Ce6304 Notes

2015AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY CE6304-SURVEYING-I UNIT-I INTRODUCTION AND CHAIN SURVEYING DEFINITION: Surveying is the art of determining the relative positions of points on, above or beneath the surface of the earth by means of direct or indirect measurements of distance, direction & elevation. Plane Survey: Surveying which the mean surface of earth regarded as plain surface and not curve it really is known as plain surveying. A following Assumption are made: (i) A level line is considered a straight line thus the plump line at a point is parallel plump line at any after point. (ii) The angles between two such lines that intersect is a plain angle and not a sphere angle. (iii) The meridian through any two points parallel. (iv) When we deal with only a small portion earths surface the above assumptions can justify. (v) The error induced for a length of an 18.5 kms it‘s only 0.0152 ms greater than sub dented chord 1.52 cm. Geodetic survey : Survey is which the shape (curvature) of the earth surface is taken in the account a higher degree of precision is exercised in linear and angular measurement is tanned as Geodetic Survey. A line connecting two points is regarded as an arc. Such surveys extend over large areas. PRINCIPLES OF SURVEYING  Location of a point by measurement from 2 points of reference  Working from whole to part. Location of a point by measurement from 2 points of reference There should be 2 points of reference say P & Q P, Q are the ground reference points and permanent points. Point R can be located by any one of the following direct methods:  Distance PR and QR can be measured and point R can be plotted by swinging the Two arcs of the same scale to which PQ has been plotted. The principle is very much used in chain surveying.  Perpendicular RS can be dropped on the reference line PQ and the lengths PS and SR are measured. The point R can be plotted using this set square. This principle is used for defining details.  The distance QR & the angle PQR can be measured and point R is plotted either by means of protractor or trigonometrically. The principle is used in traversing.  In this distance PR and QR are not measured but angle RPQ are measured with an angle measuring instrument. Knowing the distance PQ point R is plotted either by means of protrctor or by solution of triangle PQR. This principle is used in triangulation. A.MUKKANNAN M.E., A.M.I.E., DEPARTMENT OF CIVIL ENGINEERING Page 1 AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY  Angle RQP & distance PR are measured & point R is plotted either by protracting an angle & swinging an arc from P or plotted trigonometrically. Working from whole to part.  First establish a system of control points & to fix them with higher precision.  Minor control points can then be established by less precise methods & the details can then be located using these minor control points by running minor traverse etc.,  This method followed to prevent t the accumulation of errors & to control & localize minor errors. CLASSIFICATION (a)Classification based upon the nature of survey of field survey: (1) Land surveying  Topographical surveys  Cadastral surveys  City surveying Topographical surveys: This consists of horizontal & vertical location of certain points by linear & angular measurements. To determine natural features of a country such as rivers, railways, canals, towns & villages. Cadastral surveys: Fixing of property lines, calculation of land area or transfer of land property from one owner to another. To fix boundaries of municipalities & of state & federal jurisdictions. City surveying: construction of streets, water supply system sewers & other works. (2) Marine/ Hydrographic survey: Bodies of water for purpose of navigation, water supply, harbour works or for determination of mean sea level. Measurement of discharge of streams, making topographic of shores & banks, taking& locating soundings to determine depth of water, fluctuations of the ocean tide. (3) Astronomical survey: To determine absolute location of any point & direction of any line on the surface of the earth. (b) Classification based on the object of survey: (1) Engineering survey: Determination of quantities or to afford sufficient data for the designing of engineering works such as road s& reservoirs, also sewage disposal or water supply. (2) Military survey: Points of strategic importance. (3) Mine Survey: Exploring mineral wealth (4) Geological Survey: Different strata in the earth‘ s crust (5) Archaeological survey: Unearthing relics of antiquity. A.MUKKANNAN M.E., A.M.I.E., DEPARTMENT OF CIVIL ENGINEERING Page 2 . A. 5.MUKKANNAN M. details such as boundary lines. FIELD NOTES 1. establishing parallel lines & perpendicular lines 8. weather conditions. & list of equipment used. 2.M. bridges & other natural & artificial features of area surveyed. Field notes are written a record of field work made @ the time of work is done. 7. Surveying contours of land areas in which the field work involve both horizontal & vertical control. Field notes should be legible. buildings. sewers & water supply schemes.Surveying past the obstacles & carrying on a great variety of similar field work that is based on geometric or trigonometric principles. Measuring distance along the angles between the survey lines. boundaries. o Follow a consistent simple style of writing. written in clear. A.E. 6. roads.E. plain letters & figures. culverts. 2. 4. 10. Locating details of survey with respect to stations & lines between stations. Determining elevations of some existing points or establishing points @ given elevations. Never use soft pencil or ink. o Make the notes for each day‘s work on the survey complete with a title of the survey.. Establishing stations & bench marks of points of reference & thus to establish a system of horizontal & vertical control. Carrying out miscellaneous operations such as. personnel of the crew. date. streets. Rules for note-keepers: o Record directly in the field book as observations is made. roads. o Use a sharp 2H or 3H pencil. 9. Taking measurements to inaccessible points. bridges. 3. streams. Making observations on the sun or a star to determine the meridian latitude or longitude or to determine the local time. Giving lines & elevations for great variety of construction work such as that for buildings. o Use a liberal number of carefully executed sketches.I. concise & comprehensive.