Lecture Notes On Land Surveying (ES/PE 256) PDF

FACULTY OF MINERAL RESOURCES TECHNOLOGY Environmental & Safety Engineering Department Lecture Notes On Land Surveying (ES/PE 256) Compiled by: Eric Stemn January, 2015 Lecture Notes on Land...

FACULTY OF MINERAL RESOURCES TECHNOLOGY Environmental & Safety Engineering Department Lecture Notes On Land Surveying (ES/PE 256) Compiled by: Eric Stemn January, 2015 Lecture Notes on Land Surveying 2014/2015 Academic Year COURSE OUTLINE (SYLLABUS) 2014/2015 Academic Year 1. Overview of Surveying - definitions, types and procedure for surveying. 2. Measuring of Horizontal Distances - Chain Surveying 3. Angular Measurement - Compass Surveying and Applications 4. Traversing and Traverse Computation – Theodolite and Applications 5. Vertical Control – Levelling and Application 6. Area and Volume Computation 7. Modern Positioning Systems University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Page i Lecture Notes on Land Surveying 2014/2015 Academic Year COURSE OBJECTIVES 2014/2015 Academic Year The purpose of this course is to provide student with the fundamental understanding of Land Surveying. Therefore, the following are the objective of the course, the student will among other things; 1. Obtain a general overview of surveying including its purpose, principles and general operations. 2. Be familiar with the methods of measuring horizontal distances 3. Be familiar with the determination of angular measurement and direction of survey lines 4. Be able to perform traverse and conduct all necessary computations 5. Be able to perform levelling and determine the RLs of points using both the Rise and Fall and Height of Collimation Methods 6. Be able to determine the area of a closed traverse using the coordinate method. 7. Obtain an understanding of the satellite positioning and be able to use handle GPS to determine position of points. University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Page ii Lecture Notes on Land Surveying 2014/2015 Academic Year COURSE PLAN (SCHEDULE) 2014/2015 Academic Year Calendar Week Month Activity 1 REGISTRATION Course Plan and Overview of Surveying I 2 Course Plan and Overview of Surveying II Field Work 1 (Survey Instrument Identification) 3 February Course Plan and Overview of Surveying III Measurement of Horizontal Distance I 4 Quiz 1, Measurement of Horizontal Distance II Field Work 2 (Basic Survey Measurement - Linear Surveys) 5 Angular Measurement and Direction I Angular Measurement and Direction II 6 Field Work 3 (Basic Survey Measurement - Direction/Angular Surveys) Traversing and Traverse Computation I 7 Quiz 2, Traversing and Traverse Computation II March Traversing and Traverse Computation III 8 Levelling I Levelling II 9 Field Work 4 (Basic Survey Measurement - Level and Staff Usage) Quiz 3, Area and Volume Computation I 10 Area and Volume Computation II Satellite Positioning II 11 Field Work 5 (Basic Survey Measurement - GPS Surveys) April Quiz 4, Satellite Positioning II 12 Field Work (Semester Project) Field Work (Semester Project) 13 Revision Week, Report and Group Presentation 14 15 May End of Semester Examination 16 University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Page iii Lecture Notes on Land Surveying 2014/2015 Academic Year COURSE ASSESSMENT 2014/2015 Academic Year ASSESSMENT OF STUDENTS The student‘s assessment will be in two forms:  Continuous Assessment [40%] (Quizzes, Class Attendance, Assignments and Group Work)  End of Semester Examination [60%]. The results of the Continuous Assessment shall be made known to students at least one week before the start of the Semester Examinations. The End of Semester shall be marked over 60. ASSESSMENT OF LECTURER At the end of the course each student will be required to evaluate the course and the lecturer‘s performance by answering a questionnaire specifically prepared to obtain the views and opinions of the student about the course and lecturer. This exercise is schedule to take place from Monday, April 20, 2014 to Friday, April 24, 2014. Please be sincere and frank! University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Page iv Lecture Notes on Land Surveying 2014/2015 Academic Year TABLE OF CONTENTS COURSE OUTLINE (SYLLABUS) i COURSE OBJECTIVES ii COURSE PLAN (SCHEDULE) iii COURSE ASSESSMENT iv TABLE OF CONTENTS v LIST OF FIGURES ix LIST OF TABLES ix CHAPTER 1 OVERVIEW OF SURVEYING 1 1.1 Definition of Surveying 1 1.2 Classification of Surveying 2 1.2.1 Classification Based on Accuracy of Work 2 1.2.2 Classification Based on Used or Purpose 2 1.2.3 Classification Based on Instrument Used 2 1.2.3 Classification Based on Position Instrument 3 1.3 Object and Purposes of Surveying 3 1.4 Importance of Surveying 3 1.5 Principles of Surveying 4 1.5.1 Principle of Working from Whole to Part 4 1.5.2 Principles of Controls 4 1.5.3 Principle of Economy of Accuracy 5 1.5.4 Principle of Independent Check 6 1.5.5 Principle of Safeguarding 6 1.6 Stages of Survey Operation 7 1.6.1 Field Work 7 1.6.3 Office Work 8 1.6.4 Care of Instrument 8 1.7 Errors in Surveying 8 1.8 Classification of Errors 9 1.8.1 Accidental/Random Errors 9 1.8.2 Systematic Errors 9 1.8.3 Gross Errors or Mistakes 10 1.9 Units of Measurements 10 1.10 Kinds of Measurements 10 1.10.1 Linear Measures 10 1.10.2 Angular Measurements 11 1.11 Plan Scales 11 1.12 Types of Map Scales 13 1.12.1 Verbal Scale 13 University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Page v Lecture Notes on Land Surveying 2014/2015 Academic Year 1.12.2 Graphical Scale 13 1.12.3 Representative Fraction 13 1.13 Study and Review Questions 14 CHAPTER 2 MEASUREMENT OF HORIZONTAL DISTANCES 15 2.1 Introduction 15 2.2 Methods of Measuring Horizontal Distances 15 2.3 Ranging 15 2.3.1 Direct Ranging 16 2.3.2 Indirect Ranging 16 2.4 Distance Measurements by Chaining 16 2.4.1 Introduction to Chaining 16 2.4.2 Principle of Chain Surveying 17 2.4.3 Suitability and Unsuitability of Chain Surveying 17 2.4.4 Shape, Size and Arrangement of Triangles 17 2.4.5 Terminologies in Chain Surveying 18 2.4.6 Field Work in Chain Surveying 19 2.4.7 Obstacles in Chain Survey 21 2.4.8 Errors in Chain Surveying 21 2.5 Distance Measurement by Taping 22 2.5.1 Introduction to Taping 22 2.5.2 Taping on Level Ground 22 2.5.3 Horizontal Measurement on Sloping Ground 22 2.5.4 Slope Measurement 23 2.5.5 Sources of Error in Taping 24 2.6 Electronic Distance Measurement (EDM) 24 2.6.1 Introduction to EDM 24 2.6.2 Principles of EDM 24 2.7 Study and Review Questions 25 CHAPTER 3 ANGULAR MEASUREMENT AND DIRECTION 27 3.1 Introduction 27 3.2 Units of Angular Measurement 27 3.3 Kinds of Horizontal Angles 28 3.4 Direction of a Line 29 3.5 Azimuth 29 3.6 Bearing 30 3.7 Comparison of Bearing and Azimuth 30 3.8 The Compass and the Earth Magnetic Field 31 3.8 Introduction 31 3.8.2 Surveying Compass 32 University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Page vi Lecture Notes on Land Surveying 2014/2015 Academic Year 3.8.3 Magnetic Declination 33 3.8.4 Local Attraction 33 3.9 The Theodolite 34 3.9.1 Introduction 34 3.9.2 Basic Definitions 35 3.9.3 Instrumental Errors 36 3.9.4 Sources of Error 38 3.12 Study and Review Questions 39 CHAPTER 4 TRAVERSING AND TRAVERSE COMPUTATIONS 41 4.1 Introduction 41 4.2 Selecting a Traverse Station 42 4.4 Referencing Traverse Stations 42 4.5 Angular Misclosure 43 4.6 Sources of Error and Mistakes in Traversing 43 4.7 Traverse Computations 44 4.7.1 Introduction 44 4.7.2 Balancing Angles 44 4.7.3 Computation of Preliminary Bearing or Azimuth 47 4.7.4 Computation of Departures and Latitudes 48 4.7.5 Departure and Latitude Closure Condition 49 4.7.6 Traverse Linear Misclosure and Relative Precision 49 4.7.7 Traverse Adjustment 51 4.7.8 Rectangular Coordinates 53 4.7.9 Mistakes in Traverse Computations 54 4.8 Study and Review Questions 54 CHAPTER 5 LEVELLING 56 5.1 Introduction 56 5.2 Basic Definitions 56 5.3 Instruments for Levelling 58 5.3.1 Categories of Level 58 5.3.2 Telescope 58 5.3.3 Tilting Level 58 5.3.4 Automatic Level 59 5.3.5 Digital Level 60 5.3.6 Tripods 60 5.3.7 Levelling Staff 61 5.4 Fieldwork in Levelling 61 5.4.1 Making Readings 61 5.4.2 Levelling Between Two Points 61 University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Page vii Lecture Notes on Land Surveying 2014/2015 Academic Year 5.4.3 Field Booking and Reduction of Levels 63 5.5 Precision of Levelling 65 5.6 Errors in Levelling 66 5.7 Uses of Levelling 66 5.7.1 Contouring 66 5.8 Study and Review Questions 67 CHAPTER 6 AREA AND VOLUME COMPUTATION 68 6.1 Introduction 68 6.2 Methods of Measuring Area 68 6.3 Area by Coordinates 68 6.4 Method of Volume Measurement 71 6.5 Contour Area Method 71 6.6 Study and Review Questions 73 CHAPTER 7 SATELLITE POSITIONING 74 7.1 Introduction 74 7.2 GPS Segments 75 7.3 Types of GPS 76 7.3.1 Hand-held GPS 76 7.3.2 Differential Code-Phase