairs.
5. Then another angle 2 was set on the theodolite and with one end of the tape at 2m.
6. Using all the above statement, all the points were located and the curve was set
6.3. TRANSISTION CURVE
A transition curve is a curve of varying radius introduced between a straight line and a
circular curve. The passenger feels uncomfortable and even the vehicle may overturn. This
is due to causes of the centrifugal force coupled with the inertia of the vehicle. To avoid
these affects, a curve of changing radius must be introduced between the straight and the
circular curve, which is known as the transition curve.
The main function of the transition curve is as follows:
1. To accomplish gradually the transition from the tangent to the circular curve, so
that curvature increased gradually from zero to specific value.
2. To provide ea medium for the gradual introduction or change of required super
elevation.
6.4. VERTICAL CURVES:
A vertical curve is parabolic or sometimes circular curve used to join the two
intersecting grade lines of railways, highways or other routes to smooth out the
chainage in vertical motion. The vertical curve contributes to the safety, increase
sight distance; give comfort in driving and to the passengers.
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A grade, which is expressed as percentage or 1 vertical in N horizontal, is
said to be upgrade or +ve grade when elevation along it increases, while it is
termed as downgrade or –ve grade when the elevation decreases along the
direction of motion.
Assumption for calculating data which are required for setting out of Vertical
Curve:
B (apex)
‐ g 2%
+g1% P(x,y) B1 (vertex)
l y l
T1 x B2 T2 EVC
BVC L
Fig. Vertical curve.
Length of vertical curve = length of two tangent
So BT1 +Bt2 = 2l = T1B1+B1T2
Curve is assumed to be equally long on either side of the vertex. So,
T1B1=T2B2 =l
Length of vertical curve, L = no of chains, where r = rate of grade per
chain length.
Chainage of T1 = chainage of B –BT1 (l)
Chainage of T2 = chainage of B + BT2 (l)
R.L. of T1 = R.L. of B ±
R.L. of T2 = R.L. of B±
R.L. of B2 = ½(R.L. of T1 + R.L. of T2)
R.L. of B1 = ½ ( R.L. of B + R.L. of B2)
General formula for R.L. of any point is given by:
R.L. of Point i.e. P (Y) =
+ + R.L. of BVC
Method Of Setting Out Of Vertical Curve:
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Apex
B.S. H.I.
T.B.M.
R.L.
EVC
BVC Fig. Vertical Curve Setting field procedure
First of all apex point, BVC & EVC must be fixed.
Then T.B.M. must be fixed near to the area by fly levelling.
Then level instrument must be established at a commanding position.
Then back sight reading must be taken at T.B.M. for calculating H.I.
Then staff reading for each curve point must be computed by subtracting
the the R.L. of the point from R.L. of H.I.
Peg must be inserted at every point w.r.t. corresponding staff reading.
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TRANSITION CURVE:
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VII. ROAD ALIGNMENT SURVEY
7.1. Introduction
Roads are especially prepared ways between different places for the use of vehicles and
peoples. In country like Nepal, where there is less chance of airways and almost negligible chance
of waterway, roads form the major part of the transportation system. It is an important aspect in
the development of transportation network for the topographical mapping while the knowledge of
longitudinal section as well as cross sections at certain intervals of the road are essential. Also the
density of traffics should be considered before designing the road. The roadside survey was
conducted at NEATC premises .The length of the surveyed road was about 782 m.
7.2. Objectives
Road alignment survey was done to accomplish the following objectives:
To lay out the road joining from the southern part of the NEATC to the
main entrance at northern part.
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Survey Camp 2064 Group J
To choose the best possible route for the road such that there were a
minimum of number of intermediate points (I. P.) there by decreasing the
number of turns on the road.
To design smooth horizontal curves at points where the road changed its
direction in order to make the road comfortable for the passengers and the
vehicles traveling on it.
To take the sufficient data of the details including the spot height around
the road to prepare the topographical map of the area, cross section of the
road segment hence making it convenient to determine the amount of cut
and fill required for the construction of the road.
7.3. Norms (Technical Specification)
The road has to be designed for a width of 5 meter and length of 500m.
If the external deflection on the road is less then 3º the curve need not to be
fitted.
Simple horizontal curve has to be laid out where the road changed its
direction, determining and pegging the three points on the curves – the
beginning of the curve, mid of the curve and the end of the curve along the
central line of the road.
The radius of the curve should be greater then 12m.
The gradient of the road has to be maintained below 7%.
Cross‐section should be taken at the interval of 15 to 20m and also at the
beginning, middle and end of the curve along the central line of the road.
Plan of the road should be prepared in the scale of 1:500.
L‐ Section of the road has to be plotted on the scale of 1:500 on X‐ axis and
1:100 vertically.
The cross section of the road should be plotted on the scale of 1:100 for both
the axis.
7.4. Instruments required
Theodolite
Staff
Tape
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Survey Camp 2064 Group J
Level
Tripod
Arrows
Hammer
Compass with stand
7.5. METHODOLOGY
7.5.1. Reconnaissance
The Reconnaissance survey was carried out starting from the point just crossing the
river to the point where the existing road met the market place. Pegging was done at
different places and the possible I.P. were also numbered and pegged. The condition of
indivisibility was checked at each step.
7.5.2. Horizontal Alignment
The location of the simple horizontal curve were determined carefully considering
factors like the stability of the area, enough space for the turning radius etc. The I.P. was fixed
so that the gradient of the road at any place was less than 7‐10%. After determining the I.P
for the road, theodolite was stationed at each I.P. and the deflection angles measured. The
distance between one I.P. and another was measured by two way taping.
The horizontal curve was set out by angular method using theodolite at I.P. and tape.
The radius of the curve was fixed first, assuming it to be more then m. Then for that radius,
the tangent length and apex distance of the curve were calculated using the following
formulas:
Tangent Length = 2
tan ∆R
Apex Distance = ⎟⎠⎞
⎜⎝⎛ −
∆ 12
secR
Length of the Curve = 180∆Rπ
Where ∆ = External deflection angle
After performing the necessary calculation, the points T1 and T2 were fixed at a
distance equal to tangent length from the I.P. using a tape. Then the line bisecting the
internal angle at the I.P. was found out with the help of a theodolite. And on this line,
a peg was driven at mid of curve at a distance equal to the apex distance from the I.P.
Then the necessary calculation was done, thus giving the required numerical values
of different parameters.
7.5.3. Curve fitting with inaccessible
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Survey Camp 2064 Group J
The same procedure was followed for the two curves designed on the road and
hence chainage of all the points was calculated.
7.5.4. Leveling
The method of fly leveling was applied in transferring the level from the given B.M.
to all the I.P., beginnings, mid points and end of the curve as well as to the points
along the center line of the road where the cross section were taken. After
completing the work of one way leveling on the entire length of the road, fly leveling
was continued back to the B.M making before and after forming the loops should be
less than 25 K mm, where k is total loop distance in km.
7.5.5. Longitudinal section
The L‐section of the road is required to the road engineer an idea about the nature of
the ground and the variation in the elevation of the different points along the length
of the road an also to determined the amount of cutting and filling required at the
road site for maintaining a gentle slope. In order to obtain the data for L‐Section,
Staff reading was taken at a point at 25m intervals along the central line of the road
with the help of a level by the method of fly leveling. And thus after performing the
necessary calculation the level was transferred to all those point with respect R.L. of
the given B.M. Then finally the L‐Section of the road was plotted on a graph paper on
a vertical scale of 1:100 and a horizontal scale of 1:500.
7.5.6. CrossSection
Cross Section at different points is drawn perpendicular to the longitudinal section
of the road on either side its center line is order to present the lateral out line of the
ground. Cross Section is also equally useful in determining the amount of cut and fill
required for the road construction. The cross sections were taken at 25m intervals
along the center line of the road and also at point where there was a sharp change in
the elevation. While doing so, the horizontal distance of the different points from the
center line measured with the help of a tape and vertical height with a measuring
staff. The R.L. was transferred to all the points were performing the necessary
calculation and finally the cross section at different section were plotted at graph
paper on a scale of 1:100 both vertical and horizontal.