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY ( c) Classification based on instrument used: 1) Chain survey 2) Theodolite survey 3) Triangular survey 4) Triangulation survey 5) Tachometric survey 6) Plane table survey 7) Photographic survey 8) Aerial survey Field work & office work: Field work: 1. DEPARTMENT OF CIVIL ENGINEERING Page 3 . relative locations & topographic features. OFFICE WORK Drafting: Drafting consists of preparation of the plan and sections and to prepare topographic maps..30m & not 342. make it clear where they belong. that done for determining areas & volumes Designing: The surveyor may also be called upon to do some design works especially in case of route surveying. record angles as 08 06‘ 20‖ using @ least 2 digits for each part of the angle. o If measurements are put directly on the sketches.MUKKANNAN M. o Sign the notes Field notes divided into 3 parts NUMERICAL VALUES o It includes the records of all measurements such as lengths of lines & offsets. A.M.01m is measured it should recorded as 342. If a mistake is made.E. Computing: It is of 2 kinds: 1. Scale can be represented by following methods: A.E. staff readings & angles or directions. open & clear. o Sketches are almost never made to scale. rule one line through the incorrect value and the correction above the mistake.. o If length nearest to 0. Make sketches large.3m. o Always make a sketch it will help to settle any ought. SCALES Scale is the fixed ratio that every distance on the plan bears with corresponding distance on the ground. SKETCHES o Sketches are made as records of outlines. & to record such information concerning important features of the ground cover & the work done as might be of possible use later. DEPARTMENT OF CIVIL ENGINEERING Page 4 . All significant figures should be recorded.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY o Never erase. EXPLANATORY NOTES It is make clear that which is not perfectly evident from numerals & sketches.I. that done for purpose of plotting 2. Graphical scale: It is a line sub-divided into plan distance corresponding to convenient units of length on the ground. 1/1000. Types of scales: 1. From each of the divisions. A.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY NUMERICAL SCALE Engineer’s scale: One cm on the plan represents some whole number of meters on the ground. For example let a short length PQ be divided into 10 parts. 5. Divide it into ten equal parts.25mm. feet and inches etc.9-9 represents 9/10 PQ etc. Choice of scale of a map The preliminary considerations in choosing the scale are: 1. Vernier scale (a) Direct Vernier (b) Retrograde Vernier A..M. 3. Plain Scale 2. At Q draw a line QR perpendicular to PQ and of any convenient length.E. A short length is divided into a number of parts by using the principle of similar triangles in which like sides are proportional. etc. yards. Thus 1-1 represents 1/10 PQ.. Scale of chords Plain scale: A plain scale is one in which it is possible to measure two dimensions only. This type of sale is called engineer‘s scale.2. etc.I. Representative Fraction one unit of length on the plan represents some number of same units of length on the ground. 2-2 represents 2/10 PQ ……. Join the diagonal PR. it is possible to measure three dimensions such as metres. such as 1cm=10cm etc. (2) Choose as small as scale as is consistent with a clear declination of the smallest details to be plotted. 3 etc. 2. decimeters and centimeters. it will not be necessary to read the scale closer than 0. the use to which the map will be put & 2. 1. units. tenths and hundredths. 4. 1..MUKKANNAN M. thus dividing the diagonal into 10 equal parts. such as units and lengths. Vernier scale 4. the extent of territory to be represented The following 2 rules should be followed: (1) Choose a scale large enough so that in plotting or in scaling distance from the finished map. Diagonal scale: on a diagonal scale. meters and decimeters. Diagonal scale 3... This ratio of map distance to the corresponding ground distance is independent of units of measurement and is called representative fraction. DEPARTMENT OF CIVIL ENGINEERING Page 5 . miles & furlongs.E. In such case. 4. 3. 2. A. Retrograde vernier A retrograde vernier is the one which extends or increase in opposite direction as that of the main scale and in which the smallest division of the vernier is longer than the smallest division on the main scale. 5.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY Direct vernier A direct vernier is the one which extends or increase in the same direction as that of the main scale and in which the smallest division on the vernier is shorter than the smaller division on the main scale. Direct ranging is done when the two ends of the survey lines are intervisible. The diagonals of the two prisms are silvered so as to reflect the incidental rays.I. One ranging rod is erected at the point B while the surveyor stands with another ranging rod at point A holding the rod at about half metre length. c.E. To range a point P.. two ranging rods are fixed at the ends A &B. Indirect ranging Direct ranging a. till he is in line with A & B. The surveyor at A then signals the assistant to move transverse to the chain line. DEPARTMENT OF CIVIL ENGINEERING Page 6 . A handle with a hook is provided at the bottom to hold the instrument in hand to transfer the point on the ground wit the help of plumb-bob. RANGING BY LINE RANGER 1.MUKKANNAN M. Direct ranging b..M. the surveyor at P holds the line ranger very near to the line AB. The assistant then goes with another ranging rod and establishes the rod at a point approximately in the line with AB at a distance not greater than one chain length from A d. Two methods of ranging: a. b. The lower prism abc receives the rays from A which are reflected by the diagonal ac towards the observer. Let A & B be the two points at the ends of a survey line.E. ranging can either be done by eye or through some optical instrument such as a line ranger or a theodolite. RANGING AND CHAINING The process of fixing or establishing intermediate points is known as ranging. A. A line ranger consists of either two plane mirrors or two right angled isosceles prisms one above the other. AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY 6. (vi) similarly, the upper prism dbc receives the rays from B which are reflected by the diagonal bd towards the observer. Thus, the observer views the images of ranging rods at A & B. 7. the surveyor then moves the instrument sideways till the two images are in the same vertical line. 8. the point P is then transferred to the ground with the help of a plumb bob. Indirect or reciprocal ranging Indirect or reciprocal ranging is resorted to when boththe ends of the survey line are not intervisible either due to high intervening ground or due to long distance between them. In such case, ranging is done indirectly by selecting two intermediate points M1 and N1 very near to the chain line in such a way that from M1 both N1 are visible and from N1, both M1 and A are visible. 1. Two surveyors station themselves at M1 and N1 with ranging rods. The person at M1 then directs the person at N1 to move to a new position N2 in line with M1B. 2. The person at N2 then directs the person at M1 to move to a new position M2 in line N2A. Thus, the two persons are now at M2 and N2 which are nearer to the chain line than the positions M1 and N1. 