GPS (DGPS) 76 7.3.3 Carrier-Phase GPS 77 7.4 GPS Measuring Techniques 77 7.4.1 Static 77 7.4.2 Rapid Static 77 7.4.3 Real Time Kinematic 78 7.5 Study and Review Question 78 University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Page viii Lecture Notes on Land Surveying 2014/2015 Academic Year LIST OF FIGURES Figure 1.1 Example of Graphical Scale 13 Figure 2.1 Ranging a Line 16 Figure 2.2 Types of Triangle in Chain Surveying 18 Figure 2.3 Layout of a Chain Surveying 19 Figure 3.1 Basic Requirement in Determining an Angle 27 Figure 3.2 Closed Loop (Polygon) Traverse 28 Figure 3.3 Deflection Angle 29 Figure 3.4 Example of Azimuth 29 Figure 3.5 Bearing of Lines 30 Figure 4.1 Examples of Closed Traverses 41 Figure 4.2 Example of an Open Traverse 42 Figure 4.3 Example of a Traverse 45 Figure 4.4 Departure and Latitude of a Line 48 Figure 5.1 Diagram Showing Basic Levelling Terms 56 Figure 5.2 Parts of a Precise Tilting Level 59 Figure 5.3 Parts of an Automatic Level 59 Figure 5.4 Electronic Digital Level 60 Figure 5.5 Examples of Tripods 61 Figure 5.6 Principles of Levelling 62 Figure 5.7 Levelling and booking sequence 63 Figure 6.1 Area Computation by Coordinate Method 69 Figure 6.2 Traverse for Computation of Area by Coordinates 70 Figure 6.3 Illustration of the Contour-Area Method 72 Figure 8.1 GPS Segments 76 LIST OF TABLES Table 1.1 Recommended scales for use with the metric system 12 Table 3.1 Comparison of Bearing and Azimuth 31 Table 4.1 Adjustment of Angles 46 Table 4.2 Computation of Preliminary Azimuth 48 Table 4.3 Computing of Departures and Latitudes 50 Table 4.4 Balancing Departures and Latitudes by Bowditch Rule 52 Table 5.1 Rise and Fall Method 63 Table 5.2 Height of Collimation method 64 Table 6.1 Traverse for the Computation of Area by Coordinates 71 Table 6.2 Volume Computation by Contour-Area Method 73 University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Page ix Lecture Notes on Land Surveying 2014/2015 Academic Year CHAPTER 1 1 OVERVIEW OF SURVEYING 1.1 Definition of Surveying Surveying is basic to engineering. Before any engineering work can be started, there is the need to prepare a plan or map of the area showing topographical details. This involves both horizontal and vertical measurements. Surveying is defined as the science of determining the position, in three dimensions, of natural and man-made features on or beneath the surface of the Earth. These features may be represented in analogue form as a contoured map, plan or chart, or in digital form such as a digital ground model (DGM or DTM or DEM). Surveying therefore refers to those activities involved in the planning and execution of surveys for the location, design, construction, operation and maintenance of civil and other engineering projects. Surveying activities may involve the following: 1. Preparation of surveys and related mapping specifications 2. Execution of field surveys for the collection of required data including topographic and hydrographic data. 3. Calculation, reduction and plotting of survey data for use in engineering design. 4. Design and provision of horizontal and vertical control survey networks. 5. Provision of line and grade and other layout work for construction and mining activities Therefore the scope of surveying is very wide and interdisciplinary in nature. Basically it involves accurate measurements and accurate computations. In surveying we use modern sophisticated instruments, example, electronic instruments for measurements and modern computational tools, example, computers for accurate mathematical computations. Hence thorough knowledge of basic science such as, physics and mathematics is required in grasping modern surveying. University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 1 Overview of Surveying Page 1 Lecture Notes on Land Surveying 2014/2015 Academic Year 1.2 Classification of Surveying Surveying is a very old profession and can be classified in many different ways. Classification can be based on the following: 1.2.1 Classification Based on Accuracy of Work Two general classifications of surveys are geodetic and plane. In geodetic surveying the curvature of the earth is taken into account. Surveys are conducted with a high degree of accuracy. However in plane surveying except for levelling, the reference base for field work and computations is assumed to be a flat horizontal surface. The errors introduced by assuming the earth to be a plane area is not serious if the area measured is small (≤ 250 km2). 1.2.2 Classification Based on Used or Purpose Surveying can be classified based on the use and purpose of the results obtained. This classification includes the following: 1. Control surveys establish a network of horizontal and vertical points that serve as a reference framework for other surveys. 2. Topographic surveys show the natural features of a country such a river, stream, lakes, forest, hills, mountains, valleys and so on. 3. Hydrographic surveys define the shore lines and depth of water bodies such as ocean, lakes and reservoirs 4. Land, boundary or cadastral surveys establish property lines and corners 5. Route surveys are done as a preliminary to construction of roads 'and railways 6. Mine Surveys are done on, above and below ground to guide mining operation both underground and on surface. 1.2.3 Classification Based on Instrument Used In chain, theodolite, plane table, tacheometric surveys, the equipment or instrument named is the major equipment or instrument used in the survey work. University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 1 Overview of Surveying Page 2 Lecture Notes on Land Surveying 2014/2015 Academic Year 1.2.3 Classification Based on Position Instrument When measurement is done on the ground, for instant by chain, tape or electronic distance measuring instruments, it is a ground/land survey; however when photographic and remotely sensed data are taken from the air, it is an aerial survey. 1.3 Object and Purposes of Surveying The object of surveying is the preparation of plans and maps of the areas. Or is the representation of tracts of land in the form of a plan ―drawn to scale‖ upon a sheet of drawing paper, also to facilitate the calculation of areas of land. Surveying is done to locate the positions of points on or near the surface of the earth. This involves measurements of distances and angles to determine horizontal positions of arbitrary points on the earth‘s surface, heights of arbitrary points above or below a reference datum and the configuration of the ground. It also involves setting-out distances, angles and grid lines to locate construction lines for buildings, bridges, highways, drill holes and other engineering works and establishing the positions of boundary lines on the ground. Surveying, which is the art of determining the relative positions of distinctive features on the surface of the earth, by means of measurements of distances, directions and elevations are used for two distinct purposes. These are: 1. The determination of the relative positions of points (natural or artificial features) on the surface of the earth so that they may be correctly represented on maps or plans. 2. The setting-out on the ground of the positions of proposed construction or engineering works. 1.4 Importance of Surveying Surveying continues to play an extremely important role in many braches of engineering. For example, surveys are required to plan, construct, and maintain highways, railroads, rapid-transit systems, buildings, bridges, missile ranges, lunching sites, tracking stations, tunnels, canals, irrigation ditches, dams, drainage works, urban land subdivisions, water supply and sewage systems, pipelines, and mine shafts. Surveying methods are commonly University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 1 Overview of Surveying Page 3 Lecture Notes on Land Surveying 2014/2015 Academic Year employed in laying out industrial assembly lines. These methods are also used for guiding the fabrication of large equipment, such as airlines and ships, where separate pieces that have been assembled at different locations must ultimately be connected as a unit. Surveying is important in many related tasks in agronomy, archeology, astronomy, forestry, geography, geology, geophysics, landscape architecture, meteorology, paleontology, and seismology, but particularly in military and civil engineering. 1.5 Principles of Surveying Every profession must be founded upon sound practice and in this surveying is no different. Practice in turn must be based upon proven principles. The fundamental principles upon which various survey methods are based are themselves of a very simple nature. 