CONTROL SURVEYING UNIT II Control Surveying CONTENTS • • • • • • • • • • • • Working from whole to part Horizontal and vertical control methods – Triangulation Signals Base line Instruments and accessories Corrections Satellite station Reduction to.
Download ReportTranscript CONTROL SURVEYING UNIT II Control Surveying CONTENTS • • • • • • • • • • • • Working from whole to part Horizontal and vertical control methods – Triangulation Signals Base line Instruments and accessories Corrections Satellite station Reduction to.
CONTROL SURVEYING UNIT II Control Surveying CONTENTS • • • • • • • • • • • • Working from whole to part Horizontal and vertical control methods – Triangulation Signals Base line Instruments and accessories Corrections Satellite station Reduction to centre Trignometric levelling Single and reciprocal observations Modern trends Bench marking Sivapriya Vijayasimhan 2 UNIT II Control Surveying Introduction Plane Survey : Adopted for small distances Curves in earth is ignored Lines connecting two points is a straight line Figure formed by joining straight lines is plane triangle Geodetic Surveying or Trignometric Surveying Long distances and large areas Curvature of earth is taken care Joining any two points on surface of earth is curved and forms arc of circle Absolute and high precision Sivapriya Vijayasimhan 3 UNIT II Control Surveying Working from whole to part Horizontal points are established precisely Area dived into large traingles or same equilateral Large triangles are subdivided into small traingles, surveyed with less accuracy To prevent accumulation of error and to control and locate minor error Working from whole to part is effective In Part to whole, error will be magnified and uncontrollable CONTROL POINTS A system of control stations, local or universal, must be established to locate the positions of various points, objects, or details on the surface of the earth Establish system of control points with high precision Points can be vertical or horizontal Sivapriya Vijayasimhan 4 UNIT II Control Surveying Horizontal Control Points To establish supplementary control stations for use in construction surveys Supplementary control stations usually consist of one or more short traverses run close to or across a construction area to afford easy tie-ins for various projects Prevent excessive accumulation of error Forms contour and gives more details Established by means of triangulation or traversing Two systems are adopted 1.Primary Control Done by triangulation Stations are established with less precision (leads for secondary control) 2.Secondary Control Done by transit and tape traverse Horizontal Control Methods Location of points described by distance and direction from a reference point Measurement of distance using Tape, Chain, Tacheometry, Electronic Distance Measurement ,Total station, GPS Measurement of direction using Sivapriya Vijayasimhan Compass, Plane Table, Theodolite, Total Station GPS 5 UNIT II Control Surveying Vertical Control Points To determine elevation of primary control stations or to establish bench mark Precise levelling Primary stations located by triangulation and trigonometric levelling Secondary vertical control points traverse station or bench mark Done by ordinary spirit levelling Vertical Control Methods Direct Levelling Trigonometrically Levelling Tacheometry :Stadia Method Tacheometry :Tangential Method Sivapriya Vijayasimhan 6 UNIT II Control Surveying BENCH MARKS It is a relatively permanent point of reference whose elevation w.r.t some assumed datum is known. BM is used as a starting point for levelling or as point upon which to close as a check. GTS BM : Great Trigonometric Survey Bench Mark. In India, elevation of all such BMs are established w.r.t MSL at Karachi. A bronze plate provided on the top of a concrete pedestal with its elevation engraved serves as GTS BMs. GTS BMs are depicted on topo sheets published Permanent BM : Fixed points of reference , established w.r.t the GTS BM. Fixed by State Government i.e PWD. Arbitrary BM : For conducting small projects, arbitrary BMs are assumed.