3. The process is repeated till the points M and N are located in such a way that the person at M finds the person at N in line with MB, and the person at N finds the person at M in line with NA. 4. After having established M & N, other points can be fixed by direct ranging. CHAINING Two chainmen are required for measuring the length of a line which is greater than a chain length. Follower: The more experienced of the chainmen remains at the zero end or rear end of the chain and is called the follower. Leader: The other chainmen holding the forward handle is known as the leader. Unfolding the chain a. To unfold the chain, the chainmen keeps both the handles in the left hand and throws the rest of the portion of the chain in the forward direction with his right hand. b. The other chainmen assists in removing the knots etc. and in making the chain straight Lining and marking 1. The follower holds the zero end of the chain at the terminal point while the leader proceeds forward with the other end in one hand and a set of 10 arrows and a ranging rod in the other hand. 2. When he is approximately one chain length away, the follower directs him to fix his pole in line with the pole. A.MUKKANNAN M.E., A.M.I.E., DEPARTMENT OF CIVIL ENGINEERING Page 7 AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY 3. When the point is ranged, the leader makes a mark on the ground, holds the handle with both the hands and pulls the chain so that it becomes straight between the terminal point and the point fixed. 4. Little jerks given for his purpose but the pull applied must be just sufficient to make the chain straight in line. 5. The leader then puts an arrow at the end of the chain, swings the chain slightly out of the line and proceeds further with the handle in one hand and the rest of the arrows and ranging rod in the other hand. 6. the follower also takes the end handle in one hand and a ranging rod in the other hand, follows the leader till the leader has approximately traveled one chain length. 7. The follower puts the zero end of the chain at first arrow fixed by the leader, and ranges the leader who in turn, stretches the chain straight in the line & fixes the second arrow in the ground and proceeds the further. 8. The follower takes the first arrow and the ranging rod in one hand and the handle in the other & follows the leader. 9. At the end of ten chains, the leader calls for the ‗ arrows‘. 10. The follower takes out the tenth arrow from the ground, puts a ranging rod there & hands over ten arrows to the leader. 11. The transfer of ten ten arrows is recorded by the surveyor. 12. To measure the fractional length at the end of a line, the leader drags the chain beyond the end station, stretches it straight and tight the reads the links. CHAINING ON UNEVEN OR SLOPING GROUND Two methods a. Direct Method b. Indirect Method Direct method: 1. In the direct method the distance is measured in small horizontal stretches or steps. 2. for example to measure the distance between the 2 points A & B 3. The follower holds the zero end of the tape at A while the leader selects any suitable length l1of the tape and moves forward. The follower directs the leader for ranging. 4. The leader pulls the tape tight, makes it horizontal and the point 1 is then transferred to the ground by a plumb bob. 5. A special form of drop arrow is used to transfer the point to the surface. The procedure is then repeated. 6. The total length D of the line is then equal to (l1+l2+l3 ……). This method followed in case of irregular slopes. Indirect method: o Angle method A.MUKKANNAN M.E., A.M.I.E., DEPARTMENT OF CIVIL ENGINEERING Page 8 AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY  Let l1= measured inclined distance between AB and ɵ = slope of AB withhorizontal. The horizontal distance D1 is given by D1 = l 1cos ɵ1.  Similarly for BC, D2 = l 2cos ɵ2  The required horizontal distance between any two points= l cos ɵ  The slopes of the lines can be measured with the help of a clinometer.  A clinometer, in its simplest form essentially consists of a line of sight, a graduated arc, a light plumb bob with a long thread suspended at the centre.  A plumb is suspended from C, the central point. When the clinometer is horizontal, the thread touches the zero mark of the calibrated circle. To sight a point, the clinometer is tilted so that the line of sight AB may pass through the object. Since the thread still remains vertical, the reading against the thread gives the slope of the line of sight. 2. Difference in level measured 1) Sometimes, in the place of measuring the angle , the difference in the level between the points is measured with the help of a leveling instrument and the horizontal distance is computed. 2) Thus, if h is the difference in level, we have D= l2-h2 3. Hypotenusal Allowance 1) In this method, a correction is applied in the field at every chain length and at every point where the slope changes. 2) When the chain is stretched on the slope, the arrow is not put at the end of the chain but is placed in advance of the end, by an amount which allows for the slope correction. 3) BA‘ i s one chain length slope. The arrow is not put A‘ , the distance AA‘ being of such magnitude that the horizontal equivalent of BA is equal to 1 chain. TRAVERSING Traversing is that type of survey in which a number of connected survey lines form the framework and the directions and lengths of the survey lines are measured with the help of an angle measuring instrument and a tape respectively. Method of traversing: 1. Chain traversing 2. Chain and compass traversing 3. Transit tape traversing: (a) By fast needle method (b) By measurement of angles between the lines 4. Plane-table traversing Chain traversing 1. In this method the whole of the work is done with the chain and tape. No angle measuring instrument is used and the direction of the lines are fixed entirely by linear measurements. A.MUKKANNAN M.E., A.M.I.E., DEPARTMENT OF CIVIL ENGINEERING Page 9 A note on the plane also states that the 20m. This method is unsuitable for accurate work and is generally not used if an angle measuring instrument such as compass.The area of plane of an old survey platen to a scale of 10m = 1cm now measured as 19. The direction may also be fixed by external measurements such as at station B. 4. A.. 5. sextant. or theodolite is available..MUKKANNAN M.M. the direction AB and AD are fixed by internal measurements Aa1. (b) The tangent method The tangent method is a trigonometric method based upon the fact that in right angled triangle. The values of tan ɵ are taken from the table of natural tangents. prior to plotting. Chain used was 9cm short. distance between stations are laid off to scale and angles are plotted by one of the methods (1) By protractor (2) By the tangent of the angle (3) By the chord of the angle (a) The protractor method The use of the protractor in plotting direct angles.I. the length of the perpendicular being equal to basex tan ɵ. From the end of the base. This method is accurate one for plotting traverses or any other extensive system of horizontal control. the perpendicular =base x tanɵ where ɵ is the angle.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY 2. deflection angles. and a1d1. Find true area of the survey? SOLUTION: Measured Area = 19.5cm2 A. the co-ordinate method Angle & Distance method: In this method. Ad1. using the perpendicular as a base. 90 of it is plotted by erecting a perpendicular and the remainder by the tangent method. DEPARTMENT OF CIVIL ENGINEERING Page 10 . the line so obtained includes ɵ with the given side. Angles fixed by linear or tie measurements are known as chain angles. 