7.5.7. Calculations and plotting
After the work of taking the data was completed, all the necessary calculations were
done and tabulated in order to compute the Chainage of the different distinct points
of the road using the following relation:
Chainage of beginning of curve, T1=Chainage of I.P.‐Tangent length
Chainage of mid point of curve, M=Chainage of T1‐1/2*curve length
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Survey Camp 2064 Group J
Chainage of end of curve, T2= Chainage of T1+Curve length
Similarly,
Chainage of an I.P. = Chainage of previous I.P. +I.P. to distance
The R.L. of the different points was also computed using this formula.
R.L. of a point =R.L. of station + Height of instrument + H* Tan ѳ‐Mid wire reading
Where θ =Vertical Angle
Hence, with the required calculation data regarding the road site in hand, the plan
was plotted on a scale of 1:500,L‐Section on a graph paper on a scale of 1:500
horizontal and 1:100 vertical and the cross section at different points also on a
graph paper on a scale of 1:100(both vertical and horizontal).
All the data, calculation (in a tabulated from) and the drawing of the necessary plan,
longitudinal section and the cross section of the road are presented here with this
report.
7.5.8. Observation And Calculation: Reference:
Co‐Ordinate Sheet (Gales Table): Table No. 7.1 Chainage And IP calculation Sheet: Table No. 7.2 Level Transfer To IPs: Table No. 7.3 Detailing Sheet: Table No. 7.4
7.5.9. Comments And Conclusion
In spite of the different kinds of obstacles in the field, our group was successful in
completing the fieldwork as well as the office work in time. In field, we had spent quite
some time discussing the route of the road and also in designing the two curves, which led
to good results. However, the entire group members were very cautious and tried their
best to get error free data and calculations.
Moreover, after performing this road alignment survey, we were able to build confidence
in designing roads at difficult terrain taking factors like economy, convenience and its use
into consideration. We believe that such a work will be a lot of help for us in
understanding the actual situation while undertaking actual design and construction work
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Survey Camp 2064 Group J
in the future and we hope that organizes such useful field trips of the entire subject
frequently.
VIII. BRIDGE SITE SURVEY
8.1. Introduction
Bridges are the structures that are constructed with the purpose of connecting the two
places separated by rivers, streams, valleys or seas. The bridges are the network provider
for the different roads. The bridges are usually a part of road, making the road shorter and
hence economical. In Nepal where there are lots of uneven lands and plenty of rivers, the
bridges are almost the economical and efficient way to joint the two places by road in a
convenient way. The bridges are that part which connects the two impossible points, which
may be separated by some river or gorge.
Punyamata Khola was the site provided to us for the bridge site. It is situated at about 3
kilometers south of Banepa chowk. Out of 15 days of our total survey camp, 2 days were
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Survey Camp 2064 Group J
assigned for the bridge site and road site survey. Out of these three days we had to complete
the work of our bridge site in one and a half days.
8.2. Objectives
The bridge site survey was carried with the following objectives:
To develop an idea for selection of bridge axis over the river considering the factors
like convenience, economy, and geological stability.
To use the method of triangulation and reciprocal leveling, performing the necessary
calculations to calculate the length of the bridge axis using sine rule.
To prepare the topographical map of the area, cross section of the river at certain
intervals and the longitudinal section of the river including the details of the various
features and structures at the upstream and the downstream of the bridge axis.
To know the nature of the river like its discharge, velocity of flow, bed slope, higher
flood level etc.
8.3. Brief description of the site:
The site for the bridge site survey was selected on the way to Panauti at Punyamata
Khola.
The site consists of the mild vegetation including the cultivated land and few houses. To
prevent the high flood level and its devastation to land, the gabion wall has been placed at
the bank of the river as shown in the map. There is also a small bridge, which assists only
the light vehicles.
8.4. Hydrology, Geology & Soil:
The climatic condition of the Kathmandu Valley is sub‐tropical and characterized
by a seasonal pattern of monsoon that occurs mainly during rainy season from June
to September. The rainfall is generally of least during winter season. Another
important feature of this pattern is largely variation in the amount as well as on
place also.
8.5. Norms (Technical Specifications)
The following norms were followed while performing the bridge site survey:
5. Control point fixing as well as determining the length of the bridge axis had to be done by the
method of triangulation. While forming triangles, proper care had to be taken such that the
triangles were well conditioned, i.e. none of the angles of the triangle were greater than 120° or
less than 30°.
6. The triangulation angle had to be measured on two sets of readings at 0° and 90° by theodolite
and the difference between the mean angles of two sets of readings had to be within a minute.
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Survey Camp 2064 Group J
7. Transferring the level from one bank to another bank had to be done by the method of
reciprocal leveling.
8. The scale for plotting the topographical map was given to be 1:500 In order to plot the
longitudinal section of the river; data had to be taken along the riverbed up to 120 m upstream
and 60m downstream. The plot for the longitudinal section along the flow line had to be done in
a scale of 1:100 for vertical and 1:500 for horizontal. And for the cross section use the scale of
1:100 for both horizontal and vertical or 1:100 for vertical and 1:200for horizontal.
8.6. Instruments Required
The instruments required in the survey during the preparation of topographic map are as
follows:
o Theodolite o Staffs o Ranging rods o Tapes o Leveling instruments o Compass o Pegs o Marker o Tripod o Arrow
8.7. Methodology
8.7.1. Reconnaissance and site selection
The bridge site survey was done at Punyamata Khola. The first step, the
reconnaissance was done for the entire area where the bridge was to be located and
the location of the bridge axis was chosen. The site for the bridge was selected at a
location that was a continuation of the straight portion of the existing road.
8.7.2. Fixing the stations
After the completion of the recce, six stations were fixed which included the two
points of the bridge axis and it also included two points on the left hand side and two
points on the right hand side on upstream and down stream respectively. The length
of the two baselines was measured with the tape with high precision of 1:2000. The
horizontal angles were measured and the coordinates of the control points were
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Survey Camp 2064 Group J
calculated with the help of the coordinates of temporary benchmark (T.B.M.), which
was (1000.000, 1000.000, and 1456.243).
8.7.3. Topographic Survey
For the topographic survey of the bridge site triangulation was done. First the bridge
axis was set and horizontal control stations were fixed on either side for detailing.
All together six stations were fixed, with three on each bank. Thus traverse was
formed running across the river, covering the distance of 120m upstream and 60m
downstream. The interconnecting triangles were formed and angles were
measured with theodolite. The bridge axis length or span was calculated by solving
the triangles using the sine rule. Thus the horizontal control was set out.
For vertical control, the level was transferred from the TBM at the bridge near the
site by fly leveling and RL was transferred to the stations on the next bank by
reciprocal leveling. For the same bank direct level transfer method was used. For the
RL transfer for other stations then the bridge axis points the tachometric formulas
are used. The checks should be provided as far as possible. All the details were taken
by the tachometric method.
8.7.4. Longitudinal Section:
The triangulation was to determine the length of the bridge axis and to fix the
control points for detailing. The triangular stations were setup keeping in mind the
necessity of the well‐conditioned triangle. The longitudinal section of the river is
required to give an idea about the bed slope, nature of river bed, and variation of the
elevation of the different points along the length of the river. Keeping the instrument
in the control station on the river bank, the staff readings were taken at different
points along the center line of the river at an interval of 20m up to 120m upstream
and 60m downstream of the river. The elevations of the control points being known
previously, the RLs of different points at the center lines was calculated using the
tachometric formulas. Finally the L‐ section (profile) of the river bed was plotted on
the graph paper with the scale of 1:100 in Y‐axis and 1:500 in X‐axis. The graph is
attached here with the report.
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Survey Camp 2064 Group J
8.7.5. Cross Section
Cross section runs at the right angle to the longitudinal section on either side. The
cross section of the river at the particular point is the profile of the lateral from the
central line of the river. The cross sections are used to calculate the discharge and
volume of water at any section. The cross sections were taken at the interval of
about 20m extending 120m upstream and 60m downstream of the river from the
bridge axis. Staff readings of the points along the line perpendicular to the flow of
the river were taken from the station points and the elevation of the points was
calculated using the tachometric formulas. Finally the cross sections were drawn on
the graph paper at the scale of 1:100 in Y‐axis and 1:200 in X‐axis.