( 100.00m). In most of the engg. projects, difference in elevation is more important than their RL w.r.t MSL. Temporary BM : Established at the end of the day’s work, so that work can be continued from this point onward. TBM should be established on permanent points which can be identified easily next day. Sivapriya Vijayasimhan 7 UNIT II Control Surveying Azimuth: Angular distance measures towards the east from the north along the astronomical horizon to the intersection of great circle passing through the point and the astronomical zeinth with arstronmical horizon Sivapriya Vijayasimhan 8 UNIT II Control Surveying Triangulation • Proposition :that if one side and two angles of a triangle are known, the remaining sides can be computed • If the direction of one side is known, the directions of the remaining sides can be determined • Triangulation system consists of a series of joined or overlapping triangles in which an occasional side is measured and remaining sides are calculated from angles measured at the vertices of the triangles • The vertices of the triangles are known as triangulation stations • The side of the triangle whose length is predetermined, is called the base line • The lines of triangulation system form a network that ties together all the triangulation stations • Since a triangulation system covers very large area, the curvature of the earth has to be taken into account A G B O F E Sivapriya Vijayasimhan C D 9 UNIT II Control Surveying Triangulation :Objective Sivapriya Vijayasimhan 10 UNIT II Control Surveying Triangulation Principle •Consider two interconnected triangles ABC and BCD. All the angles in both the triangles and the length L of the side AB, have been measured. •Also the azimuth θ of AB has been measured at the triangulation station A, whose coordinates (XA, YA), are known. •The objective is to determine the coordinates of the triangulation stations B, C, and D by the method of triangulation Sivapriya Vijayasimhan 11 UNIT II Control Surveying Sivapriya Vijayasimhan 12 UNIT II Control Surveying Sivapriya Vijayasimhan 13 UNIT II Control Surveying Sivapriya Vijayasimhan 14 UNIT II Control Surveying Steps in Triangulation Survey 1. 2. 3. 4. 5. 6. 7. Reconnaissance Selection of stations and base line Decision of triangle formation Erecting of signals and towers Measurement of base line Horizontal angles of the triangles are measured Computations of various sides of triangles 1.Reconnaissance - Short and rapid survey - Factors to be considered Terrain selection Selection of site for base line Suitable triangulation stations - Needs Great skill, experience and judgment - Instruments used Angle measuring instrument : Theodolite Bearing Measuring instrument :prismatic compass Elevation measuring Instrument : Aneroid barometer Intervisibility testing Tape, chains, telescope, drawing instrument Sivapriya Vijayasimhan 15 UNIT II Control Surveying 2.Selection of Triangulation Stations - - Well conditioned traingles nearly equilateral triangles (less than 300 and not more than 1200 ) Stations should be clearly visible from all adjacent stations Stations should be accessible Communication facilities Transportation facilities Length of site should neither too long nor too small Selection of station to cover a wide area from main triangulation station so number substations may be controlled Location should be on firm ground Line sight should pass through areas free from atmospheric disturbances Forest area: cutting of woods shld be minimised Cost of erection of scaffolds and signals shld be minimum All stations shld be shown on topographic plan on area along their latitudes and longitudes considering RL of station w.r.t to MSL Sivapriya Vijayasimhan 16 UNIT II Control Surveying 3.Selection of Triangulation figure or system - Magnitude of angles in each individual triangles Arrangement of triangles Classification of Triangulation •First-order triangulation is used to determine the shape and size of the earth or to cover a vast area like a whole country with control points to which a second-order triangulation system can be connected. •Second-order triangulation