3. Diameter of a good form of protractor is 10 to 60 cm. At A.E. PLOTTING Two principle methods of plotting are 1. PROBLEMS: 1. bearings and azimuths requires no explanation.5cm only.5cm2 as found by plane meter. The station point is joined to the point so obtained. The plan is found to have shrunk that a line originally 10cm long now measures 9. a perpendicular is set off. Co-ordinate method: Survey stations are plotted by calculating their co-ordinates. The biggest advantage in this method of plotting is that the closing error can be eliminated by balancing. The ordinary protractor is seldom divided more finely than 10‘ or 15‘ which accords with the accuracy of compass traversing but not of theodolite traversing.E. the angle & distance method 2. If the angle is little over 90 . 5/10)2 x 19.00 m = (30.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY Actual length of paper -> 10cm. A.85m LA = 30..E.5cm. = (9.9 m² 2.9 = 19.A field was measured using 30 m chain which was 15m too long. Later it was found that the chain is 15 cm too long calculate the true area.15 = 30.15 m LA = 30.A) M.cm.A) M. 1cm2 = 1 x 1cm.59 x 100 m² = 1759.cm = 17.8 m² Correction = 30 +0.A = 316.85 /30)² x Measured Area (M. Data: True area = (true length/ measured length) ² X measured area A = 320 m² LE = 30 – 0.8 = 1743. 99 m² 3.I.E. The area was calculated as 320m² after applying correction. Later it was found that the chain is 15 cm too short calculate the true area. Data: A = 320 m² LE = 30 + 0.8 True area = 319.15 m LA = 30.15 /30)² x Measured Area (M.8m² Area is field when measured with = 1759.M. DEPARTMENT OF CIVIL ENGINEERING Page 11 . The area was calculated as 320m² after applying correction.15 = 29.15 / 30)² x 316.8m² A chain (L) = 20m Error (L1) = 20 – 0.A = 323.91 / 20)² x 1759.00 m True area 320 m² = (29. Measured error length -> 9. = 10m x 10m = 100m2 2 17.91m True area = (19.00 m True area 320 m² = (30.A field was measured using 30 m chain which was 15m too short..MUKKANNAN M.15 = 30.59 cm2 Scale -> 10cm = 1.21m² A. True Area = (L1/L)2 x measured Area.5 = 17. The fare temperature cared. DEPARTMENT OF CIVIL ENGINEERING Page 12 .E. A. E = young‘s modulus 2.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY Correct = 30 -0.00 m = (29.21 True area = 319. True length = (L1/L) X Measured length Where L1 is corrected length of chain or tape L is observed length of chain or tape Correction for slope :The distance measured along the slope is always greater than the horizontal distance between the print. Correction for slope CSL = h2/2L Correction for slope CSL = L – D Cos θ = D /L D = L cos θ Correction for tension (or) pull :It the pull applied the tape during measurement is more than the standard pull at which the tape was standard is length increases take the distance measured becomes less than the actual. the distance is measured on the slope it must be immediately reduced to its corresponding horizontal distance. CP = (P – PO / AE) X L Were PO is standard pull P = pull applied during measurement A = Area of Cr s of tap. 99 m² Tape corrections that can be applied for the measured length: Corrections :Depending on the accuracy requires certain correction are to be made to the original measurements correction for Error in chain Length : Before using tape the axial length is ascertain by comparing with the std tape of known length.15 = 29.M. …. Hence correction for pull.. A correction will have to be applied to the measured length. If the axial tape button is not equal to the value.85 / 30)² x 323.. CT = α (Tm – To) L Tm is mean Temp during measurement To is Temp at which the tape is sodalist A.E.85 m LA = 30.1 x 105 N/m² for steel L is the tape length` Correction for Temp :The tape length changes due to changes with temperature while take a measurements.MUKKANNAN M.I.. E.5 x 10-6°c.8N.1 x 106 Kg/Cm2 A = 0.5 x 106 and E is of take 2.I. Calculate axial level between the ends it temperature during measurement is 25°c pull a the tape 100N and E=2.A.057775 + 0. A line was measured with a steel tape which exactly 30m at a temperature 20°c and pull of 10 Kg.11 x 105N /n2 Given: L = 30M Correction for temperature: CT = ∂ (Tm -To ) L A.MUKKANNAN M. A..1 x106) 1650 x 102 = 15.025 Cm² & = 40°c is 3. E = 2.215m 2. the measure length 1650 m. The three supports being at the same level. CSC = W² L1 / 24P² W = weight of tap P = pull apply in new tan‘s spans L1 = measurement length of tape between spans Sag correction will be always negative ie it has to be always subtracted from the measured length. 1.065cm² total weight 15. And the co-efficient expansion being 11.S. DEPARTMENT OF CIVIL ENGINEERING Page 13 . Sag Correction : When the tape is stretch between two points.05775 ms. The measured length is more than the actual length. temperature during measured 30°c and pull apply was 15 Kg.025 x 2. Given:Lt = 30 To = 20°c Tn =30°c Po = 10kg Pr = 15Kg Pm = 1650 ∂ = 3.00000122 m/oc for invar.M.5x10-6 x (30°c -20°c )1650 = 0.. It takes be form d catenae. CP = P – PO /AE x L = 15 – 10 /(0. of tape was 0. The tape its stretch on two support 30M append it‟s also supports in the tape.5 x 10-6 M/sec. Assure to a parabola considerately. tin the true length of live C. Ct= ∂ (Tm -To ) L = 3.E.157 kg/cm True length = 1650 + 0.025 Cm².157 = 1650.1 x 106 Kg/Cm².AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY α = co-efficient of thermal expansion α = 0.A steel tape is 30 m long between the end graduation 30m long between the at a temp 15°c when its horizontal and the ground when sectional area = 0.0000032 m/oc for steel = 0.71 kg/cm = 0. the leader holds the zero end of the tape at the point „P‟ to be located and the follower carry the tape box and swing the tape along the chain.065 x 271 x 105 x 30 = 0. During the adjustment of chain etc. In this method. the point or object is located by measurement of a distance and angle from a point on the chain line.00034M Sag Correction: C sag = (7. These errors may be caused due to. (ii) Bending of links.0034 + 0. A. bad starting and wrong lining. Compensating errors are proportional to the square route of length of the line. A. DEPARTMENT OF CIVIL ENGINEERING Page 14 .MUKKANNAN M.0039M Pull Correction: CP = (P – PO) / AE x L = 100 – 0 / 0. When temperature will churn measurement is different from temperature during calends. (i) Incorrect holding & marking of the arrows (ii) Incorrect plumbing while chaining on slopes. knot‘s.M.99 m Cumulative Error:These are errors.E. Perpendicular offset When the angle of offset is 90°. Offsets:An offset is the lateral distance of an object or ground feature measured from a survey line. (v) Bad range. By method of offsets. The position of the offset on the chain is located by the point where the arc is t a n g e n t i a l to the chain. (iii) Not applying slope correction to the length measured in the slopes. These are errors.