8.7.6. Detailing
Detailing of the entire bridge site was done by the tachometric method, the
readings being taken from theodolite stationed at the different control stations. All
the horizontal distance and the RLs of the detailed points were calculated by the
tachometric method. The calculations are drawings related to the bridge site are
presented in this report.
8.7.7. Reciprocal Leveling
Reciprocal leveling is the process in which the difference in elevation between the
two points is calculated accurately by two sets of observation when it is not possible
to set he instrument between the two points. For the transfer of RL across the bridge
axis, the reciprocal leveling was done.
Reciprocal levelling must be used to obtain accuracy and to eliminate the
following points.
Error in instrument adjustment
Combined effect of earth’s curvature and the refraction of the atmosphere.
Variation in the average refraction.
Line of sight
H a H b
A River B
Line of sight
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Survey Camp 2064 Group J
H a’ H b’
A River B
Fig. Reciprocal levelling
True difference in elevation between A and B = H = Ha‐ (H b‐e)
Also the true difference in elevation = H = ( h a’‐e)‐H b’
Taking the average of the two difference we get the the difference in elevation
i.e. The Exact R.L. of Q1 = (1456.243-1.632) =1454.611 m
8.8. Observation and Calculation:
Reference:
Co‐ordinate Sheet (Gales table): Table No.8.1
Angular Correction And Calculation Sheet: Table No. 8.2
Distance and Bearing Obvs. And Calculation Sheet: Table No. 8.3
R.L. Transfer And Calculation Sheet: Table No.8.4
Angular Observation Sheet: Table No.8.5
Detailing Sheets: Table No. 8.6
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Survey Camp 2064 Group J
8.9. Computation and Plotting
The bearing of TBM from one of the axis station was taken and the detailing of
the TBM was also done from the same station. By the help of these two the bearing
of all the lines (outer frame joining the control points) was determined. The length
of the two base lines was measured with the tape and the rest is calculated by using
the sine rule in different triangles. From the bearing and the length the coordinates
of all the stations were calculated with reference to the coordinate of TBM.
The horizontal and vertical distances were calculated using the tachometric
formulas.
The formula for the horizontal distance is,
H =KSCos2θ
The formula for the vertical distance is,
V = 2K S Sin2θ
Where K = 100
S = Staff intercept = (Top reading – Bottom reading)
After the completion of all the calculation and the computation, the plotting of
topographic map was done in the scale of 1:500 with the help of proper gridlines.
Then the L‐section and cross sections were done.
8.10. Comments and Conclusion
Bridge site provided to us was quite steep area so it was difficult to take the staff
readings the different points that were required, so all the necessary data were assumed.
After the completion of the bridge site survey and calculation it was found that the bridge
span was 58.153m. The bridge site survey provided great knowledge to us about the
construction of the bridge. After the completion of the bridge site survey we had the idea
about the selection of the bridge axis. It also helped us to know the value of teamwork
with which the completion of the work was not possible. Finally, all maps, graphs and all
the necessary calculations are attached here with the report.
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Survey Camp 2064 Group J
IX. CONCLUSION AND RECOMMENDATIONS
9.1. Conclusion
The two weeks of surveying have been most educative. As far as field knowledge is
concerned, the traversing and the detailed surveying performed at NEATC, Kharipati helped
to understand better the fundamental principle of surveying working from the whole to
part. The vertical control of the major traverse stations was selected with high degree of
precision. Hence the degree of accuracy achieved was also of great order.
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Survey Camp 2064 Group J
The topographical survey done at the Punyamata Khola was able to impart a preliminary
knowledge on how to select the bridge axis for the construction of the bridge and the
collection of the data for performing the preliminary office work for bridge construction.
Road survey done at the same site was also helpful for the knowledge required on the
design of road and also and setting the curve.
The selection of members for each group for the survey camp were done by teachers with
the objective that each student should adjust with every other student and know the value
of teamwork. And the objective was greatly fulfilled.
9.2. Recommendations
Survey camp was almost good and also it gives a lot of experiences and helped us to build
up the confidence. Due to limited time, we had to perform every work in hurry due to which
some error were committed in the field but it may be due to instrumental error, whatever it
may be, the main thing is that all the errors were in the permissible limits and were
corrected or distributed. Rather the table work was more than the fieldwork. All the group
members were equally active and co‐operative so we completed our work in time.
X. BIBLIOGRAPHY
1. A Text Book of Surveying. (R.Agor)
2. A Text Book of Surveying (Vol I & II). (Dr. B.C. Purnima)
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Survey Camp 2064 Group J
3. A Text Book of Surveying (Vol I & II). (David Clark)
4. Surveying (Vol I & II). S.K. Duggal
5. Surveying A. Bannister & S. Raymond
Surveying‐II Traversing
1
A traverse may be defined as the course taken measuring a connected series of straight lines, each joining two points on the ground; these points are called traverse stations. The straight line between two consecutive traverse stations is called traverse leg, the angle at any station is called traverse angle. The traverse leg are measured by direct chaining Or taping and angles at any station is measured with a Theodolite is called Theodolite traversing. According to the nature of the starting or closing station there are two types of traverse.
• Closed traverse
• Open traverse
PRINCIPLE OF THEODOLITE SURVEY: According to the accuracy aimed and nature of the ground, the length of the traverse leg are measured directly on the ground either by Chaining or taping. The traverse angles are measured with Theodolite by setting up the Theodolite on each station. If the co‐ordinates of the one station and the true bearing of the traverse leg connected to it, are known the co‐ordinates of the other traverse station may be calculated with the following formulae:
X co‐ordinate of B= Co‐ordinate of A+lsinθ Y co‐ordinate of B=Y co‐ordinate of A+lcosθ
N B(x, y) L Θ A(x, y) E
METHOD OF THEODOLITE TRAVERSING : On the basis of measuring relative directions of traverse legs, the method of Theodolite traversing may be divided into two groups.
a) By measuring the direct angle between two consecutive traverse leg. b) By measuring the direct bearing of the traverse leg.
THEODOLITE TRAVERSING BY ANGLE MEASUREMENT: This method is generally adopted for long traverse when higher degree of accuracy is required. In this method, bearing of the starting and closing traverse legs are generally determined by making astronomical observations to pole, sun or star. In this method, angle between relative directions of traverse legs, are directly measured with Theodolite. Direct angles measured at different traverse stations may be either included angles or deflected angles. Theodolite traversing by observing included angles: The included angles are those angles which measured on the left side of the direction of traverse. It is customary to run a closed traverse in an anticlockwise direction in which only interior angles are measured. In closed circuits, the accuracy of
Surveying‐II Traversing
2
the angular measurement is easily checked by summing up all the included angles as their total sum should be equal to (2n±4)*90°, where n is no. of traverse legs, the +ve sign is used for exterior angles and negative sign is used for interior angles. Arrows shows the direction of traverse. N F E
A s D B C Fig: ‐ A closed traverse with interior angles. B C LATITUDE AND DEPARTURE:‐ The latitude or Northing (N) of a survey line is defined as the co‐ordinate measured parallel to the assumed meridian. The Departure or Easting of a survey line is defined as the co‐ordinate measured at right angle to the assumed meridian. The negative latitude is Southing and Positive Latitude is Northing. Similarly the–ve, Departure is Westing and positive departure is Easting. To calculate the Latitude (L) and Departure (D), the following relation is applied. Latitude (L) =l*cosθ Departure (D) =l*sinθ Where l & θ are length and reduced bearing of traverse leg. CALCULATION OF CLOSING ERROR: In a complete circuit, the sum of the north Latitudes must be equal to the sum of the south latitudes; the sum of easting must be equal to the sum of westing. If linear as well as angular measurement of the traverse along with their computations is correct. If not the distance between the starting station and position obtained by the calculation is called closing error. The closing error can be expressed as a fraction which is: Closing Error/Perimeter of traverse Where, Closing error= √ (∆x2+∆y2) BALANCING THE CONSECUTIVE COORDINATES: Generally, there are two methods of balancing the consecutive co‐ordinates.
a) BOWDITCH’S METHOD: ‐ This method is employed when linear and angular measurements of the traverse are of equal accuracy.