system consists of a network within a first-order triangulation. It is used to cover areas of the order of a region, small country, or province. •Third-order triangulation is a framework fixed within and connected to a second-order triangulation system. It serves the purpose of furnishing the immediate control for detailed engineering and location surveys. Sivapriya Vijayasimhan 17 UNIT II Control Surveying “ Sivapriya Vijayasimhan 18 UNIT II Control Surveying Arrangements of Triangles 1.Single chain of triangles 2.Double chain of triangles 3.Central point of figures 4.Quadrilateral or interlacing triangles 1.Single Chain of Triangles Narrow strip of terrain Economical and rapid Adjustment is relatively small Not accurate for primary work Sivapriya Vijayasimhan 19 UNIT II Control Surveying 2.Double chain of triangles Economical and rapid Similar to single chain 3.Central Point Figure Cover more area on flat terrain Figures may be quadrilateral, pentagon or hexagon Adequate checks Program is slow Sivapriya Vijayasimhan 20 UNIT II Control Surveying 4.Quadrilateral or interlacing triangles Four corner station and observed signal Forms best figure Suitable for hilly terrain Length can be determined by different combination of sides and angles System is accurate Selection of best system 1.Atleast one route should be well conditioned triangle 2.Very long length is neglected 3.Independent routes are available Sivapriya Vijayasimhan 21 UNIT II Control Surveying C Well Conditioned Triangles Error in measurement of angle have minimum effect upon length of calculated sides Error in another two sides may affect rest of figure Two sides are equally accurate: equal length and isosceles triangle A θ c B Δ ABC is an isosceles triangle with AB of known length Sides BC and CA are computed Triangles is isosceles A = B By Sine rule 𝑺𝒊𝒏 𝑨 𝒂 = 𝒄 𝑺𝒊𝒏 𝑪1 δA, error in angle measurement δa1 , error in side a. Differentiate eq 1 by A 𝜹𝒂𝟏 = 𝒄 𝑪𝒐𝒔 𝑨 𝜹𝑨 𝑺𝒊𝒏 𝑪 𝜹𝒂𝟏 𝑪𝒐𝒔 𝑨 = 𝜹𝑨 = 𝜹𝑨 𝐜𝐨𝐭 𝑨 𝒂 𝑺𝒊𝒏 𝑨 Sivapriya Vijayasimhan 2 22 UNIT II Control Surveying δC, error in angle measurement C δa2 , error in side a. Differentiate eq 1 by C 𝜹𝒂𝟐 = - 𝑺𝒊𝒏 𝑨 𝑪𝒐𝒔 𝑪 𝜹𝑪 𝑺𝒊𝒏𝟐 𝑪 𝜹𝒂𝟐 𝑪𝒐𝒔 𝑪 = - 𝑺𝒊𝒏 𝑪 𝜹𝑪 𝒂 = −𝜹𝑪 𝑪𝒐𝒔 𝑪 δA and δC probable errors in angles and are equal to ± β Probable fraction error in side a = ±𝜷 𝑪𝒐𝒕𝟐 𝑨 + 𝑪𝒐𝒕𝟐 𝑪 𝑪 = 𝟏𝟖𝟎° − 𝑨 − 𝑩 = 𝟏𝟖𝟎° − 𝟐𝑨 (𝑪𝒐𝒕𝟐 𝑨 + 𝑪𝒐𝒕𝟐 𝑪shld be minimum) Differentiate the above equation wrt A and equating to zero 𝟒𝑪𝒐𝒔𝟐A + 2 𝑪𝒐𝒔𝟐 𝑨 − 𝟏 = 𝟎 A = 56⁰14’ (Approximately) For Practical purpose, equilateral triangle is most suitable Triangles angle smaller than 300 or greater than 1200shld be avoided Sivapriya Vijayasimhan 23 UNIT II Control Surveying Strength of Figure The U.S. Coast and Geodetic Surveys has developed a convenient method of evaluating the strength of a triangulation figure It is based on the fact that computations in triangulation involve use of angles of triangle and length of one known side The other two sides are computed by sine law – For a given change in the angles, the sine of small angles change more rapidly than those of large angles. (Angles less than 30° should not be used in the computation of triangulation If angles less than 30° is used, then it must be ensured that this is not opposite the side whose length is required to be computed for carrying forward the triangulation series) Factor to be considered during Triangulation – Triangulation system within a desired degree of precision – Deciding the layout of a triangulation system The square of the probable error (L²) that would occur in the sixth place of the logarithm of any side, if the computations are carried from a known side through a single chain of triangles after the net has been adjusted for the side and angle conditions. The expression for L² is L² = (4/3)d ²R d - probable error of an observed direction in seconds of arc R - shape of figure Sivapriya Vijayasimhan 24 UNIT II Control Surveying 1 1 Sivapriya Vijayasimhan 25 UNIT II Control Surveying Sivapriya Vijayasimhan 26 UNIT II Control Surveying Signals and Towers - Device erected to define the exact position of an observed station - A tower is a structure over a station to support the instrument and the observer, and is provided when the station or the signal, or both has to be elevated Requirements of Signals 1. 