Advanced Surveying - Theory and Practice.pdf

1|Page 2|Page Advanced Surveying: Theory & Practice Authors Dr. Ramakant Agrawal, Mr. Parshottam Sarathe, Professor and Head, Asstt. Professor, Department...

1|Page 2|Page Advanced Surveying: Theory & Practice Authors Dr. Ramakant Agrawal, Mr. Parshottam Sarathe, Professor and Head, Asstt. Professor, Department of Civil Engineering, Department of Civil Engineering, Oriental Institute of Science and Oriental Institute of Science and Technology, Bhopal Technology, Bhopal Reviewer Dr. Sirisha Uppaluri, Associate Professor, Department of Civil Engineering Christ (Deemed To Be University), Bengaluru All India Council for Technical Education Nelson Mandela Marg, Vasant Kunj, New Delhi, 110070 3|Page BOOK AUTHOR DETAILS Dr. Ramakant Agrawal, Professor and Head, Department of Civil Engineering, Oriental Institute of Science and Technology, Bhopal Email ID: [email protected] Mr. Parshottam Sarathe, Asstt. Professor, Department of Civil Engineering, Oriental Institute of Science and Technology, Bhopal Email ID: [email protected] BOOK REVIEWER DETAILS Dr. Sirisha Uppaluri, Associate Professor, Department of Civil Engineering Christ (Deemed To Be University), Bengaluru Email ID: [email protected] BOOK COORDINATOR (S) – English Version 1. Dr. Amit Kumar Srivastava, Director, Faculty Development Cell, All India Council for Technical Education (AICTE), New Delhi, India Email ID: [email protected] Phone Number: 011-29581312 2. Mr. Sanjoy Das, Assistant Director, Faculty Development Cell, All India Council for Technical Education (AICTE), New Delhi, India Email ID: [email protected] Phone Number: 011-29581339 November, 2022 © All India Council for Technical Education (AICTE) ISBN : 978-81-959863-3-0 All rights reserved. No part of this work may be reproduced in any form, by mimeograph or any other means, without permission in writing from the All India Council for Technical Education (AICTE). Further information about All India Council for Technical Education (AICTE) courses may be obtained from the Council Office at Nelson Mandela Marg, Vasant Kunj, New Delhi-110070. Printed and published by All India Council for Technical Education (AICTE), New Delhi. Laser Typeset by: Printed at: Disclaimer: The website links provided by the author in this book are placed for informational, educational & reference purpose only. The Publisher do not endorse these website links or the views of the speaker / content of the said weblinks. In case of any dispute, all legal matters to be settled under Delhi Jurisdiction, only 4|Page 5|Page Acknowledgement The authors are grateful to the authorities of AICTE, particularly Prof. Anil D. Sahasrabudhe, Chairman; Prof. M. P. Poonia, Vice-Chairman; Prof. Rajive Kumar, Member-Secretary and Dr Amit Kumar Srivastava, Director, Faculty Development Cell for their planning to publish the books on (Advanced Surveying-Theory&Practice). We sincerely acknowledge the valuable contributions of the reviewer of the book Dr. Sirisha Uppaluri, Associate Professor, Dept. of Civil Engineering, Christ (Deemed To Be University), Bengaluru- 560074, Karnataka for giving valuable inputs and suggestions to bring this book in present form. The authors are thankful to Dr. Sadhna Agrawal, Amber, Akshat, Ms.Swati and Aryansh for their cooperation and patience during writing this book. This book is an outcome of various suggestions of AICTE members, experts and authors who shared their opinion and thought to further develop the engineering education in our country. Acknowledgements are due to the contributors and different workers in this field whose published books, review articles, papers, photographs, footnotes, references and other valuable information enriched us at the time of writing the book. Dr. Ramakant Agrawal Parshottam Sarathe (v) 6|Page Preface The book titled “Advanced Surveying – Theory & Practice” is an effort of the authors to present their vast experience of teaching in the simplest form specially for diploma students strictly as per syllabus prescribed by AICTE New Delhi. The level and presentation of the book is kept in such a manner that diploma students can understand the subject easily. Efforts are made to explain the fundamentals of the subject in the simplest possible way. During the writing of various chapters of the book, various standard textbooks, web materials and you tube content were referred and accordingly we have divided the book into six chapters. The subject matter is clearly explained through definitions, principles, illustrations, and figures. The solved and unsolved numerical problems are included to explain the subject clearly, wherever necessary. The multiple-choice questions, short and long questions are included for preparations of various types of the examinations. Know more section is included in each chapter to teach the students the content beyond the syllabus. This will enable the students to learn latest knowledge, supplementary knowledge and history to update themselves and making the content interesting. Dynamic QR codes are provided at the end of each chapter to learn the subject in depth including interesting Videos to explain the subject elaborately and clearly. We expect that the book will be useful for diploma students and will inspire them to learn and discuss the applications of various surveying instruments and techniques. Every effort is made to minimise the errors in the content and numerical work, in spite that some errors may remain, and authors would be thankful to the readers if they point out the same. We would appreciate all constructive comments and suggestions which will contribute to the improvement of the book Dr. Ramakant Agrawal Parshottam Sarathe (vi) 7|Page Outcome Based Education For the implementation of an outcome based education the first requirement is to develop an outcome based curriculum and incorporate an outcome based assessment in the education system. By going through outcome based assessments, evaluators will be able to evaluate whether the students have achieved the outlined standard, specific and measurable outcomes. With the proper incorporation of outcome based education there will be a definite commitment to achieve a minimum standard for all learners without giving up at any level. At the end of the programme running with the aid of outcome based education, a student will be able to arrive at the following outcomes: Programme Outcomes (POs) are statements that describe what students are expected to know and be able to do upon graduating from the program. These relate to the skills, knowledge, analytical ability attitude and behaviour that students acquire through the program. The POs essentially indicate what the students can do from subject-wise knowledge acquired by them during the program. As such, POs define the professional profile of an engineering diploma graduate. National Board of Accreditation (NBA) has defined the following seven POs for an Engineering diploma graduate: PO1. Basic and Discipline specific knowledge: Apply knowledge of basic mathematics, science and engineering fundamentals and engineering specialization to solve the engineering problems. PO2. Problem analysis: Identify and analyses well-defined engineering problems using codified standard methods. PO3. Design/ development of solutions: Design solutions for well-defined technical problems and assist with the design of systems components or processes to meet specified needs. PO4. Engineering Tools, Experimentation and Testing: Apply modern engineering tools and appropriate technique to conduct standard tests and measurements. PO5. Engineering practices for society, sustainability and environment: Apply appropriate technology in context of society, sustainability, environment and ethical practices. PO6. Project Management: Use engineering management principles individually, as a team member or a leader to manage projects and effectively communicate about well-defined engineering activities. PO7. Life-long learning: Ability to analyse individual needs and engage in updating in the context of technological changes. (vii) 8|Page Course Outcomes By the end of the course the students are expected to learn: CO-1: Prepare plans using Plane Table Surveys CO-2: Prepare plans using Theodolite Survey CO-3: Find distances and elevations using Tacheometer CO-4: Prepare plans using Total Station instrument CO-5: Locate coordinates of stations using GPS Mapping of Course Outcomes with Programme Outcomes to be done according to the matrix given below: Expected Mapping with Programme Outcomes (1- Weak Correlation; 2- Medium correlation; 3- Strong Correlation) Course Outcomes PO-1 PO-2 PO-3 PO-4 PO-5 PO-6 PO-7 CO-1 3 2 2 3 1 2 3 CO-2 3 3 3 3 1 2 3 CO-3 3 3 3 3 1 2 3 CO-4 3 2 2 3 1 2 3 CO-5 3 2 2 3 1 2 3 (viii) 9|Page Guidelines for Teachers To implement Outcome Based Education (OBE) knowledge level and skill set of the students should be enhanced. Teachers should take a major responsibility for the proper implementation of OBE. Some of the responsibilities (not limited to) for the teachers in OBE system may be as follows:  Within reasonable constraint, they should manoeuvre time to the best advantage of all students.  They should assess the students only upon certain defined criterion without considering any other potential ineligibility to discriminate them.  They should try to grow the learning abilities of the students to a certain level before they leave the institute.  They should try to ensure that all the students are equipped with the quality knowledge as well as competence after they finish their education.  They should always encourage the students to develop their ultimate performance capabilities.  They should facilitate and encourage group work and team work to consolidate newer approach.  