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY = 11. Therefore the actual length can be found by separating the error from measure. which are liable to occur in the same direction and to accumulate. links removal of links.. (iv) Not applying temperature correction.9)2 x 15 / 24 x (1002) = 0. the it is called Perpendicular offset or simply offset. Compensative Error. which are liable to occur in both the direction and tend to compensate.0039 x 2 + 0.I.. These error may be caused an (i) The length of chain is shorted then the standard length. The length of the offset is the shortest distance from the object to the chain obtained by swinging the tape about the object as Centre.E.219 = 29.5x10-6 (25°c -15°c )30 = 0.219m True length = 30 – 0. one unit of length on the plan represents some number of same units of length on the ground.. DEPARTMENT OF CIVIL ENGINEERING Page 15 . A. etc. Ill conditioned Triangles:The triangles having angles less than 30° and more than 130° are known ill condition triangle. refraction and magnetic declination are called Natural Error. (ii) Chain and compass traversing(loose needle method) (iii) Transit Tape Traversing: (a) By fast needle method. it is called open traverse. Pantograph: Pantograph is an instrument used for reproducing . (i) Chain Traversing. Personal Error. humidity.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY Oblique offset when the angle is other than 90° then it is called an oblique offset Well conditioned Triangle:The triangles having internal angles between 30° & 130° are known as well condition triangle. Closed Traverse and Open Traverse: When the survey lines form a circuit which ends at the starting point. Representative Fraction (R. Lack of perfection in human sight. gravity.E. The improper adjustments of the plate level are called Instrumental Error... (b) By measurement of angles between the lines. (iv) Plane –table traversing. Imperfection in construction and adjustment of the instrument.I.E. A. It is based on the principle of similar triangles.M. such as 1/1000. the incorrect graduation. SOURCES OF ERRORS IN CHAIN SURVEYING: Instrumental Error The Error due to. If the circuit ends elsewhere. enlarging and reducing the maps. Well-conditioned Triangle:The triangles having internal angles between 30° & 130° are known as well condition triangle ILL conditioned Triangles:The triangles having angles less than 30° and more than 130° are known ill condition triangle. Methods of Traversing. is called Closed Traverse. This ratio of map distance to the corresponding ground distance is independent of units of measurement and is called Representative Fraction. Natural Error The Error due to Variations in Natural phenomena such as Temperature.MUKKANNAN M. The Error due to.F): If. Lack of perfection in and setting the instruments are called personal Error. 20M Slope is 14.5 (3) the differential elevation. DEPARTMENT OF CIVIL ENGINEERING Page 16 .5 tan θ = 0.17m θ = tan-1 0. (iv) Plane –table traversing.E.45 D = L – 2.M.55 A. If angle of slope 10° D = L cos θ = 250 cos 10° D = 246. A.22 = 12°24‘‘ CSL = h² /2L = 35² / 2x 250 = 2. If (1) Angle of slope 10° (2) slope is 14.5 tan θ = opp x d / adjust x d = 1 / 4.I..AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY Methods of Traversing: (i) Chain Traversing.54 = 244.45 = 247. (b) By measurement of angles between the lines. PROBLEM The distance P & Q measured along a slope is 250M fink horizontal distance between P.E. (ii) Chain and compass traversing(loose needle method) (iii) Transit Tape Traversing: (a) By fast needle method.22 D = 250 cos 12°..MUKKANNAN M. MUKKANNAN M. PRISMATIC COMPASS Prismatic compass is a instrument used to measure the bearing of a line.M. both being hinged to the box. This type of survey can be used to measure large areas with reasonable speed and accuracy. THE PRISMATIC COMPASS 1. therefore. so that bearing of the magnetic meridian is read as 0°. The object vane consists of a vertical hair attached to a suitable frame while the eye slit consists of a vertical slit cut into the upper assembly of the prism unit.E. DEPARTMENT OF CIVIL ENGINEERING Page 17 . DIP When a magnetic needle is suspended freely it always points north. 4. The 0°or 360° reading is. The included angle between magnetic north and true north is called dip or declination. When the line of sight is also in the magnetic meridian. The magnetic needle is attached to the circular ring or compass card made up of aluminum.magnetic substance. The area below the magnetic needle is graduated between 0 to 360 degrees. A. Due to certain factors magnetic needle may not point true north. 6.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY UNIT-2 COMPASS SYRVEYING AND PLANE TABLE SURVEYING COMPASS SURVEY The branch of surveying in which direction of survey line are determine by a compass and their length by a chain or tape is called compass surveying. When the needle is on the pivot it will orient itself in the magnetic meridian and. the N and S ends of the ring will be in this direction. engraved on the South end of the ring. A triangular prism is fitted below the eye slit having suitable arrangement for focusing to suit different eye sights. both attached to the compass box. The line of sight is defined by the objective vane and the eye slit. a non. A.. When an object is sighted. The instrument cover consists of a sighting vane and vertical hair to align the compass along the instrument station and the staff station. the sight vanes wilt rotate with respect to the NS end of ring through an angle which the line makes with the magnetic meridian. 7. Prismatic compass is the most convenient and portable of magnetic compass which can either be used as a hand instrument or can be fitted on a tripod. The prism has both horizontal and vertical faces convex. It consists of a magnetic needle pivoted at the center and is free to rotate.E. 3. The object vane presses against a bent lever which lifts the needle off the pivot and holds it against the glass lid. 8. it points at a direction away from north called magnetic north.. 2. so that a magnified image of the ring graduation is formed.I. 5. the South end ring comes vertically below the horizontal face of the prism. therefore. 9. Thus. cannot be straightened. A. The card is graduated in quadrant system having 0 at N and S ends and 90East and West ends. as was the case in the prismatic compass.. thus.a plane. 2. TEMPORARY ADJUSTMENTS Centering: Centering is the process of keeping the instrument exactly over the station. Bearing of a line is its direction relative to a given meridian. It.MUKKANNAN M. Focusing the Prism: The prism attachment is slided up or down for focusing till the readings are seen to be sharp and clear. passing that point and the north and south pt. it must in hand in such a way that graduated disc is swinging freely appears to be level as judged from the top edge of the ease. passes through the north and south. the graduated card or ring is not oriented in the magnetic meridian. intersects with surface of the earth. A. Taking when the line has a bearing of 90° in East direction. the object is to be sighted first with the object and eye vanes and the reading is then taken against the North end of the needle. BEARING. 11. The object vane is similar to that of prismatic compass. DEPARTMENT OF CIVIL ENGINEERING Page 18 . The edge bar needle freely floats over the pivot. Since no prism is provided.The sight vanes are generally not adjustable THE SURVEYOR‟S COMPASS The graduated ring is directly attached to the box and not with needle. When line of sight is in magnetic meridian. a light spring fitted inside the box can be brought into the contact with the edge of the graduated ring to damp the oscillations of the needle when about to take the reading. 