2. 3. 4. Clearly visible against any background Feasible to centre accurately over the station mark Suitable for accurate bisection Free from Phases Types of Signals 1. 2. 3. Daylight or Non-luminous Signals Sun or Luminous Signals Night Signals Sivapriya Vijayasimhan 27 UNIT II Control Surveying Requirements of Signals -It should be conspicuous and clearly visible against any background. To make the signal conspicuous, it should be kept at least 75 cm above the station mark. -It should be capable of being accurately cantered over the station mark. -It should be suitable for accurate bisection from other stations. -It should be free from phase, or should exhibit little phase Sivapriya Vijayasimhan 28 UNIT II Control Surveying 1. Daylight or Non-luminous Signals - Timber post, Masts and tin-cone Used for sight upto 30 km For less than 6 km, pole signals are used 2. Sun or Luminous Signals - Sun rays reflected to the theodolite (Heliographs and Hebiostats) Length of sight exceeds 30 km 3. Night Signals - Observing the angles of the triangulation system during night Oil lamps and acetylene lamps Phase of Signals - Error of bisection of some type of signals when they are in partly light and partly in shade -Common when there are cylindrical signals and when the observer sees the illuminated portions and bisect it - Leads to apparent displacement of the centre of signals - Corrections is required (for bright portion and bright line) Sivapriya Vijayasimhan 29 UNIT II Control Surveying 1.Observation made on Bright Portion A – Position of observer B – Centre of Signal FD – Visible portion of illuminated surface AE – line of Sight E – Mid portion of FD β –phase correction Θ1 and Θ2 – angles which extremities of visible portion make with A α –angle which the direction of sun makes AB r-radius of signal D- distance of AB β = θ1 + ( ) 1 1 θ 2 θ1 = (θ1 +θ 2 ) 2 2 r radians D r sin(90° α) r cosα θ1 = = radians D D θ2 = β= Sivapriya Vijayasimhan 1 r cosα r r (1 +cosα) + = = 2 D D 2D 206265r cos2 D 1 α 2 sec onds 30 UNIT II Control Surveying 2.Observation made on Bright Line Let β be equal to ΔEAB SE and S1A are parallel ΔSEA = 180⁰-(α-β) ΔBEA = 1 ΔSEA =180° 1 [180° (α β)]= 90°+ 1 (α β) 2 2 2 ( ) 1 ΔEBA =180° (β +ΔBEA) =90° α +β 2 r cosα 206265r cosα 2 radians= 2 sec β= D D Correction is applied to observed angle according to the relative position of sun and signal Common in cylindrical signals Sivapriya Vijayasimhan 31 UNIT II Control Surveying INTERVISIBILITY AND HEIGHT OF STATIONS • Distance between stations is more or difference in elevation is less – intervisibility is checked • Hence raise both instrument and signal to overcome the curvature of earth and intervening obstruction Following condition decide the height of instrument and signal 1. Distance between stations 2. Elevation of stations 3. Intervening Ground Sivapriya Vijayasimhan 32 UNIT II Control Surveying 1.Distance between stations No intervening ground Horizontal distance of visible horizon from station of known elevation D2 h (1 - 2m) 2R h – height of station above datum D – distance to visible horizon R – mean radius of earth m– co-efficient of refraction 0.07 for sights over land 0.08 for sights over sea Taking D and R in km, m=0.07 h = 0.06735D 2 Sivapriya Vijayasimhan h in m 33 UNIT II Control Surveying 2.Elevations of Stations No Obstruction due to intervening ground Elevation of station at a distance may be calculated, when it can be visible from another station of known elevation D2 h (1 2 m) 2R h 0.0 6 7 3 5D 2 m=0.07 and R in km h1 0.0 6 7 3 5D12 h1 – known elevation of station A above datum D1- distance from A to point of tangency D – known distance between A and B D1 = h1 0 .0 6 7 3 5 D1 = 3.8 5 3 h1 Knowing D1, D2=D - D1 Knowing D2, h2 , the elevation of B above datum is h2 0.06735D22 (m) Line of sight shld be atleast 2 to 3 m above Sivapriya Vijayasimhan 34 UNIT II Control Surveying 3. Intervening Ground Condition 1 (hc>hc’) Signal