They should follow Blooms taxonomy in every part of the assessment. Bloom’s Taxonomy Teacher should Student should be Possible Mode of Level Check able to Assessment Students ability to Create Design or Create Mini project create Students ability to Evaluate Argue or Defend Assignment justify Students ability to Differentiate or Project/Lab Analyse distinguish Distinguish Methodology Students ability to Operate or Technical Presentation/ Apply use information Demonstrate Demonstration Students ability to Understand Explain or Classify Presentation/Seminar explain the ideas Students ability to Remember Define or Recall Quiz recall (or remember) Guidelines for Students Students should take equal responsibility for implementing the OBE. Some of the responsibilities (not limited to) for the students in OBE system are as follows:  Students should be well aware of each UO before the start of a unit in each and every course.  Students should be well aware of each CO before the start of the course.  Students should be well aware of each PO before the start of the programme.  Students should think critically and reasonably with proper reflection and action.  Learning of the students should be connected and integrated with practical and real life consequences.  Students should be well aware of their competency at every level of OBE. (ix) 10 | P a g e Abbreviations and Symbols List of Abbreviations General Term Abbreviations Full form Abbreviations Full form N-S North – South W.C.B Whole Circle Bearing LOS Line of Sight R.B. Reduced Bearing LOC Line of Collimation P.C. Point of Curve L Latitude P.T. Point of Tangency D Departure P.I. Point of Intersection s Staff Intercept EDM Electromagnetic Distance Meter/ Measurement f Focal Length of the CAD Computer Added objective Design GIS Geographical RS Remote Sensing Information System GPS Global Positioning TS Total Station system LED Liquid Crystal Diode EM Electromagnetic LCD Light Emitting Diode List of Symbols Symbols Description Symbols Description α (R ) Right Deflection angle Λ Web length β (L) Left Deflection angle Φ Phase Angle of web ∆ Deflection Angle N Number of Sides k Multiplying Constant in E Closing Error in Tacheometer Traverse Da, Dc Degree of Curve I Stadia Hair Interval f Focal Length C Additive Constant in Tacheometer (x) 11 | P a g e List of Figures Page No. Unit 1 Plane Table Surveying Fig. – 1.1 Plane Table Fig. – 1.2 Plain Alidade Fig. – 1.3 Telescopic Alidade Fig. – 1.4 Plumbing fork with U‐ frame Fig. – 1.5 Trough Compass Fig. ‐ 1.6 Spirit Level Fig. – 1.7 Radiation Method Fig.‐ 1.8 Intersection Method Fig.‐ 1.9 Traversing Method Fig ‐ 1.10 Radiation Method – Seven‐sided closed traverse Fig. 1.11– Locating Details by Intersection Method Fig. 1.12 – Locating Details by Traversing Method Unit 2 Theodolite Surveying Fig. No. ‐ 2.1 Components of transit theodolite Fig. No. 2.2 – Vertical circle with verniers and telescope Fig. No. 2.3 – Parts of Vertical Frame Fig. No. – 2.4 Cross‐ section along the length through upper and lower plate Fig. No. – 2.5 Photograph of Transit Theodolite Fig. No. – 2.6 ‐ Fundamental Axes of Transit Theodolite and their Relation Fig. No. ‐ 2.7 Reading of Vernier of Transit Theodolite Fig No. – 2.8 Levelling with three‐foot screw Fig No. 2.9 Levelling with four‐foot screw Fig No.‐ 2.10 Measurement of horizontal angle Fig. No. 2.11 Measurement of vertical angle Fig No.‐ 2.12 Measurement of Direct Angle Fig. No. – 2.13 Measurement of Deflection Angle Fig. No. –2. 14 Measurement of Magnetic Bearings Fig. No. – 2.15 Prolonging a Straight Line (xi) iii | P a g e Fig. No. – 2.16 Included angle method ‐Interior angle measured clockwise Fig. No. – 2.17 Included angle method ‐ Exterior angle measured clockwise Fig. No. – 2.18 Checks for open traverse‐ case 1 Fig. No. – 2.19 Checks for open traverse‐ case 2 Fig. No. – 2. 20 Calculations of Bearing from Angles Fig. No. – 2.21 Latitude and Departure Fig. No. – 2.22 Closing Error in Traverse Fig. No. –2. 23 Determination of interior angles Fig. No. – 2.24 Determination of length of survey lines. Fig. No. –2. 25 Determination of lengths & bearings of lines Fig. 2.26 – Determination of bearings of lines Fig. 2.27 – Determination of horizontal angle Fig.‐ 2.28 ‐ Determination of vertical angle Fig 2.30‐ Jesse Ramsden's Great Theodolite of 1787 Fig 2.31‐ A theodolite of 1851 Fig 2.32 ‐A transit theodolite with six‐inch circles, manufactured in Britain in 1910 by Troughton & Simms Fig 2.33 ‐ Wild T2 theodolite developed by Heinrich Wild in 1919 Unit 3 Tacheometric Surveying Fig No.‐ 3.1 Principle of Tacheometry Fig. No. – 3.2 Patterns of stadia diaphragm Fig. No. ‐ 3.3 Stadia Rod Fig. No. – 3.4 Principle of Stadia Method Fig. No. – 3.5 Anallatic Lens Fig. No. – 3.6 Elevated line of sight (Vertical holding of staff) Fig. No. – 3.7 Depressed line of sight (Vertical holding of staff) Fig. No. – 3.8 Determination of horizontal distance and R.L. Fig. No. – 3.9 Determination of horizontal distance and R.L. – Inclined sight Fig. No. – 3.10 Stadia Cross Hairs Fig. No. – 3.11 Computation of horizontal distance and R.L. Unit 4 Curve Fig No. – 4.1 Simple Circular Curve Fig No. ‐ 4.2 Compound Curve Fig No. ‐ 4.3 Reverse Curve Fig – 4.4 Transition Curve Fig – 4.5 Elements of Circular Curves Fig No. ‐ 4.6 Designation of curve Fig No. ‐ 4.7 Offsets from the long chord method Fig No. ‐ 4.8 Rankine’s method of deflection angle Fig No. ‐ 4.9 Setting out Circular Curve by Rankine’s Method i (xii) iv | P a g e Unit 5 Advanced Surveying Equipment Fig No. – 5.1 Sinusodial Wave in harmonic sinusoidal fashion Fig. No. – 5.2 Distance Measurement by EDM Fig. No. – 5.3 Photograph of Micro‐Optic Theodolite Fig. No. – 5.4 Photograph of Electronic Theodolite Fig. No. 5.5 – Basic Measurements by Total Station Unit 6 Remote Sensing, GPS and GIS Fig. No. – 1 Electromagnetic Spectrum Fig. No. – 2 Remote Sensing System (xiii) ii iii | P a g e CONTENTS Foreword iv Acknowledgement v Preface vi Outcome Based Education vii Course Outcomes viii Guidelines for Teachers ix Guidelines for Students ix Abbreviations and Symbols x List of Figures xi Contents Page No. CHAPTER‐1: Plane Table Surveying UNIT SPECIFICS RATIONALE PRE‐REQUISIT UNIT OUTCOMES 1.1 INTRODUCTION 1.2 PRINCIPLE OF PLANE TABLE SURVEYING 1.3 INSTRUMENTS USED IN THE PLANE TABLE SURVEYING 1.3.1 The Plane Table 1.3.2 Alidade 1.3.3 Plumbing Fork and Plumb Bob 1.3.4 Trough Compass 1.3.5 Spirit Level 1.4 Working Operations 1.4.1 Fixing the table on the tripod 1.4.2 Setting out of the table 1.4.3 Sighting the stations/objects 1.5 Methods of Plane Table Surveying 1.5.1 Radiation Method 1.5.2 Intersection Method 1.5.3 Traversing Method 1.6 Merits and Demerits of Plane Table Surveying 1.6.1 Merits 1.6.2 Demerits UNIT SUMMARY EXERCISES PRACTICAL KNOW MORE REFERENCES AND SUGGESTED READINGS DYNAMIC QR CODE FOR FURTHER READING CHAPTER‐2: Theodolite Surveying UNIT SPECIFICS i (xiv) iv | P a g e RATIONALE PRE‐REQUISITES UNIT OUTCOMES 2.1 INTRODUCTION 2.2 CLASSIFICATION OF THEODOLITE 2.2.1 Classification Based on Movement of Telescope: 2.2.2 Classification Based on Arrangement of Reading Observations 2.3 Components of Transit Theodolite 2.3.1 The Telescope 2.3.2 The Vertical Circle 2.3.3 The Index Frame or Vernier Frame 2.3.4 The Standards 2.3.5 The Upper Plate 2.3.6 The Lower Plate ‐ 2.3.7 Plate Level 2.3.8 The Levelling Head 2.3.9 Tripod: 2.3.10 Plumb Bob: 2.4 Technical Terms used in Transit Theodolite 2.5 Fundamental Axes of Transit Theodolite and Their Relationship 2.6 Reading of Vernier of Transit Theodolite 2.7 Temporary Adjustment of Transit Theodolite 2.7.1 Setting of Theodolite 2.7.2 Levelling of Theodolite 2.7.3 Elimination of parallax 2.8 Measurement of horizontal angle by Transit Theodolite 2.8.1 Direct Method 2.8.2 Method of repetition 2.9 Measurement of Vertical Angle by Transit Theodolite 2.10 Some Field Applications of Transit Theodolite 2.10.1 Measurement of Direct Angle 2.10.2 Measurement of Deflection Angle 2.10.3 Measurement of Magnetic Bearings 2.10.4 Prolonging a Straight Line 2.11 Theodolite Traversing 2.11.1 Traversing by Included Angles 2.11.2 Traversing by Deflection Angles 2.12 Checks in Traversing 2.12.1 Checks in Closed Traverse 2.12.2 Checks in Open Traverse 2.13 Calculations of Bearing from Angles 2.14 Traverse Computations 2.14.1 Consecutive Co‐ordinates: Latitude and Departure 2.14.2 Independent Co‐ordinates 2.14.3 Closing Error in Traverse 2.15 Balancing of Traverse 2.15.1 Bowditch method 2.15.2 Transit Method 2.16 Gales Traverse Table ii (xv) v|Page UNIT SUMMARY EXERCISES PRACTICAL KNOW MORE REFERENCES AND SUGGESTED READINGS DYNAMIC QR CODE FOR FURTHER READING CHAPTER‐3: Tacheometric Surveying UNIT SPECIFICS RATIONALE PRE‐REQUISIT UNIT OUTCOMES 3.1 Introduction 3.2 Principle of Tacheometry 3.3 Instruments Used in Tacheometry 3.3.1 Tacheometer 3.3.2 Stadia Rod 3.4 Systems of Tacheometric Measurement 3.5 Principle of Stadia Method 3.6 Field Methods for Determining Constants of Tacheometer 3.7 Anallatic Lens 3.8 Determination of Horizontal and Vertical Distances by Tacheometer 3.9 Limitation of Tacheometry UNIT SUMMERY EXERCISES PRACTICAL KNOW MORE REFERENCES AND SUGGESTED READINGS Dynamic QR Code for Further Reading CHAPTER‐4 UNIT SPECIFICS RATIONALE PRE‐REQUISITES UNIT OUTCOMES 4.1 Introduction 4.2 Classification of Curve 4.3 Simple circular curve 4.3.1 Elements of circular curves 4.3.2 Designation of curve 4.3.3 Methods of setting simple circular curves UNIT SUMMERY EXERCISES PRACTICAL KNOW MORE REFERENCES AND SUGGESTED READINGS DYNAMIC QR CODE FOR FURTHER READING i (xvi) vi | P a g e CHAPTER‐5: Curve UNIT SPECIFICS RATIONALE PRE‐REQUISIT UNIT OUTCOMES 5.1 Introduction 5.2 Principle of EDM 5.3 Component Parts and Their Function 5.4 Types and Uses Of EDM Instruments 5.5 Micro‐Optic Theodolite 5.6 Electronic Digital Theodolite 5.7 Total Station 5.7.1 Fundamental