Land Surveying @Kwesi PDF

UNIVERSITY OF MINES AND TECHNOLOGY UMaT-TARKWA FACULTY OF MINERAL RESOURCES TECHNOLOGY GEOMATIC ENGINEERING DEPARTMENT LAND SURVEYING (GL/MN/ES 262) Compiled by Michael Aduah (PhD) February, 2017 Course Outline (Syllabus)  INTRODUCTION TO LAND SURVEYING  CHAIN SURVEYING  COMPASS SURVEYING  THEODOLITE SURVEYING  OPTICAL DISTANCE MEASUREMENTS – TACHEOMETRY  ELECTRONIC DISTANCE MEASUREMENTS – EDM  LEVELLING Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana i ASSESSMENT OF STUDENTS Student’s assessment will be in two forms; quizzes/practicals/homework; 40% and end of Semester Examination 60%. UMaT GRADING POLICIES Raw Total Score (%) Letter Grade Interpretation 80 – 100 A Excellent 70 – 79.99 B Very Good 60 – 69.99 C Good 50 – 59.99 D Pass Below – 50 F Fail - I Incomplete. Schedule for Semester Week Date Subject 1 1-Feb Introduction to Landsurveying 2 8-Feb Chain surveying 3 15-Feb 4 22-Feb Compass surveying 5 1-Mar 6 8-Mar Levelling 7 15-Mar 8 22-Mar Theodolite surveying 9 29-Mar 10 5-Apr Optical distance measuremt 11 12-Apr 12 19-Apr Electronic distance measurment 13 26-Apr Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana ii Acknowledgements My sincere thanks go to Messrs. Edward Nenya Kwesi and P.E. Baffoe and Drs. B. Kumi- Boateng and S. Mantey for writing previous editions of this handout. Many thanks also goe to those whose material have been used in this handout, but their names are not mentioned for lack of information; they will also be acknowledged in subsequent editions, when their identities are known. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana iii Table of contents ASSESSMENT OF STUDENTS................................................................................................................ii Course Objectives.....................................................................................................................................vii 1. INTRODUCTION TO LAND SURVEYING..................................................................................... 1 1.1. PURPOSES OF LAND SURVEYING (Agor, 2005)................................................................. 1 1.2. BRANCHES OF LAND SURVEYING...................................................................................... 2 1.2.1. CADASTRAL SURVEYING............................................................................................. 2 1.2.2. ENGINEERING SURVEYING.......................................................................................... 3 1.2.3. TOPOGRAPHIC SURVEYING......................................................................................... 3 1.2.4. HYDROGRAPHIC SURVEYING..................................................................................... 4 1.2.5. GEODETIC SURVEYING................................................................................................. 4 1.3. COORDINATE SYSTEMS FOR SURVEY COMPUTATIONS.............................................. 4 1.3.1. THE RECTANGULAR COORDINATE SYSTEM........................................................... 4 1.3.2. COMPUTATIONS OF RECTANGULAR COORDINATES............................................ 6 1.4. BASIC PRINCIPLES AND TECHNIQUES OF SURVEYING................................................ 6 1.4.1. WORKING FROM THE WHOLE TO THE PART........................................................... 6 1.4.2. APPROPRIATE METHOD FOR REQUIRED RESULT.................................................. 6 1.4.3. PROVISION OF ADEQUATE CHECKS.......................................................................... 7 1.6 BASIC METHODS IN LAND SURVEYING.................................................................................. 8 1.6.1 INTERSECTION............................................................................................................... 8 1.6.2 RESECTION....................................................................................................................... 9 1.6.3 BEARING AND DISTANCE.......................................................................................... 10 1.10 THE PRACTICE OF LAND SURVEYING................................................................................ 11 2. CHAIN SURVEYING...................................................................................................................... 12 2.1. BASIC PRINCIPLES AND FEATURES................................................................................. 12 2.2. BOOKING THE SURVEY MEASUREMENTS..................................................................... 14 2.3. ORIENTATION / NORTH DIRECTION................................................................................. 16 2.4. ABSTRACTION OF MEASUREMENTS............................................................................... 16 2.5. PLOTTING THE SURVEY...................................................................................................... 16 2.6. CHECK MEASUREMENT...................................................................................................... 17 2.7. APPLICATION OF COLOUR AND INKING......................................................................... 17 2.8. LETTERING / ANNOTATION................................................................................................ 17 2.9. MAKING COPIES / REPRODUCTIONS................................................................................ 18 2.10. CONVENTIONAL SIGNS AND LEGEND......................................................................... 18 2.11. CHAIN / TAPE SURVEYING EQUIPMENT..................................................................... 21 3. COMPASS SURVEYING................................................................................................................ 23 3.1. SOME BASIC TERMINOLOGIES IN COMPASS SURVEYING......................................... 23 3.2. TYPES OF REFERENCE DIRECTIONS (MERIDIANS) AND BEARINGS........................ 24 3.3. FORWARD AND BACK BEARINGS......................................................................................... 25 3.4. RECORDING OF READINGS........................................................................................................ 26 Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana iv 3.4.1. WHOLE CIRCLE BEARING (W. C. B).......................................................................... 26 3.4.2. QUADRANTAL BEARING (Q.B).................................................................................. 27 3.5. CONVERSION OF BEARING FROM ONE SYSTEM TO ANOTHER................................ 28 3.6. COMPASSES............................................................................................................................ 29 3.7. DESCRIPTION OF THE PRISMATIC COMPASS................................................................ 31 3.7.1. FIELD OBSERVATIONS................................................................................................ 32 3.7.2. MAGNETIC DECLINATION AND ITS CORRECTION............................................... 32 3.7.3. CORRECTION FOR DECLINATION............................................................................. 33 3.7.4. WORKED EXAMPLES................................................................................................... 35 3.8. LOCAL ATTRACTION........................................................................................................... 37 3.8.1. CORRECTION FOR LOCAL ATTRACTION................................................................ 37 3.9. COMPASS TRAVERSE SURVEY.......................................................................................... 37 3.9.1. TRAVERSING WITH THE PRISMATIC COMPASS.................................................... 38 3.9.2. TRAVERSE BOOKING................................................................................................... 39 3.9.3. BOOKING OF DETAILING............................................................................................ 39 3.9.4. PLOTTING THE TRAVERSE......................................................................................... 40 3.10. USES / APPLICATIONS OF COMPASS OBSERVATIONS............................................. 42 3.10.1. CALCULATING ANGLES FROM BEARINGS............................................................. 42 3.10.2. CALCULATION OF COORDINATES AND AREAS.................................................... 43 3.10.3. COMMON MISTAKES IN COMPASS MEASUREMENTS......................................... 43 3.11. PRECAUTIONS IN COMPASS SURVEYING................................................................... 43 3.12. SAMPLE QUESTIONS........................................................................................................ 43 4. THEODOLITE SURVEYING.......................................................................................................... 45 4.1. INTRODUCTION..................................................................................................................... 45 4.2. DIRECTION AND ANGLE MEASUREMENTS.................................................................... 47 4.3. BOOKING AND COMPUTATION OF DIRECTIONS AND ANGLES................................ 48 4.4. CHECKS ON ANGLE MEASUREMENTS (ANGULAR CLOSURE).................................. 49 4.5. THEODOLITE TRAVERSING................................................................................................ 50 4.5.1. TRAVERSE COMPUTATION AND ADJUSTMENT................................................... 50 4.6. PLOTTING OF TRAVERSE.................................................................................................... 53 4.6.1. AREA OF TRAVERSE.................................................................................................... 53 5. OPTICAL DISTANCE MEASUREMENT:TACHEOMETRY....................................................... 54 5.1. INTRODUCTION..................................................................................................................... 54 5.2. EQUIPMENT............................................................................................................................ 54 5.3. METHOD AND PRINCIPLE OF STADIA TACHEOMETRY.............................................. 55 5.4. INCLINED SIGHTS................................................................................................................. 57 5.5. PERMISSIBLE APPROXIMATIONS..................................................................................... 58 5.6. COMPUTATIONS (REDUCTIONS) IN STADIA TACHEOMETRY................................... 59 6. ELECTRONIC DISTANCE MEASUREMENTS (EDMs).............................................................. 61 1. Fig. 5.1 Illustration of the EDM Principle........................................................................................ 61 6.1. BASIC PRINCIPLES................................................................................................................ 62 Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana v 6.2. RELATIVE ADVANTAGES OF EDM................................................................................... 63 7. LEVELLING..................................................................................................................................... 64 7.1. BASIC DEFINITIONS.............................................................................................................. 64 7.1.1. Vertical Line...................................................................................................................... 64 7.1.2. Horizontal Line................................................................................................................. 65 7.1.3. Level Line......................................................................................................................... 65 7.1.4. Level Surface..................................................................................................................... 65 7.1.5. Elevation............................................................................................................................ 65 7.2. DESCRIPTION OF THE LEVEL INSTRUMENT.................................................................. 65 7.3. TYPES OF LEVELS................................................................................................................. 66 7.3.1. Dumpy Level..................................................................................................................... 66 7.3.2. Tilting Level...................................................................................................................... 67 7.3.3. Automatic Level................................................................................................................ 68 7.4. TRIPOD..................................................................................................................................... 69 7.5. LEVELLING STAFF................................................................................................................ 69 7.6. FIELDWORK IN LEVELLING............................................................................................... 70 7.6.1. Making a Reading............................................................................................................. 70 7.6.2. Levelling Between Two Points......................................................................................... 70 7.6.3. Field Booking and Reduction of Levels............................................................................ 71 7.6.4. Rise and Fall Method........................................................................................................ 72 7.6.5. Adjustment:....................................................................................................................... 72 7.6.6. Height of Collimation Method.......................................................................................... 73 7.7. PRECISION OF LEVELLING................................................................................................. 74 7.8. INVERTED STAFF.................................................................................................................. 74 7.9. ERRORS IN LEVELING.......................................................................................................... 74 7.9.1. Errors in Equipment.......................................................................................................... 75 7.9.2. Field Errors........................................................................................................................ 75 7.10. CLASSIFICATION OF LEVELING.................................................................................... 75 7.10.1. Spirit Levelling.................................................................................................................. 75 7.10.2. Barometric Levelling......................................................................................................... 75 7.11. DIFFICULTIES IN LEVELING........................................................................................... 76 7.11.1. Levelling Across a Lake.................................................................................................... 76 7.11.2. Levelling Across an Intervening High Wall...................................................................... 77 7.11.3. Inverted Staff Levelling..................................................................................................... 78 7.11.4. Reciprocal Levelling......................................................................................................... 79 7.12. PRECISE LEVELING.......................................................................................................... 82 7.13. USES OF LEVELLING........................................................................................................ 82 7.13.1. Contouring......................................................................................................................... 82 7.13.2. Sectioning.......................................................................................................................... 82 Cross sections.................................................................................................................................... 83 Drawing cross-sections and profiles................................................................................................. 83 Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana vi Longitudinal sections........................................................................................................................ 85 Plotting the profile............................................................................................................................ 86 Cross – sectioning............................................................................................................................. 87 8. REFERENCE BOOKS...................................................................................................................... 88 Course Objectives This course aims to provide students with an understanding of Land Survey. Thus the following objectives are set out, that the student will among other things:  Understand the science and technology as well as know the importance of Land surveying,  Be familiar with the theory/principle of chain surveying, compass surveying, theodolite surveys and know how to measure angles and distances in surveying  Conduct simple Land surveys using tapes, compasses, levels, theodolites and EDM instruments. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana vii 1. INTRODUCTION TO LAND SURVEYING Land surveying is the science, technology and art of determining relative positions of features/phenomena on or near the Earth surface and depicting these features on maps (two dimensional surfaces). Land surveying involves the measurement of horizontal and vertical distances between points as well as the angles subtended by these points. The elevations of features are represented on maps as contours. In addition to the measurements, mathematical calculations are fundamental in land surveying as coordinates, elevations, areas, and volumes are computed from survey data. Majority of the information from land survey fieldwork is also portrayed graphically by the construction of maps, profiles, cross sections, and diagrams. Land surveying is an important field in the development and security of a nation as no project can take place without first conducting land survey and it is also through land surveying that boundaries of lands are determined, whether it is boundary between communities, regions or countries. The land surveying process follows the following stages: 1. Office planning and reconnaissance 2. Field reconnaissance 3. Station selection and line Clearing 4. Station marking 5. Field observations and measurements 6. Field booking 7. Adjustments 8. Computations 9. Plotting. 10. Covering report 1.1. PURPOSES OF LAND SURVEYING (Agor, 2005)  To conduct feasibility studies to determine the suitability of sites for projects,  Establish boundaries of land/properties based on available records,  To determine accurately the relative heights/depths of points on the Earth surface,  To determine relative positions of features on or near the Earth surface, Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 1  Produce accurate maps/plans or sections/profiles by plotting measured horizontal distances/coordinates or angles/directions and distances as well as elevations of features/objects,  Accurate setting out (on the ground) of civil engineering project drawings (e.g. roads, bridges, buildings, dams) and to control construction processes from start to finish (finished projects should match design drawings),  To compute quantities including distances between points, areas and volumes of earthworks and materials in engineering projects. 1.2. BRANCHES OF LAND SURVEYING Land surveying has been classified into several branches namely, cadastral surveying, engineering surveying, topographic surveying, hydrographic surveying and geodetic surveying. Land surveying can also be classified based on the type of instruments used. Under this classification we have chain surveying, compass surveying, theodolite surveying, levelling and GPS surveys. The different classes of surveying are discussed further below; with more details provided for the survey methods based on instruments. 1.2.1. CADASTRAL SURVEYING Cadastral surveying deals with the surveying and demarcation of land boundaries, where only the horizontal positions of land parcels are concerned. In Cadastral surveying, the Land Surveyor measures directions of all the sides of the parcel of land as well as all the lengths of the sides of the parcel. In modern Land surveying practice, GPS is often used to determine the horizontal position (X,Y coordinates) of all the boundary points of a parcel of land. However, regardless of the method/instruments used for cadastral surveying, after processing the data, all the directions/bearing as well as the lengths of the sides must be shown on the cadastral plan. The Cadastral plan (e.g Figure 1.1) must also show the adjacent plots of lands and any leading road to the site. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 2 Figure 1.1: A section of a cadastral plan 1.2.2. ENGINEERING SURVEYING Land surveys carried out for the purpose of executing engineering projects such as roads, railines, buildings etc. It involves determination of both horizontal and vertical (elevations) position of points/features. Engineering surveys are usually carried over small areas and short distances (e.g distances with in a town) and does not take the curvature of the Earth into account. In engineering surveying, high accuracies are required to ensure that design drawings are adhered to as accurately as possible; hence large scales (e.g. 1:500, 1:1000, 1:1500) are often used. Surveys related to mining activities also come under engineering surveys. Mine survey consists of the specialized application of survey techniques to positions determination of surface and underground mine workings or structures (e.g. exploration, pit, earthworks, and monitoring surveys). 1.2.3. TOPOGRAPHIC SURVEYING Topographic surveying is a type of Land surveying which is used to determine position (XYZ) of natural and artificial features (buildings, roads, rivers, lakes, mountains, vegetation etc.) on the ground. The maps produced through this process are called topographic maps. Topographic maps typically show the horizontal position of features using conventional symbols and their elevations using contours/spot heights. To produce topographic maps, the horizontal as well as elevations of points/objects are required and these can be measured using Land surveying Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 3 instruments such as theodolites, total stations, levels. However, modern topographic maps are often produced using aerial photography through the process of Photogrammetry. The scales of topographic maps range from 1:25000 to 1:1000 000. 1.2.4. HYDROGRAPHIC SURVEYING Hydrographic surveying is a branch of surveying for determination of positions of features underwater. Hydrographic surveys produce nautical charts/maps required for safe marine/river navigation, marine/river construction, offshore oil drilling and dredging of water bodies/ports. Hydrographic surveying is also an expensive practice as it requires the use of specialised boast/ships and survey instruments and sensors. 1.2.5. GEODETIC SURVEYING Geodetic surveying is a branch of Land survey which deals with the determination of positions and heights over larges areas and long distances (e.g. the whole of West Africa), hence the curvature of the Earth is taken into account in the measurement and calculations. Geodetic surveys provide precise control network upon which surveys of less-precision (e.g. topographic and cadastral surveys) depend. For example in Geodetic surveying, the distance between Accra and Bolgatanga in Ghana, will not be a straight line, but a curved line on the surface of the Earth (Geodesic), since the Earth is spheroid. Geodetic surveys require extremely accurate instruments and methods to deliver the required precision; hence the practice of geodetic surveying is expensive because of the high cost of the appropriate instruments and in developing countries the practice is limited to only National survey agencies such as the Survey and Mapping Division of Ghana. Determination and mapping country boundaries also come under Geodetic surveys. For example the techniques that are being used to determine the sea and land boundary between Ghana and Ivory Coast are Geodetic techniques. 1.3. COORDINATE SYSTEMS FOR SURVEY COMPUTATIONS 1.3.1. THE RECTANGULAR COORDINATE SYSTEM For most plane surveys (e.g. mining and engineering) surveys, the horizontal positions of control points and other objects are defined in terms of rectangular coordinates regardless of the method used for the survey. An understanding of the use of the coordinates is therefore very Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 4 necessary for a surveyor. The coordinate system adopted for most survey purposes is the plane rectangular coordinate system, which consist of two axes intersecting at right angles as in the ordinary mathematical Cartesian coordinates. One axis is designated North (N) corresponding to the Y-axis and the other is Eastern (E) = the X-axis. The scale along both axes is always equal/ the same. As can be shown in Figure 1.2, any point P (x, y) on a plane to which such a rectangular system has been designed, therefore becomes associated with two coordinate values, one for North and the other for East, called Eastings and Northings respectively. The position of each point on such a plane relative to all other points is identified by its Eastern and Northern coordinates and the bearing or direction of each line is also related to the North axis of the coordinate system. For all types of surveys the origin is taking at the extreme south and west of the area, so that all coordinates become positive. N(Y) 120.00m 100.00m d2 D 80.00m C c2 A a2 60.00m 40.00m b2 B a1 d1 b1 c1 20.00m 80.00m 100.00m 120.00m 140.00m 160.00m 180.00m 200.00m 220.00m E (X) Figure 1.2: Rectangular coordinate system There must be specific North direction for every system that one adopts. Such a North direction is usually the true geographical North, or may be the magnetic North or any arbitrary direction of one’s choice. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 5 1.3.2. COMPUTATIONS OF RECTANGULAR COORDINATES The rectangular coordinate system is the most widely used coordinate system in modern Land surveying. For any two points, if one is known, the other can be computed as shown below. If A has coordinates A (EA, NA), the coordinates of B can be computed as: EB = EA+∆EAB = EA+DABSinβAB, NB = NA+∆NAB = NA+DABCosβAB. Where βAB = Bearing of line AB and DAB is the horizontal distance. 1.4. BASIC PRINCIPLES AND TECHNIQUES OF SURVEYING Surveying consists of many different operations and techniques, but underlying them are some basic principles that provide a unity and a discipline to the subject. These principles are few and simply stated, and while they do not possess the status of natural laws, they have developed from generations of experience to provide the most expeditious and effective basis for conducting surveys. 1.4.1. WORKING FROM THE WHOLE TO THE PART The first principle is to work from the whole to the part. This means that, for any particular survey, whether it is of an entire country or of a field, the main framework of the survey should be set out on as large a scale as possible, and involves the minimum possible number of measurements. The concept of framework, or control, will become clearer in later chapters, when triangulation and other forms of control are described. At this stage the principle may be explained by reference to a simple example. 1.4.2. APPROPRIATE METHOD FOR REQUIRED RESULT The second principle is always to choose the method of survey appropriate to the required result. At first sight this might appear to be a statement of the obvious but some of its implications make it worth closer examination. Every survey is performed for some particular purpose, which may range from the topographical mapping of an entire country, to the setting- Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 6 out of a new highway. For such purpose suitable specifications for the accuracy of the required survey must be devised. It is clear that the more refined the techniques and instruments employed, the greater the accuracy obtained. However, the relationship between effort and accuracy in surveying is not linear, and the effect of, say, halving the permitted tolerances will usually more than double the cost of the survey. This means that, in the interests of speed and economy, the surveyor should work as close to the limits of allowable error as he can. Once again, adopting the simplest possible example as illustration, if the survey of a small area is to be plotted as a scale of 1/1000, then, assuming that distances may be plotted on the plan to 0.25 mm, which represents 25 cm on the ground, it is pointless to measure and record distances to points of detail to greater precision than 0.25 m. If, on the other hand the plan is at the scale of 1 /100, then 2.5 cm is just plottable, and the precision of the detail measurement must be increased accordingly. 1.4.3. PROVISION OF ADEQUATE CHECKS The third and final principle relates to the provision of adequate checks. Until some experience has been gained it is difficult to appreciate how easily errors can be made in every aspect of surveying, including operating and reading instruments, recording the observations and calculating and plotting the result. Furthermore, although the frequency of such errors does decrease with increasing experience, the possibility of making errors always exists. A survey must therefore be designed in such a way that it is impossible for such errors to pass undetected, and this necessitates the inclusion of checks. In fieldwork these take the form of measurements in excess of the minimum necessary to fulfil the geometrical requirements of the survey. Figure 1.3 shows a control framework ABCD in which the sides of the two triangles ABC and BCD have been measured. If the diagonal AD is measured, a comparison of the measured and plotted values provides a check on the validity of the measurements. Methods of recording observations and of computation are designed in a similar manner to show up errors in these processes. For measuring face left and face right during angular measurements. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 7 B D A C Figure 1.3: Example control network 1.6 BASIC METHODS IN LAND SURVEYING Practically all methods of surveying involve the measurement, to varying degrees of accuracy, of angles and distances, in both the horizontal and vertical planes. The location of points in these planes is then obtained by applying various geometrical processes to these measured quantities. In surveying, the different processes are known by distinctive names. The methods for fixing position in the horizontal plane are:  Intersection,  Resection and  Bearing and distance. 