Surveying‐II Traversing
3
If, l=length of leg ∑l=perimeter of legs ∑L=Total error in Latitude ∑D=Total error in Departure ∂L=Correction to the Latitude of the leg ∂D=Correction to the Departure of the leg. Then, ∂L= l/∑l *∑L ∂D = l/∑L *∑D b) Transit Rule: ‐ If angular accuracy is more than linear accuracy, then
transit rule is applied. According to this rule, Correction to the latitude of leg=Total error in latitude/Sum of Latitude*Latitude of that leg Correction to the departure of leg = Total error in departure/sum of departure*Departure of that leg Title:‐ Detailing by Tachometric Method:
Purpose: To locate the necessary details of a given area by the traverse stations. T Instrument Required: T’
• Theodolite with tripod M θ S • Staff B B’ • Plumb bob
Theory:‐ A θ
Fig. Stadia measurement by a tachometer.
Calculation of distance from the Theodolite centre to the staff position is based on similar triangles. Distance from Theodolite to the position of the staff intersected by middle hair, AM in figure= K(S*Cosθ) +C Where, S cosθ=T’B’=staff intercept normal to the line of sight.
Surveying‐II Traversing
4
K=multiplying factor of theodolite which depends upon the focal length and length between top and bottom hair in the lens. C= additive constant= f+d Where, f= focal length D= distance from objective lens to centre of theodolite For horizontal sight, Horizontal distance between theodolite centre and staff station is, H=KS+C (where k=100 &C=0) generally For inclined line of sight, H=KS* Cos2θ. Where, θ= angle with horizontal S= staff intercept For vertical distance, from centre of theodolite to the middle hair position in staff. V=KS Cosθ*Sinθ= (KS Sin2θ)/2 If horizontal angle is taken, H=KS Sin2θ and V=1/2*KS Sin2θ Field Procedure:
1. Zero angles are set at the back sight to the traverse station. 2. Staff reading is taken i.e., bottom, middle and top at the necessary
position. 3. Staff man is allowed to go to the next position. 4. Vertical and horizontal angles are taken. 5. Height of instrument should be taken initially.
Now, the horizontal and vertical distances are obtained using formulas. Then by use of horizontal angles and distance we can plot the necessary details. The vertical distance is reduced to calculate the RL of staff stations which will serve for rough contouring in the topographic map.
Surveying‐II Traversing
5
45
Compound Curve:
IP (1+200m)
∆ 30˚30’40’’
TL D
(1+152.23 M) S (1+244.71 m)
N Φ E SC CS F
(1+122.23m) T1 G T2 (1+274.71m)
(TS) (ST)
A R R
Φ ∆‐2Φ Φ
∆
C
Fig. Compound curve with (Transition, Spiral and Circular curves)
46
6.4. Transition Curves:
A non‐ circular curve introduced between a straight and a circular curve is known as a transition curve. The curvature of transition curve varies from zero at its beginning to a definite value at it’s junction with the circular curve. The transition curve has the following advantages:
It enables to introduce super‐elevation in proportion to the rate of change of curvature. It avoids the danger of derailment at the point of commencement if full amount of super‐elevation is suddenly applied at the point.
It avoids over turning and side slipping of the moving vehicles. It eliminates discomforts caused to the passengers while negotiating a curve. Various types of transition curves are:
I. Cubical Spiral II. Cubic Parabola III. The Lemniscate curve
Cubical spiral and cubic parabolic transition curves are best suited to railway curves and Lemniscate
curves fro highway curves.
I. Cubical Spiral: The standard equation of a cubical spiral curve is given by
x =
Where, L = Total length of the transition curve T1 R = radius of the circular curve l x l =distance measured along the curve L x = perpendicular offset from the tangent Fig. Cubic spiral
II. Cubic Parabola : The standard equation of a cubic parabola is given by :
X=
y x where, y = distance measured along the tangent Fig. Cubic Parabola
III. The Lemniscate curve: The equation of this type of curve is given by:
r =
45˚ ρ
Where, r = radius of the curvature <α ρ = Polar ray of any point. Fig. The Lemniscate Curve α= Polar deflection angle i.e. angle between the polar ray and the straight.
47
The transition curve is introduced between a straight and a circular curve in order to introduce superelevation gradually from zero at the point of commencement of the transition curve and the full amount at the junction of transition curve and the circular curve. If h is the amount of superelevation in centimeters and 1 in n be the rate of superelevation over the transition curve, L is the length of the transition curves in meters. Then,
a. D = i.e. L =
b. L =
c. L = c is rate of change of centrifugal acceleration in m/sec3, R is radius in meter and v is velocity of vehicle
in m/sec.
Superelevtion (h) = where, h = superelevation rise and G = gauge of the railway track.
Here, 1. The angle between the back tangent and tangent at the junction of the transition curve with the
circular curve is called Spiral angle. i.e. (Φ) where, Φ = radian
I.e. Φ = degree
2. The distance through which main circular curve is shifted inward to accommodate the transition
curve is known as shift. Its value is S=
3. The tangent length of the combined curve : Total tangent length = (R+S) Tan (∆/2) +L/2
4. Length of combined curve : The central angle for the circular curve = ∆‐2Φ
The length of the circular curve = ∆
˚
Total length of the combined curve = L + length of Circular curve +L
=2 ∆
˚
5. Deflection angle :
For circular curve, D = . where, c = Length of chord
For transition curve δ =
Where, R = radius of circular curve L = Length of transition curve l = distance from the point of commencement of transition curve.
6. Chainage: Chainage of i.e. T1 (TS) =Chainage of IP – TL Chainage of SC = Chainage of TS +L Chainage of CS = Chainage of Sc + length of circular curve, Chainage of ST = Chainage of CS + L
Chainage of T2= Ch of T1 + 2L ∆˚
48
Field Procedures:
1. The instrument was set at T1 and compound deflection angles were adjusted on the
theodolite.
2. An arrow with tape at a distance of chord was ranged at that angle.
3. Different points of the transition curve were obtained in similar manner.
4. Then the instrument was shifted at back tangent point and the points were obtained
similarly as above.
5. The remaining portion of the curve was circular part was set by Rankine’s method.
Intersection Group J
INTERSECTION
Objectives: To find the coordinate of unknown point by observing from the points of known coordinates.
Intersection is the process of determining the coordinate of unknown point by observing from the
points of known co‐ordinates. Intersection is done when the co‐ordinate of the feature for future use is needed & we have to place the coordinate of the point from the known co‐ordinates.
The main purpose is: • To establish the control points around the area.
The position of unknown point can be calculated by the following way: For the correctness & more accuracy the ideal angle of intersection should be 90° & the range is (60°‐
120°). Let A (XA, YA) & B (XB, YB) are the two points on the ground of known co‐ordinate. We have to fix C (xc,yc) now the distance & bearing of AB can be computed as follows:
Distance AB = 2 C(Xc,Yc)
Bearing of AB = tan
In ∆ABC, knowing a & b, Sine law can be applied. b a <C=180°‐(Γ+β) Then, θ β Γ A(Xa, Ya) C B(Xb,Yb)
=
=
D
a =
& b=
Now, F.B. of AC = F.B. of AB ‐ <Γ F.B. of BC = F.B. of BA + <β In ∆ABC, Then coordinates of C w.r.t. A Xc =Xb +a Sinθ1 Yc =Ya+b Cosθ1 Co‐ordinate of C w.r.t. B Xc = Xb+a Sin θ2 Yc = Yb+ a Cos θ2 Mean of two results can be used for more accurate coordinates.
Intersection Group J
INTERSECTION OF WATER TANK TOP AT NEATC, KHARIPATI, BHAKTAPUR
Group J
Now, the coordinates i.e. (E, N, R.L.) Of stations are as follows:
i.e. <CP2CP1W.T. =8˚30’50’’ <CP1CP2W.T. = (360˚‐193˚46’15’’) =166˚13’45’’
<CP2W3W.T. = (360˚‐243˚40’25’’) =116˚19’35’’
Now, From ∆CP1CP2W.T, <CP1+<CP2+<β =180˚ i.e. 8˚30’50’’+166˚13’45˚+<β =180˚ i.e. <β =5˚15’25’’ Now, Length of CP1CP2 = 50.5947 m From ∆CP1CP2W.T,
˚ ’ ’’
= . .