Quantities Measured by Total Station 5.7.2 Control Panel of Total Station 5.7.3 Common softkey functions 5.7.4 Orientation and Location of the Instrument 5.7.5 Sighting of the Object and Display of the Result 5.7.6 Traversing by Total station 5.7.7 Contouring by Total station UNIT SUMMARY EXERCISES PRACTICAL KNOW MORE Dynamic QR Code for Further Reading CHAPTER‐6: Advanced Surveying Equipment UNIT SPECIFICS RATIONALE PRE‐REQUISIT UNIT OUTCOMES 6.1 Introduction 6.2 Remote Sensing: Overview 6.3 Remote Sensing System 6.4 Application of Remote Sensing in Civil Engineering 6.4.1 Land use/ land cover mapping 6.4.2 Disaster Management 6.5 GPS Instruments 6.5.1 Elements of GPS 6.5.2 Use of GPS Instruments 6.5.3 Principle of GPS 6.6 Geographical Information System (GIS) 6.6.1 Components of GIS 6.6.2 Application of GIS 6.6.3 GIS software 6.7 Introduction to Drone Surveying UNIT SUMMARY EXERCISES PRACTICAL ii (xvii) vii | P a g e KNOW MORE REFERENCES AND SUGGESTED READINGS DYNAMIC QR CODE FOR FURTHER READING CO AND PO ATTAINMENT TABLE Index i (xviii)  1 Plane Table Surveying d UNIT SPECIFICS Through this unit we have discussed the following aspects:  Principle of plane table surveying  Instruments used in plane table surveying  Working operations of plane table surveying  Methods of plane table surveying  Merits and demerits of plane table surveying RATIONALE This unit describes purpose, principle, and methodologies of plane table surveying. The instruments used in the plane table survey and their uses are stated with neat diagrams. This unit discusses working operations of plane table survey including fixing of table, levelling, centring and orientation of table and sighting of objects. The survey by the plane table is done for locating various ground feature and plane table stations and plotting them on the sheet. The field observations and plotting on sheet are done simultaneously in this survey. The methods of plane table survey include radiation, intersection, traversing and resection. Nowadays the utility of plane table survey is limited with invention of electronic distance measurement methods and plotting/drawing software. PRE-REQUISIT Basic Surveying (Third Semester Diploma) UNIT OUTCOMES List of outcomes of this unit is as follows: U1-O1: State the principle of plane table survey UI-O2: Describe the instruments used in plane table survey U1-O3: Explain the operations of plane table survey U1-O4: Apply methods of plane table survey U1-O5: List the merits and demerits of plane table survey 2|Page EXPECTED MAPPING WITH COURSE OUTCOMES Unit-1 (1- Weak Correlation; 2- Medium correlation; 3- Strong Correlation) Outcomes CO-1 CO-2 CO-3 CO-4 CO-5 U1-O1 2 1 1 1 1 U1-O2 3 1 1 1 - U1-O3 3 1 1 1 - U1-O4 3 2 1 1 - U1-O5 3 - - - - MA 1.1 Introduction The plane table surveying is a graphical method of surveying in which ground field work and plotting on sheet are done simultaneously. The beauty of this survey is that it omits recording of data on the field and using it for plotting on sheet. This survey is suitable for small to medium size of field. It is the most useful in magnetic areas where compass survey does not work. 1.2 Principle of Plane Table Surveying The principle of plane table survey is based on parallelism. It states (i) A line joining the points on the plane table are made to lie parallel to its corresponding line joining the ground stations during working at each station. (ii) The plane table at each station must be placed identical, i.e. at each ground station the table must be oriented in some fixed direction. 1.3 Instruments Used in The Plane Table Surveying The instruments used are as follows: 1.3.1 The plane table It is a wooden table mounted on tripod. It may be rotated about its vertical axis and may be fixed at any position. The sizes of plan table available are 600 mm x 500 mm, 750 mm x 600 mm or 100 mm x750 mm. The height of tripod used is usually 1200 mm. (Fig.-1.1). ii 3|Page Fig. – 1.1 Plane Table 1.3.2 Alidade The Alidade may be two types. (i) Plain Alidade (ii) Telescopic Alidade The plain Alidade consists of a wooden or metal rule has two edges. One straight and other one is bevelled. The straight edge is made of gunmetal or brass and used as a ruler. The bevelled edge is known the fiducial edge. It has two vanes at the both ends. The vanes are hinged at the ends and may be folded when the alidade is not in use. One of the vanes is the eye vane or the sight vane provided with narrow silt. The other vane is called as object vane. It is open and carries a hair or thin wire. The surveyor looks through the narrow silt towards the object or station coinciding the hair of object vane and establishes a horizontal line of sight parallel to the ruler. The problem with a simple alidade is that it can be used only to take horizontal sight to the objects at alidade level. (Fig.-1.2) Fig. – 1.2 Plain Alidade Telescopic alidade is used to take inclined sights to the objects at above or below plane table level. It is used to enhance the accuracy of the sight taken. It consists of a wooden or metal rule provided with a spirit level tube and a telescope so that the alidade can be levelled with the working station and telescope provides inclined line of sight. A scale is marked on the horizontal axis and lines are drawn along the straight ruler. It is also mounted with a vertical circle that measures the angle of the object with the horizontal axis. (Fig.-1.3) i 4|Page Fig. – 1.3 Telescopic Alidade 1.3.3 Plumbing Fork and Plumb Bob Plumbing fork is used for centring the table over the station occupied by the plane table when the position of that station is already plotted on the sheet. In other words, it is used for transferring the ground point on the sheet so that the plotted point and ground station are in same vertical line. It is a U-shaped metal frame that has two different arms. Upper arm is horizontal and the lower is inclined at a certain angle. The upper arm is provided with a pointer at the end while the lower arm has a hook at the end, from which plumb bob is suspended. The upper arm is kept on the sheet. The table is so placed that plumb bob touches the ground station, then pointer of upper arm defines plotted position of the ground station. (Fig. No.1.4). ii 5|Page Fig. – 1.4 Plumbing fork with U- frame 1.3.4 Trough Compass A trough compass is used to orient the table to magnetic north. A trough compass consists of a long, narrow rectangular box with a long narrow magnetic needle mounted on a pivot. The long sides are used as ruler to draw a arrow along magnetic north. (Fig. No. -1.5) Fig. – 1.5 Trough Compass 1.3.5 Spirit Level Spirit level is used to level the table. The table is levelled by keeping the level on the board in two mutually perpendicular directions and getting the bubble in centre in both directions. (Fig. No. -1.6) i 6|Page Fig. - 1.6 Spirit Level 1.4 Working Operations Following operations are carried out during plane table survey 1. Fixing the table on the tripod 2. Setting out the table It consists of three activities (a) Levelling the table (b) Centring (c) Orientation 3. Sighting the stations/objects 1.4.1 Fixing the table on the tripod The tripod is unfolded, and legs are spread so that its height is approximately 1.2 metre above the ground level. The plane table is placed on tripod top and clamp screw is tightened into brass annular ring of the plane table. 1.4.2 Setting out of the table It consists of three activities (a) Levelling - The table is levelled by putting the level on the table in two mutual perpendicular direction and getting the bubble in centre in both directions by tilting of board and adjusting the legs of the tripod. (b) Centring - The table is so placed over the station on the ground that the point plotted on the sheet corresponding to the station occupied must be exactly over the station on the ground. This is called centring of the plane table. The centring is done by plumbing fork, the procedure is described earlier in instruments section. (c) Orientation - Orientation is a process of putting the plane table into the fixed direction so that a line on the plane table and corresponding line on ground show the same direction This is a necessary when more than one instrument station are used. If the orientation is not done, the table will not be parallel to itself at different positions, that will result in a complete distortion of the map. Main methods of orientation (i) Orientation by trough compass (ii) Orientation by back sighting. (i) Orientation by trough compass In this method, the trough compass is so placed on the plane table that the needle freely floats and rests in N-S direction. A line is drawn along the long side of the compass box. This line shows magnetic north. When the table is to be oriented on another station, the compass is to be placed along this line showing ii 7|Page magnetic north and table is oriented by rotating it until the needle rests in N-S direction. The table is then fixed in the position. In both positions the table is parallel to each other. This method is fast but less accurate. (ii) Orientation by back sighting Let the table is placed at any fixed direction at station A, represented by a point ‘a’ on sheet. Now the table is to be oriented in same direction at station B. Put the table on station A and draw a line ab towards station B with the help of alidade, point ‘b’ shows station B. Place the table on station B and keep the alidade along line ba and rotate the table in such a way that the line of sight passes through the station A. In this position ground line AB will coincide with plotted line ab and table thus oriented and is clamped in this position. 