2. In doing so. the pointer of the needle remains fixed in position while 0° N graduation of the card moves in a clockwise direction. The eye vane consists of a simple metal vane with a fine slit. Levelling: If the instrument is a hand instrument.I.. A meridian is any direction such as : · True meridian · Magnetic Meridian · Arbitrary Meridian. In order to sight the point B. Let us take the case of a line AB which is in NorthEast quadrant.M.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY 10.E. 1. The permanent adjustments of prismatic compass are almost the same as that of the surveyor‘s except that there are no bubble tubes to be adjusted and the needle. the pointer appears to move by 90 from the 0° N graduation in anti-clockwise direction. by looking vertically through the top glass. The meridian through a point is the line in which .E. the North and south ends of the needle will be over the 0° N and 0° S graduations. The greatest advantage of prismatic compass is that both sighting he object as well as reading circle can be done simultaneously without hanging the position of the eye. PERMANENT ADJUSTMENTS 1. The circle is read at the reading at which the hair line appears to cut the graduated ring. By pressing knob or break pin placed at the base of the object vane. the box will have to be rotated about the vertical axis. (1) True Meridian. R.=180 +R.E.= 180 -W.B. (2) Magnetic Meridian Magnetic meridian through a is the direction shown by a freely floating and balanced magnetic needle free from all other attractive forces..= 360 .B.B 270 & 360 “Add the measured clockwise angles to the bearing of the previous line.B. Magnetic Bearing The magnetic bearing of a line is the horizontal angle which it makes with the magnetic meridian passing through one of the extremities of the line.C.C.B= R. deduct 180°.MUKKANNAN M.B SE 180 & 270 R.B 0 & 90 W.C.B.B. the true bearing of a line is a constant quantity.= 180 . True bearing of a line is the horizontal angle which it makes with the true meridian through one of the extremities of the line. A.C.=W.B.B.B. INTO R.B.B.B.C.180 SW 270 & 360 R.I. 0 & 90 R. INTO W.C. Arbitrary meridian is any convenient direction towards a permanent and prominent mark or signal.B. such as a church spire or top of a chimney.C. CONVERSION OF W.R. If the sum is less than 180°. NW CONVERSION OF R. Arbitrary bearing Arbitrary bearing of a line is the horizontal angle which it makes with any arbitrary meridian passing through one of the extremities..B 90 & 180 W. DEPARTMENT OF CIVIL ENGINEERING Page 19 .=W.B NE 90 & 180 R. 180 & 270 W.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY True Bearing..C.C.E.M.= 360 -W.C. (3) Arbitrary Meridian.B. W. Since the direction of true meridian through a point remains fixed. add 180°” EXAMPLES ON ANGLES AND BEARINGS Example : (a) Convert the following whole circle to quadrantal bearings (i) 22°30‘ (ii) 170º 12‘ A.B. If the sum is more than 180. = 360° — R.= 180° + R. QUADRENTAL BEARING (QB ) These are bearings of lines from north or south towards east or west.B.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY (iii) 211°54‘ (iv) 327°24‘ .B.C.M. WHOLE CIRCLE BEARING (WCB) In this method bearings of lines are observed from magnetic north and are observed directly from the prismatic compass.E. B.C.B.= 180° + 68° 6‘ = 248º 6‘ (iv)W.B.= W.B.MUKKANNAN M.= W.170 12‘=S 9° 48‘ E (iii) R. If the magnetic meridian is to the right side (or eastern side) of the true meridian. if it to be the left side (or western side). (b) Convert the following quadrantal bearing to whole circle bearings (i) N12°24‘E (ii) S31°36‘ E (iii) S 68 6‘W (iv) N5°42‘W Referring to fig above and tables given: (i) R.CB =22°30‘=N22°30‘E (ii) R. C.= 360° —W.=360° —327° 24‘ =N 32° 36‘ W (i)WCB= RB=12°24‘ (ii) WCB = 180° — RB = 180° — 31° 36‘ =148º 24‘ (iii)W. B.B.E.. the declination is said to be western or negative. =180° ..B.= 180° —W. C. = 360° — 5°42‘ = 354°18‘ EARTH‟ S MAGNETIC FIELD AND DIP The horizontal projections of the lines of force define the magnetic meridian. It can be used to tie topography by existing control and to carry its own control systems by triangulation or traverse and by lines of levels. — 180°=211° 54—180 °=S 31° 54‘W (iv) R.C.B. It is means of making a manuscript map in the field while the ground can be seen by the topographer and without intermediate steps of recording and transcribing field Notes.I. Plane Table Surveying Definition Plane tabling is a graphical method of survey in which the field observations and plotting proceed simultaneously. The angle which these lines of force make with the surface of the earth is called the angle of dip or simply the dip of the needle. DEPARTMENT OF CIVIL ENGINEERING Page 20 .B. A. A. declination is said to be eastern or positive. MAGNETIC DECLINATION Magnetic declination at a place is the horizontal angle bet the true meridian and the magnetic meridian shown by the ne at the time of observation. These values are usually reduced from observed whole circle bearing for the ease of calculation of included angles and plotting. f. A.M.I. d. The table is levelled by adjusting tripod legs.E.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY Instruments used The following instruments are used in plane table survey a.E. Alidade A plane table alidade is a straight edge with some form of sighting device.MUKKANNAN M. The head consists of a ball-and-socket joint and a vertical spindle with two thumb screws on the underside. A. Johnson Table This consists of a drawing board usually 45x60cm or 60x75 cm. o The two vanes or sight are hinged to fold down on the rule when the alidade is not in use. e. The levelling of the table is done very accurately with the help of the three foot screws. the table may be rotated about the vertical axis and can thus be oriented. Plumbing fork and plumb bob. the table may be tilted about the ball-and socket for levelling. Two types are used: (i) Plain alidade (ii) Telescopic alidade. Plain Alidade. The Coast Survey Table The table is superior to the above two types and is generally used for work of high precision. DEPARTMENT OF CIVIL ENGINEERING Page 21 . usually by eye-estimation. (b) rotation about vertical axis. The clamp is then tightened to fix the board in a horizontal position. Drawing paper with a rainproof cover. Spirit level. b. The table can be turned about the vertical axis and can be fixed in any direction very accurately with the help of a clamp and tangent screw. Alidade for sighting c. When the lower screw is loosened. The plane table with levelling head having arrangements for (a) levelling.. When the upper screw is free. The Plane Table Three distinct types of tables having devices for levelling the plane table and controlling its Orientation are in common use: Traverse Table The traverse table consists of a small drawing board mounted on a light tripod in such a way that the board can be rotated about the vertical axis and can be