˚ = . .
˚
i.e.
.˚ ’ ’’
= . .
˚= . .
˚ ,
i.e. CP2W.T. =81.754 m
INTERSECTION OF WATER TANK TOP AT NEATC, KHARIPATI, BHAKTAPUR
Group J
& CP1W.T. =131.4474 m
Bearing of CP2W.T. = 38˚30’5.47’’+193˚46’15’’‐180˚ =52˚16’20.47’’ (w.c.b.)
Bearing of CP1W.T. =38˚30’5.47’’+8˚30’50’’ =47˚0’55.47’’ (w.c.b)
Now , Co‐ordinate of water tank top with respect to CP1 = Easting of W.t. (Xw.t.) =Xcp1+Lcp1w.t. *Sin (47˚0’55.47’’) = 1000+131.4474 Sin (47˚0’55.47’’) = 1096.1586 m Northing of W.t. (Yw.t.) = Ycp1+Lcp1w.t.* Cos (47˚0’55.47’’) = 1000+131.4474 Cos (47˚0’55.47’’) = 1089.6210 m Co‐ordinate of water tank top with respect to Cp2 = Easting of W.t. (Xw.t.) = Xcp2+Lcp2w.t. *Sin (52˚16’20.47’’) = 1031.497+81.754 Sin (52˚16’20.47’’) = 1096.1586 m Northing of W.t. (Yw.t.) = Ycp2+ Lcp2w.t.*Cos (52˚16’20.47’’) = 1039.595+81.754 Cos (52˚16’20.47’’) =1089.6209 m Now, <W3CP2W.T. =Bearing of CP2 W.t. – Bearing of CP2W3 = 52˚16’20.47’’‐21˚58’59.61’’ = 30˚17’20.86’’ From ∆CP2W3W.T, <CP2+<W3+<α =180˚ i.e. <α = 180˚‐30˚17’20.86’’‐116˚19’35’’ = 33˚23’4.14’’ Now, Length of CP2W3 = 50.1502 m From ∆CP2W3W.T,
˚ ’ . ’’ ’
= . .
˚ ’ ’’=
. .˚ ’ . ’’
i.e.
.˚ ’ . ’’
= . .
˚ ’ ’’ = . .
˚ ’ . ’’
i.e. CP2W.T. = 81.6871 m, and W3W.T. =45.9677 m
Now, Easting of W.t. w.r.t. CP2 = Easting of CP2+ L Sin (52˚16’20.47’’)
= 1031.497+81.6871 Sin (52˚16’20.47’’)
= 1096.1056 m
Northing of W.t. w.r.t. CP2 = Northing of Cp2 + L Cos (52˚16’20.47’’)
= 1039.595+ 81.6871 Cos (52˚16’20.47’’) = 1089.5800 m
INTERSECTION OF WATER TANK TOP AT NEATC, KHARIPATI, BHAKTAPUR
Group J
Now, Bearing of W3W.t. = 21˚58’59.61’’+243˚40’25’’‐180˚ =85˚39’24.61’’ (w.c.b.) Easting of W.t. w.r.t. W3 = Easting of W3+LSin (85˚39’24.61’’) = 1050.270 +45.9677 Sin (85˚39’24.61’’) = 1096.1057 m Northing of W.t. w.r.t. W3 = Northing of W3+ L Cos (85˚39’24.61’’) = 1086.099+45.9677 Cos (85˚39’24.61’’) = 1089.5801 m
FOR ALTITUDE CALCULATION:
Vertical angle from CP1 i.e.α1 = 11˚30’20’’ Now, Elevation difference between instrument station Cp1 and Water tank top i.e. H1 =D Tanα1 (D= Cp1W.T.) = 131.4474 Tan (11˚30’20’’) = 26.7565 m H.I. of CP1 = 1.44 m R.L. of W.t. w.r.t. Cp1 = R.L. of CP1+1.44+H1 =1336.304+1.44+26.7565 = 1364.500 m And, vertical angle from CP2 i.e. α2 = 17˚54’10’’ H2 = D Tan α2 (D= Cp2W.t.) = 81.754 Tan (17˚54’10’’) = 26.4101m H.I. of CP2 = 1.51 m R.L. of W.t. w.r.t. CP2 = R.L. of CP2 +1.51+ H2 = 1336.606+1.51+26.4101 = 1364.526 m And, Vertical Angle from W3 i.e. α3= 29˚41’55’’ H3= D Tan α3 (D= W3W.t.) = 45.9677 Tan (29˚41’55’’) = 26.2180 m H.I. of W3 = 1.48 m R.L. of W.t. w.r.t. W3 = R.L. of W3+1.48+ H3 = 1336.818 +1.48+26.2180 = 1364.516 m Now the Exact R.L. of W.t. = Average of R.L. from three station observation
= . . .
= 1364.514 m
Result: Hence the co‐ordinate of water tank top at NEATC is found as follows: S.N. Easting(m) Northing(m) Mean
Easting (m) Mean
Northing (m) Reduced Level (m)
Mean Reduced level (m)
Remarks
1 1096.1586 1089.6210 1096.1409m
1089.6073m
1364.500 1364.514m
Obs. from CP1
2 1096.1586 1089.6209 1364.526 Obs. from Cp2
3 1096.1057 1089.5801 1364.516 Obs. from W3
INTERSECTION OF WATER TANK TOP AT NEATC, KHARIPATI, BHAKTAPUR
αi=573li^2/RLs(minute)Calculated Theodolite Reading(10" least
count)(360˚‐angle)
(For Transition & circular(TC) one left half part i.e.(TS‐SC)
(For circular & spiral(CS)to one right half part (ST) i.e.(CS‐ST)
COMBINED CURVED SETTING DATA:
αi=573li^2/RLs(minute)Calculated Theodolite Reading(10" least
count)
Curve SettingGroup J
45
Compound Curve:
IP (1+200m)
∆ 30˚30’40’’
TL D
(1+152.23 M) S (1+244.71 m)
N Φ E SC CS F
(1+122.23m) T1 G T2 (1+274.71m)
(TS) (ST)
A R R
Φ ∆‐2Φ Φ
∆
C
Fig. Compound curve with (Transition, Spiral and Circular curves)
46
6.4. Transition Curves:
A non‐ circular curve introduced between a straight and a circular curve is known as a transition curve. The curvature of transition curve varies from zero at its beginning to a definite value at it’s junction with the circular curve. The transition curve has the following advantages:
It enables to introduce super‐elevation in proportion to the rate of change of curvature. It avoids the danger of derailment at the point of commencement if full amount of super‐elevation is suddenly applied at the point.
It avoids over turning and side slipping of the moving vehicles. It eliminates discomforts caused to the passengers while negotiating a curve. Various types of transition curves are:
I. Cubical Spiral II. Cubic Parabola III. The Lemniscate curve
Cubical spiral and cubic parabolic transition curves are best suited to railway curves and Lemniscate
curves fro highway curves.
I. Cubical Spiral: The standard equation of a cubical spiral curve is given by
x =
Where, L = Total length of the transition curve T1 R = radius of the circular curve l x l =distance measured along the curve L x = perpendicular offset from the tangent Fig. Cubic spiral
II. Cubic Parabola : The standard equation of a cubic parabola is given by :
X=
y x where, y = distance measured along the tangent Fig. Cubic Parabola
III. The Lemniscate curve: The equation of this type of curve is given by:
r =
45˚ ρ
Where, r = radius of the curvature <α ρ = Polar ray of any point. Fig. The Lemniscate Curve α= Polar deflection angle i.e. angle between the polar ray and the straight.
47
The transition curve is introduced between a straight and a circular curve in order to introduce superelevation gradually from zero at the point of commencement of the transition curve and the full amount at the junction of transition curve and the circular curve. If h is the amount of superelevation in centimeters and 1 in n be the rate of superelevation over the transition curve, L is the length of the transition curves in meters. Then,
a. D = i.e. L =
b. L =
c. L = c is rate of change of centrifugal acceleration in m/sec3, R is radius in meter and v is velocity of vehicle
in m/sec.