1.4.3 Sighting the stations/objects After setting of the table i.e. completing of levelling, centring and orientation , the objects or points to be located are sighted by the alidade. Keeping alidade pivoted about the plotted location of the plane table station and turning the alidade in such a way that the line of sight bisects the object or signal at the point to be plotted. A line is drawn along the ruler of the alidade from the plotted position of the station. 1.5 Methods of Plane Table Surveying There are four methods of plane table surveying 1. Radiation Method 2. Intersection Method 3. Traversing Method 4. Resection Method First two methods used for locating the details while last two methos are more accurate, used for locating plane table stations. Here first three methods are described. 1.5.1 Radiation Method This method of plane table surveying is suitable for locating the details from single station and when distances of objects are small. The direction of the objects or the points to be located are indicated by drawing radial lines by sighting the objects or the points with the help of alidade. The horizontal distance between instrument and stations are then measured and stations are located on the sheet to some scale Procedure: 1. Set up the plane table at a station X, after levelling, transfer the ground point X on the sheet by plumbing fork as ‘x’. 2. Keeping alidade pivoted at x, sight object A. Draw the ray (xa) along fiducial edge of the alidade. Similarly draw the rays towards stations B, C,D,E etc.by sighting them. 3. Measure ground distances XA, XB, XC, XD etc. and plot them to some scale along their corresponding rays (xa,xb,xc,xd etc.) and mark points a,b,c,d etc. i 8|Page Fig. – 1.7 Radiation Method Table – 1.1 Radiation Method Instrument Alidade pivoted Sight to Draw the resector Remarks at about X x A xa Mark a,b,c,d,e X x B xb to the scale as per ground X x C xc distances and Join a,b,c,d,e.f X x D xd X x E xe X x F xf ii 9|Page 1.5.2 Intersection method The intersection method is suitable when distances of objects to be located, are large or cannot be measured properly due to ground conditions. This method is preferred in small survey work and for mountainous regions. The objects are located by sighting them from two plane table stations whose positions are already plotted and rays are drawn towards the objects. The intersection of rays towards the objects from two different plane table stations determines the plotted position of the objects. Procedure: 1.Set the table at station A, after levelling ,transfer the ground point A on the sheet as ‘a’ with the help of plumbing fork then clamp the table. 2.Mark the north direction on the paper using trough compass. 3. Keeping alidade pivoted at a, sight it towards station B and a ray is drawn. By measuring ground distance AB, plot along the ray to some scale and mark point b corresponding station B thus line ab drawn. 4. Keeping alidade pivoted at a, sight objects P, Q, R etc and corresponding rays are drawn. 5.Shift the table at station B. 6. After levelling, orient it by back sighting A. Keeping alidade pivoted at b, sight object P, Q, R etc and corresponding rays are drawn. 7. The intersection of corresponding rays towards the objects P,Q, R etc. from two different plane table stations A and B determines the plotted position of the objects P.Q,R etc., thus p,q,r etc are drawn on the paper. Fig.- 1.8 Intersection Method i 10 | P a g e Table 1.2 Intersection Method Instrument Alidade pivoted Sight to Draw the resector Remarks at about A A P ap A A Q aq A A R ar A A S as A A T at B B A - Orientation B B P bp p,q,r,s,t are marked by B B Q Bq intersection of resectors from B B R Br stations A and B. B B S Bs B B T Bt 1.5.3 Traversing Method The method of traversing is used when the stations have not been plotted previously. In this method, traverse stations are first selected then the stations are plotted by method of radiation by taking back sight on the previous station and a fore sight to the next station. The location of stations are plotted by measuring the distance between two stations as done in radiation method. Procedure:- 1. Set the table at station A, after levelling ,transfer the ground point A on the paper as ‘a’ with the help of plumbing fork. 2. Mark the north direction on the paper using trough compass. 3. Keeping alidade pivoted at a, sight it towards station B and a ray is drawn. By measuring ground distance AB, plot along the ray to some scale and mark point b corresponding station B thus line ab is drawn. Similarly draw the ray towards E, measure AE and thus line ae is drawn 4. Shift the table at station B. After levelling, orient it by back sighting A. 5. Keeping alidade pivoted at b, sight it towards station C and a ray is drawn. By measuring ground distance BC, plot along the ray to some scale and mark point c corresponding station C thus line bc is drawn. Similarly, the table is shifted at other stations and the traverse is completed. ii 11 | P a g e Fig.- 1.9 Traversing Method Table – 1.3 Traversing Method Instrument Alidade pivoted Sight to Draw the resector Remarks at about A a B ab A a E ae B ba A - Orientation B b C bc C cb B - Orientation C c D cd C c, e E - Check D dc C - Orientation D b B - Check D E E de i 12 | P a g e 1.6 Merits and Demerits of Plane Table Surveying 1.6.1 Merits 1. The observation and plotting are done simultaneously. All ground features remain before the eyes of surveyor, hence there is no possibilities of omitting necessary measurements. 2. The errors in plotting the details can be checked by drawing checklines 3. As the area is in view, irregular objects can be plotted with great accuracy 4. No great skill is required 5. It is cheaper than theodolite survey 6. It is the most useful in magnetic areas where compass survey does not work. 1.6.2 Demerits 1. It is not suitable in rainy season and densely wooded areas 2. As field measurements are not recorded, it is highly inconvenient if the survey is to be plotted to some different scale. 3. It is not suitable for accurate work. 4. The apparatus with accessories is inconvenient to carry due to heaviness 5. There are many small accessories, hence likely to be lost. ii 13 | P a g e UNIT SUMMARY  Principle of plan table survey is based on parallelism.  Plan table survey is graphical method in which plotting, and field work are done simultaneously.  Sizes of plane table usually available are 600mmx500mm, 750mmx600mm and 1000mmx750mm.  Purpose of the plane table accessories (i) Plane table – Used for fixing the drawing sheet. (ii) Tripod – Used to support the plane table at required height (iii) Trough Compass – To mark the direction on drawing sheet (iv) Alidade – Used to draw the line of sight (v) Spirit Level – used to check the levelling of plane table (vi) Plumb bob- used to mark the centre point on the ground. (vii) Plumbing-fork – Used to transfer the ground point on drawing sheet.  Plane table survey is most suitable for small scale map.  It is recommended in magnetic areas because there is no effect of magnetic field.  Limitations - It is not suitable in rainy season.  Methods of plan table (i) Radiation (ii) Intersection (iii) Traversing (iv) Resection i 14 | P a g e EXERCISES Multiple Choice Questions. 1. Plan table survey is based on the method of………………………… a) Ranging b) Contouring c) Traversing d) Triangulation 2. U- Frame is used for a) For Focusing b) For Levelling c) For Centring d) For Orientation 3. What is the purpose of the alidade in plane table survey? a) For Sighting b) For Levelling c) For transferring the point to ground d) All the above 4. What is the advantage of plane table survey? a) Accurate output b) Suitable for wet climate c) Used in magnetic areas d) Suitable for large area 5. Following method is not the example of plane table survey. a) Radiation b) Intersection c) Trisection d) Traversing 6. Following method of plane table survey requires two instruments station. a) Traversing b) Radiation c) Intersection d) Resection 7. Following methods of plane table are used to locating the details of the survey a) Resection, Intersection b) Radiation, Intersection c) Radiation, Resection d) Traversing, Resection 8. In the magnetic area which type of survey can be preferred a) Compass Survey b) Theodolite Survey c) Plan table survey d) All the above ii 15 | P a g e 9. Plane table survey is more suitable for wet climate a) True b) False 10. Error occurred due to the orientation in plane table survey can be checked by a) Calculating area b) Measuring Bearings c) Calculating Volume d) Measuring Angles 11. How many methods of plane table survey are there? a) 3 b) 1 c) 4 d) 2 12. Which instrument is used for levelling in a plane table survey? a) U- Frame b) Compass c) Plumb bob d) Spirit level 13. In plane table surveying, plotting and observations are done simultaneously. a) True b) False 14. The plane table survey is the ………………… method a) Mathematical b) Graphical c) Analytical d) None of above 15. Trough compass is used for a) Centring b) Orientation c) Levelling d) Sighting Answers To Multiple Choice Questions 1(c), 2(c), 3(a), 4(c), 5(c), 6(c), 7(b), 8(c), 9(b), 10(d), 11(c), 12(d), 13(a), 14(b), 15(b) i  16 | P a g e Short and Long Answer Type Questions Short Questions: 1. Explain briefly, plane table survey 2. Explain the principle of plane table survey 3. What is the difference between simple alidade and telescopic alidade? 4. Write the advantages and disadvantages of the plane table survey 5. Explain the orientation of the plane table survey Long Questions: 1. Describe the following methods of plane table surveying (i) Radiation (ii) Intersection (iii) Traversing 2. Explain each accessory used in plane table survey 3. Discuss the working operations of plane table survey 4. Discuss the differences between radiation and Intersection methods ii 17 | P a g e PRACTICAL Experiment No. – 1 Objective: Use plane table survey to prepare plans of a plot of seven-sided closed traverse by Radiation Method. Required Accessories: 1. Drawing Board 2. Tripod stand 3. Alidade 4. Spirit Level 5.Trough Compass 6. Plumbing fork with plumb- bob 9.Drawing Sheet 10.Tape for distance measurement 11. Pencil, Eraser, Clamp or Scotch tape etc. Procedure:  Fix the plane table on tripod at station ‘O’ and paste the drawing sheet on plane table.  