station B has to raised Intervening ground at C is obstructed by the intervisibility between stations A and B DA =3.853 hA Distance DT of peak C from the point of tangency T, DT DA - Dc Sivapriya Vijayasimhan 35 UNIT II Control Surveying From ΔA’C’C’ and A’B’B” we get B” hc " hB " Dc D D hB " hc " Dc hc " hc - hc ' The required height of signal above station Bo, BoB” = (BB’ + B’B”) - BBo = (hB’ + hc”) - hB Condition 2 (hc’>hc) Line of sight is clear and assumed it is not obstructed by ground Sivapriya Vijayasimhan 36 UNIT II Control Surveying Station Mark The triangulation stations should be permanently marked on the ground so that the theodolite and signal may be centred accurately over them. The following points should be considered while marking the exact position of a triangulation station : - The station should be marked on perfectly stable foundation or rock. Generally, a hole 10 to 15 cm deep is made in the rock and a copper or iron bolt is fixed with cement. - If no rock is available, a large stone is embedded about 1 m deep into the ground with a circle, and dot cut on it. A second stone with a circle and dot is placed vertically above the first stone. - A G.I. pipe of about 25 cm diameter driven vertically into ground up to a depth of one meter which serves as a good station mark. - The mark may be set on a concrete monument. The station should be marked with a copper or bronze tablet. The name of the station and the date on which it was set, should be stamped on the tablet. - In earth, generally two marks are set, one about 75 cm below the surface of the ground, and the other extending a few centimeters above the surface of the ground. The underground mark may consist of a stone with a copper bolt in the centre, or a concrete monument with a tablet mark (Fig 1) Sivapriya Vijayasimhan 37 UNIT II Control Surveying -The station mark with a vertical pole placed centrally, should be covered with a conical heap of stones placed symmetrically. This arrangement of marking station, is known as placing a cairn (Fig 2) - Three reference marks at some distances on fairly permanent features, should be established to locate the station mark, if it is disturbed or removed. - Surrounding the station mark a platform 3 m × 3 m × 0.5 m should be built up of earth. Figure 1 Sivapriya Vijayasimhan Figure 2 38 UNIT II Control Surveying BASE LINES Longest of the main survey lines. – Main reference line for fixing the positions of various stations and also to fix the direction of other lines. – Accuracy of entire triangulation critically depends on this measurement. Length of depends on magnitude of triangulation Check bases are provided at suitable intervals Location of Base lines - Ground shld be flat terrain - Triangulation shld be visible from both ends of base line - Well proportioned triangles - Site shld be free from obstructions - Ground shld be firm( no water gaps and not wider than the length of tape) - Site shld be possible for extension to primary triangulation Standards of Length - International meter - Meter is marked on three platinum-iridium bars kept in standard conditions Disadvantage: standard length in metal changes its dimensions Sivapriya Vijayasimhan Great Britain 1 Imperial Yard = 0.91439482 m United States 1 meter = 39.37 inch India 10 feet bar = 9.9999566 British feet 39 UNIT II Control Surveying Forms of base measuring apparatus 1.Standarad Tape -Steel and invar tapes -Length : 30 to 50 m -co-eff of expansion does not exceed 9 x 10-7 /0C 2.Straining Device -End of tape attached to hook of a chain which passes over a block -Load applied at bottom of chain 3.Spring Balance -Sensitive and accurate spring balance 4.Thermometers -To measure temperature of steel tape 5.Steel tape -For spacing of tripods or stakes 6.Tripod -For marking and supporting Sivapriya Vijayasimhan 40 UNIT II Control Surveying Corrected Length of Base Line 1. Correction for absolute length 2. Correction for temperature 3. Correction for pull or tension 4. Correction for Sag 5. Correction for slope or vertical alignment 6. Correction for horizontal alignment 7. Reduction to mean sea level 1.Correction for absolute length Actual length of tape ≠ designated length of tape Ca Lc l Ca – correction for actual or absolute length L- measured length of line C-correction per tape length I-nominal or designated length of tape Condition 1. Actual length of tape > nominal length, then then length is too short & correction is additive 2. Actual length of tape < nominal length, then length is too great and correction is subtractive Sivapriya Vijayasimhan 41 UNIT II Control Surveying 2. Correction for temperature Ct αTm - To L Ct – correction for temperature α- coeff of thermal expansion Tm-mean temperature in field during measurement To-temperature during standardisation of the tape L- measured length of line Condition 1. Field Temperature > Standardised tape temperature : measured distance is less and correction is additive 2. Field Temperature < Standardised tape temperature : measured distance is more and correction is subtractive Sivapriya Vijayasimhan 42 UNIT II Control Surveying 3. Correction for Pull or tension P P0 Cp L AE Cp – correction for pull P- pull applied during measurement (kg) P0-standarad Pull (kg) A-cross section area of the tape (cm2) E-Young’s modulus of elasticity (kg/cm2) L- measured length of line (m) Condition 1. Pull applied > Standardised tape pull: measured distance is less and correction is additive 2. Pull applied< Standardised tape pull : measured distance is more and correction is subtractive Pull applied in field should be less than 20 times the weight of tape Sivapriya Vijayasimhan 43 UNIT II Control Surveying 4. Correction for Sag -sags due to self weight and takes horizontal catenary -horizontal length is less than length along the curve Sag correction = horizontal length – measured length 2 8 h l1 d1 1 d 3 l 8 h2 C s1 d1 - l1 3 d1 1 2 wl1 d1 wl1d1 2 4 8 wl1d1 h 8P Ph 3 (Sub the value of h in eqn 1) Substituting the values of h in eqn 2 2 2 8 1 wl1d1 l1 ( wl1 ) 2 l1W Cs1 3 d1 8 P 24P 2 24P 2 If l is total length of tape and it is suspended in ‘n’ equal intervals, then the sag correction is as follows Cs nCs1 Sivapriya Vijayasimhan 2 nlW 24P 2 Cs – tape correction per tape length W – total weight of tape l -total length of tape n -number of equal spans P -pull applied 44 UNIT II Control Surveying 5. Correction for slope or Vertical Alignment Distance measured along slope > horizontal distance ( correction is subtractive) AB – measured inclined length ‘L’ AB1 - horizontal length h – difference in elevation between ends Cv – slope correction due to vertical alignment h2 h2 C AB AB1 L L h L L1 2 4 2 L 8L 2 2 h2 h4 3 ..... Slope flatter than 1 in 25, second term is neglected 2 L 8L h2 C 2L L1,L2 etc length of successive uniform gradients H1,h2 etc difference in elevation between the ends Total slope correction = h 2 2L If the slope angle θ is measured instead of h, then correction Cv L L cos L(1 cos ) Sivapriya Vijayasimhan Cv 2 L sin 2 2 45 UNIT II Control Surveying 6.Correction for Horizontal Alignment In case of base line with obstructions – broken base Ac – Straight base AB and BC two section of broken base Β – exterior angle measured at B Correction for horizontal alignment,Ch = (a + c) – b By Sine rule b is given as , b 2 a 2 c 2 2ac cos (subtractive) a 2 c 2 b 2 2ac cos 2 4 ac sin 1 2 By adding 2ac on both sides of equation we get (a c) b ( a c) b 4ac sin 2 1 2 Ch acb Sin 1/2β ~ 1/2β and express β in minutes and b ~ (a+c) ac 2 Ch 4.2308108 ac Sivapriya Vijayasimhan 46 UNIT II Control Surveying 7.Reduction to Mean Sea Level AB – measured horizontal distance A’B’ –equivalent length at MSL (D) h-mean equivalent of base line above MSL R-radius of earth Θ – angle subtended at centre of earth, by AB D L R Rh 1 R Lh h DL 1 L Rh R R Correction, Cmst L D Lh R Sivapriya Vijayasimhan (Subtractive) 47 UNIT II Control Surveying Measurement of Horizontal Angles Methods: 1. Repetition Method and 2. Reiteration Method 1.Repetition Method P R 1. Measure angle between PQR. Station at Q 2. Use upper screw and tangent set vernier A reading zero and note vernier B reading 3. Unclamp the upper clamp, turn instrument clockwise about