Superelevtion (h) = where, h = superelevation rise and G = gauge of the railway track.
Here, 1. The angle between the back tangent and tangent at the junction of the transition curve with the
circular curve is called Spiral angle. i.e. (Φ) where, Φ = radian
I.e. Φ = degree
2. The distance through which main circular curve is shifted inward to accommodate the transition
curve is known as shift. Its value is S=
3. The tangent length of the combined curve : Total tangent length = (R+S) Tan (∆/2) +L/2
4. Length of combined curve : The central angle for the circular curve = ∆‐2Φ
The length of the circular curve = ∆
˚
Total length of the combined curve = L + length of Circular curve +L
=2 ∆
˚
5. Deflection angle :
For circular curve, D = . where, c = Length of chord
For transition curve δ =
Where, R = radius of circular curve L = Length of transition curve l = distance from the point of commencement of transition curve.
6. Chainage: Chainage of i.e. T1 (TS) =Chainage of IP – TL Chainage of SC = Chainage of TS +L Chainage of CS = Chainage of Sc + length of circular curve, Chainage of ST = Chainage of CS + L
Chainage of T2= Ch of T1 + 2L ∆˚
48
Field Procedures:
1. The instrument was set at T1 and compound deflection angles were adjusted on the
theodolite.
2. An arrow with tape at a distance of chord was ranged at that angle.
3. Different points of the transition curve were obtained in similar manner.
4. Then the instrument was shifted at back tangent point and the points were obtained
similarly as above.
5. The remaining portion of the curve was circular part was set by Rankine’s method.
KATHMANDU ENGINEERING COLLEGEKalimati, Kathmandu
l
Station I.S. Rise Fall R.L. RemarksTBM1 22 1.006 0.896 0.786 1348.122 TBM1
Instrument At: W7Ht. of instrument axis : 1.455MSighted to
Face H.Dist.
d m s d m s d m s d m s d m s d m s T M Bw6 L 0 0 20W8 L 127 38 0 89 32 0 0 28 0 1.44 1.085 0.73 70.995W8 R 307 39 0 270 28 20 0 28 20 1.25 0.895 0.54 71.000W6 R 180 1 40W6 L 90 0 0W8 L 217 38 0W8 R 7 38 0W6 R 240 0 40
Instrument At: W8Ht. of instrument axis : 1.454MSighted to Face Staff Reading H.Dist.
d m s d m s d m s d m s d m s d m s T M BW7 L 0 0 0W9 L 197 29 40 87 40 0 2 20 0 1.2 0.923 0.65 55.408W9 R 17 29 40 272 20 20 2 20 20 1.09 0.815 0.54 55.000W7 R 180 0 20W7 L 90 0 20W9 L 287 29 20W9 R 107 30 0W7 R 270 0 20
H.C.R. H.A. Mean H.A. V.C.R. V. Angle
V. Angle
Mean V. Angle
37 20
127 37 30
0
V.C.R. Staff Reading
KATHMANDU ENGINEERING COLLEGEKalimati, Kathmandu
THEODOLITE FIELD OBSERVATION SHEET(THEODOLITE TRAVERSING)
(SURVEY Camp 2064‐B, Kharipati, Bhaktapur)
H.C.R. H.A. Mean H.A.
20
127 37 40
127
Mean V. Angle
37 2028 10
127 37 40
127
197 29 20
197 29 20
197 29 0
197 29 40
197 29
2 20 10
Group j
Horizontal Angle Observation Sheet
Instrument At: W9
Ht. of instrument axis : 1.462Sighted
to Face Staff Reading H.Dist.
d m s d m s d m s d m s d m s d m s T M BW8 L 0 0 0W10 L 183 26 20 91 24 0 1 24 0 1.2 0.865 0.53 66.960W10 R 3 27 20 271 24 20 1 24 20 1.3 0.965 0.63 67.000W8 R 180 1 40W8 L 90 0 20W10 L 273 26 0W10 R 93 26 0W8 R 270 0 20
Instrument At: W10Ht. of instrument axis : 1.5Sighted to
Face Staff ReadingH.DIST.
d m s d m s d m s d m s d m s d m s T M BW9 L 0 0 20W11 L 157 39 10 89 58 20 0 1 40 1.9 1.545 1.19 70.995W11 R 337 39 20 271 58 0 0 58 0 1.8 1.45 1.1 70.000W9 R 180 0 20W9 L 90 0 20W11 L 247 39 20W11 R 67 39 20W9 R 270 0 20
157 39 20
39 0
183 26 0
183 26 20
183 25
183
157 39 0
157
40
V. AngleH.C.R. H.A. Mean H.A. V.C.R.
40
10
Mean V. Angle
Mean V. Angle
24
H.C.R. H.A. Mean H.A. V.C.R. V. Angle
1
183 552525
290 50
157 39 2.5
157 38 50
Group j
Horizontal Angle Observation Sheet
Instrument At: W11Ht. of instrument axis : 1.43Sighted to
Face Staff ReadingH.Dist.
d m s d m s d m s d m s d m s d m s T BW10 L 0 0 20W12 L 117 38 20 117 38 0 95 51 0 5 51 0 1.2 0.83 0.46 73.231W12 R 297 38 0 264 9 0 5 51 0 1.2 0.833 0.47 72.736W10 R 180 0 0 117 38 0W10 L 90 0 20W12 L 207 38 0 117 37 40W12 R 27 38 20W10 R 270 0 20 117 38 0
Instrument At: W12Ht. of instrument axis : 1.455Sighted to
Face Staff ReadingH.DIST.
d m s d m s d m s d m s d m s d m s T M BW11 L 0 0 20 0W13 L 158 58 20 158 58 0 93 36 20 3 36 20 1.2 0.863 0.53 67.500W13 R 338 58 40 266 19 50 3 40 0 3.12 2.78 2.44 67.727W11 R 180 0 20 158 58 20W11 L 90 0 20W13 L 248 58 40 158 58 20W13 R 68 58 40W11 R 270 0 0 158 58 40
158 58 20
3 38 10
H.C.R. H.A. Mean H.A.
H.C.R. H.A. Mean H.A.
51 0
117 37 55
V.C.R. V. Angle
5
Mean V. Angle
V.C.R. V. AngleMean V. Angle
Group j
Horizontal Angle Observation Sheet
Instrument At: W13Ht. of instrument axis : 1.38Sighted Face Staff Reading H.DIST.
d m s d m s d m s d m s d m s d m s T M BW12 L 0 0 20W14 L 204 56 50 204 56 30 89 20 10 0 39 50 0.9 0.618 0.34 56.500W14 R 24 57 20 270 39 50 0 39 50 1.1 0.818 0.54 56.494W12 R 180 0 40 204 56 40W12 L 90 0 20W14 L 294 56 20 204 56 0W14 R 114 56 40W12 R 270 0 20 204 56 20
Instrument At: W14Ht. of instrument axis : 1.39Sighted to Face Staff Reading H.DIST.
d m s d m s d m s d m s d m s d m s T M BW13 L 0 0 20W15 L 165 24 40 165 24 20 94 23 20 4 23 20 1.2 0.906 0.61 58.800W15 R 345 24 30 265 36 0 4 23 40 1.2 0.905 0.61 58.654W13 R 180 0 0 165 24 30W13 L 90 0 20W15 L 255 24 40 165 24 20W15 R 75 24 0W13 R 270 0 20 165 23 40
23 30
165 24 12.5
204 22.556
0 34 50
H.C.R. H.A. Mean H.A. V.C.R. V. Angle Mean V. Angle
H.C.R. H.A. Mean H.A. V.C.R. V. Angle Mean V. Angle
4
Group j
Horizontal Angle Observation Sheet
Instrument At: W15Ht. of instrument axis : 1.4Sighted to
Face Staff ReadingH.DIST.
d m s d m s d m s d m s d m s d m s T M BW14 L 0 0 20W16 L 178 40 40 178 40 30 268 37 0 1 23 0 1.2 0.845 0.49 71.000W16 R 358 38 20 91 22 40 1 22 40 1.3 0.945 0.59 70.959W14 R 179 57 40 178 40 40W14 L 90 0 20W16 L 268 45 0 178 44 40W16 R 88 45 40W14 R 270 2 40 178 43 0
Instrument At: W16Ht. of instrument axis : 1.31Sighted to
Face Staff ReadingH.DIST.
d m s d m s d m s d m s d m s d m s T M BW15 L 0 0 20W17 L 107 44 20 107 44 0 95 6 0 5 6 0 0.8 0.508 0.22 58.500W17 R 287 44 20 264 22 20 5 37 40 1 0.705 0.41 58.584W15 R 180 0 0 107 44 20W15 L 90 0 0W17 L 197 44 0 107 44 0W17 R 17 44 40W15 R 270 0 40 107 44 0
12.542
V. AngleMean V. Angle
107 44 10
5 21 50
1 22 50
V.C.R.