Level the plane table using the spirit level by tilting the board and adjusting the legs of tripod.  Transfer the ground station ‘O’ on the drawing sheet as ‘o’ with the help of plumbing fork using plumb bob.  Mark the north direction on the drawing sheet with the help of trough compass.  Pivot the alidade on ‘o’ and draw the line of sight towards objects A, B, C, D, E, F and G by sighting with the help of alidade.  Measure the distances OA, OB, OC, OD, OE, OF and OG and mark the points on drawing sheet to some scale as a, b, c, d, e, f and g respectively.  Join the points to complete traverse abcdefga. i 18 | P a g e Fig - 1.10 Radiation Method – Seven-sided closed traverse ii 19 | P a g e Experiment No. – 2 Objective: Use plane table survey to prepare plans, locate details by Intersection Method. Required Accessories: 1. Drawing Board 2. Tripod stand 3. Alidade 4. Spirit Level 5.Trough Compass 6. Plumbing fork with plumb- bob 9.Drawing Sheet 10.Tape for distance measurement 11. Pencil, Eraser, Clamp or Scotch tape etc Procedure:  Fix the plane table on tripod at station ‘P’ and paste the drawing sheet on plane table.  Level the plane table using the spirit level by tilting the board and adjusting the legs of tripod.  Transfer the ground station ‘P’ on the drawing sheet as ‘p’ with the help of plumbing fork.  Select another station Q and draw a ray from P towards Q by sighting with the help of alidade. Measure the distance PQ on ground and to some scale mark the point q.  Draw the rays from A towards objects X1, X2, X3, X4 and X5 by sighting with the help of alidade.  Set the plane table on station Q such that station Q is exactly below the sheet point q using plumbing fork. Level the table and orient it by back sighting P.  Draw the rays from Q towards object X1, X2, X3, X4 and X5 by sighting with the help of alidade.  The intersection of corresponding rays towards the object X1, X2, X3, X4 and X5 from two different plane table stations P and Q determines the position of corners of plan x1 x2 x3 x4 x5.  Join x1, x2, x3, x4 and x5. to complete the plan x1 x2 x3 x4 x5. i 20 | P a g e Fig. 1.11– Locating Details by Intersection Method ii 21 | P a g e Experiment No. – 3 Objective: Use plane table survey to prepare plans, locate details by Traversing Method. Required Accessories: 1. Drawing Board 2. Tripod stand 3. Alidade 4. Spirit Level 5.Trough Compass 6. Plumbing fork with plumb- bob 9.Drawing Sheet 10.Tape for distance measurement 11. Pencil, Eraser, Clamp or Scotch tape etc. Procedure:  Fix the plane table on tripod at station ‘P’ and paste the drawing sheet on plane table.  Level the plane table using the spirit level by tilting the board and adjusting the legs of tripod.  Transfer the ground point P on the sheet as ‘p’ with the help of plumbing fork.  Mark the north direction on the sheet using trough compass.  Draw the ray from P towards Q by sighting with the help of alidade. Measure ground distance PQ and to some scale mark the point ‘q’and draw the line pq. Similarly draw the ray towards T, measure PT and to some scale mark the point ‘t’ and draw the line pt.  Shift the table at station Q. After levelling, orient it by back sighting P.  Draw the ray from Q towards R by sighting with the help of alidade. Measure ground distance QR and to some scale mark the point ‘r’and draw the line qr.  Similarly, the table is shifted at other stations and the traverse is completed. i 22 | P a g e Fig. 1.12 – Locating Details by Traversing Method ii 23 | P a g e KNOW MORE Resection Method of Plane Table survey The fourth method of plane table survey is resection method, which is more accurate method than other methods of plane table surveying. It is used for locating the plane stations. Resection is the method of determining the plotted position of the station which is occupied by the plane table by sighting known stations whom locations have already been plotted. The resection problem can be solved by following methods. 1. Resection after orientation by compass 2. Resection after orientation by back sighting 3. Resection by three-point problem 4. Resection by two-point problem Errors in Plane Table Survey. (i) Instrumental Error 1. Error due to inclined plane table 2. Error due to fiducial edge might not be straight 3. Plane table is not properly tight with tripod. 4. Needle of trough compass is not properly balanced. 5. Error due to imperfection of Spirit level 6. Object vane and eye vane may not be vertical (ii) Errors in Operations 1. Plane table may not be perfectly levelled. 2. Inaccurate centring of plane table 3. Inaccurate orientation of plane table 4. Imperfect bisection of objects (iii) Plotting errors 1. Taking wrong scale by mistake 2. Incorrect linear measurement Types of Plane Table Following three types of plane table are used. 1. Traverse Table – It is the ordinary plane table, which can be mounted on tripod stand by tightening clamp screw of tripod into brass annular ring of the plane table. It is levelled by adjusting the legs of the tripod. 2. Johnsons Table - It is provided with additional ball and Socket arrangement for levelling purpose. 3. Coast Survey table - It is high quality table provided with three levelling screw arrangement similar to the levelling instruments. i 24 | P a g e Dynamic QR code for Resection method REFERENCES AND SUGGESTED READINGS 1. B.C Punmia, Surveying Vol –II, Laxmi Publication (P) Ltd, 2023. 2. N.N. Basak, surveying & Levelling,McGraw hill Iindia, Private Limited, Noida, 2017. 3. Bhavikatti SS, Surveying and Levelling Vol. II, I.K International Publishing House Pvt. Ltd, 2016. 4.R. Agor, A Text Book of Surveying & Levelling, Khanna Publication, 2015. 5. S.K. Duggal, Surveying Vol. I, McGraw Hill Publishing Company Ltd., 2013. 6. C. Venkatramaiah, Textbook of Surveying, University Press (India) Limited, 2011. 7. Saikia MD, Das BM, Das MM, Surveying, Prentice Hall India Learning Limited, 2010. 8. T.P. Kanetkar and S.V. Kulkarini, Surveying and Levelling, Vidyarthi Griha Prakashan, 1967. 9.NPTEL video link - https://youtu.be/vT_7OmzFiSE 10. Notes Link- https://www.madeeasy.in/Uploads/examsolution/Surveying.pdf ii 25 | P a g e Dynamic QR Code for Further Reading Following QR codes are given for further study of plan table surveying. 1. Dynamic QR code for plan table survey (Theory) 2. Dynamic QR code for Accessories used in plane table (Video) 3. Dynamic QR Code for Radiation method (Video) 4. Dynamic QR Code for Intersection method (Video) i 26 | P a g e 5. Dynamic QR Code for Traversing method (Video) ii 27 | P a g e 2 Theodolite Surveying d UNIT SPECIFICS Through this unit we have discussed the following aspects:  Purpose and types of Theodolites  Different parts of transit Theodolite and their function  Working of transit Theodolite  Temporary adjustment of Theodolite  Measurement of horizontal and vertical angle by transit Theodolite  Some field applications of Theodolite  Traversing by Theodolite  Traverse Computations RATIONALE This unit describes the purpose and types of Theodolites. The Theodolite is most precise instrument used to determine horizontal and vertical angle. This chapter presents various parts of transit theodolite with their functions. The terminology used in Theodolite including transiting, face left , face right and fundamental axes of transit theodolite are defined clearly. The temporary adjustment of Theodolite is necessary before taking observations. The direct and repetition methods of measurement of horizontal angle and measurement of vertical angle by Theodolite are discussed in this chapter. The various uses of theodolite including measurement of magnetic bearing of line, prolonging, and ranging a line and measurement of deflection angle are dealt in this chapter. This chapter also discusses Theodolite traversing which includes checks for open and closed traverse, calculation of bearing from angles. Traverse computation including determination of latitude, departure, consecutive & independent coordinates and balancing the traverse by Bowditch’s rule and transit rule, is also discussed. The Gale’s traverse table is also presented. PRE-REQUISITES Mathematics: Basic knowledge of Trigonometry Basic Surveying (Third Semester Diploma) UNIT OUTCOMES List of outcomes of this unit is as follows: U2-O1: State the uses and types of Theodolites U2-O2: Explain the working of Theodolite U2-O3: Determine horizontal and vertical angle by using Theodolite U2-O4: Perform field work using Theodolite U2-O5: Apply methods of traversing using Theodolite i 28 | P a g e EXPECTED MAPPING WITH COURSE OUTCOMES Unit-1 (1- Weak Correlation; 2- Medium correlation; 3- Strong Correlation) Outcomes CO-1 CO-2 CO-3 CO-4 CO-5 U2-O1 1 3 2 2 1 U2-O2 1 3 2 2 1 U2-O3 1 3 2 2 1 U2-O4 1 3 2 2 1 U2-O5 1 3 2 2 1 2.1 Introduction The Theodolite is the most versatile and precise instrument widely used for the measurement of horizontal and vertical angle. It has wide application in the field such as locating points on a line, laying grades, finding difference in elevation, setting out curves, prolonging survey lines etc. In this chapter vernier theodolite is discussed as the basic features of a Theodolite may be illustrated conveniently by simplified diagram of a vernier Theodolite although Digital Theodolites are more accurate, compact and convenient and used nowadays. 