1.5.1 Principle of Working from Whole to Part In most types of survey the ruling principle is to work from the whole to the part. Thus, in fairly extensive surveys, such as those of a large estate or of a town, the first-thing to be done is to establish a system of control points. The positions of these points are fixed with a fairly high standard of accuracy, but, between them the work may be done by less accurate and consequently, by less expensive methods. The main idea of working from whole to the part is to prevent accumulation of errors and to localize minor errors within the frame work of the control points. On the other hand, if survey is carried out from the part to the whole, the errors would expand to greater magnitudes and the scale of the survey will be distorted beyond control. In general practice the area is divided into a number of large triangles and the positions of their vertices are surveyed with greater accuracy, using sophisticated instruments. These triangles are further divided into smaller triangles and their vertices are surveyed with lesser accuracy. 1.5.2 Principles of Controls A control network is the framework of survey stations whose coordinates have been precisely determined and are often considered definitive. The stations are the reference monuments, to which other survey work of a lesser quality is related. By its nature, a control survey needs to be precise, complete and University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 1 Overview of Surveying Page 4 Lecture Notes on Land Surveying 2014/2015 Academic Year reliable and it must be possible to show that these qualities have been achieved. This is done by using equipment of proven precision, with methods that satisfy the principles and data processing that not only computes the correct values but gives numerical measures of their precision and reliability. Since care needs to be taken over the provision of control, it ought to be planned to ensure that it achieves the numerically stated objectives of precision and reliability. It must also be complete as it will be needed for all related and dependent survey work. Other survey works that may use the control will usually be less precise but of greater quantity. Examples are setting out drill holes, detail surveys of a site or of an as-built development and monitoring many points on a structure suspected of undergoing deformation. The practice of using a control framework as a basis for further survey operations is often called working from the whole to the part. 1.5.3 Principle of Economy of Accuracy Surveys are carried out for a specific purpose and so should be as accurate as they need to be. In spite of modern equipment, automated systems, and statistical data processing the business of survey is still a manpower intensive one and needs to be kept to an economic minimum. Once the requirement for a survey or some setting out exists, then part of the specification for the work must include a statement of the relative and absolute accuracies to be achieved. From this, a specification for the control survey may be derived and once this specification has been achieved, there is no requirement for further work. While control involves working from the whole to the part the specification for all survey products is achieved by working from the part to the whole. The specification for the control may be derived from estimation based upon experience using knowledge of survey methods to be applied, the instruments to be used and the capabilities of the personnel involved. Such a specification defines the expected quality of the output by defining the quality of the work that goes into the survey. Alternatively a statistical analysis of the proposed control network may be used and this is the preferable approach. In practice a good specification will involve a combination of both methods, statistics University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 1 Overview of Surveying Page 5 Lecture Notes on Land Surveying 2014/2015 Academic Year tempered by experience. The accuracy of any survey work will never be better than the control upon which it is based. You cannot set out drill holes to 5 mm if the control is only good to 2 cm. 1.5.4 Principle of Independent Check The independent check is a technique of quality assurance. It is a means of guarding against a blunder or gross error and the principle must be applied at all stages of a survey. Failure to do so will lead to the risk, if not probability of ‗catastrophic failure‘ of the survey work. If observations are made with optical or mechanical instruments, then the observations will need to be written down. A standard format should be used, with sufficient arithmetic checks upon the booking sheet to ensure that there are no computational errors. The observations should be repeated, or better, made in a different manner to ensure that they are in sympathy with each other. For example, if a rectangular building is to be set out, then once the four corners have been set out, opposite sides should be the same length and so should the diagonals. The sides and diagonals should also be related through Pythagoras‘ theorem. Such checks and many others will be familiar to the practising surveyor. Checks should be applied to ensure that stations have been properly occupied and the observations between them properly made. Data abstraction, preliminary computations, data preparation and data entry are all areas where transcription errors are likely to lead to apparent blunders. Ideally all these activities should be carried out by more than one person so as to duplicate the work and with frequent cross-reference to detect errors. Every human activity needs to be duplicated if it is not self-checking. Wherever there is an opportunity for an error there must be a system for checking that no error exists. If an error exists, there must be a means of finding it. 1.5.5 Principle of Safeguarding Since survey can be an expensive process, every sensible precaution should be taken to ensure that the work is not compromised. Safeguarding is concerned with the protection of work. Observations which are written down in the field must be in a permanent, legible, unambiguous and easily understood form so that others may make good sense of the work. Observations and other data University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 1 Overview of Surveying Page 6 Lecture Notes on Land Surveying 2014/2015 Academic Year should be duplicated at the earliest possible stage, so that if something happens to the original work the information is not lost. This may be by photocopying field sheets, or making backup copies of computer files. Whenever the data is in a unique form or where all forms of the data are held in the same place, then that data is vulnerable to accidental destruction. In the case of a control survey, the protection of survey monuments is most important since the precise coordinates of a point which no longer exists or cannot be found are useless. 1.6 Stages of Survey Operation The entire work of a survey operation may be divided into three district stages, namely: 1. Field work 2. Office work 3. Care of the instrument 1.6.1 Field Work The fieldwork involve the measurement of distances and angles required for plotting to scale and also keeping a systematic record of what has been done in the form of a field book or measurement book. In survey operation, field work involves the following: 1. Reconnaissance: Here the surveyor goes to the area to fix a number of stations, ensuring necessary intervisibility to establish a system of horizontal control. It is just a familiarization tour of the area. A preliminary inspection of the area is Recce. 2. Observations: The surveyor makes necessary observations with survey instruments for linear and angular measurements. 3. Field Records: All the measurements made are recorded in a field book. Every care is made to ensure correct entries of all the observations otherwise the survey may be useless. University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 1 Overview of Surveying Page 7 Lecture Notes on Land Surveying 2014/2015 Academic Year 1.6.3 Office Work The field notes are brought to the office and necessary drafting, computing, adjustment and designing work are done manually or electronically using a computer. 1.6.4 Care of Instrument A great care is required to handle survey instruments. A beginner should always be made familiar with care and adjustment of the instruments and its limitation. Precision instruments such as theodolite, level, and prismatic compass need more care than the equipment such as chains, arrows, ranging rods, etc. 1.7 Errors in Surveying The basic task in land surveying is establishment of three-dimensional controls using linear and angular measurements and more recently through the use of satellites (GPS). Such measurements contain errors, since no measurement is free of errors. True value of a measurement can therefore, never be found, even though such a value exist. The true value is determined statistically after repeated measurements. Since the true value of a measurement is not known it follows that exact error will also never be known. It must be understood that no measurement in a survey is ever exact – every measurement, whether linear or angular, contains errors. There are basically three main sources of errors, namely natural, instrumental and personal. 