Mean V. AngleV. AngleV.C.R.Mean H.A.H.A.H.C.R.
Mean H.A.H.A.H.C.R.
178
Group j
Horizontal Angle Observation Sheet
Instrument At: W17Ht. of instrument axis : 1.45Sighted to
Face Staff ReadingH.DIST.
d m s d m s d m s d m s d m s d m s T M BW16 L 0 0 20W18 L 105 22 40 105 22 20 81 43 0 8 17 0 1.6 1.343 1.09 51.500W18 R 285 24 0 278 16 40 8 16 40 1.6 1.34 1.08 50.921W16 R 180 0 20 105 23 40W16 L 90 0 20W18 L 195 23 40 105 23 20W18 R 15 23 20W16 R 270 1 10 105 22 10
Instrument At: W18Ht. of instrument axis : 1.45Sighted to
Face Staff ReadingH.DIST.
d m s d m s d m s d m s d m s d m s T M BW17 L 0 0 20W19 L 196 0 40 196 0 20 88 49 40 1 10 20 1.1 0.775 0.45 65.000W19 R 16 0 40 271 9 40 1 9 40 1.2 0.875 0.55 64.973W17 R 18 0 30 196 0 10W17 L 90 0 20W19 L 286 0 40 196 0 20W19 R 106 0 20W17 R 269 59 40 196 0 40
196 0 22.5
1 10 0
H.C.R. H.A. Mean H.A. V.C.R. V. AngleMean V. Angle
V. AngleMean V. Angle
105 22 52.5
8 16 50
H.C.R. H.A. Mean H.A. V.C.R.
Group j
Horizontal Angle Observation Sheet
Instrument At: W19Ht. of instrument axis : 1.4Sighted to
Face Staff ReadingH.DIST.
d m s d m s d m s d m s d m s d m s T M BW18 L 0 0 20CP1 L 158 49 0 158 48 40 81 24 50 8 35 10 1.69 1.343 1 68.500CP1 R 338 45 20 279 24 20 9 24 20 1.89 1.534 1.18 68.581W18 R 179 58 0 158 47 20W18 L 90 0 20CP1 L 248 44 10 158 43 50CP1 R 68 50 10W18 R 269 58 30 158 51 40
Instrument At: CP1Ht. of instrument axis : 1.54Sighted to
Face Staff ReadingH.DIST.
d m s d m s d m s d m s d m s d m s T M BW19 L 0 0 0CP2 L 206 1 0 206 1 0 90 18 30 0 18 30 1.24 0.987 0.73 50.600CP2 R 26 1 0 269 41 40 0 18 20 1.51 1.254 1 50.699W19 R 180 0 0 206 1 0W19 L 90 0 0CP2 L 296 1 20 206 1 20CP2 R 116 1 20W19 R 270 0 0 206 1 20
45
H.C.R. H.A. Mean H.A. V.C.R. V. AngleMean V. Angle
158 47 52.5
H.C.R. H.A. Mean H.A. V.C.R. V. AngleMean V. Angle
206 1 10
250 18
8 59
Group j
Horizontal Angle Observation Sheet
Instrument At: CP2Ht. of instrument axis : 1.5Sighted to
Face Staff ReadingH.DIST.
d m s d m s d m s d m s d m s d m s T M BCP1 L 0 0 20W3 L 163 29 40 163 29 30 81 52 20 8 7 40 1.32 1.064 0.81 50.300W3 R 343 29 40 278 7 30 8 7 30CP1 R 180 0 20 163 29 20CP1 L 90 0 20W3 L 253 29 40 163 29 20W3 R 73 29 20CP1 R 270 0 50 163 28 30
Instrument At: W3Ht. of instrument axis : 1.32Sighted to
Face Staff ReadingH.DIST.
d m s d m s d m s d m s d m s d m s T M BCP2 L 0 0 0W4 L 236 6 20 236 6 20 90 11 0 0 11 0 0.8 0.49 0.18 62.000W4 R 56 6 0 269 49 0 0 11 0CP2 R 180 0 0 236 6 0CP2 L 90 0 20W4 L 326 6 40 236 6 20W4 R 146 6 40CP2 R 270 1 0 236 6 40
236 6 5
V.C.R. V. AngleMean V. Angle
0 11 0
163 29 10
H.C.R. H.A. Mean H.A.
H.C.R. H.A. Mean H.A. V.C.R. V. AngleMean V. Angle
8 7 35
Group j
Horizontal Angle Observation Sheet
Instrument At: W4Ht. of instrument axis : 1.32Sighted to
Face Staff ReadingH.DIST.
d m s d m s d m s d m s d m s d m s T M BW5 L 0 0 20W3 L 117 9 40 117 9 20 90 6 50 0 6 50 1.4 1.05 0.71 69.000W3 R 297 8 40 269 53 0 0 7 0 1.5 1.05 0.81 69.000W5 R 180 0 0 117 8 40W5 L 90 0 20W3 L 207 9 40 117 9 20W3 R 27 9 40W5 R 270 0 20 117 9 20
Instrument At: W5Ht. of instrument axis : 1.42Sighted to
Face Staff ReadingH.DIST.
d m s d m s d m s d m s d m s d m s T M BW4 L 0 0 20W6 L 139 51 50 139 51 30 90 50 0 0 50 0 0.9 0.595 0.29 61.000W6 R 319 51 20 269 54 90 0 4 30 1 0.695 0.39 60.996W4 R 120 0 20 139 51 0W4 L 90 0 20W6 L 229 51 20 139 51 0W6 R 49 51 40W4 R 270 0 20 139 51 20
V. AngleMean V. Angle
117 9 10
H.C.R. H.A. Mean H.A. V.C.R.
V.C.R. V. AngleMean V. Angle
0 6 55
H.C.R. H.A. Mean H.A.
15
139 51 25
0 27
Group j
Horizontal Angle Observation Sheet
Instrument At: W6Ht. of instrument axis : 1.45Sighted to
Face Staff ReadingH.DIST.
d m s d m s d m s d m s d m s d m s T M BW5 L 0 0 20W7 L 137 33 40 137 30 20 90 18 40 0 18 40 1.7 1.414 1.13 57.200W7 R 317 33 40 269 40 40 0 19 20 1.8 1.513 1.23 57.498W5 R 180 0 20 137 33 20W5 L 90 0 20W7 L 227 33 30 137 33 10W7 R 47 33 20W5 R 270 0 0 137 33 20
H.C.R. H.A. Mean H.A. V.C.R. V. AngleMean V. Angle
d m s d m s Top middle BottomIP5/1.41M T1 0 0 0 97 43 0 0.9 0.539 0.178 70.898 ‐9.607 1324.5120+313.553 L5 26 11 0 97 42 20 1.6 1.500 1.400 19.640 ‐2.657 1330.501
Zero Set At:IP7 R.L.OF IP8:1337.807MInst.Stn./HI. Staff Point
Horizantal distance
Vertical distance R.L. Remarks
d m s d m s Top middle BottomIP8/1.40 IP9 151 0 30 89 20 0 1.5 1.143 0.786 71.390 0.831 1338.895m 0+580 0 0 0 89 54 0 1.8 1.713 1.626 17.400 0.030 1337.524
Exact R.L.of W8=1339.042mObserved R.L.of W8=1339.062merror=(1339.062-1339.042)=0.02m=20mm error +ve correction is negativeprecission=25√K mm where k is kilometer.