2.2 Classification of Theodolite Theodolites may be classified two ways 2.2.1 Classification based on movement of telescope: (i) Transit Theodolite (ii) Non-transit Theodolite Transit Theodolite In transit Theodolite, the telescope can be rotated through 180 0 in the vertical plane about its horizontal axis i.e. line of sight can be reversed. A transit theodolite is simply called ‘transit’. It is widely used. Non-transit Theodolite In Non-transit Theodolite, the telescope cannot be transited, i.e., cannot be resolved through 180 0. The non-transit theodolites have now become obsolete. 2.2.2 Classification based on arrangement of reading observations (i) Vernier Theodolite (ii) Micrometer Theodolite (iii) Optical Theodolite (iv) Electronic or Digital Theodolite Vernier Theodolite In this type of Theodolite, vernier is used for reading horizontal and vertical graduated circles. The least count of vernier Theodolite is 20”. Micrometer Theodolite In this type of Theodolite, micrometre is used for reading horizontal and vertical graduated circles. The least count of micrometer Theodolite is 1”. Optical Theodolite In optical theodolite, graduated glass circle is used, and the reading is reflected to observer eye by means of a system of prisms and lenses. ii 29 | P a g e Electronic or Digital Theodolite In Electronic or Digital Theodolite, the reading of angle is found in digital form. These types of theodolites are accurate and more convenient, hence other types of Theodolites have become obsolete. 2.3 Components of Transit Theodolite The transit theodolite consists of following components (see Fig. No. -2.1) Fig. No. - 2.1 Components of transit theodolite 1. Telescope 2. Vertical clamp 3. Arm of the vertical circle clamp 4. Standard 5. Line of sight 6. Upper clamp 7. Axis of plate bubble 8. Upper plate 9. Lower plate 10. Lower clamp 11.Upper Tribrach plate 12. Foot screw 13. Lower Tribrach plate 14. Tripod top 15. Plumb bob 16. Vertical axis 17.Tripod clamping screw 18. Levelling head i 30 | P a g e 19. Horizontal graduated arc 20. Plate level 21. Vernier frame 22. Horizontal or Trunnion axis 23. Altitude bubble 24. Vertical circle 2.3.1 The Telescope - The telescope (1) is mounted on a spindle. The spindle coincides with horizontal axis, it is also called trunnion axis (22). The telescope provides horizontal as well as inclined line of sight (5). Generally internal focusing telescope is used. 2.3.2 The Vertical Circle – The vertical circle (24) is a graduated circular arc fixed with telescope. The centre of circular arc coincides with trunnion axis, the vertical circle rotates with telescope. It can be locked at any position by vertical clamp (2), and fine adjustment may be done by vertical tangent screw. The vertical circle is graduated from 00 to 3600, sometimes it is divided into four quadrants from 00 to 900. Fig. No. 2.2 – Vertical circle with verniers and telescope 2.3.3 The Index Frame or Vernier Frame – Vernier Frame (21) is also called T frame as it is T-shaped, consisting of a vertical leg called as clipping arm and a horizontal arm called as index arm or vernier arm. Two verniers are provided at both ends of index arm to read the vertical circle. The centre of index arm is coincided by trunnion axis. The index frame remains fixed in front of the vernier circle. When telescope is rotated in vertical plane, the vertical circle also moves relative to verniers facilitates reading of main scale of vertical circle. However, the index arm may be rotated slightly for adjustment purpose by a clip screw fitted on the clipping arm. Glass magnifiers are placed above each vernier to magnify the reading. A bubble tube is fixed on the top of the index frame, it is also called altitude bubble (23). [See Fig. No.- 2.3] ii 31 | P a g e Fig. No. 2.3 – Parts of Vertical Frame 2.3.4 The Standards - Two standards (4) are provided on upper plate. They are A- shaped, hence also called A- frame , they support telescope and allow it to rotate about trunnion axis. 2.3.5 The Upper Plate - This is also known as vernier plate (8). It is attached to inner spindle and carries two verniers with glass magnifier at opposite ends. It carries upper clamp (6) for locking it to the lower plate and a tangent screw for finer adjustment. When the upper clamp is tightened, both upper and lower plates are attached and moves together. 2.3.6 The Lower Plate- This is also called as scale plate (9) as it carries horizontal circular graduated arc (19) graduated from 00 to 3600. It is attached to the outer spindle and carries lower clamp (10) and a tangent screw. If lower clamp is loosened and upper clamp is tightened, both plates will rotate together. Similarly, if lower clamp is tightened and upper clamp is loosened then, only upper plate will move and lower plate will be fixed with tribrach plate. 2.3.7 Plate Level - Plate level (20) is carried by the upper plate which is parallel to the trunnion axis. The plate level is used for levelling the instrument. i 32 | P a g e Fig. No. – 2.4 Cross- section along the length through upper and lower plate ii 33 | P a g e 2.3.8 The Levelling Head- The levelling head (18) is provided with two parallel triangular plates known as tribrach plates. The upper triangular plate is known as upper tribrach plate (11) and is used to level the instrument with the help of foot screws (12) provided at its three corners. The lower triangular plate is called as lower tribrach plate or foot plate (13) and is attached to the tripod top to support the instrument on the tripod. Fig. No. – 2.5 Photograph of Transit Theodolite 2.3.9Tripod - The Theodolite is supported on tripod (14). The tripod head carries an external screw (17), which is screwed to internal screw of foot plate of levelling head. 2.3.10 Plumb Bob- Plumb bob (15) is used to place the Theodolite on the ground station in such a way that vertical axis (16) of the instrument is exactly above the ground point. The bob is suspended from the hook fitted at inner spindle touching the ground. Moving the tripod and adjusting the legs of it , the bottom tip of the bob is brought exactly on ground point. This process is called centering. 2.4 Technical Terms used in Transit Theodolite (i) Transiting- Transiting is also known as reversing or plunging. It is a process of rotating the telescope about its i 34 | P a g e horizontal axis through 1800 in the vertical plane. (ii) Swinging the telescope- It is turning the telescope about its vertical axis in the horizontal plane. A swing is called right if the telescope is rotated in clockwise direction and a swing is called left if the telescope is rotated in anti-clockwise direction. (iii) Face Left: If the vertical circle of the instrument is on the left side of the observer while sighting an object, the position is called the face left and the observation taken during this position is called as the face left observation. (iv) Face Right -If the vertical circle of the instrument is on the right side of the observer while sighting an object, the position is called the face right and the observation taken during this position is called as the face right observation. 2.5 Fundamental Axes of Transit Theodolite and Their Relationship Fundamental Axes – 1. Axis of the Level Tube / Bubble Line: It is a tangent to the longitudinal curve of the level tube at the centre of the tube. It is horizontal when the bubble is in the centre of the bubble tube. 2. Vertical Axis: It is the axis about which the telescope can rotate in the horizontal plane. The upper and lower plates rotate about this axis. 3.Horizontal Axis / Trunnion Axis: It is the axis about which the telescope can rotate in the vertical plane. 4. Line of Sight (LOS)/Line of Collimation (LOC) : It is an imaginary line joining the intersection of the cross- hairs of the diaphragm to the optical centre of the objective and its continuation Fig. No. – 2.6 - Fundamental Axes of Transit Theodolite and their Relation ii 35 | P a g e Relationship – (see Fig. No. 2.6)  The axis of the level tube must be perpendicular to the vertical axis.  The line of collimation must lie in a plane perpendicular to the horizontal axis. Line of collimation, Vertical axis and Horizontal axis must intersect at a point.  The Horizontal axis must be perpendicular to the Vertical axis.  The axis of altitude level must lie in a plane parallel to the line of collimation 2.6 Reading of Vernier of Transit Theodolite A theodolite is provided with two verniers diagonally opposite to each other (at 180 0 difference) on the upper plate. For ordinary work, reading of only one is taken, whereas for precise work, reading of both verniers are taken. Later practice minimises errors due to imperfection of subdivisions and eccentricity of circular scale. The main scale is circular, placed on lower plate , graduated from 00 to 3600. Each degree is divided in three equal parts, hence least count of main scale is 20’. The vernier scale is graduated from 0’ to 20’. Each minute is divided into three equal parts, hence least count of vernier is 20”. For taking observation, first reading of main scale is taken in degrees and minutes against the zero of the vernier, then vernier reading would be coinciding division of vernier with any main scale division multiplied by the least count of the vernier. The main scale reading is added to vernier scale reading to get the final reading. For example, main scale reading against the zero of vernier is 1550 20’and coinciding division of vernier is 43 then final reading would be 1310 20’ + 43x20” = 1310 34’20” (Fig No. – 2.7) i 36 | Plan Table Survey Fig. No. - 2.7 Reading of Vernier of Transit Theodolite 2.7 Temporary Adjustment of Transit Theodolite Temporary adjustments of theodolite include – 1. Setting on the station 2. Levelling Up 3. Parallax Elimination 2.7.1 Setting of theodolite Firstly, fix the instrument on the tripod and keep the instrument over the station by spreading the legs of the tripod ensuring convenient height of the tripod. Now do the centring of instrument with the help of plumb-bob, by moving the tripod in such a way that the bottom tip of plumb-bob should touch ground point of the station. Sometimes centring is done in windy areas with the help of optical plummet by moving the tripod in such a way that narrow laser beam should exactly fall on ground point of the station. Then approximate levelling is done by adjusting the legs of the tripod. ii  37 | P a g e 2.7.2 Levelling of Theodolite Accurate levelling of the theodolite is done with the help of foot screws and plate level. Two types of levelling screws heads are used by which levelling is done; the process is as under. Three levelling screws head 1. Place the plate level parallel to a line joining any two levelling screws ( say A &B) by turning the upper plate. 