1. Natural Sources of error may be caused by adverse or variable weather conditions examples of which are; expansion or contraction of steel tapes due to temperature changes, refraction of light rays, variation in the speed of electromagnetic waves through the atmosphere, etc. 2. Instrumental errors are caused by imperfect construction and adjustment of equipment used in surveying 3. Personal errors results from the inability of the individual to make exact observations due to limitations of human sight, touch and hearing. University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 1 Overview of Surveying Page 8 Lecture Notes on Land Surveying 2014/2015 Academic Year 1.8 Classification of Errors Errors can be classified into the following: 1. Accidental Errors 2. Systematic Errors 3. Gross Errors or Mistakes 1.8.1 Accidental/Random Errors This does not mean errors arising from accidents in the field. Accidental errors are those small errors about which nothing can be done – variations in the eyesight of persons using instrument telescopes, sudden changes in temperature altering the length of a steel tape, slight imperfections in instruments, and so on. The surveyor‘s efforts should be directed principally at eliminating mistakes and keeping systematic errors to the minimum, according to the type of survey and the accuracy required. Random Errors are associated with the skill and vigilance of the surveyor. They are introduced into each measurement mainly because no human can perform perfectly. Thus equipment and our observations are imperfect. They represent the residual error after all other errors have been eliminated. They are compensating and generally unavoidable. They are usually conforming to the law of probability. Taking the mean of repeated observations minimizes their effects. 1.8.2 Systematic Errors These are errors which always recur in the same instrument or operation, and they are cumulative, that is to say, their effect will increase throughout the survey. As an example, if a nominal 20 m chain has been stretched (by hard usage) by an amount of 0.05 m, then every time it is laid on the ground there will be an error in distance measurement of 0.05. If, in measuring the length of a line, the chain is laid down ten times, the length of the line will be noted as 200 m, but the true length will be 20.05 m. The error will have accumulated to 10 x 0.05 m = 0.5m. These errors may be guarded against by using suitable operational methods, by standardizing equipment, and by applying appropriate corrections to the actual measurements. University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 1 Overview of Surveying Page 9 Lecture Notes on Land Surveying 2014/2015 Academic Year 1.8.3 Gross Errors or Mistakes These are serious mistakes made by the surveyor, such as reading a level staff as 2.415 m instead of 3.415m, or noting a distance measured with the chain as 5.45 m instead of 15.45 m. These can only be eliminated by the use of suitable methods of observing and booking and checking both operations. Mistakes can be detected and eliminated by repeated or check measurements. This also improves the precision. 1.9 Units of Measurements Several systems of units of measurement have been in use throughout the world, including the metric system, the imperial (British) system and American units. The American units are basically the same as the British, with some differences in weight and volume. The republic of Ghana and many other countries have adopted the international system of units, abbreviated to SI. In the metric system, the unit of measurement of distance is recommended in metre and centimetre for the execution of surveys whilst that of the imperial system is in feet and inches. It must be noted that the Survey and Mapping Agency of Ghana still have survey data in feet. 1.10 Kinds of Measurements There are two kinds of measurements in plane surveying: 1. Linear measurement, i.e. Horizontal or vertical distances 2. Angular measurement, i.e. Horizontal or vertical angles. 1.10.1 Linear Measures The basic length unit in S.I. is the metre. Basic units of length, S. I. 10 millimetres = 1 centimetre (cm) 10 centimetre = 1 decimetre (dm) 10 decimetres = 1 metre (m) 10 metres = 1 decametre (dam) 10 decametre = 1 hectometre Basic units of area University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 1 Overview of Surveying Page 10 Lecture Notes on Land Surveying 2014/2015 Academic Year The accepted units are the square kilometre (Km2), the hectare (ha) and the square metre (m2). All of these may be used in surveying as appropriate. 10 000 m2 = 1 hectare 1 000 000 m2 = 1 Km2 100 ha = 1 Km2 Volume Units Quantities of materials, such as excavation, rock, sand, and so on, are expressed in cubic metres (m3) liquid volumes are stated in litres. 1 litre = 0.001 m3 (Note that 0.001 m3 is actually one cubic decimetre). The sub- multiple of the litre is the millilitre (ml), and 1000 ml = 1 litre = 0.001 m3. The millitre was formerly known as ―Cubic centimetre‖ and was often indicated by the symbol ―cc‖ instead of the international symbol ―cm3‖. 1.10.2 Angular Measurements An angle may be defined as the difference in directions of two intersecting lines, or it is the inclination of two straight lines. The agreed angle unit in S.I. is the radian (rad). A radian is the angle subtended at the centre of a circle by an arc of length equal to the radius of the circle. Then, 2 π radians = 1 revolution = 4 right angles. The radian is useful in many branches of mathematics and in some survey calculations. The practical unit of angle measure in Ghana is degree and its sub-divisions, the minutes and the second. Then, 60 seconds = 1 minutes 60 minutes = 1 degree 360 degree = 1 revolution Angles may be expressed in degrees, minutes and seconds; example 273˚25'30" or in degrees and minutes and decimals of a minutes or decimal degree; example 273.425. For the conversions between degrees and radians, 1 rad = 57.29 degrees = 206265 seconds 1.11 Plan Scales A map scale is the ratio between a distance on a map and the corresponding distance in the terrain. Or it is also an expression of how much the area represented has been reduced on the map. Scale is considered to be the single University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 1 Overview of Surveying Page 11 Lecture Notes on Land Surveying 2014/2015 Academic Year most critical mathematical feature of any map and, because of its importance, scale is often used as a primary means of categorising maps - from large-scale maps of 1: 10,000 to atlases of 1:1,000,000. The scales recommended by the international organization for standardization (I.S.O) are shown Table Table 1.1 Recommended scales for use with the metric system USE SCALE 1: 1 000 000 1: 500 000 Maps 1: 200 000 1: 100 000 1: 50 000 1: 50 000 1: 20 000 Town Surveys 1: 10 000 1: 5 000 1: 2 500 1: 2 500 1: 2 000 Surveys and Layouts 1: 1 250 1: 1 000 0.388888889 1: 1 250 Site Plan 1: 1 000 0.388888889 0.180555556 Location drawings 0.111111111 1:50 1:20 Components and assembly detail drawings 1:10 1:05 1:01 Scales may be said to be large or small, but there is no definite dividing point. One scale may be said to be larger than another, if the numerical value of the first scale‘s R.F is greater than that of the second scale, e.g. comparing scales of 1: 100 and 1: 200, 1 1  0.01 and  0.005 100 200 Since 0.01 is greater numerically than 0.005, the 1:100 scale is said to be larger than the 1:200 scale. The distinction between maps and plans should be understood. A plan is a true to scale representation. A map is drawn to such a University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 1 Overview of Surveying Page 12 Lecture Notes on Land Surveying 2014/2015 Academic Year small scale that some of the features shown on it cannot be drawn to scale. It must be noted that scales are also generally grouped into two, namely; 1. Numerical scales 2. Graphical 1.12 Types of Map Scales We can relate map and ground with three different types of scale; 3. Verbal scale 4. Graphical scale 5. Representative fraction 1.12.1 Verbal Scale Verbal scale expresses in words as the relationship between a map distance and a ground distance. Usually it is along the lines of: One inch represents 16 miles. Here it is implied that the one-inch is on the map, and that one-inch represents 16 miles on the ground. Verbal scales are commonly found on popular atlases and maps. 1.12.2 Graphical Scale The second type of scale is a graphic scale, or bar scale. This shows directly on the map the corresponding ground distance. Figure 1.1 Is an example of a graphical scale. Figure 1.1 Example of Graphical Scale The main drawback of bar scales is that they are usually short compared to the map itself, and hence measuring longer distances is difficult. 