1.6.1 INTERSECTION Referring to Fig. 1.4, if the positions of two points A and B are known either in the form of rectangular co-ordinates or as positions on a map or plan, then the position of C can be determined by measuring the angles BAC and ABC. Knowing the side length AB, the position of C is obtained either by plotting the two angles, or by using the sine rule of plane trigonometry to calculate the side lengths AC, BC. So far, it has been implicitly assumed that the distance AB is the length of the straight line joining A and B, and the observed angles lie in the plane containing A, B and C. However, for many reasons it is convenient to project all points on the limited area of the earth's surface that we are considering onto a horizontal plane. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 8 Intersection by angles is the basis of the method of providing networks of horizontal control points known as triangulation. In this, each calculated side length provides a known horizontal distance in adjoining triangles such as BCD and ACE in Fig. 1.4 and if the base angles of the triangles are measured, the calculated side lengths AE, CE, BD, and CD are available as bases for additional triangles. In this way a whole network of points, based on a single initial known distance, is built up. In each triangle the necessary check is provided by observing the third angle of the triangle, while the network as a whole is checked by including more than just one known distance. Referring again to Fig. 1.4 (a), the position of C can be determined from A and B by measuring the horizontal distances AC and BC alone and plotting or calculating the intersection of these distances. As with triangulation, this process can be extended to adjacent triangles, to build up a network of control points, with no measured angles. This is known as trilateration. Intersection by both angles and distances can also be used to fix points of detail. Figure 1.4: Intersection 1.6.2 RESECTION This is the method of determining the horizontal position of a point solely by angular observations at the point to a minimum of three fixed points. If, in Fig. 1.5 the positions of three points A, B and C are known and the horizontal angles APB and BPC are measured, then the position of D may be determined either graphically or by calculation. A check is provided by observing extra angles (such as CPD) in addition to the minimum of three points A, B, C. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 9 B C D A P Figure. 1.5: Resection 1.6.3 BEARING AND DISTANCE This is the most direct way of determining position. In Fig. 1.5, A and B are points of known position, and it can be seen that measurement of the horizontal angle BAP and horizontal distance AP is sufficient to fix the point P. P A D Figure. 1.6: Bearing (or Angle) and Distance Method Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 10 1.10 THE PRACTICE OF LAND SURVEYING The practice of surveying is complex. No amount of theory will make a good Land surveyor unless the requisite skill in the art and science of measuring in the field and sound application of office procedures is obtained. The practical phases of the subject are very important, and this requires a lot of field exercises and practice. In addition to those who will major in the field, surveying is one of the basic courses taught to students in the engineering and earth sciences programmes. Although such students may not practice surveying after school, they should understand that the education received in the art and science of measuring and computing, and in the practice of surveying and mapping, will contribute directly to success in other subjects, regardless of their chosen fields. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 11 2. CHAIN SURVEYING 2.1. BASIC PRINCIPLES AND FEATURES Chain surveying is a method of producing a plan of a limited area, not more than a few hundred square metres in extent, using only simple instruments. The principle of chain surveying is that an area to be surveyed is covered by one or more triangles, whose sides are measured. The triangles may be drawn at some selected plan scale by means of a simple geometrical construction. From the control framework on the ground (using working from whole to part principle), measurements are made to points of detail(features), and these can then be located in their correct relative positions by constructing the corresponding scaled distances on the plan. The main figures of the control network should be as large and simple as possible, and measurements in excess of the minimum number that are strictly necessary to plot the survey should be made, in order to provide the necessary checks. The basic equipment of chain surveying is the 20 m surveyor's chain, chaining arrows, ranging poles, a 30 m plastic tape, an optical square and on steeply sloping sites, an abney level. In Figure 2.1(a), ABC, ACD are two triangles, marked by pegs in the ground, forming the framework of a chain survey. The points B and D are not inter-visible, so that checks are provided by measuring the distances BE and DE to a point E on the line AC. The position of this point on the ground will have been established during the reconnaissance for the survey, and the distances of E from A and C are determined during the chaining of the distance AC. To plot the framework, the longest side, or alternatively one of the longer sides, is drawn at the required scale on a sheet of drawing paper. In this example we select the side AC. Then with a pair of compasses, or a beam compass for longer distances, draw arcs with centre A and radii equal to the scale distances AD and AB in the approximate locality of D and B respectively. Repeating the process at C with arcs of radius CD and CB gives intersections representing the positions of D and B. Mark the position of E on AC by scaling its distance from A. Join E to B and D and scale off the distance EB and ED. These scaled distances should corre- spond, to within plottable accuracy, to the distances, measured on the ground. Exactly the same procedure is used for plotting more complicated frameworks, the guiding principles throughout being to work from the whole to the part., and to ensure that an independent check is available for each figure. The layout of the framework on the ground is always designed with these principles in mind. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 12 In some cases, although it may be possible to devise a strong and simple framework covering the area of the survey, the main chain lines are not well situated for survey of the details. In these circumstances a subsidiary framework is added specifically to facilitate the detail survey. For example, in Fig. 2.1(b) the lines FG, HI, JK, LM, NO, UV and WX have been chosen to pass near the main detail. (a) (b) Figure 2.1: Framework for chain survey The principal method of fixing points of detail is by means of perpendicular offsets from the lines of the control framework. In Figure 2.1(a), the corner of the building, Q, is fixed by measuring the distance PQ, where P is the foot of the perpendicular from Q on to the line CD. The offset measurements are made while the line CD is actually being chained. If YZ represents the third chain length along the line CD, then all the detail within a reasonable taping distance - Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 13 say one, two or possibly even three 30 m tape lengths - that happens to lie between perpendiculars to CD through Y and Z is surveyed by rectangular offsets. The chain is actually lying on the ground between Y and Z, which has been lined-in between C and D and which is marked with chaining arrows. The position of P, the foot of the perpendicular from Q onto the chain between Y and Z, is determined by the eye if the distance PQ is less than a tape length or by means of the optical square if it is longer. When P has been located, the chain reading at P, corresponding to the distance YP, is noted and added to the distance CY to give the total distance CP, known as the chainage of P. Thus each detail point Q is fixed by two known distances, one in a given direction and the other perpendicular to it. It may happen that the perpendicular from a detail point to the chain line is obstructed, so that the perpendicular offset cannot be measured. In this case the detail point is fixed by means of tie lines. In Fig. 2.1(a), S is such a detail point. On the chain line two points R and T are located such that the unobstructed lines RS and TS can be chained. S can be plotted as the intersection of the compass arcs, centres R and T and radii the measured distances RS and TS. R and T are, of course, located by their chainages from C. 2.2. BOOKING THE SURVEY MEASUREMENTS The recording, or booking, of survey measurements is an extremely important aspect of all survey operations, whether they relate to chain survey measurements or to work of the highest precision. The principle of all booking methods is that the field notes must be capable of unambiguous interpretation by a person other than the surveyor who actually carried out the survey, as in many organisations the office work of surveying is performed by specialised computing and draughting staff. The method of booking in chain surveying follows a fairly well-established convention. The field book has two vertical parallel lines ruled in the centre of each page, and the chainages along a chain line are entered between these parallel lines. Figure 2.2 represents a field-book page. Entries commence at the bottom of the page and proceed upwards. Opposite each chainage entered, the point of detail to which it refers is sketched in, and the length of the rectangular offset to it is written level with the chainage. When surveying a building the fact that corners are generally rectangular is used to fix the parts of it that do not face onto the chain line. For this purpose the dimensions of buildings are measured and recorded on the field-note sketch. To ensure that there is no possibility of such dimensions being subsequently confused with rectangular offsets, the former are, by convention, Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 14 prefixed with a plus sign (often known as PLUS measurements), it being understood that the sign has no arithmetical significance when used in this context. In addition to recording the minimum number of dimension measurements necessary to fix all the points on a building, it is worth including few extra ones, to provide a check on the chainages and offsets. Apart from its use in the sense, just described, the plus convention is also applied to any detail measurement that is not an offset. Conversely, any measurement that is not prefixed by a plus sign originates at the chain line. This is of particular importance when two offsets relate to the same chainage point. Figure 2.2: Chain survey field book Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 15 2.3. ORIENTATION / NORTH DIRECTION In any survey, no matter what its purpose or the methods employed, it is desirable to have some idea of orientation, however approximate, and in chain surveys this can be provided by observing a magnetic compass bearing along one of the sides. The direction of magnetic north, and if the magnetic variation is known, true north can then be indicated on the plan. 2.4. ABSTRACTION OF MEASUREMENTS In order to be able to plot the survey efficiently, it is convenient, as the survey progresses, to abstract the measurements relating to the main and subsidiary frameworks, and show them on separate diagrams. These diagrams, which need not be drawn to scale, serve also as an index of the field notes, since, against each line in the diagram can be written the numbers of the field-book pages on which the measurements relating to the line are recorded. 2.5. PLOTTING THE SURVEY The main and subsidiary control frameworks of the survey are plotted as already described in Section 2.1. To plot the detail that has been surveyed in relation to a chain line, the field - book chainages are marked off along the plan representation of the line. Then with a set - square short lines (no longer than the longest offset at the appropriate scale) are drawn faintly in pencil, through the chainage marks and perpendicular to the chain line. The rectangular offset distances are then scaled off along the perpendicular lines. To plot detail that has been fixed by tie lines, each tie line distance is set on a pair of compasses, and arcs, centred on the appropriate chainage points, are drawn, the intersection giving the position of the detail point. When the offsets and tie lines have been plotted, the plus measurements are inserted to complete the plotting of the detail. The construction lines can then be erased. An alternative method of plotting rectangular offsets is by means of an offset scale. This is a small scale about 5 cm long which is graduated identically to the full length scale that is being used to plot the survey. The ends of the offset scale are cut exactly at right angles to the graduated edges, and the graduations commence exactly at one of the ends. To plot the offsets, the full-length scale is laid along the plotted chain line, the zero of the scale coinciding with the point at which the chainages commence, and is fixed in position with heavy paper-weights. The end of the offset scale at which the graduations commence is placed Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 16 against the graduated edge of the main scale, and slid along it, stopping at each scale graduation that corresponds to a field-book chainage, and marking the associated offset on the set scale. It is necessary to carry out this process twice for each chain line in order to plot the detail on both sides of the line. To avoid this, the full-length scale may be set off to one side of the chain line, parallel to it and sufficiently distant to allow the longest offset to be plotted. 2.6. CHECK MEASUREMENT An occasional check measurement to detail points is desirable and can often be included with little extra effort. 2.7. APPLICATION OF COLOUR AND INKING When the plotting is complete, the detail may be inked-in, different colours being used to differentiate types of detail, if desired. It is preferable to show the control framework separately, on a transparent overlay, but if it is necessary to indicate it on the plan, it should be made as unobtrusive as possible, using, for example, pale brown ink. If it is desired to differentiate between surfaces, such as water, tarmac, gravel or grass, colour washes may be used. These should be in very pale water colours, and in mixing them they should always be made far paler than the desired result, as they dry to much darker shades, and stark colours ruin the appearance of a well-drawn plan. Crayons and fibre pens should never be used. 2.8. LETTERING / ANNOTATION Appropriate items of detail, such as buildings and roads should be named. While it is not usually expected that a field Surveyor's lettering should be of the same standard as that of a trained draughtsman, it must be neat and regular, and in a simple style. For all lettering, three equally spaced parallel pencil lines should be drawn as guides, to be erased when the lettering has been done. Irregularities and imperfections in lettering are less apparent if an italic style sloping about 15° from the vertical, is adopted― Eg a b c d e f g h i j k l m n o pq r s t u v w x yz; 1234567890. Alternatives to free-hand lettering are stencils and pre-printed stick-down lettering and if the surveyor's plan is to be photographed for distribution, it is probably preferable to use these. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 17 2.9. MAKING COPIES / REPRODUCTIONS Normally a Surveyor's plan is fair-drawn by a draughtsman and put into a suitable form for reproduction, by dyeline or lithographic printing. 2.10. CONVENTIONAL SIGNS AND LEGEND In addition to descriptions by lettering, some items of detail such as trees or railway lines, may be indicated by conventional signs, some examples of which are shown in Figure 2.3. To complete the plan or map, the following items should also be shown: 1. Title of the plan (e.g. Chain Survey of UMaT farm). 2. Scale - both as a representative fraction (e.g. I :2500) and in graphic form. 3. North point - an indication of magnetic north, true north or grid north. Preferably the plan should be so orientated that north is up wards, parallel to the sides of the paper. 4. Legend - providing a key to the conventional signs. 5. Land Surveyor's name and date of survey. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 18 Figure 2.3: Conventional symbols Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 19 Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 20 2.11. CHAIN / TAPE SURVEYING EQUIPMENT Arrows or pins A set of ten arrows or pins is essential in chaining, for marking off chain lengths as measured. These are 12 or 15 in. long, made of steel wire, with one end pointed and the other end formed into a ring for convenience in carrying. A strip of red clot h should be attached to the ring so that the arrow can be easily observed. Tapes A tape is used for taking subsidiary measurements. It is usually made of linen, or of linen interwoven with fine metal wires, or of steel, with feet and inches marked on one side and links on the other. The linen tape is convenient to work with and light to carry, but it soon wears and stretches and is adversely affected by damp. For very accurate work a steel tape 33 or 66 ft long may be used. The tape is very suitable for taking offsets, which are measurements made perpendicular to the chain line, to fix points adjacent thereto, as on a boundary. All measurements taken with the tape , when it is used in conjunction with the Gunner's chain, should be noted, unless for a specia l reason. The tape, whether of linen or of steel, should be clean and dry when it is wound up, or its life will be short. Ran gi n g Pol es These are used for marking the main survey points or stations and intermediate points between the stations as required. Ranging roles are made in various lengths, 6, 8, and 10 ft being most common; they can also be obtained 10 links long (6 ft 7.2 in.). They are usually made of wood, about 1 inch thick, shod with steel and are generally circular in section but an octagonal section is obtainable and is preferred by some surveyors. They are painted in alternate bands of colour; red, white, and black, the bands being a foot broad, thus enabling offset measurements to be made with the pole. Ten or twelve ranging poles will usually suffice for a survey. S etti n g -ou t Ri gh t An gl es Right Angles.-The surveyor, especially in chain surveying, has frequent need for setting out or measuring right angles; and for this she has the choice of several instruments. Over short distances, i.e. those less than about 15 ft, they may be judged by eye, but over any greater distance some instrument like the cross-staff should be used. Pl u mb -b ob A plumb-bob is used for various purposes in surveying such as chaining over hilly ground. The plumb-bob is usually a pear-shaped piece of gun-metal, weighing about 0.45 kg, with the lower end pointed and with a ring on the broad end to which a cord is Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 21 attached. They may be improvised with a stone and string bun for marking the exact spot under the point of suspension. Fi el d B ook A field book is also required by the Land Surveyor to record sketches and measurements. It may be oblong in shape, of a convenient size for the pocket, of plain paper with a single red line ruled down the centre of each page, or with two parallel lines about 4 in. apart. The actual type of book employed, however, largely depends on individuals. The method of recording the field measurements in the book has been illustrated. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 22 3. COMPASS SURVEYING Compass Surveying is one of the basic techniques of land surveying, involving both direction and distance measurements. It provides only planimetric information. The main instruments employed are the compass, tapes and ranging poles. 3.1. SOME BASIC TERMINOLOGIES IN COMPASS SURVEYING Bearing This is a basic term used in describing directions in land surveying. The bearing (βop) of a line OP is the horizontal angle, measured clockwise from a given reference point R or line (OR) with the observer (O) as the centre of rotation/angular displacement (Figure 3.1). Such reference directions or lines, used in surveying for bearings, are termed meridians R R R P βop P βop O O O βop P Fig. 3.1: Bearing βop of point P from point O w. r. t. direction OR Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 23 3.2. TYPES OF REFERENCE DIRECTIONS (MERIDIANS) AND BEARINGS There are four main types of bearings, depending on the reference direction or meridian used for measuring the bearing namely true/Astronomical bearing, magnetic/compass bearing, grid /map bearing, local/arbitrary bearings True / Geographical / Astronomical Bearing This is bearing measured with respect to the true/geographical/astronomical meridian — the line passing through or joining the north and south poles of the Earth as well as the observer’s position. This meridian is determined by astronomical observations. Magnetic / Compass Bearing This is bearing taken with respect to the magnetic meridian of the Earth—the lines joining the observer’s position and the magnetic north and south poles of the Earth. This line is determined with the aid of a compass and this is why it is also called compass meridian and compass bearing. It is much easier to determine this meridian and hence measure directions of other points/lines from it in surveying than the true meridian. Grid / Map Bearing These are bearings defined with respect to a grid meridian or any line parallel to a grid meridian. A grid meridian at a point is a line that is tangential to a longitude (true meridian) at that point. As far as plane surveying is concerned, grid bearings are the most important of all these three major bearings considered. This is so because the position of points in plane surveying are often expressed in terms of plane rectangular grid systems (x-y axis) consisting of straight parallel lines along the x-axis and y-axis respectively and not curved lines as in the case of true and magnetic meridians. Local / Arbitrary Bearings These are bearings taken with respect to any assumed or chosen reference direction. This is usually advantageous for small surveys especially in areas where the true meridian is yet to be established. This artificially assumed direction is usually in a direction from a survey station to some well-defined permanent object or along the longest side or orientation of a piece of land being surveyed and in relation to the way engineering activities are designed to take place in that area. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 24 Relationships between True and Magnetic Meridian These do not usually coincide; the deviation of the magnetic meridian from the true meridian is termed the magnetic declination. This difference changes in magnitude and direction from time to time and from place to place. The isogonic chart is one of the means by which declination can be estimated and corrected in compass surveying. Inter-relationship between True and Grid Meridians / North /Bearing Difference exists between these bearings and this is called the angle of convergence. To convert one bearing into the other type, the existing difference between them and the corresponding lines of measurement and the rates of changes should be known. Inter-relationship between True and Magnetic Bearings For magnetic bearing (Mβ) and true bearing (Tβ), we have Tβ=Mβ+d, where  for the whole circle bearing system, d is taken to be positive for east declination and negative for west declination,  for the quadrant system, d is positive for east declination in the 1st and 3rd quadrant and negative in the 2nd and 4th quadrants; for west declination d is positive in the 2nd and 4th and negative in the 1st and 3rd quadrants. 3.3. FORWARD AND BACK BEARINGS The direction of a line with reference to the magnetic meridian can be found by taking a bearing at either end of the line. In Figure 3.2 the bearing of the line AB taken at A is the angle θ1, and the bearing at B is the angle θ2. The bearing of a line such as AB taken at A is called a forward bearing, and the bearing of the same line taken at B is called a back or reverse bearing. The meridian through A may, for this purpose, be taken as being parallel to the meridian through B, so evidently dl = θ2 - 180°, i.e. the bearings of a line observed from either end should differ by 180°; if they do not, local attraction must be suspected. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 25 N N βpo = θ2 B A βop = θ1 Fig 3.2: Forward and Back Bearings 3.4. RECORDING OF READINGS Bearings/directions can be recorded using either quadrantal bearing system (Q.B) or whole-circle bearing (W.C.B) systems. 3.4.1. WHOLE CIRCLE BEARING (W. C. B) In this system, bearing of a line is measured from the true north or magnetic north in clockwise direction. This is sometimes known as Azimuthal system. The valve of a bearing may vary from 0˚ to 360˚, utilizing the whole circle of graduations. Prismatic compass is graduated on whole circle bearing system. To establish the direction of a line between two points on the ground, its bearing has to be determined. The whole-circle bearing (WCB) of a line is measured in a clockwise direction in the range 0º to 360º from a specified reference or north direction. Examples of whole-circle bearings are given as: Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 26 N B D N θ α Θ =whole circle α =whole circle C bearing of line AB bearing of line CD A Figure 3.2: Bearing systems Whole circle bearing is the standard way of defining a bearing in survey practice. The whole circle bearing of a line AB is defined as the clockwise angle from 0º to 360º at A between the reference meridian and line AB. 3.4.2. QUADRANTAL BEARING (Q.B) In quadrantal bearing system, bearing of survey lines are measured eastward or westward from North and south, whichever is nearer. In this system, both north and south directions are used as reference meridians and bearings reckoned either clockwise or anticlockwise, depending upon the position of the line. Surveyor’s compass is graduated in quadrantal bearing system. This is also known as reduced bearings. If the cardinal point of a compass is drawn and labelled north, east, south and west moving clockwise, the whole 360º circle would have been divided into four quadrants of 90º (Figure 3.3). The quadrants are known as north east, south east, south west and North West. The quadrant bearing of any line is the angle it makes with the north-south axis. Q.B of a line is defined as the angle lying between 0º and 90º between the direction to the North or south and the direction of the line. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 27 Figure 3.3: Whole circle bearings and quadrant bearings 3.5. CONVERSION OF BEARING FROM ONE SYSTEM TO ANOTHER i. If the whole circle lies between 0º and 90º, the quadrant bearing has the same numerical value in the North east quadrant, ii. If the WCB lies between 90º and 180º, the quadrant bearing is (180 – WCB) and lies in the south east quadrant, iii. If the WCB lies between 180º and 270º, the quadrant bearing is (WCB - 180) and lies in the south west quadrant, iv. If the WCB lies between 270º and 360º, the quadrant bearing is (360 - WCB) and lies in the north-west quadrant, The conversion of bearings from one system to another may be easily done by drawing a diagram. This shall be illustrated during lectures. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 28 Based on the above conversion system, fill in the blank spaces of Table 3.1 Table 3.1 : Converting WCB to QB Line WCB QB AB 98 BC 275 CD 129 EF 217 FG 38 GH 230 IJ 86 JK 341 KL 254 3.6. COMPASSES Compass is one of the most ancient of surveying instruments; with the exception of linear measuring rods. The simplest form of compass consists of a magnetic needle balanced on a hardened steel point and having an agate bearing, mounted in a circular case with a glass cover. Fig.3.4 shows some of the modern forms of compasses. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 29 Figure 3.4: Compasses Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 30 3.7. DESCRIPTION OF THE PRISMATIC COMPASS The Prismatic Compass consists of an ordinary magnetic needle carrying a light metal or card dial rigidly affixed. The alignment of the survey line across the dial is given by a sighting slot on one side of the box and a sight vane directly opposite on the other. In order that the scale may be read without losing the alignment, the sighting slot is combined with a prismatic reading glass, which reflects the reading of the scale without the compass being moved from the eye. The prismatic compass is shown in Figure 3.5. Figure 3.5: The Prismatic Compass To use the instrument, hold it to the eye with the tips of the fingers, keeping the index finger free to press in the stud or brake underneath the vane. With the reading glass to the eye, turn the instrument until the sight vane and the distant station coincide, keeping the compass as level as possible, and the feet firmly planted, one on each side of the chain-line. If the compass card swings freely, the brake may be applied gently to steady its swing, but it should not actually be stopped. By lowering the glance the scale may be read off at each end of its swing, using the sight vane as the index line. The mean of two readings is then taken and booked as the bearing. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 31 Several types of compasses have been introduced in recent years, including oil, luminous, lensatic and gyroscopic compasses, each having distinct advantages for certain types of work, but the prismatic compass here described will be found quite convenient for ordinary land surveying. The prismatic compass is a more or less "local" instrument, constructed to be used only in the latitude for which it is made, and, if restricted to that latitude, it will need no adjustment in itself. (The bearings will, of course, all be magnetic bearings, and the declination of the needle must be allowed for when plotting, as explained earlier). If the compass is taken far out of its original latitude, it will be found that the needle tends to tilt or "dip" out of the horizontal, the "dip" increasing as the pole is approached, until: it would eventually-when right over the pole-stand vertically. The compass is also liable to be deflected by metal about the person, by local magnetic attraction, and by small changes in the position of the needle at different hours of the day, as well as by the slow changes which occur from year to year and from place to place. 3.7.1. FIELD OBSERVATIONS Around the outer edge of the bottom of the box are engraved the cardinal points and sub- divisions of degrees or groups of degrees, according to the size of the compass. To obtain a bearing with this type of instrument one would stand over the line, with the compass held steadily in both hands at about the level of the waist, as nearly horizontal as possible, twisting the case round until the north on the scale and the like end of the needle correspond. 3.7.2. MAGNETIC DECLINATION AND ITS CORRECTION This is the angle between the north directions of the earth. It is true or geographical or astronomical meridian and is the magnetic or compass meridian at a given location at a particular time. This angle varies in magnitude and direction from place to place and from time to time. (Figure 3.6). Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 32 Magnetic direction TN MN at point A at time of observation W A E Figure 3.6: Magnetic Declination 3.7.3. CORRECTION FOR DECLINATION Since the declination, and hence magnetic bearings change with time, the latter are often converted into time bearings by correcting for the declination. This is done by the expression: Tβt = Mβt + dt for east declinations Tβt = Mβt - dt for west declinations and Where Tβt, Mβt, dt denote true bearing, magnetic bearing and declination of a point/place at a given time t. 3.7.3.1. ISOGONIC CHART This is a graph (Figure 3.7) of lines that shows places/points of equal declinations and their annual rate of changes. It is produces usually by national/international survey body/firms/organizations and published periodically. Like a topographical map, issogonic charts are used / needed in determining the declination and the rate of changes in declination of places so that magnetic bearings of places can be corrected for changes due to time lapses and/or converted into true bearings. When magnetic directions are used to obtain coarse estimates for bearings or when an old survey must be retraced, it is necessary to reduce the magnetic directions to true bearings or azimuths. Conversion from magnetic to true azimuths, or vice versa, is most easily accomplished by using azimuths. Consider the following examples. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 33 Figure 3.7: Isogonic chart of North and South America Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 34 3.7.4. WORKED EXAMPLES In order to facilitate understanding of what has been discussed, we will take some worked examples and re-compute them ourselves to see how we can apply the knowledge in solving problems. Example 1 A magnetic azimuth of 54°30' was observed along line AD in June 1977. The declination for the area surveyed is found by interpolation from an isogonic chart dated 1970 to be 17°30'E with an annual change of 1' westward. Compute the true azimuth of line AD. Solution: First draw a careful sketch of the relationship among true north, magnetic north, and the direction of the line as illustrated by Fig. 3.8a. Solution to Example 1 Magnetic Bearing AD 54˚30′ Declination in 1970 17˚30′ Change in Declination (= 7 yrs * 1′/yr ) -7′ (westward) Declination in 1977 =17˚30′-7′ True Bearing 71˚ 53′ Figure 3.8: Worked example 1 Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 35 Example 2 Magnetic bearing of N34°30'W is recorded on an old survey plan dated August 20, 1910. It is desired to re-establish this direction on the site in 1977. The 1970 isogonic chart shows a declination of 10°W for the area, with an annual change of 2' eastward. Determine the magnetic bearing that must be used to relocate the direction of the line in the field. Solution: As before, sketch the lines involved, as shown in Fig. 3.9. Magnetic North True North 1910 1970 1977 9˚46 36˚44′ ′ 10˚00′ 34˚30′ B 12˚00′ W E A S Solution to Example 2 Figure 3.9 b: Worked example 2 Declination (D) in 1970 10˚00′ W Change D in 60 yrs (= 60yrs * 2′/yr ) 02˚ 00′ (Eastwards +) Declination in 1910 12˚ 00′ W Mag. bearing in 1910 N34˚30′ W True bearing of line N46˚ 30′ W Decl. in 1977 9˚ 46′ W Mag. bearing 1977 N36˚44′W Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 36 3.8. LOCAL ATTRACTION Objects of iron or steel, or some kinds of iron ore and currents of direct electricity alter the direction of the lines of magnetic force in their vicinity and hence are likely to cause the compass needle to deviate from the magnetic meridian. The deviation arising from such local sources is called local attraction or local disturbance. In certain localities, particularly in cities, its effect is so pronounced as to render the magnetic needle of no value for determining directions. It is not likely to be the same at one point as at another, even though the points may be but a short distance apart. It is even affected by such objects as the steel tape, chaining pins, axe, and small objects of iron or steel that is on the person. Usually, its magnitude can be determined, and directions observed with the compass can be corrected accordingly. Local attraction can usually be detected by observing the compass bearing of a line at two or more points on the line. 3.8.1. CORRECTION FOR LOCAL ATTRACTION This is done by taking the bearing of any line from both its ends or from intermediate points on the line. If the two bearings agree it is probable that there is no local magnetic disturbance. If the two do not agree it remains to discover which is correct. 3.9. COMPASS TRAVERSE SURVEY A traverse is a sequence of connected straight lines, the directions and lengths of which have been measured. The directions may be measured by a compass or by a theodolite, giving rise to a compass traverse or a theodolite traverse. Different methods of measuring the lengths of the lines may also be adopted, chain, tape, tacheometry or pacing. Traverses may also be classified as closed, or open. A traverse which returns to its starting point or ends at a point whose position (relative to the starting point) is known is called a closed traverse. A traverse which does not return to some known point, and one whose finish is connected to its starting point only by the traverse is called an open traverse. An example of a closed traverse is a survey of a pond. In such a figure, the angles at the junctions of the survey lines are measured by chain / tape, but they can be measured more quickly and accurately with a theodolite; or the directions of the lines might be measured with a prismatic compass, the differences of the directions giving the angles of intersection of the lines. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 37 An example of an open traverse might be a reconnaissance survey for a planned road or railway in unmapped country; starting probably at a known point but then wandering off into unknown country. 3.9.1. TRAVERSING WITH THE PRISMATIC COMPASS When the direction of a line is to be determined, the compass is set up on line and leveled. The needle is released and the compass is rotated about its vertical axis until a range pole or other object on line is viewed through the slits in the two sight vanes. When the needle comes to rest, the bearing is read. Ordinarily, the sight vane at the end of the compass box marked "S" is held next to the eye; in this case the bearing is given by the north end of the needle. Fig. 4.0 shows a lake with an island, of which a plan is required. Stations A, B, C, D, and E are chosen so that the lines joining them are as long as possible without diverging too much from the lake side (thus keeping the offsets to the side short), and ranging poles are inserted. B C F A D E Figure 4.0: Lake with Island The bearings and the lengths of the lines have to be measured and also the offsets to the lake side. It is quite practicable to make these measurements together, but usually it will be found better to, take all the bearings, in turn, as one operation and then carry out the chaining and offset measuring as another. The first operation is carried out as follows: at A the forward bearing to B is observed and the back bearing to E, in addition the bearing to a conspicuous tree, F, on the island is observed. Similarly at the other stations the forward and back bearings are observed and as many as are required to fix F (or any other points of inaccessible detail). All the bearings are booked as shown at Table 3.2. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 38 3.9.2. TRAVERSE BOOKING This is usually in a tabular form (Table 3.2). The remarks column is for noting things or events that may have influence on the field measurements or their interpretation. It can include names of control points used in the traversing and any objects that may cause local attractions in bearings. Table 3.2: Compass Traverse Booking Line Forward Back Back Forward Remarks Bearing Bearing Distance Distance ° ° AB 49.5 230.5 280.90 281.00 Narrow corner of pond BC 086.5° 266.0° 273.01 273.00 Iron pole close-by CD 159.5° 341.0° 337.00 336.95 Wooden peg DE 254.5° 074.5° 341.98 342.01 Concrete pillar EA 307.0° 128.0° 346.05 345.94 Survey Pillar 3.9.3. BOOKING OF DETAILING The booking is done up the page just as it is done for chain survey bookings and all the bearings as well as the lengths of the traverse lines are entered. These lengths are linear measurements, the booking of which is done as described in chain Surveying. It will be noted that if the back bearing agrees with the forward bearing to 0.5o, it is underlined, but if the two bearings disagree by more than that the mean bearing is written alongside the length of the line and underlined. (If the difference is excessive the bearing observations should be repeated) The tree, F in Figure 4.0, is fixed by the intersection of the bearings from A and E, with a check bearing from B; when plotted these three bearings should cut in a point. (Actually, since BF and EF are nearly in a line, it would be better to take the check bearing from C). If it seems likely that local attraction exists at a station, e.g. suppose D is close to a steel fence, bearings should not be observed there, but from auxiliary stations carefully aligned; situated, for the back bearing to C, a little way back on the line DC and, for the bearing to E, a short way along DE. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 39 In a compass traverse angular errors are not cumulative, so an error in the direction of one line will not affect the directions of subsequent lines (as happens in a theodolite traverse). Figure 4.1: Booking of compass traverse details 3.9.4. PLOTTING THE TRAVERSE First make a rough sketch, approximately to scale, to ascertain the shape of the survey and how best it may be fitted on the paper. Having decided the position of A on the paper, draw the line AB in the direction indicated by the rough sketch. Its direction (from the booking) was 050°, so set back this angle from AB (Figure 4.2) with the protractor and rule in the magnetic meridian through A. Then rule light lines parallel to this, and about 2 in. apart, to represent other meridians from which subsequent bearings may be protracted. Using the scale, prick off B on the line AB, then lay off the bearing BC, and prick off C, and so on, until the plotting has returned to A. If an open traverse is being drawn nothing remains but to plot the outline from the offset measurements and complete the plan, but in a closed traverse such as has been discussed, it is quite likely that the polygon will not close, because the end of the line EA does not coincide with the point A. This is referred to as a closing error. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 40 B C C B A D A E D E Figure 4.2: Plotting by Protractor and Scale A large closing error indicates faulty chaining or plotting, and if the work is to be of any value the lines should be checked. A small closing error, however, may be eliminated by slightly modifying the shape of the polygon and so closing the traverse. This is called adjusting the traverse. In Figure 4.2, the traverse as plotted is represented by AB'C'D'E'A', and A'A represents the closing error. If this was adjusted simply by joining E' to A it would result in a serious displacement and difference in length of the line EA. The error is therefore distributed round the traverse by shifting each station proportionately to its total distance from the start of the traverse in a direction parallel to the closing. This is the method of least distortion, popularly called the BOWDITCH ADJUSTMENT method. The above procedure is best done graphically. Through each plotted station, draw lines parallel to AA; then construct a triangle as shown in Figure 4.3 below. The measured lengths AB, BC, etc are to any convenient scale along a base line, and a perpendicular to AA, equal in length to the closing error, is established. The other perpendiculars, BB, CC, etc, give the distances through which B, C, etc, must be moved along the short lines drawn parallel to the closing error. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 41 A E D C B A B C D E A Figure 4.3: Error Correction Graph 3.10. USES / APPLICATIONS OF COMPASS OBSERVATIONS Compass observations can be used for computations of angles, coordinates and areas. 3.10.1. CALCULATING ANGLES FROM BEARINGS In calculating the angle between two lines, it is necessary only to remember that the bearing is always counted from the meridian, either N or S, toward the E and W points. Example: If the bearing of line OA is 500 and that of line OB is 345 °,. find the angle between them. Solution The angle between them is evidently 345'-500 = 295°, which is the external angle AOB. The internal angle AOB = 360° - 295° = 65°. It is advisable to draw a sketch of the given conditions when determining the angle to avoid confusion. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 42 3.10.2. CALCULATION OF COORDINATES AND AREAS Calculations of rectangular coordinates and areas from bearings are the same as those used when theodolite is employed for measuring angles. 3.10.3. COMMON MISTAKES IN COMPASS MEASUREMENTS  Reading the wrong end of needle,  Not letting needle down on pivot,  Reading the wrong side of the loth degree, viz., reading 61° instead of S9°. 3.11. PRECAUTIONS IN COMPASS SURVEYING At each observation the compass box should be tapped lightly as the needle comes to rest, so that the needle may swing freely. In order not to confuse the north and south ends of the needle when taking bearings, the observer should always note the position of the counterbalancing wire (which is on the south end in the northern hemisphere). Since the precision with which angles may be read depends on the fragility of the needle, special care should be taken to avoid shaking between the jewel bearing of the needle and the pivot point. Before moving the instrument, one should be certain that the needle is lifted and clamped. Sources of magnetic disturbance such as chaining pins and axe should be kept away from the compass, while a reading is being taken. Care should be taken not to produce static charges of electricity by rubbing the glass; a moistened finger pressed against the glass will remove such charges. Ordinarily the amount of metal around the instrument man is not large enough to deflect the needle significantly, but a change of position between two readings should be avoided. 3.12. SAMPLE QUESTIONS Q1 A magnetic bearing of 146°30'00"E is recorded on a 1970 map from point A to B. It is desired to reestablish this direction on the site during January 2000. The 1970 Issogonic Chart shows a declination of 10° W for the area with an annual change of 2'eastwards. (a) (i) Determine the bearing that must be used to re-locate the direction of the line with a compass. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 43 (ii) If in the field, point B is first found, what bearing will be used to locate point A?. Give this answer in the whole circle system. (b) If the coordinates of A are (50.00, 100.00) and the distance between A and B is 40.00 m, find: (i) the polar coordinates of point B with respect to point A. (ii) the departure and latitude of the distance AB. (iii) the rectangular coordinates of point B. (c) Examine the following compass traverse data to see if there are any errors that need to be adjusted and do so. Which of these errors will you attribute to local attraction and why? What can be the causes of these errors?. Line Forward Bearing Back Bearing AB 98°30° 278°.00 BC 275°40 95°30 CD 308050 129°10 Q2 (a) (i) Explain the term surveying. (ii)What basic observable quantities are necessary in position determination and fixing and what is the role of reference control systems in doing this. (b) With the aid of clear diagrams, explain how the position of points may be determined and fixed relative to others by: (i) angles only (ii) distances only (iii) a combination of directions and distances. (iv) Show how each may be extended to provide a system of horizontal controls and state the general survey name for it. (v) provide two instruments each for measuring directions, distances and elevations. Q3. Briefly explain the following land survey terms and their importance. (i) Reconnaissance and station marking. (ii) Control points and control network systems (iii)Direction, Distance and Elevation measurements. (iv) Detailing. (v) Booking and (vi) Plotting. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 44 4. THEODOLITE SURVEYING 4.1. INTRODUCTION In theodolite surveying the theodolite is the main instrument used. The theodolite is the main survey instrument used for direction and angle measurements. The angles are derived from the direction measurements. The instrument is also used to measure vertical and horizontal distances during Tacheometric surveys. Survey techniques in which the theodolite features prominently are traversing, trigonometry, intersection, resection and setting out surveys. Figure 4.1 and 4.2 shows a theodolite and its parts. Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 45 (a) (b) Figure 4.1: Optical (a) and electronic (b) theodolites Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 46 Figure 4.2: Theodolite circles and angle measurement 4.2. DIRECTION AND ANGLE MEASUREMENTS Figures 4.4a and b illustrates angle measurement with the theodolite. The theodolite is set up at point B and the targets at points A, O and C. The theodolite is focused on each of the targets and horizontal circle readings are taken as RA, RO, RC, respectively. This may be repeated a number of times and the means taken. The angles are the deduced as follows: θABO = RO - RA ; θOBC = RC - RO and θABC = RC - RA = θABO + θOBC O A RO RA C RC θABO θOBC B Figure 4.4 a: Angle measurement with the Theodolite Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 47 Figure 4.4b: Accessories of the theodolite during field measurements 4.3. BOOKING AND COMPUTATION OF DIRECTIONS AND ANGLES Different booking formats are adopted by different survey firms and organisations. One format that is generally used in Ghana by the Survey and Mapping Division of Lands Commission is discussed in the following tables. Table 4.1 (a): Booking and computation of directions and angles (Two measures of an angle, one on each face by simple reversal) Traverse point Horizontal angles Inst. Target Face Left Face Right o o ' '' ' '' A (1) 00 02 43 (3) 180 02 43 B C (2) 102 45 46 (4) 282 45 52 Angles 102 43 03 102 43 09 Mean 102 43 06 Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 48 Table 4.1 (b): Booking and computation of directions and angles (Four measures of an angle, two on each face, using two zeros- reiteration measurements) Inst. Target Face Left Face Right Mean Angle Stn. o ' '' o ' '' L+R A 00 26 48 180 26 42 00 26 45 B 57 08 51 C 57 35 42 237 35 30 57 35 36 A 90 38 24 270 38 30 90 38 27 B 57 08 55.5 C 147 47 24 327 47 21 147 47 22.5 Mean 57 08 53 4.4. CHECKS ON ANGLE MEASUREMENTS (ANGULAR CLOSURE) There are mathematical formulae associated with the geometrical shapes of survey traverses that are used to check and correct errors in the angles of a traverse by a theodolite or compass. Three of these formulae are as follows: 1. Check on the sum of the interior angles of a loop traverse: ∑θc = (n-2)* 180 2. Check on the sum of the exterior angles of a loop traverse: ∑θc = (n+2)*180 The total angular error in a traverse is obtained by ∆θ = [ ∑θc - (n+2) 180 ]. This is then distributed evenly over all the angles in the traverse. The angular error per angle in a traverse is given by δ = (∆θ/n) The correction for each angle is given as -δ. NB: θ0= observed angle, θc= computed angle, θa= adjusted angle C Michael Aduah (PhD) Geomatic Engineering Department, UMaT, Tarkwa, Ghana 49 325.24 m 87055'40'' 241.95 m 87055'40'' B D 87055'40'' N 210.05 m 301.32 m 87055'40'' Bearing A N44031'10''E Reference Meridian Figure 4.5: Angle Measurement in Theodolite Traversing 4.5. THEODOLITE TRAVERSING A traverse is a series of interconnected straight lines, whose directions or angles and distances have been measured. Most of the traversing in surveying is done with the theodolite, because its angular measurements are relatively of higher accuracy than those of the compass. The directions of the traverse lines are measured with the theodolite, but these are not generally referenced to the true or magnetic meridian. The distances are measured with tape, or EDM, or tacheometry. Theodolite traversing is applied in providing control surveying, topographical surveying and cadastral surveying to determine the boundaries and sizes of land parcels. 4.5.1. TRAVERSE COMPUTATION AND ADJUSTMENT This involves the computations of the partial coordinates (latitudes and departures of the lines) using the adjusted distances and angles of the lines. The latitudes (change in northings) and departures (change in ea

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