2. Now, rotate these two screws (A&B) in opposite directions uniformly until the bubble of the plate level comes in the centre. 3. Rotate the upper plate by 900 4. Now, rotate the third levelling screw in such a way, that the bubble of plate level comes in the centre 5. Repeat steps (1) to (4) till the bubble is in centre in both positions (2) and (4) simultaneously 6. Now rotate the instrument by 1800 if the bubble remains in the centre, then the instrument is called levelled. If not, it needs permanent adjustment. (a) (b) Fig No. – 2.8 Levelling with three-foot screw Four levelling screws head 1. Place the plate level parallel to a line joining any two diagonally opposite levelling screws ( say B &D) by turning the upper plate. 2. Now, rotate these two screws (B&D) in opposite directions uniformly until the bubble of the plate level comes in the centre. 3. Rotate the upper plate by 900 so that the plate level is parallel to the line joining to other two diagonally opposite screws ( say A&C) 4. Now, rotate these two screws (A&C) in opposite directions uniformly until the bubble of the plate level comes in the centre. 5. Repeat steps (1) to (4) till the bubble is in centre in both positions (2) and (4) simultaneously. 6. Now rotate the instrument by 1800 if the bubble still remains in the centre of its run, then the instrument is called levelled. If not, it needs permanent adjustment. i  38 | Plan Table Survey (a) (b) Fig No. 2.9 Levelling with four-foot screw 2.7.3 Elimination of parallax The parallax occurs if the image formed by the objective doesn’t lie in the plane of the cross hair and the object is not clearly visible through telescope. The parallax can be eliminated by focusing of the eyepiece and the objective. Focusing of the eyepiece This can be done by placing the piece of white paper in front of the objective or towards the sky and rotate the eyepiece in such a manner that the cross hairs are visible clearly. Focusing of the objective This can be done with the help of a focusing screw. Sight the telescope of theodolite towards the object to be viewed and rotate the focusing screw in such a manner that the object is visible clearly while sighting through the eyepiece. The image so formed is in the plane of cross-hairs. 2.8 Measurement of Horizontal Angle by Transit Theodolite 2. 8.1 Direct Method The measurement of angle POQ is done as under (Fig. No. -2.10) 1. Set up the Theodolite on station O and level it 2. Keep the vertical circle at left (face left case) 3.Release the upper clamp and turn upper plate till the zero of any vernier (say A) of upper plate coincides with the zero of main scale of lower plate. Tighten the clamps of both the plates and coincide the two zeros exactly by turning the upper tangent screw. Take the readings of both verniers. The readings of verniers A and B would be 00 and 1800 respectively. 4.Release the lower clamp and sight the station P by swinging the telescope. Tighten the lower clamp and bisect the station point P accurately by lower tangent screw. 5.Release the upper clamp and swing the telescope in clockwise direction and sight the station point Q Tighten the upper clamp and bisect the point Q accurately by upper tangent screw. ii 39 | P a g e 6.Take readings of both verniers. The reading of vernier A gives the angle POQ directly while reading of vernier B gives the angle POQ by deducting 1800. Take average of the two values of angle POQ 7.Keep the vertical circle at right by transiting the telescope (face right case) and repeat the above process and determine the angle POQ. 8. Take mean value of angle POQ obtained by steps (6) and (7) Note- The zero of the vernier is initially set on zero of main scale for convenience purpose only, it can be set at any convenient reading. Fig No.- 2.10 Measurement of horizontal angle 2.8.2 Method of Repetition To measure a horizontal angle more accurately than that is obtained by the least count of the vernier, the method repetition is used. In this method the angle is measured twice or more times with the vernier to remain clamped at the end of each measurement instead of setting it back at 00 when sighting previous station. Hence the angle reading is multiplied by number of repetitions mechanically. The multiplied reading is divided by number of repetitions to get the mean angle. The measurement of angle POQ is done as under 1.Set up the Theodolite on station O and level it 2.Keep the vertical circle at left (face left case) 3.Release the lower clamp and turn upper plate till the zero of any vernier (say A) of upper plate coincides with the zero of main scale of lower plate. Tighten the clamps of both the plates and coincide the two zeros exactly by turning the upper tangent screw. Take the readings of both verniers. The reading of vernier A would be 00, note the reading of vernier B. 4.Release the lower clamp and sight the station P by swinging the telescope. Tighten the lower clamp and bisect the station point P accurately by lower tangent screw. 5.Release the upper clamp and swing the telescope in clockwise direction and sight the station point Q.Tighten the upper clamp and bisect the point Q accurately by upper tangent screw. 6.Take readings of both verniers. The reading of vernier A gives the angle POQ directly while reading of vernier B gives the angle POQ by deducting 1800. Take average of the two values of angle POQ i 40 | Plan Table Survey 7.Release the lower clamp of lower plate and sight the station P again by swinging the telescope in clockwise direction. Tighten the clamp of lower plate and bisect the station point P accurately by tangent screw of lower plate. In this operation, vernier readings will not be changed as there is no relative motion between upper and lower plate. 8.Release the upper clamp and swing the telescope in clockwise direction and sight the station point Q. Tighten the upper clamp and bisect the point Q accurately by upper tangent screw. Take the readings of the verniers. The vernier will read twice the angle POQ. 9.Repeat the process for required number of times, say 03 and average angle for face left case will be equal to final reading divided by 03 10.Keep the vertical circle at right by transiting the telescope (face right case) and repeat the above process 03 more times and determine the average angle for face right case by dividing the final reading by 03 11.Determine average horizontal angle by taking mean of two angles obtained by steps (9) and (10) for face left and face right case. Errors eliminated by method of repetition (i) The errors due to eccentric centres of the plates and eccentricity of verniers are rectified by taking both verniers readings. (ii) The error due to the line of collimation is not being perpendicular to the trunnion axis is eliminated by taking both face readings (iii) The error due to inaccurate graduation is rectified by reading the angle at different parts of the graduated circle. (iv) Errors due to inaccurate bisection of the objects are counter balanced to some extent in different observations. 2.9 Measurement of Vertical Angle by Transit Theodolite A vertical angle is defined as an angle which the inclined line of sight to an object makes with the horizontal. If the object to be sighted is above the horizontal plane, then the angle subtended is called as the angle of elevation and if object is below the horizontal plane, then the angle is called angle of depression. The measurement of vertical angle is done as under (Fig. No. 2.11) 1. Set the instruments at the station B and level it with the plate level 2. Release the vertical clamp and rotate the telescope in vertical plane till zero of any vertical vernier coincides with the zero of vertical circle. Tighten the vertical clamp and coincide the two zeros exactly by turning the vertical tangent screw. Check bubble of altitude level, if it is not in centre, bring it in centre with the help of the clip screw. 3. Release the clamp of vertical circle and rotate the telescope in vertical plane to sight the object A. Tighten the vertical clamp and use vertical tangent screw to bisect the object accurately. 4. Read both the vertical verniers C and D. The mean of readings of two verniers will give the value of the required angle 5. Change the face and repeat the process to get another value of required angle 6. Take average of the two values of required angle obtained in steps (4) and (5). ii 41 | P a g e Fig. No. 2.11 Measurement of vertical angle 2.10 Some Field Applications of Transit Theodolite 2.10.1 Measurement of Direct Angle An angle measured from previous line to next line in clockwise direction is called Direct Angle. The angle ABC is measured as under (Fig. No. -2.12) (i) Set the instrument at B and level it. Set the reading of graduated circle to zero against vernier A by turning the upper plate with face left. (ii) Release the lower clamp and swing the telescope to sight station A. Tighten the lower clamp and bisect A accurately by lower tangent screw (iii) Release the upper clamp and swing the telescope clockwise to sight the station C. Tighten the upper clamp and bisect station C accurately by upper tangent screw. Take readings of both verniers (iv) Release the lower clamp and swing the telescope to sight station A again and lock the lower clamp. (v) Release the upper clamp and swing the telescope clockwise to sight the station C again. (vi) The angle measured is double of the required angle ABC, hence final reading is divided by two to get more accurate value of angle ABC. i 42 | Plan Table Survey Fig No.