Unit 3 Triangulation Surveying PDF

UNIT III Triangulation Prof. R.V. Langote  SYLLABUS Triangulation : Principles, classification of triangulation system, triangulation figures, their choice of station, phase of signals, towers, satellite station, reduction to center, field work, Reco...

UNIT III Triangulation Prof. R.V. Langote  SYLLABUS Triangulation : Principles, classification of triangulation system, triangulation figures, their choice of station, phase of signals, towers, satellite station, reduction to center, field work, Reconnaissance, Intervisibility, angular measurements. Base line and its measurements. Basenet, extension of Basenet, corrections to base line measurement, adjustment of field observation, errors in observation, method of least square, weighted observations, figure adjustment (Triangle only). Prof. R.V. Langote Q? 1. What are the basic classification of triangulation system? Mention the basic specification of primary triangulation ? 2. Draw various common triangulation figures and their uses? 3. What are the point to be kept in view for selecting the site for base line in large survey? 4. Explain the procedure to reduction to centre of satellite station. 5. What do you understand by a satellite station and reduction to centre. Prof. R.V. Langote 5. The triangulation stations A and B, 50 km apart, have elevations 243 and 258m respectively. The intervening ground may be assumed to have a uniform elevation of 216m. Find the minimum height of the signal required at B, so that the line of sight may not pass nearer the ground than 2.4m. 6. The triangulation stations A and B, 60 km apart, have elevations 240 and 280m respectively. Find the minimum height of the signal required at B, so that the line of sight may not pass nearer the ground than 2m. The intervening ground may be assumed to have a uniform elevation of 200 metres. 6. The elevation of two triangulation stations A and B, 100 km apart are 180m and 450m respectively. The intervening obstruction situated at C, 75 km from A has an elevation of 259 m. Ascertain if A and B are intervisible. If not, by how much B should be raised so that the line of sight must nowhere be less than 3m above the surface of the ground, assuming A as the ground station? Prof. R.V. Langote 7. The altitude of two proposed station A and B 100 km apart are respectively 420 m and 700m. The intervening obstruction situated at C, 70 km from A has an elevation of 478.0 m. Ascertain if A and B are intervisible and if necessary by how much B should be raised, so that the line of sight must be no where less than 3.0 m above the surface of the ground. 8. Find the most probable value of A from the following observations: A = 40o32’33’’ weight 2 3A = 121o42’12’’ weight 3 9. Find the most probable value of the angle A and B and the summation angle A+B from the following observation from the following observations: A = 42o20’30’’.4 weight 1 B = 36o18’25’’.2 weight 2 A +B = 78o38’50’’.3 weight 3 Prof. R.V. Langote 10. From an eccentric station S, 12.25 m to the west of the main station B, the following angles were measured : LBSC = 76o25’32’’ LCSA = 54o32’20’’ The station S and C are to the opposite sides of the line AB. Calculate the correct angle ABC. The length AB and BC are 5286.50 m. and 4932.20 m respectively. 11. The angles of triangle ABC were recorded as follows : A = 77o14’20’’ weight 4 B = 49o40’35’’ weight 3 C = 53o04’52’’ weight 2 Give the corrected value of the angles. Prof. R.V. Langote  Principle of Triangulation In triangulation, the system consists of a number of interconnected triangles in which the length of only one line called the base line, and the angles of triangles - are measured very precisely. Knowing the length of one side and three angles, the length of other two sides of each triangle can be computed. The apexes of the triangles are known as triangulation stations and whole figure is called as triangulation system or triangulation figure. Prof. R.V. Langote  The defect of triangulation is that it tends to accumulate errors of length and azimuth of the preceding line. To control the accumulation of errors, subsidiary bases are also selected. Prof. R.V. Langote  OBJECTIVES 1. To provide the most accurate system of horizontal control points on which the less precise triangles may be based, which in turn may form a framework to which cadastral, topographical and other related surveys may be referred. 2. To assist in determination of the size and shape of the earth by making observations for latitude, longitude and gravity. Prof. R.V. Langote  Classification of Triangulation System Triangulation systems of different accuracies depend upon the extent and the purpose of the survey. The accepted grade of triangulation are : 1. First order or Primary Triangulation 2. Second order or Secondary Triangulation 3. Third order or Tertiary Triangulation Prof. R.V. Langote  1. First order or Primary Triangulation It is of highest order and is employed either to determine earth’s figure or to furnish the most precise control points to which secondary triangulation may be connected. Primary triangulation embraces(adopt) the vast area. Every precaution is taken in making linear and angular measurement and in performing the reductions. Following are general specification of primary triangulation 