1.12.3 Representative Fraction The third type of scale is a representative fraction, or ratio scale. Compared to the first two, it is the most abstract, but also the most versatile. A representative fraction, or RF, shows the relationship between one of any unit on the map and one of the same unit on the ground. RFs may be shown as an actual fraction, for example 1/24,000, but are usually written with a colon, as in 1:24,000. In this example, one unit of any length (one mm, one cm, one University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 1 Overview of Surveying Page 13 Lecture Notes on Land Surveying 2014/2015 Academic Year inch, one foot, etc.) on the map represents 24,000 of those same units on the ground (24,000 mm, 24,000 cm, 24,000", 24,000', etc.). Examples 1. If 1 centimetre on a map represents 10 metres on the ground, what will be the RF? 2. The scale of a plan is 1:4. If a square on the plan measures 3 by 3 units what is the corresponding ground area? 3. An area was measured on a plan by, 250 mm x 175 mm. Calculate the ground area in metres if the scale is (a) 1:2000 (b) 1: 500 1.13 Study and Review Questions 1. Explain surveying and state three surveying activities 2. Name the four main ways upon which surveying can be classified? Under each of the classifications state and explain two sub- classifications 3. State the object as well as the two main purpose of surveying? 4. Give three importance of surveying 5. State and explain three of the principles of surveying 6. What is reconnaissance in surveying 7. What the three main sources of errors in surveying? Explain each of them 8. Errors in surveying can be classified into three classes, name and explain each of these classes 9. Name the kinds of measurements in surveying 10. What is a plan scale? Name the three different kinds of scale in surveying 11. If 1 centimetre on a map represents 10 metres on the ground, what will be the RF? University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 1 Overview of Surveying Page 14 Lecture Notes on Land Surveying 2014/2015 Academic Year CHAPTER 2 2 MEASUREMENT OF HORIZONTAL DISTANCES 2.1 Introduction One of the most important operations in surveying is measurement of horizontal distance between two points. Distance measurement is generally regarded as the most fundamental of all surveying observations. In plane surveying, the distance between two points means the horizontal distance. If the points are at different elevations, the distance is the horizontal length between vertical lines at the points. 2.2 Methods of Measuring Horizontal Distances Depending on the accuracy desired and time available for measurement, there are many methods of measuring horizontal distances. In surveying, linear measurements have been obtained by many different methods. These include (1) pacing, (2) odometer readings, (3) optical rangefinders, (4) tacheometry (stadia), (5) subtense bars, (6) chaining and taping, (7) electronic distance measurement (EDM), (8) satellite systems, and others. Of these, surveyors most commonly use taping, EDM and satellite systems today. 2.3 Ranging The process of marking a number of intermediate point a survey line joining two stations in the field so that the line between them may be measured correctly, is called ranging. When the line is short or its end station is clearly visible, the chain may be laid in true alignment. If the line is long or its end station is not visible due to undulating ground, it is required to mark a number of points with ranging rod such as a, b, c, d, etc. along chain lines prior to chaining the distance between A and B as shown in Figure 2.1. University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 2 Measurement of Horizontal Distances Page 15 Lecture Notes on Land Surveying 2014/2015 Academic Year d c B b a A Figure 2.1 Ranging a Line Ranging may be done either by eye estimation or by using line ranger or theodolite. Theodolites are generally used in important works only. Ranging may be classified as 1. Direct ranging 2. Indirect ranging 2.3.1 Direct Ranging When intermediate ranging rods are fixed along the chain line, by direct observations from either end station, the process is known as ―Direct ranging‖ 2.3.2 Indirect Ranging When end stations are not intervisible and the intermediate ranging rods are placed in line by interpolation or by reciprocal ranging or by running an auxiliary line (or random line) the process is known as indirect ranging. Indirect ranging is resorted to the following situations. 1. When the end stations of a line are not distinctly visible due to a large distance 2. When the end station of a line are not visible due to raised ground. 2.4 Distance Measurements by Chaining 2.4.1 Introduction to Chaining Chain surveying is one of the methods of land surveying. It is the system of surveying in which sides of various triangles are measured directly in the field and no angular measurements are taken. Almost all surveying is based on the triangle, and to reproduce a given triangle three things must be known: either University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 2 Measurement of Horizontal Distances Page 16 Lecture Notes on Land Surveying 2014/2015 Academic Year (a) the lengths of the three side, or (b) two sides and an angle, or (c) one side and two angles. Chain survey is based on the first of these three. 2.4.2 Principle of Chain Surveying The principle of chain surveying is to divide the area into a number of triangles of suitable sides. As a triangle is the only simple plane geometrical figure which can be plotted with lengths of its sides alone, a network of triangles is preferred to in chain surveys. 2.4.3 Suitability and Unsuitability of Chain Surveying Chain surveying is most suitable in the following cases 1. When the ground is fairly level and open with simple details 2. When large scale plans are required such as those for a factory size. 3. When the area is comparatively small in extent Chain surveying is unsuitable in the following cases 1. It is unsuitable for large areas 2. It is unsuitable for areas crowded with many details 3. It is unsuitable for wooded areas 4. It is unsuitable for undulating areas. 2.4.4 Shape, Size and Arrangement of Triangles In chain surveying all the three sides of a triangle are liable to error. Hence, all the side of the triangle should preferably be equal having each angle nearly 60˚. An equilateral triangle is also more accurately plottable than an obtuse angled triangle. Hence, to ensure minimum destruction due to errors in measurement and plotting, the best shaped triangle is an equilateral triangle. Due to the configuration of the ground, it is not always possible to have equilateral triangles. An attempt should therefore be made to have triangles which are very nearly equilateral. Such triangles are known as well conditioned or well shaped triangles. A well-conditioned triangle should not contain any angle smaller than 30˚ and greater than 120˚. Figure 2.2 shows the different types of shape and size of triangles in chain surveying. University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 2 Measurement of Horizontal Distances Page 17 Lecture Notes on Land Surveying 2014/2015 Academic Year Z Z Z 75 15 60 145 Y 60 60 Y X 30 20 X 75 Y X An Ideal Triangle Well-Conditioned Triangle Ill-Conditioned Triangle Figure 2.2 Types of Triangle in Chain Surveying The triangle having angle smaller than 30˚ or greater than 120 ˚, are known as ill-conditioned triangles. Ill conditioned triangles should always be avoided. In case, ill-conditioned triangles are unavoidable, greater care must be taken in their chaining and plotting. The size of a triangle depends upon the nature of the detail and the terrain. If the terrain is open with lesser details, large triangles may be adopted. On the other hand, if the terrain is crowded with details, small sized triangles may be suitable. 2.4.5 Terminologies in Chain Surveying The following are the some basic terminologies in chain surveying. 1. Main survey station – The point where two sides of a main triangle meet is called, main survey station. Main survey station is a point of importance at the beginning and at the end of a chain line. The chain lines joining the main survey stations are known as main survey lines. 