- 2.12 Measurement of Direct Angle 2.10.2 Measurement of Deflection Angle An angle measured from prolongation of previous line to next line is called Deflection Angle. When the angle measured clockwise, it is called right (R) deflection angle whereas measured anti-clockwise, it is called left(L) deflection angle. The value of deflection angle varies from 00 to 1800. In Fig. No. 2.13, the deflection angle is α (R ) at Q and β(L) at R. The deflection angle is measured as under. (i) Set the theodolite at station Q and level it. (ii) Set the reading of graduated scale to zero against vernier A by turning upper plate and with the help of upper clamp and tangent screw. (iii) Take back sight at station P ensuring vernier A reads zero (iv) Transit the telescope keeping line of sight is in the direction of PQ produced keeping vernier A reads zero. (v) Release the upper clamp and rotate the telescope clockwise to sight station R with finer adjustment by tangent screw. (vii) Take readings of both verniers (viii) Release the lower clamp and turn the telescope to sight P again keeping the verniers to read same readings and lock lower clamp. (ix) Transit the telescope and release the upper clamp and rotate the telescope to sight station R. Take readings of vernier. (x) The angle measured is double of the required angle PQR, hence final reading is divided by two to get more accurate value of angle PQR. ii 43 | P a g e Fig. No. – 2.13 Measurement of Deflection Angle 2.10.3 Measurement of Magnetic Bearings The magnetic bearing of a line OP can be measured as under (Fig. No. -2.14) (i) Set the instrument at station O (ii) Fit the trough compass on the theodolite and release its needle (iii) Set the vernier to read zero on graduated circle by turning upper plate using upper clamp and tangent screw (iv) Release the lower clamp and rotate the lower plate till magnetic needle rest in N-S direction. Lock the lower clamp and bring the needle in true magnetic north by lower tangent screw. (v) Release the upper clamp and bring the telescope in the line of station P. Lock the upper clamp and bisect station P accurately using upper tangent screw. Take readings of both verniers (vi) Change the face of the instrument and repeat the steps from (ii) to (v) The average of two values obtained from readings of two faces is correct value of the bearing of line OP i 44 | Plan Table Survey Fig. No. –2. 14 Measurement of Magnetic Bearings 2.10.4 Prolonging a Straight Line The prolonging the line AB can be done as under (Fig. No. – 2.15) (i) Set the theodolite at A and level it (ii) Sight B accurately by turning lower plate and using lower clamp and tangent screw (iii) Looking from telescope, direct the surveyor to bring the ranging rod exactly at C such that B and C in a line. (iv) Shift the instrument at B and repeat above steps (v) Continue the process until last point E is established.. Fig. No. – 2.15 Prolonging a Straight Line 2.11 Theodolite Traversing Traversing is a type of surveying which consists of number of connected survey lines. The direction of the lines is measured with the help of chain, compass and theodolite whereas length is measured by tape or chain. A traverse is said to be closed if it returned to starting point whereas it is called open traverse if it does not return to starting point and ends elsewhere. The closed traverse is suitable to locate the boundaries of ponds, lakes, forests etc. whereas open traverse is useful for locating long narrow strips of land for roads, canals and coastal lines. When theodolite is used for direction or angle measurement, it is called theodolite traversing. Theodolite traversing is done by following methods 2.11.1 Traversing by Included Angles In this method, the angle between two survey lines is measured directly by taking backsight at preceding station. The greater accuracy is obtained by taking readings of both verniers, taking both face observations, and using method of repetition. It is preferred to measure the angles clockwise as the graduations on graduated circle are marked in clockwise direction. The angle measured clockwise from previous station may be interior angle or exterior angle depending on direction of progress of survey. If direction of progress of work is anticlockwise, angle measured clockwise will be interior angle ( Fig. No. 2.16) and if direction of progress of work is clockwise, angle measured clockwise will be exterior angle (Fig. No. 2.17 ) ii 45 | P a g e Fig. No. – 2.16 Included angle method -Interior angle measured clockwise Fig. No. – 2.17 Included angle method - Exterior angle measured clockwise 2.11.2 Traversing by Deflection Angles The deflection angle and method of its measurement is described in section (). The traversing by this method is suitable where survey lines make small deflection angles like roads, railways and pipelines etc. The attention must be given in recording and plotting of correct deflection angle whether it is right or left deflection angle. It is preferred to read included angles clockwise from back station except in specialised work where deflection angles are required to read. The lengths of lines are measured by high quality steel tape. 2.12 Checks in Traversing 2.12.1 Checks in Closed Traverse – The errors occur in in closed traverse may be two types (i) Linear errors (ii) Angular errors Linear errors may be checked by chaining each survey line twice , preferably in reverse direction second time on different dates and by different surveyors. Angular errors may be checked as under (a) Traversing by included angles – The sum of interiors angles of traverse should be equal to (2N- 4) right angles and sum exterior angles should be equal to (2N+4) right angles. (b) Traversing by deflection angles – The algebraic sum of the deflection angles of traverse should be equal to 3600 provided right -hand deflection angles are taken as positive and left -hand deflection angles are taken as negative (c ) Traversing by direct observation of bearings - The difference of fore bearing of the last line of a traverse and its back bearing measured at initial station, should be equal to 1800. i 46 | Plan Table Survey 2.12.2 Checks in Open Traverse – There is no direct check of angular errors in open traverse available. Indirect checks can be used as under (a) In Fig. No. – 2.18, ABCDE is an open traverse. Join AE, measure bearing of AE at A, similarly measure bearing of EA at E, the difference of two bearings should be 1800. (b) In Fig. 2.19 ABCD is an open traverse. Take any point P as shown in the Fig., read the bearings of P from consecutive stations A,B,C and D and draw lines AP, BP, CP and DP by measured bearings and as a check, these lines should pass through one point. Fig. No. – 2.18 Checks for open traverse- case 1 Fig. No. – 2.19 Checks for open traverse- case 2 2.13 Calculations of Bearing from Angles If in a traverse included angles between successive lines are known, the bearings of the lines may be calculated if bearing of any one line is also known. In an open traverse ABCDEF, the bearing of line AB is θ1 and included angles between lines measured clockwise are α, β, γ and δ then The bearing of the next line BC = θ2 = θ1+ α -1800 The bearing of the next line CD = θ3 = θ2+ β -1800 The bearing of the next line DE = θ4 = θ3+ γ -1800 The bearing of the next line EF = θ5 = θ4+ δ +1800 ii 47 | P a g e Fig. No. – 2. 20 Calculations of Bearing from Angles It is clear in the Fig. 2.20 that ( θ1+ α) ,( θ2+ β) and ( θ3+ γ ) are more than 1800 whereas (θ4+ δ ) is less than 1800 , hence following fact can be concluded for calculation of bearing of next line “Add the included clockwise angles to the bearing of previous line, if sum is more than 1800, deduct 1800 if sum is less than 1800, add 1800”. 2.14 Traverse Computations 2.14.1 Consecutive Co-ordinates : Latitude and Departure The latitude (L) of a survey line is defined as co-ordinate length of the line measured parallel to a assumed meridian direction.The assumed meridian may be true north or magnetic north or any reference direction. The departure (D) of a survey line is defined as co-ordinate length of the line measured perpendicular to an assumed meridian direction. The following sign convention is adopted. Consecutive Co-ordinate Direction Sign Termed as Latitude Northward or upward Positive Northing Latitude Southward or downward Negative Southing Departure Eastward Positive Easting Departure Westward Negative Westing The Latitude and Departure of a line PQ having length l and reduced bearing θ are given as L= + l cos θ and D= +l sin θ (Fig. No. – 2.21) They are also called Consecutive Co-ordinates i 48 | Plan Table Survey Fig. No. – 2.21 Latitude and Departure It is necessary to convert the bearing of a line in quadrantal system to determine its Latitude and Departure. The following table indicates the signs of Latitude and Departure for a line located in various quadrants. W.C.B R.B. Quadrant Latitude Departure 0° to 90° NθE I + + 90° to 180° SθE II - + 180° to 270° SθW III - - 270° to 360° NθW IV + - 2.14.2 Independent Co-ordinates The total latitude and departure of a point with respect to a common origin are called as independent co-ordinates or total co-ordinates of that point. A set of vertical and horizontal axes passin