1. Average triangle closure : less than 1 sec. 2. Maximum triangle closure : not more than 3 sec. Prof. R.V. Langote 3. Length of base line : 5 to 15 Km 4. Length of side of triangles : 30 to 150 Km. 5. Actual error of base : 1 in 3,00,000 6. Probable error of base : 1 in 10,00,000 7. Discrepancy between two measures of a section : 10 mm √km 8. Probable error of computed distance : 1 in 60,000 to 1 in 2,50,000 9. Probable error in astronomic azimuth (angular distance from north or south point of the horizon to the point at which a vertical circle passing through the object intersects the horizon) : 0.5 sec Prof. R.V. Langote  2. Second order or Secondary Triangulation The secondary triangulation consists of number of points fixed within the framework of primary triangulation. The stations are fixed at close intervals so that the sizes of the triangles formed are smaller than the primary triangulation. The instruments and method used are not of the same utmost refinment. The general specification of the secondary triangulation are: 1. Average triangle closure : 1 sec. 2. Maximum triangle closure : 8 sec. Prof. R.V. Langote 3. Length of base line : 1.5 to 5 Km 4. Length of side of triangles : 8 to 65 Km. 5. Actual error of base : 1 in 1,50,000 6. Probable error of base : 1 in 5,00,000 7. Discrepancy between two measures of a section : 20 mm √km 8. Probable error of computed distance : 1 in 20,000 to 1 in 50,000 9. Probable error in astronomic azimuth : 2.0 sec Prof. R.V. Langote  3. Third order or Tertiary Triangulation It consists of number of points fixed within the framework of secondary triangulation and forms the immediate control for detailed engineering and other surveys. The sizes of triangle are small and instrument with moderate precision may be used. The specifications for a third order triangulation are as follows: 1. Average triangle closure : 6sec. 2. Maximum triangle closure : 12 sec. Prof. R.V. Langote 3. Length of base line : 0.5 to 3 Km 4. Length of side of triangles : 1.5 to 10 Km. 5. Actual error of base : 1 in 750,000 6. Probable error of base : 1 in 2,50,000 7. Discrepancy between two measures of a section : 25 mm √km 8. Probable error of computed distance : 1 in 5,000 to 1 in 20,000 9. Probable error in astronomic azimuth : 5.0 sec Prof. R.V. Langote  Comparative Specifications of First order, Second order and Third Order Triangulation Prof. R.V. Langote  Specifications First Order Second Order Third Order Average triangle closure less than 1 sec 1 sec 6sec. Maximum triangle closure not more than 3 sec 8 sec 12 sec. Length of base line 5 to 15 Km 1.5 to 5 Km 0.5 to 3 Km Length of side of triangles 30 to 150 Km 8 to 65 Km 1.5 to 10 Km Actual error of base 1 in 3,00,000 1 in 1,50,000 1in 1,00,000 Probable error of base 1 in 10,00,000 1 in 5,00,000 1 in 2,50,000 Discrepancy between two 10 mm √km 20 mm √km 25 mm √km measures of a section Probable error of computed 1 in 60,000 to 1 in 2,50,000 1 in 20,000 to 1 in 50,000 1 in 5,000 to 1 in 20,000 distance Probable error in astronomic 0.5 sec 2.0 sec 5.0 sec azimuth Prof. R.V. Langote  Triangulation Figures or Systems A Triangulation figure is a group or system of triangles such that any figure has one side, and only one, common to each of the preceding and following figures. The common figures or systems are :- 1. Single chain of triangles 2. Double chain of triangles 3. Central point figures 4. Quadrilaterals Prof. R.V. Langote 1. Single chain of triangles This figure is used where a narrow strip of terrain is to be covered. Though the system is rapid and economical, it is not so accurate for primary work since the number of conditions to be fulfilled in the figure adjustment is relatively small. It is not possible to carry the solution of triangles through the figures by two independent routes. If the accumulation of errors is not be become excessive, base lines must be introduced frequently. Prof. R.V. Langote 2. Double chain of triangles It is used to cover greater area. Prof. R.V. Langote 3. Central Point Figures Centred figures are used to cover larger area, and give very satisfactory results in flat country. The centred figures may be quadrilaterals, pentagons, or hexagons with central stations. The system provides the desired checks on the computations. However, the progress of work is slow due to more settings of the instrument. Prof. R.V. Langote 4. Quadrilaterals The quadrilateral with four corner stations and observed diagonal forms the best figures. They are best suited for hilly country. Since the computed lengths of the sides can be carried through the system by different combinations of sides and angles, the system is most accurate. Prof. R.V. Langote Criteria for selection of figure: 1. The figure should be such that the computations can be done through two independent routes. 2. The figure should be such that at least one, and preferably both routes should be well-conditioned. 3. All the line in a figure should be of comparable length. Very long lines should be avoided. 4. The figure should be such that least work may secure maximum progress. 5. Complex figures should not involve more than about twelve conditions. Prof. R.V. Langote Signals and Towers Prof. R.V. Langote 1. Towers A tower is a structure erected over a station for the support of the instrument and observing party and is provided when the station, or the signal, or both are to be elevated. The amount of elevation depends upon character of terrain and length of sight desired. The triangulation tower must be built in duplicate, securely founded and braced and guyed. The inner tower support the instrument only and outer support the observer and the signal. Prof. R.V. Langote Bilby Steel Tower Prof. R.V. Langote  The two tower should be entirely independent to each other. Towers may be of masonry, timber, or steel. For small heights, masonry structure are most suitable, but otherwise they are economical. Timber scaffolds are most commonly used, and have been constructed to heights over 50 metres. Steel tower made of light sections are very portable and can be easily erected and dismantled. Bilby is a portable type of tower made of steel section and rods which can be assembled and dismantled very easily. Bilby tower can raise the observer and the lamp to a height of 30 m or even 40m with a beacon 3m higher. Five men can erect the tower, weighing 3 tonnes, in 5 hours. Prof. R.V. Langote 2. Signals A signal is a device erected to define the exact position of an observed station. The signal may be classified as under : 1. Daylight or nonluminous (opaque) signal; 2. Sun or luminous signal and 3. Night signal Prof. R.V. Langote  1. Daylight or nonluminous (opaque) signal; It consist of various forms of mast, target or tin cone types, and are generally used for direct sights less than 30 km. For sights under 6 km pole signals consisting of round pole painted black and white in alternate section and supported on a tripod or quadripod may be used. A target signal consists of a pole carrying two square or rectangular targets placed at right angles to each other. The targets are made of cloth stretched on wooden frames. Prof. R.V. Langote  The signal should be of dark colour for visibility against the sky and should be painted white, or in white and black strip. The top of the mast should carry a flag. To make signal conspicuous, its height above the station should be roughly proportional to the length of longest sight upon it. A height in the vertical plane corresponding to at least 30’’ is necessary. Following rules may serve as a guide: Diameter of signal = 1.3D to 1.9 D, where D is in km. Height of signal in cm = 13.3 D Where, D is in km. Prof. R.V. Langote 2. Sun or luminous signal Sun signals are those in which the sun rays are reflected to the observing theodolite either directly as from a beacon or indirectly from a target. They are generally used when the length of sight exceeds 30 km. The heliotrope and heliograph are the special instruments used as sun signals. The heliotrope consists of a plane mirror to reflect the sun rays and a line of sight to enable the attendant to direct the reflected rays towards the observing station. The line of sight may be either telescopic or in the form of a sight vane with an aperture carrying crosswire. Prof. R.V. Langote  The heliotrope is centred over the station mark, and the line of sight is directed upon the distant station by the attendant at the heliotrope. Flashes are sent from the observing station to enable the direction to be established. Because of the motion of sun, the heliotroper must adjust the mirror every minute on its axes. Another form of heliotrope is the ‘ Galton Sun Signal’. Prof. R.V. Langote 3. Night Signal Night signals are used in observing the angles of a triangulation system at night. Various forms of night signals used are : 1. Various forms of oil lamps with reflectors or optical collimators for lines of sight less than 80 kilometers. 2. Acetylene lamp designed by captain G.T. McCaw for lines of sight up to 80 kilometers. Prof. R.V. Langote  PHASE OF SIGNALS It is the error of bisection which arises from the fact that, under lateral illumination, the signal is partly in light and partly in shade. The observer sees only the illuminated portion and bisect it. It is thus apparent displacements of the signal. The phase correction is thus necessary so that the observed angle may be reduced to that corresponding to the centre of the signal. The correction can be applied under two conditions: When the observation is made on the bright portion When the observation is made on the bright line. Prof. R.V. Langote  When the observation is made on the bright portion Fig. shows the case when observation is made on bright portion FD. Let, A = position of observer B = center of the signal (in plan) FD = visible portion of the illuminated surface. AE = line of sight E = mid point of FD ß = phase correction Θ1 & Θ2 = angle which the extremities of the visible portion make with AB. α = the angle which the direction of sun makes with AB r = radius of the signal D = distance AB Prof. R.V. Langote The phase correction ß = Θ1 + ½ (Θ2- Θ1) = ½ (Θ1+ Θ2) But Θ2 = r/D Θ1 = r sin (90o- α)/D = (r cos α/D) radians 𝑟 cos α 𝑟 𝑟 (1:cos α) ß=½ { + } = 𝐷 𝐷 2𝐷 1 𝑟 (cos22α) ß= 𝑟𝑎𝑑𝑖𝑎𝑛𝑠 𝐷 Or 1 𝑟 (cos22α) ß= 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 𝐷 sin 1′′ 1 206265 𝑟 cos2 2 α [ß = 𝐷 seconds ] Prof. R.V. Langote  When the observation is made on the bright line Let observation be made on bright line formed by the reflected rays as indicated by path SE. AE is the observed line of sight. Let,