clamped in any position. o It generally consists of a metal or wooden rule with two vanes at the ends. 2. The balland-socket joint is operated by the upper thumb screw.. o It is used for ordinary work. and (c) clamping in any required position. Compass. o The elevation of the point can also be computed by using usual tacheometric relations. Both the slits thus provide a definite line of sight which can be made to pass through the object to be sighted.I. o The horizontal axis rests on a A-frame fitted with vernier fixed in position in the same manner as that in a transit.E.MUKKANNAN M. one side of which is used as the working edge along which line may be drawn.. is meant for centring the table over the point or station occupied by the plane table when the plotted position of that point is already known on the sheet. o Thus. o It essentially consists of a small telescope with a level tube and graduated arc mounted on horizontal axis. o Also the accuracy and range of sights are increased by its use. o It is essential to have the vanes perpendicular be the surface of the sheet.. A. o The alidade can be rotated about the point representing the instrument station on the sheet so that the line of sigh passes through the object to be sighted. A. o The telescopic alidade is used when it is required to take in lined sights. Telescopic Alidade.E. The inclination of the line of sight can be read on the vertical circle. o The horizontal distance between the instrument and the point sighted can be computed by taking stadia readings on the staff kept at the point. to facilitate calculation work. o A string joining the tops of the two vanes is sometimes provided to use it when sights of considerable inclination have to be taken. o In the beginning of the work it is meant for transferring the ground point on to the sheet so that the plotted point and the ground station are in the same vertical line. o Sometimes. o The same geometric principle apply to the alidade as to the transit. o All the parts are finally supported on a heavy rule. o A line is then drawn against the working edge (known as the fiducial edge) of the alidade. the observer can very quickly and easily obtain the true horizontal distance from the plane table to a levelling staff placed at the point and the difference in elevation between them.M. Plumbing Fork o The plumbing fork is used in large scale work. 3. but the adjustments are somewhat modified in accordance with the lower degree of accuracy required. DEPARTMENT OF CIVIL ENGINEERING Page 22 . o The alidade is not very much suitable on hilly area since the inclination of the line of sight is limited.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY o One of the vanes is provided with a narrow slit while the other is open and carries a hair or thin wire. a Beaman stadia are may be provided as an extra. 5.E. o For work of accuracy. Spirit Level o A small spirit level may be used for ascertaining if the table is properly level. DEPARTMENT OF CIVIL ENGINEERING Page 23 . 6. o For work of high precision. o The fitting can be placed with the upper arm lying on the top of the table and the lower arm below it.M. o To overcome this difficulty. o Single sheet must be seasoned previous of the use by exposing it alternatively to a damp and a dry atmosphere. fibre glass sheets or paper backed with sheet aluminium are often used. Drawing Paper o The drawing paper used for plane tabling must be of superior quality so that it may have minimum effect of changes in the humidity of the atmosphere. an ordinary spirit level may be used. A.E. o The compass used with a plane table is a trough compass o In which the longer sides of the trough are parallel and flat so that either side can be used as a ruler or laid down to coincide with a straight line drawn on the paper. 4.  sighting the points Levelling o For small-scale work. o The table is levelled by placing the level on the board in two positions at right angles and getting the bubble central in both positions. levelling is done by estimation.  Setting : (i)Levelling the table (ii)Centring (iii)Orientation. Compass o The compass is used for orienting the plane table to magnetic north. sometimes two sheets are mounted with their grains at right angles and with a sheet of muslin between them. o The table being centred when the plumb-bob hangs freely over the ground mark and the pointed end of the upper arm coincides with the equivalent point on the plan. in which a plumb-bob is suspended from the end of the lower-arm. essentially with a flat base so that it can be laid on the table and is truly level when the bubble is central. A. o The changes in the humidity of the atmosphere produce expansion and contraction in different directions and thus alter the scale and distort the map..MUKKANNAN M..AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY o The fork consists of a hair pin-shaped light metal frame having arms of equal length. AJUSTMENTS OF COMPASS Three operations are needed  Fixing : Fixing the table to the tripod. o The level may be either of the tubular variety or of the circular type.I. The processes of centring and orientation are dependent on each other. (ii) Orientation by back sighting Orientation can be done precisely by sighting the points already plotted on the sheet. A. Two cases may arise (a) When it is possible to set the plane table on the point already plotted on the sheet by way of observation from previous station.M. (b) When it is not possible to set the plane table on the point.I.E. If precise work requires that the plotted point should be exactly over the ground point.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY o The table is levelled by placing the level on the board in two positions at right angles and getting the bubble central in both directions. the table will have to be rotated about its vertical axis. 4.. thus disturbing the centring. 2. If orientation is not done. Intersection. Orientation by means of back sighting (i) Orientation by trough compass The plane table can be oriented by compass under the following conditions (a) ) When speed is more important that accuracy. Orientation by means of trough compass. Radiation. (d) For approximate orientation prior to final adjustment (e) In certain resection problems. the table will not be parallel to itself at different positions resulting in an overall distortion of the map. (b) When there is no second point available for orientation. o For more precise work..MUKKANNAN M. There are two main methods of orienting the plane table 1. METHODS OF PLANE TABLING Methods of plane tabling can be divided into four distinct 1. Centring The table should be so placed over the station on the ground that the point plotted on the sheet corresponding to the station occupied should be exactly over the station on the ground. (c) When the traverse is so long that accumulated errors in carrying the azimuth forward might be greater than orientation by compass. A. repeated orientation and shifting of the whole table are necessary. Orientation Orientation is the process of putting the plane-table into some fixed direction so that line representing a certain direction on the plane is parallel to that direction on the ground. For orientation. Traversing. 