Θ inner axis towards R. Clamp upperclamp and bisect R .Vernier A and B readings are noted Q 4. Unclamp lower clamp. Turn clockwise to view the target P. Bisect P using lower tangent screw 5. Unclamp the upper clamp, turn telescope clockwise and sight R. Bisect R by upper tangent screw Elimination of errors 1.Eccentricity of verniers and centres : both vernier readings 2. Inadjustments of line of collimation and trunnion axis are eliminated by taking both face reading 3. Inaccurate graduation :readings at different parts of circle 4.Inaccurate bisection of object: taking different obervations Sivapriya Vijayasimhan 48 UNIT II Control Surveying 2.Reiteration Method A 1.Signals are bisected successively and a value is obtained for each direction of several rounds of observation 2.Several angles at station are measured in terms of direction of their sides from sn initial station 3.Direction of theodolite are provide with optical micrometer 4.Primary work B C O D Elimination of errors 1. Eccentricity errors of vertical axis and microscope are rectified by taking micrometers 2. Imperfect adjustments of line of collimation and horizontal axis are eliminated by both face readings 3. Graduations are eliminated by reading values of each angle on different parts 4. Error due to manipulation: ½ the observation from left to right and ½ observation from right to left 5. Accidental error due to bisection and reading are eliminated by taking number of observation Sivapriya Vijayasimhan 49 UNIT II Control Surveying Satellite Station - Reduction to Centre - To obtain well-conditioned triangle or better visibility, object such as church pier, steeples, flag pole, tower etc., are selected as triangulation stations. - Setting up instrument over the such station and observations is difficult to take - Subsidiary stationary can be termed as satellite station or eccentric station or false station is selected near to the main stations and measurements are taken Observations are taken to other triangulation station with same precision of measurements - Satellite station is not preferred in primary triangulation - Corrections are later applied Correction applied to eccentricity of station – reduction to centre Distance between true station and satellite station is determined by trigonometric levelling or by triangulation Sivapriya Vijayasimhan 50 UNIT II Control Surveying Let A,B,C - triangulation station S - satellite station d-BS – eccentricity between B and S (determined by trignometric levelling or by triangulation) Θ-ΔASC = observed angle at S α-true angle at B γ-ΔCSB –observed angle at S β1- ΔSAB β2-ΔSCB O-point of intersection of lines AB and CS Sides AB and BC of ΔABC can be calculated using Sine rule, BC = 𝒂 = 𝒃𝑺𝒊𝒏 𝑪𝑨𝑩 𝑺𝒊𝒏𝑨𝑩𝑪 and AB=𝒄 = 𝒃𝑺𝒊𝒏𝑨𝑪𝑩 𝑺𝒊𝒏𝑨𝑩𝑪 SB sin ASB d sin( ) AB c SB sin BSC d sin CBS , sin 2 BC a sin 1 d sin( ) d sin( ) 1 206265 sin 1" c sin 1" c sin 2 d sin d sin 2 206265 sin 1" a sin 1" a ABS, sin 1 Sivapriya Vijayasimhan 51 UNIT II Control Surveying ABC AOC 2 1 2 d sin( ) d sin c sin 1" a sin 1" Conditions Case I : S1 left to B (Figure a) 1 2 Case II : S2 right to B (Figure b) 1 2 Case III : S3 between Ac and B (Figure c) 1 2 Case IV : S4 below to B (Figure d) 1 2 Sivapriya Vijayasimhan 52 UNIT II Control Surveying TRIGONOMETRIC LEVELLING - Observation to find small elevations and short distances (plane survey) - Observations to find higher elevations and large distances (geodetic survey) Curvature and Refraction Effect of Curvature : To make objects sighted to appear lower than the real position Effect of Refraction: To make objects sighted to appear higher than the real position Correction Plane Survey : curvature or refraction or combined correction is applied linearly to the observed staff reading Geodetic Survey : curvature or refraction or combined correction is applied to the observed angles Sivapriya Vijayasimhan 53 UNIT II Control Surveying Correction for Refraction Angle measure at A towards B Corrected angle BAO' A' AO'O' AB 1 r Angle measure at B towards A Corrected angle ABB2 B' BB2 B' BA 1 r Correction for refraction is subtractive to angle of