2. The station /subsidiary survey station – The station which are selected on the main survey lines for running auxiliary lines are called subsidiary stations. The chain lines joining the subsidiary survey stations are known as auxiliary, subsidiary or more commonly as tie lines. These are provided to locate the interior details which are far away from the main lines. 3. Base line – The longest of the main survey lines is called a base line. Various survey stations are plotted with reference to the base line 4. Check lines – The lines which are run in the field to check the accuracy of the field work are called check lines. If the measured length of a check line agrees with the length scaled off the plan, the survey is accurate. Figure 2.3 illustrates these terminologies University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 2 Measurement of Horizontal Distances Page 18 Lecture Notes on Land Surveying 2014/2015 Academic Year Base Line: AC A Main Survey Lines: AB, BC, CD and AD Main stations: A, B, C and D Subsidiary Stations: E and F Subsidiary or Tie Lines: BE and FD Check Lines: HG and MN D M E N F Road H G B C Figure 2.3 Layout of a Chain Surveying 2.4.6 Field Work in Chain Surveying The field work of chain surveying is carried out in the following steps Reconnaissance It is always useful and often absolutely necessary for the surveyor to make a preliminary inspection of the area before commencing his actual detail survey for the purpose of fixing the survey stations and forming a general plan for the network of the chain lines. On arriving at the field, the surveyor first of all walks around and thoroughly examines the ground, with the view to determining how best he may arrange the work. The positions of the stations can be selected and marked, the poles being used to test intervisibility. During recce, the surveyor should prepare a sketch showing the arrangement of lines and the numbering or lettering of the stations. University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 2 Measurement of Horizontal Distances Page 19 Lecture Notes on Land Surveying 2014/2015 Academic Year Selection of Station In examining the ground for a good arrangement of survey lines, the surveyor should endeavour to meet the following requirements.  Survey lines should be as few as practicable and such as to form a geometrically sound framework.  Triangle should be well conditioned and angles less than 30 ˚ should be avoided if possible.  There should be an adequate numbers of check line and if these can be used to pick up some details, so much the better.  Offsets should be kept short especially those to important features.  Lines should lie over the more level ground Stations Marking Stations should be marked so that they can be found again at any time during the survey. In soft ground wooden pegs about 0.3 m by 30 mm square may be driven in flush and made conspicuous by dabs of paint or chalk. For marking a permanent station, a stone of any standard shape may be embedded in the ground and fixed with cement mortar. A brief description of each survey station is given and reference sketches are drawn in the field book. Running the Survey Line On completion of preliminary work, survey lines are run as detailed below: 1. Ranging is done between the end stations of the base line. 2. A chain/tape is stretched in true alignment keeping one end of the chain at the stating station 3. An arrow is fixed at the other end of the chain while it is kept lying on the ground. 4. The surveyor walks along the chain line and takes offsets to adjacent detail points on the right and left sides of the chain lines. 5. Chainages and offsets are recorded in the field book 6. Process of chaining and offsetting, is repeated until the end of the base line is reached 7. Other lines are similar completed University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 2 Measurement of Horizontal Distances Page 20 Lecture Notes on Land Surveying 2014/2015 Academic Year Note keeping The book in which chainages, offset measurements and sketches of detail points are recorded, is generally called a field book. At the beginning of a chain line, the following information is recorded in the field book: 1. The name or number of the chain line 2. The name or number of the survey station 3. The symbol denoting the station mark 4. The direction of the survey lines starting from or ending at the station. 5. The initial chainage which is generally zero is enclosed in the symbol. The complete record of the chain survey should include the following: a. A general plan of lines b. The details of lines c. The date of survey d. Names of surveyor and assistant Plotting the Survey After the field work, the data that was obtained is then plotted to produce a map or plan of the survey. 2.4.7 Obstacles in Chain Survey Various types of obstacles generally met during chaining may be overcome by any one of the following methods. Obstacles to chaining may be classified as under: 1. Obstacles which obstruct ranging but not chaining 2. Obstacles which obstruct chaining but not ranging 3. Obstacles which obstruct both ranging and chaining. 2.4.8 Errors in Chain Surveying All measurements made with tapes and chains are subject to some form of error, no matter how carefully any line is measured. The error may be due to surveyor‘s carelessness or inexperience; it may be due to prevailing climatic conditions, or it may be inherent in the instrument being used. Errors can be divided into several classes which are: University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 2 Measurement of Horizontal Distances Page 21 Lecture Notes on Land Surveying 2014/2015 Academic Year Gross Errors These are mistakes arising from inexperience, carelessness or fatigue in the observer. Examples are, miscounting of chain lengths, displacement of arrows from their true position and faulty booking of field information (3.02 m instead of 13.02 m). These can only be eliminated by proper and careful methods of observing booking. Systematic/Cumulative/Constant errors These are errors whose magnitude and algebraic sign can be determined. They always recur in the same instrument or operation. They include misalignment of the tape, error due to sag of the chain in stepping operations, the chain not being true to length and the chain not being pulled straight. Accidental/Human errors These are caused by variations in the eye sight of persons using the instrument and sudden changes of temperature or wind and atmospheric disturbances. They are usually small and not cumulative. 2.5 Distance Measurement by Taping 2.5.1 Introduction to Taping Observation of horizontal distances by taping consists of applying the known length of a graduated tape directly to a line a number of times. Two types of problems arise: (1) observing an unknown distance between fixed points, such as between two stakes in the ground and (2) laying out a known or required distance with only the starting mark in place. Tapping can be applied on both level and sloping grounds. 2.5.2 Taping on Level Ground Taping on levelled ground can be performed in six steps: (1) lining in, (2) applying tension, (3) plumbing, (4) marking tape lengths, (5) reading the tape, and (6) recording the distance. 2.5.3 Horizontal Measurement on Sloping Ground In taping on uneven or sloping ground, it is standard practice to hold the tape horizontally and use a plumb bob at one or perhaps both ends. On steeper University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 2 Measurement of Horizontal Distances Page 22 Lecture Notes on Land Surveying 2014/2015 Academic Year slopes, where a long length cannot be held horizontally without plumbing from above shoulder level, shorter distances are measured and accumulated to total a full tape length. This procedure, called breaking tape, is illustrated in Figure 2.4. Figure 2.4 Procedure for Breaking Tape 2.5.4 Slope Measurement In measuring the distance between two points on a steep slope, rather than break tape every few meters, it may be desirable to tape along the slope and compute the horizontal component. This requires measurement also of either the altitude angle α or the difference in elevation d (see Figure 2.5). Figure 2.5 Slope Measurement In Figure 2.8, if altitude angle is determined, the horizontal distance between points A and B can be computed from the relation: H  Lcos eqn. 2.1 University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 2 Measurement of Horizontal Distances Page 23 Lecture Notes on Land Surveying 2014/2015 Academic Year Where H is the horizontal distance between points, L the slope length separating them, and α is the altitude angle from horizontal, usually obtained with an Abney hand level and clinometer. If the difference in elevation d between the ends of the tape is measured, which is done by levelling, the horizontal distance can be computed using the following expression derived from the Pythagorean Theorem: H  L2  d 2 eqn. 2.2 2.5.5 Sources of Error in Taping There are three fundamental sources of error in taping namely 1. Instrumental errors: A tape may differ in actual length from its nominal graduated length because of a defect in manufacture or repair, or as a result of kinks. 2. Natural errors: The horizontal distance between end graduations of a tape varies because of the effects of temperature, wind, and weight of the tape itself. 3. Personal errors: Tape-persons setting pins, reading the tape, or manipulating the equipment. 2.6 Electronic Distance Measurement (EDM) 2.6.1 Introduction to EDM A major advance in surveying instrumentation occurred with the development of electronic distance measuring (EDM) instruments. These devices measure lengths by indirectly determining the number of full and partial waves of transmitted electromagnetic energy required in traveling between the two ends of a line. In practice, the energy is transmitted from one end of the line to the other and returned to the starting point; thus, it travels the double path distance. Multiplying the total number of cycles by its wavelength and dividing by 2, yields the unknown distance. 2.6.2 Principles of EDM In Section 2.6.1, it was stated that distances are observed electronically by determining the number of full and partial waves of transmitted University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 2 Measurement of Horizontal Distances Page 24 Lecture Notes on Land Surveying 2014/2015 Academic Year electromagnetic energy that are required in traveling the distance between the two ends of a line. In other words, this process involves determining the number of wavelengths in an unknown distance. Then, knowing the precise length of the wave, the distance can be determined. This is similar to relating an unknown distance to the calibrated length of a steel tape. The procedure of measuring a distance electronically is depicted in Figure 2.6, where an EDM device has been centred over station A by means of a plumb bob or optical plumbing device. Figure 2.6 Generalised EDM Procedure The instrument transmits a carrier signal of electromagnetic energy to station B. A reference frequency of a precisely regulated wavelength has been superimposed or modulated onto the carrier. A reflector at B returns the signal to the receiver, so its travel path is double the slope distance AB. In the figure, the modulated electromagnetic energy is represented by a series of sine waves, each having wavelength λ. The unit at A determines the number of wavelengths in the double path, multiplied by the wavelength in feet or meters, and divided by 2 to obtain distance AB. 2.7 Study and Review Questions 1. Explain five methods the are used for linear measurement University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 2 Measurement of Horizontal Distances Page 25 Lecture Notes on Land Surveying 2014/2015 Academic Year 2. What is ranging in surveying? Name the two types of ranging 3. What is chain surveying 4. What is the principle of chain surveying 5. Under what conditions can chain surveying be said to be suitable 6. Name three situations the makes chain surveying unsuitable 7. What is a well-conditioned and an ill-conditioned triangle 8. What should be the size, shape and arrangement of triangles during chain surveying 9. Explain the following terms as they are applied in chain surveying a. Main surveying line b. Baseline c. Check lines d. Subsidiary survey station 10. Explain how chain surveying is carried out in the field 11. What are the main obstacles that may be encountered in chain surveying 12. Explain how you would overcome obstacle the obstruct chaining but not ranging 13. Compute the horizontal distance of a line with a slope distance of 500 m and an altitude angle of 70˚ 14. Name the sources of errors in taping 15. Explain the principle of EDM University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 2 Measurement of Horizontal Distances Page 26 Lecture Notes on Land Surveying 2014/2015 Academic Year CHAPTER 3 3 ANGULAR MEASUREMENT AND DIRECTION 3.1 Introduction Determining the locations of points and orientations of lines frequently depends on the observation of angles and directions. In surveying, directions are given by azimuths and bearings. Angles measured in surveying are classified as either horizontal or vertical, depending on the plane in which they are observed. Horizontal angles are the basic observations needed for determining bearings and azimuth. Vertical angles are used in trigonometric levelling, stadia and for reducing slope distances to horizontal. Three basic requirements determine an angle. As shown in Figure 3.1, they are (1) reference or starting line, (2) direction of turning, and (3) angular distance (value of the angle). Figure 3.1 Basic Requirement in Determining an Angle 3.2 Units of Angular Measurement A purely arbitrary unit defines the value of an angle. The sexagesimal system which is used in many countries is based on degrees, minutes, and seconds, with the last unit further divided decimally. In other countries (mainly Europe), the grad or gon is commonly used. Radians may be more suitable in computer computation. University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 3 Angular Measurement and Direction Page 27 Lecture Notes on Land Surveying 2014/2015 Academic Year 3.3 Kinds of Horizontal Angles The kinds of horizontal angles most commonly observed in surveying are (1) interior angles (angles to the left and right), (2) exterior angles (angles to the left and right), and (3) deflection angles. Since they differ considerably, the kind used must be clearly indicated in field notes. Interior angles, shown in Figure 3.2, are observed on the inside of a closed polygon. Normally the angle at each apex within the polygon is measured. A check can be made on their values because the sum of all interior angles in any polygon must equal (n- 2)180˚ where n is the number of angles. Exterior angles, located outside a closed polygon, are complements of interior angles. The advantage to be gained by observing them is their use as another check, since the sum of the interior and exterior angles at any station must total 360˚. The sum of the exterior angles for a closed polygon traverse must equal (n+2)180˚. a. Angles to the right b. Angles to the left Figure 3.2 Closed Loop (Polygon) Traverse Deflection angles (see Figure 3.3) are observed from an extension of the back line to the forward station. They are used principally on the long linear alignments of route surveys. University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 3 Angular Measurement and Direction Page 28 Lecture Notes on Land Surveying 2014/2015 Academic Year As illustrated in the figure, deflection angles may be observed to the right (clockwise) or to the left (anticlockwise) depending on the direction of the route. Clockwise angles are considered plus and anticlockwise ones minus, as shown in the figure. Deflection angles are always smaller than 180˚ and appending an R or L to the numerical value identifies the direction of turning. Figure 3.3 Deflection Angle 3.4 Direction of a Line The direction of a line is defined by the horizontal angle between the line and an arbitrarily chosen reference line called a meridian. Different meridians are used for specifying directions including (a) geodetic (also often called true), (b) astronomic, (c) magnetic, (d) grid, and (e) assumed. 3.5 Azimuth Azimuths are horizontal angles observed clockwise from any reference meridian. In plane surveying, azimuths are generally observed from north, but astronomers and the military have used south as the reference direction. Examples of azimuths observed from north are shown in Figure 3.4. Figure 3.4 Example of Azimuth University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 3 Angular Measurement and Direction Page 29 Lecture Notes on Land Surveying 2014/2015 Academic Year As illustrated, they can range from 0° to 360° in value. Hence, the azimuth of OA is 70°, of OB is 145°, of OC is 235°, and of OD is 330°. A line‘s forward direction can be given by its forward azimuth and its reverse direction by its back azimuth. In plane surveying, forward azimuths are converted to back azimuths, and vice versa, by adding or subtracting 180°. For example, if the azimuth of OA is 70°, the azimuth of AO is 70°+180° = 250°. 