3. The operation is known as centring the plane table. 2. DEPARTMENT OF CIVIL ENGINEERING Page 24 .E. a Johnson Table or Coast Survey Table may be used. Resection. level it and transfer the point on to the sheet by means of plumbing fork. sight the details C. table stations. The distance between the two instrument stations is measured and plotted on the sheet to some scale.I. the distance is measured between the instrument station and that point. level it and transfer the point A on to the sheet by way of plumbing fork. D. No linear measurement other. in the field and plot their distances to some scale along the corresponding rays. The method has a wider scope if the distances are obtained tacheometrically with the help of telescopic alidade. a ray is drawn from the instrument station towards the point. and draw the corresponding rays along the edge of the alidade to intersect with the previously drawn rays in c. mark the north direction on the sheet. Similarly. 3. TE etc. TC. INTERSECTION (GRAPHIC TRIANGULATION) Intersection is resorted to when the distance between the point and the instrument station is either too large or cannot be measure accurately due to some field conditions. and draw the corresponding rays.. Evidently. E etc.M. and draw corresponding rays. E etc. Due to this reason. and the point is located by plotting to some scale the distance so measured. than that of the base line is made. The point of intersectior of the two rays forms the vertex of a triangle having the two rays as two sides and the base line as the third line of the triangle. The intersection of these rays will give the position of the object. RADIATION In this method. Clamp the table. e etc. sight it to B. (2) With the help of the trough compass.E. d. Set the table at T. (3) Pivoting the alidade about a. The positions of the points are thus mapped by way of intersection. D.. It is therefore very essential to have at least two instrument stations to locate any point. (4) Pivoting the alidade about a.. DEPARTMENT OF CIVIL ENGINEERING Page 25 .MUKKANNAN M. D. TD.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY The first two methods are generally employed for locating the details while the other two methods are used for locating the plane table stations. Draw the ray along the fiducial edge of the alidade. Clamp the table. (5) Shift the table at B and set it there. 2. intersection is also sometimes known as graphic triangulation. Join these if needed. Measure AB and plot it along the ray to get b. Measure TA. The following steps are necessary to an instrument station to locate the points from an instrument station: 1. d. A. thus getting a.E. Orient the table roughly by compass and finally by back sighting A. TB. sight the details C. The base line ab is thus drawn.. thus getting point t representing T. Procedure The following is the procedure to locate the points by the method of intersection: (1) Set the table at A. Keep the alidade touching t and sight to A. sight different points B. A. E etc. The line joining the two instrument stations is known as the base line. b. (6) Pivoting the alidade about b. C. the method is more suitable when the distances are small and one single instrument can control the points to be detailed. e etc. The location of an object is determined by sighting at the object from two plane table stations and drawing the rays. c. E. A. draw a resector (ray) towards A. Resection after orientation by backsighting If the table can be oriented by backsighting along a previously plotted backsight line. DEPARTMENT OF CIVIL ENGINEERING Page 26 . Resection after orientation by compass The method is utilized only for small-scale or rough mapping for which the relatively large errors due to orienting with the compass needle would not impair the usefulness of the map. the required point. (1) Let C be the instrument station to be located on the plan.. (iv) Resection after orientation by two-point problem. The only difference is that in the case of radiation the observations are taken to those points which are to be detailed or mapped while in the case of traversing the observations are made to those points which will sub sequently be used as instrument stations. Procedure. sight to C.I. sight it to B and draw the ray. similarly.MUKKANNAN M. Similarly draw a ray towards E. Draw the direction of magnetic meridian with the help of trough compass. Measure BC and plot it on the drawn ray to the same scale. (3) Shift the table to B and set it. RESECTION Resection is the process of determining the plotted position of the station occupied by the plane table. (2) With the alidade pivoted about a. Clamp the table. (2) Pivoting the alidade about a. Clamp the table. Orient the table accurately back sighting A. A. The following are the four methods of orientation: (i) Resection after orientation by compass. the required point. Use plumbing fork for transferring A on to the sheet. (ii) Resection after orientation by back sighting.M. Measure AB and scale off ab to some scale. (1) Set the table at A. the table will have to be set on at least (n — 1) stations to know the error of closure though the traverse may be closed even by setting it on (n — 2) stations. sight B from b and draw a resector.. Let A and B be two visible stations which have been plotted on the sheet as a and b. (5) It is to be noted here that the orientation is to be done by back sighting (6) If there are n stations in a closed traverse. Similarly. the station can be located by the intersection of the backsight line and the resector drawn through another known point. (iii) Resection after orientation by three-point problem. by means of sights taken towards known points. measure AE and plot e. The intersection of the two resectors will give c. the table can be set at other stations and the traverse is completed. (4) Pivoting the alidade about b. locations of which have been plotted. Set the table at C and orient it with compass.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY TRAVERSING Plane table traverse involves the same principles as a transit traverse. of the two resectors will give c.E. the data must consist of either (a) Three visible points and their plotted positions (The three.E. it is necessary to set the table on one of the known points and draw the ray towards the station to be located. sight C and draw a ray. Keep the alidade on the line c1 a and orient the table by back-sight to A. Clamp the table which has been oriented. o Let P be the instrument station and A. (4) Pivoting the alidade about b.I. B. of the station occupied by the plane table by means of observations to three well-defined points whose positions have been previously plotted on the plan o In other words.. b and c meet at a point and not in a triangle. orientation and resection are accomplished in the same operation.fore. DEPARTMENT OF CIVIL ENGINEERING Page 27 . THE THREE-POINT PROBLEM Statement: Location of the position. Set the table at A and orient it by backsighting B along ab. A. are inevitable. the first method is rarely used as the errors due to local attraction etc.point problem). Thus. (2) