UNIT 2 TACHEOMETRIC SURVEYING Tacheometric Surveying Structure 2.1 Introduction Objectives 2.2 Principles of Tacheometry 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.2.6 2.2.7 2.3 Advantages of Tacheometry Tacheometer Stadia Rods Systems of Tacheometric Measurements Basic Principle of Stadia Method Movable Hair Method Anallactic Lens Methods of Tacheometry 2.3.1 Various Cases – Inclined Sights with Staff Vertical and Staff Normal to the Line of Sight 2.3.2 Tangential Method 2.3.3 Subtense Bar Method 2.3.4 Tacheometric Traversing 2.4 Summary 2.5 Answers to SAQs 2.1 INTRODUCTION Generally, horizontal distances are measured by direct methods, i.e. laying of chains or tapes on ground. These methods are not always convenient if the ground is undulating, rough, difficult and inaccessible. Under these circumstances, indirect methods are used to obtain distances. One such method is “Tacheometry”. Using tacheometric methods, elevations can also be determined. It is in fact a branch of angular surveying in which both the horizontal and vertical positions of points are determined from the instrumental observations, the chain surveys being entirely eliminated. Objectives After studying this unit, you should be able to • explain the principle of tacheometry, • describe various tacheometric methods, • learn stadia principles, • learn fixed hair and movable hair methods, and • carry out tacheometrical surveying. You will also be learning principles of anallactic lens which makes the calculations simple. Staff vertical and staff normal cases are also discussed. You will also understand tangential tacheometry and subtense bar methods including tacheometrical traversing. 37
Advanced Survey 2.2 PRINCIPLES OF TACHEOMETRY 2.2.1 Advantages of Tacheometry Since both the quantities viz., horizontal distances and the difference of elevations are determined indirectly in tacheometric surveying, it has a number of advantages over the direct methods of measurement of these quantities. In terrain where direct methods are not convenient, tacheometric methods can be used. Tacheometric methods are convenient for reconnaissance surveys of routes, for hydrographic surveying and for filling in details in a traverse. There is considerable saving in time and money with the use of tacheometric methods. 2.2.2 Tacheometer A tacheometer is similar to an ordinary transit theodolite, generally a vernier theodolite itself, fitted with two stadia wires in addition to the central cross-hair. The stadia diaphragm has three horizontal hairs viz., a central horizontal hair and upper and lower stadia hairs. The upper and lower stadia hairs are equidistant from the central horizontal hair. Stadia hairs are sometimes called stadia lines. For the purpose of tacheometry, even though an ordinary transit can be employed, accuracy and speed are increased if the instrument is specially designed for the work. The magnification of the telescope in tacheometer should be at least 20 to 30 diameters, with an aperture of at least 40 mm for a sufficiently bright image. The magnifying power of the eyepiece is also greater than for an ordinary transit to produce a clearer image of a staff held far away. Further, the altitude bubble is made more sensitive, since vertical angles form an important part of the data for calculation of elevation differences. Figure 2.1 shows a more commonly used pattern of stadia diaphragm. i Figure 2.1 : Stadia Diaphragm 2.2.3 Stadia Rods For short sights of about 100 m or less, an ordinary levelling staff may be used. For long sights, special staff called stadia rod is generally used. The graduations are in bold type (face about 50 mm to 150 mm wide and 15 mm to 60 mm thick) and the stadia rod is 3 m to 5 m long. To keep the staff or stadia rod vertical, a small circular spirit level is fitted on its backside. It is hinged to fold up. 2.2.4 Systems of Tacheometric Measurements The underlying principle common to various systems of tacheometry is that the horizontal distance between an instrument station P and a point Q, as well as the elevation of Q relative to the instrument, can be deduced from 38 (a) the angle at P subtended by a known small distance at Q, and (b) the vertical angle from P to Q.
This basic principle is applied in different ways in different tacheometric methods. There are basically three systems of tacheometric measurements such as stadia system, tangential system, and subtense bar system. Tacheometric Surveying Stadia System This is the more extensively used system of tacheometry particularly for detailed work, such as those required in engineering surveys. In this system, a tacheometer is first set up at a station, say P, and a staff is held at station Q, as shown in Figure 2.2. The difference of upper hair reading and lower hair reading is called staff intercept s. All the three hairs including central cross hair are read, and s is determined. Vertical angle, θ, corresponding to the central hair is also measured. These measurements enable determination of horizontal distance between P and Q and their difference in elevation. There are two different types of systems in stadia method. These are as follows : Fixed Hair Method In this method, the distance between the upper hair and lower hair, i.e. stadia interval i, on the diaphragm of the lens system is fixed. The staff intercept s, therefore, changes according to the distance D and vertical angle θ. Movable Hair Method In this method, the stadia interval ‘i’ can be changed. The stadia hairs can be moved vertically up and down by using micrometer screws. The staff intercept s, in this case, is kept fixed. Two vanes (targets) are fixed on the staff at a fixed interval of 2 m or 3 m. The fixed hair method is the one which is commonly used and, unless otherwise mentioned, stadia method means fixed hair method. Movable hair method is not in common use due to difficulties in determining the value of i accurately. s Q θ h P D Figure 2.2 : The Stadia System Tangential System 39
Advanced Survey In this system, observations are not taken on stadia hairs. Instead vertical angles θ1 and θ2 to the two targets fixed on a staff are recorded (Figure 2.3). The targets are at a fixed distance s. Vertical angles θ1, θ2 and staff intercept s enable horizontal distance D and the difference of elevations to be determined. In Figure 2.3, both the vertical angles θ1 and θ2 are the angles of elevations. There may be two more cases where either both the angles may be angles of depression or one of the angles is angle of elevation and another is angle of depression. s Q θ1 P θ2 h D Figure 2.3 : Tangential System Subtense Bar System Subtense bar is a bar of fixed length generally 2 m fitted with two targets at the ends. The targets are at equal distance apart from the centre. The subtense bar can be fixed on a tripod stand and is kept horizontal. As shown in Figure 2.4, angle α subtended by the two targets at station P is measured by a theodolite. The distance s between the targets and the angle α enable the distance D between station P and Q to be determined. P α Q s D Figure 2.4 : Subtense Bar System (Shown in Plan) 2.2.5 Basic Principle of Stadia Method We will derive distance and elevation formulae for fixed hair method assuming line of sight as horizontal and considering an external focusing type telescope. In Figure 2.5, O is the optical centre of the object glass. The three stadia hairs are a, 40