elevation Correction for refraction is additive to angle of depression Co-efficient of refraction(m) m=angle of refraction (r) angle of subtended at centre of earth (θ) Methods to Determine ‘m’ 1.Distance d small and H large 2.Distance d large and H small Sivapriya Vijayasimhan 54 UNIT II Control Surveying 1.Distance d small and H large 1 1 (1 2m) 2.Distance d large and H small 1 1 (1 2m) CORRECTION FOR CURVATURE Correction = 2 (+ve for angle of elevation and -ve for angle of depression) COMBINED CORRECTION Combined angular correction = (1 2m)d sec 2 R sin 1" (+ve for angle of elevation and -ve for angle of depression) Sivapriya Vijayasimhan 55 UNIT II Control Surveying AXIS SIGNAL CORRECTION If the height of the signal is not same as that of height of instrument axis but above the station ( s2 h1 ) cos2 tan1 d cos / 2 ( s1 h2 ) cos2 tan 2 d (Subtractive) (Additive) If vertical angles α and β are very small, t an 1 1 s 2 h1 sec d sin 1" s h2 1 sec d sin 1" 1 2 After calculating δ1 and δ2 , Sivapriya Vijayasimhan 1 (elevation) 1 1 (depression) 2 56 UNIT II Control Surveying Difference in elevation Difference of elevation between the stations A and B. 1.Single Observation 2.Reciprocal Observation 1.Single Observation i. Correction for curvature ii. Correction for refraction iii. Correction for axis signal (Sign of correction depends on angle of elevation or angle of depression) Sivapriya Vijayasimhan 57 UNIT II Control Surveying Angle of elevation d H d tan1 (1 2m) 2R sin 1" Sivapriya Vijayasimhan Angle of Depression H d tan1 (1 2m) d 2 R sin 1" 58 UNIT II Control Surveying Correction to linear Measurement If α is the observed angle, uncorrected for curvature, refraction, axis signal H= d tan α – (Height of signal) - (height of instrument) + Curvature correction) (Refraction correction) d 2 m d2 H d tan ( s1 h2 ) 2R R For angle of depression β, H= d tan α + (Height of signal) - (height of instrument) - Curvature correction) + (Refraction correction) d2 H d tan ( s1 h2 ) (1 2m) 2R Sivapriya Vijayasimhan 59 UNIT II Control Surveying Reciprocal Observation Observation made from both the station so that the refraction effect is same More accurate, when ‘m’ value is not known 1 d sin 1 2 H 1 cos 1 2 2 1 d sin 1 2 H 1 cos 1 2 2 Sivapriya Vijayasimhan +ve for angle of elevation -ve for angle of depression 60 UNIT II Control Surveying BASE NET Base lines are shorter than average length of triangle sides - When there in no possibility to get a favourite site for a longer base - Difficult and expensive to measure long base line Connecting shorter base lines to the main triangulations. These group of triangles meant for extending the base is called base net Points to be considered 1. Small angles opposite the known side must be avoided 2. Net should have sufficient redundant lines to provide 3 to 4 equations 3. Quickest extension with fewest stations Sivapriya Vijayasimhan 61 UNIT II Control Surveying Various forms of Base Extension Sivapriya Vijayasimhan 62 UNIT II Control Surveying Criteria for selection of triangulation stations • Triangulation stations should be inter-visible. For this purpose the station points should be on the highest ground such as hill tops, house tops, etc. • Stations should be easily accessible with instruments. • Station should form well-conditioned triangles. • Stations should be so located that the lengths of sights are neither too small nor too long. • Small sights cause errors of bisection and centering. • Long sights too cause direction error as the signals become too indistinct for accurate bisection. • Stations should be at commanding positions so as to serve as control for subsidiary triangulation, and for possible extension of the main triangulation scheme. • Stations should be useful for providing intersection points and also for detail survey. • In wooded country, the stations should be selected such that the cost of clearing and cutting, and building towers, is minimum. • Grazing line of sights should be avoided, and no line of sight should pass over the industrial areas to avoid irregular atmospheric refraction. Sivapriya Vijayasimhan 63