25√0.895=23.651mm o.k. within permissible limit
RemarksBS FSDistances corrected R.L.
correction(-)Station IS HI R.L.
Level Transfer for Road
s.n.Total length
Mean Length Precision
From To1 Q6 Q4 77.36 77.35 1 in 38672 Q4 Q6 77.343 Q1 Q2 91.1 91.09 1 IN 45544 Q2 Q1 91.085 Q4 TBM 23.43 23.425 1 IN 23426 TBM Q4 23.42
Survey Camp 2064 Resection Theory & Calculation Group J
RESECTION: Object: To determine the position of unknown point i.e. instrument station by Resection Resection is the process of determining the position of unknown points by observing the horizontal and vertical
angle from instrument position to at least three well defined points of known position (i.e. coordinates). This problem can be tackled either by two point problem or by three point problem according to the availability of known points. Significance of resection is given below:
To establish the control points around the survey area. For measuring the map whose plans are development with respect to common origin. For joining the map with national grid line.
The position of unknown point is calculated by three point problem by the following methods: There may be two conditions according to the position of the resection point p.
a) When P is inside the ∆ABC i.e. α+β>180° b) When P is outside the ∆ABC i.e. α+β<180°
Case I: α+β>180° Case II: α+β<180° Let A, B, C & D are the well defined points of known coordinates. Angle α, β, Γ and δ be the measured horizontal angle from A to B, C, D & A (measuring with horizon. Closed). In ABCD, <X+<Y+<α +<β+<B =360° <B can be computed by using cosine law. <α & <β are measured angle. <X+<Y=360°‐[<α +<β+<B] Now, <X+<Y = ф ……………………….. (i) i.e. value can be known. From ∆ABP & ∆BPC:‐
, =
……………………….. (ii)
By combining equations (i) and (ii) <X = ф‐<Y from equation (i)
ф
= K
& ф ф
= K
Sin ф Cot Y‐Cos ф = K
Sin ф Cot Y = K+Cos ф or, Cot Y = ф
ф
Or, Cot Y = K Cosecф+Cotф or, <Y =cot ф ф
) or <y = tan ф ф
Survey Camp 2064 Resection Theory & Calculation Group J
And, <X = ф ‐tan ф ф)
When angle <x & <y are computed then we can calculate the coordinate of unknown point P by using sine law for distance, Latitude & departure computation. Here, CP1, CP2 and W3 are three known points where coordinates is already computed and we have supposed these three points as S, D and H respectively. Let P be the unknown or instrument point whose coordinate is to be computed with the help of these known points. Here, we have the following data. From observation table: <JM4PW13 =46˚48’18.3’’=<α <W13PW12 =99˚36’33.3’’=<β <W12PJM4 =213˚35’8.34’’=<Г Here, α+β<180˚
FOR JM4W13: Length of JM4W13= 13 4 13 4
= 842.24 882.477 1014.587 991.863
= 40.237 22.724 =46.2103 m Easting of JM4W13 =Easting of W13‐ Easting of Jm4 =842.24‐882.477 =‐40.237 m Northing of JM4W13 = Northing of W13‐ Northing of JM4 =1014.587‐991.863 = 22.724 m
Length of W13W12 = 814.175 842.24 1076.203 1014.587
= 28.065 61.616 =67.7065 M Easting of W13W12 = Easting of W12‐ Easting of W13 = 814.175‐842.24 =‐28.065 m Northing of W13W12 = Northing of W12‐ Northing of W13
FOR W12JM4: Length of W12JM4 = 882.477 814.175 991.863 1076.203
= 68.302 84.34 =108.5283 m
Easting of W12JM4 = Easting of JM4‐ Easting of W12 = 882.477‐814.175 =68.302 m W12 (814.175, 1076.203) Northing of W12JM4 = Northing of JM4‐ Northing of W12 = 991.863‐1076.203 <Y = ‐84.34 m
JM4 (882.477, 991.863) Now, <W13 = (360˚‐ Bearing of W13W12) + Bearing of W13JM4 = (360˚‐335˚30’41.66’’) + (299˚27’20.72’’‐180˚) =24˚29’18.34’’+119˚27’20.72’’ =143˚56’39.06’’ Now from JM4PW12W13, <X+<Y+<α+<β+<W13=360˚ And, <x+<y = 360˚‐<α+<β+<W13 =360˚‐(46˚48’18.3’’+99˚36’33.3’’+143˚56’39.06’’) =360˚‐290˚21’30.66’’ i.e.Φ =69˚38’29.34’’ Now we have, in ∆ PW12W13 &∆ PJM4W13, Using Sine law,
And
Or, PW13 = =
Or,
Or, K=
Or, K =˚ ’ . ’’˚ ’ . ’’
.
.
OR, k= 1.083361229 We have,
<Y = tan
Survey Camp 2064 Resection Theory & Calculation Group J
= tan ˚ ’ . ’’. ˚ ’ . ’’
= tan 0.65504 i.e. <Y = 33˚13’35.57’’ Now, <X = Φ‐<Y =69˚38’29.34’’‐33˚13’35.57’’ i.e. <X =36˚24’53.77’’ Now, from ∆PW12W13, Using Sine rule,
˚ ’ . ’’ ˚ ’ . ’ ˚ ’ . ’’
Or, . ˚ ’ . ’’ ˚ .
i.e. PW12 = 50.356 m
And, from ∆PW13JM4, Using Sine rule,
13 446˚48’18.3’’
4180 46˚48’18.3’’ 36˚24’53.77’’
Or, . ˚ ’ . ’’ ˚ .
i.e. PJM4 =62.943 m
Now, Bearing of JM4P =Bearing of W13JM4+<X+180˚ = (299˚27’20.72’’‐180˚) +36˚24’53.77’’+180˚ =335˚52’14.49’’ Easting of P w.r.t. JM4 =Easting of JM4 +Lsinθ =882.477 +62.943*sin (335˚52’14.49’’) = 856.746 m Northing of P w.r.t. JM4 = Northing of JM4+LCosθ =991.863+62.943*Cos (335˚52’14.49’’) =1049.3064 m I.e. the coordinate of B with respect to JM4 are: Easting(m) Northing(m) 856.746 1049.3064
Similarly, Easting of W13P = LW13p*Sinθ Now,
PW13 = 13 4
PW13 = ˚ ’ . ’’˚ ’ . ’’
46.2103 =37.6278 m
Bearing of W13P = bearing of W13JM4 – (180˚‐(46˚48’18.3’’+36˚24’53.77’’)) = (299˚27’20.72’’‐180˚)‐(96˚46’48’’) =22˚40’32.72’’ (W.C.B.) Easting of P w.r.t. W13 =Easting of W13 + L Sinθ = 842.24+37.6278*sin (22˚40’32.72’’) =856.746 m Northing of P w.r.t. W13 = Northing of W13+ LCosθ
Survey Camp 2064 Resection Theory & Calculation Group J
=1014.587+37.6278*Cos (22˚40’32.72’’) =1049.3062 m Hence, Co‐ordinate of P w.r.t. W13 are: Easting(m) Northing(m) 856.746 1049.3064 Similarly, Easting of W12P = LW12p*Sinθ Bearing of W12P = Bearing of W13W12 +<Y‐180˚ = 335˚30’41.66’’+ (360˚‐33˚13’35.57’’)‐540˚ = 122˚17’6.09’’ Easting of P w.r.t. W12 = Easting of W12 + L Sinθ =814.175+L*sin (188˚44’17.23’’)
Here, ˚ ˚ ’ . ’’ ˚ ’ . ’’
W12p = ˚ .˚ ’ . ’’
67.7065 = 50.356 M
Easting of P w.r.t. W12= 814.175+50.356 Sin (122˚17’6.09’’) =856.746 m Northing of O w.r.t. W12 = 1076.203+50.356 Cos (122˚17’6.09’’) =1049.3063 m Hence the Co‐ordinate of P w.r.t. W12 are: Easting(m) Northing(m) 856.746 1049.3063 Result: Hence the actual Co‐ordinate of Resection Point (P) is as follows:
S.N. Easting (m) Northing (m) Mean Easting (m) Northing (m)