3.6 Bearing Bearings are another system for designating directions of lines. The bearing of a line is defined as the acute horizontal angle between a reference meridian and the line. The angle is observed from either the north or south toward the east or west, to give a reading smaller than 90°. The letter N or S preceding the angle, and E or W following it shows the proper quadrant. Thus, a properly expressed bearing includes quadrant letters and an angular value. An example is N80°E. Figure 3.5 shows the bearing of different lines. Figure 3.5 Bearing of Lines In the figure above, all bearings in quadrant NOE are measured clockwise from the meridian. Thus the bearing of line OA is N70°E. All bearings in quadrant SOE are anticlockwise from the meridian, so OB is S35°E. 3.7 Comparison of Bearing and Azimuth Since bearings and azimuths are encountered in so many surveying operations, the comparative summary of their properties given in Table 3.1 University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 3 Angular Measurement and Direction Page 30 Lecture Notes on Land Surveying 2014/2015 Academic Year should be helpful. Bearings are readily computed from azimuths by noting the quadrant in which the azimuth falls, then converting as shown in the table. Table 3.1 Comparison of Bearing and Azimuth 3.8 The Compass and the Earth Magnetic Field 3.8 Introduction The branch of surveying in which directions of survey lines are determined by a compass and their lengths by chaining or taping directly on the surface of the earth is called compass surveying. Method of chain surveying is preferred to if the area to be surveyed is small in extent and higher accuracy is aimed at. On the other hand, if the area is comparatively large, with undulations, University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 3 Angular Measurement and Direction Page 31 Lecture Notes on Land Surveying 2014/2015 Academic Year compass surveying is adopted. Before recommending the compass survey for any area, it must be ascertained that area is not magnetically disturbed. 3.8.2 Surveying Compass Figure 3.6 shows the surveyor’s compass and the prismatic compass. The instrument consists of a metal baseplate (A) with two sight vanes (B) at the ends. The compass box (C) and two small level vials (D) are mounted on the baseplate, the level vials being perpendicular to each other. When the compass was set up and the bubbles in the vials centred, the compass box was horizontal and ready for use. b. Surveyor Compass a. Surveyor Compass d. Prismatic Compass c. Compass Box Figure 3.6 Types of Surveying Compasses University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 3 Angular Measurement and Direction Page 32 Lecture Notes on Land Surveying 2014/2015 Academic Year 3.8.3 Magnetic Declination Magnetic declination is the horizontal angle observed from the geodetic meridian to the magnetic meridian. An east declination exists if the magnetic meridian is east of geodetic north; a west declination occurs if it is west of geodetic north. East declinations are considered positive and west declinations negative. The relationship between geodetic north, magnetic north, and magnetic declination is given by the expression geodetic azimuth = magnetic azimuth + magnetic declination eqn. 3.1 Since the magnetic pole positions are constantly changing, magnetic declinations at all locations also undergo continual changes. One way of determining the magnetic declination at a point is to interpolate it from an isogonic chart. An isogonic chart shows magnetic declinations in a certain region for a specific epoch of time. Lines on such maps connecting points that have the same declination are called isogonic lines. Examples Assume the magnetic bearing of a property line was recorded as S43˚30'E in 1862. At that time the magnetic declination at the survey location was 3˚15'W. What geodetic bearing is needed for a subdivision property plan? 3.8.4 Local Attraction This is a local anomaly caused from such things as power lines, railroad tracks, metallic belt buckles, and so on that affect the direction a compass needle points at any location. As an example, when set up beside a streetcar with overhead power lines, the compass needle would swing toward the car as it approached, then follow it until it is out of effective range Local attraction is present if the forward and back bearings of a line differ by more than the normal observation errors. Consider the following compass bearings read on a series of lines as shown in Table 3.4. University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 3 Angular Measurement and Direction Page 33 Lecture Notes on Land Surveying 2014/2015 Academic Year Table 3.2 Compass Bearing of a Series Lines Line Bearing AB N24˚15'W BC N76˚40'W CD N60˚00'E DE N88˚35'E BA S24˚10'E CB S76˚40'E DC S61˚15'W ED S87˚25'W Forward-bearing AB and back-bearing BA agree reasonably well, indicating that little or no local attraction exists at A or B. The same is true for point C. However, the bearings at D differ from corresponding bearings taken at C and E by roughly to the west of north. Local attraction therefore exists at point D and deflects the compass needle by approximately to the west of north. It is evident that to detect local attraction, successive stations on a compass traverse have to be occupied and forward and back bearings read. 3.9 The Theodolite 3.9.1 Introduction The theodolite is a very useful instrument for engineers. It is used primarily for measuring horizontal and vertical angles. However, the instrument can be used for other purposes like (i) Prolonging a line, (ii) Measuring distances indirectly and (iii) Levelling. Theodolites these days are all transit theodolites. Here the line of sight can be rotated in a vertical plane through 180˚ about its horizontal axis. This is known as transitting and hence the name "transit". There are basically two types of theodolite, the optical mechanical type and the electronic digital type, both of which may be capable of reading directly to 1', 20", 1" or 0.1" of arc, depending upon the precision of the instrument. Figure 3.9 shows the main part of a theodolite University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 3 Angular Measurement and Direction Page 34 Lecture Notes on Land Surveying 2014/2015 Academic Year Figure 3.7 Main Parts of a Theodolite The telescope is of measuring type, has an object glass, a diaphragm and an eyepiece and is internal focussing. When elevated or depressed, it rotates about its transverse horizontal axis (trunnion axis) which is placed at right angles to the line of collimation and the vertical circle which is connected to the telescope rotates with it. The vertical circle is rigidly connected to the transverse axis of the telescope and moves as the telescope is raised or depressed. The vertical circle is graduated in degrees with graduations. 3.9.2 Basic Definitions Line of collimation: It is an imaginary line joining the intersection of the cross hairs with the optical centre of the objective. Face left condition: If the vertical circle is on the left side of the observer it is known as face left condition. Since normally the vertical circle is on the left side it is also known as normal condition. University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 3 Angular Measurement and Direction Page 35 Lecture Notes on Land Surveying 2014/2015 Academic Year Face right condition: If the vertical circle is on the right side of the observer, the theodolite is in the face right condition. The telescope is then in the inverted form and hence the condition is known reverse condition. Changing face: It is the operation of changing face left to face right and vice versa. Double sighting or double centring: It is the operation of measuring an angle twice, once with telescope in the normal condition and another in the reverse condition. Plunging the telescope: This is also known as transitting or reversing. It is the process of rotating the telescope through 180˚ in the vertical plane. By this process the direction of objective and eyepiece ends are reversed. Swinging the telescope: It is the process of turning the telescope clockwise or anticlockwise about its vertical axis. Clockwise rotation is called swing right and anticlockwise rotation is called swing left. 3.9.3 Instrumental Errors In order to achieve reliable measurement of the horizontal and vertical angles, one must use an instrument that has been properly adjusted and adopt the correct field procedure. In a properly adjusted instrument, the following geometrical relationships should be maintained 1. The plane of the horizontal circle should be normal to the vertical axis of rotation. 2. The plane of the vertical circle should be normal to the horizontal transit axis. 3. The vertical axis of rotation should pass through the point from which the graduations of the horizontal circle radiate. 4. The transit axis of rotation should pass through the point from which the graduations of the vertical circle radiate. 5. The principal tangent to the plate bubble should be normal to the main axis of rotation. University of Mines and Technology (UMaT) – Tarkwa, Ghana Eric Stemn Chapter 3 Angular Measurement and Direction Page 36 Lecture Notes on Land Surveying 2014/2015 Academic Year 6. The line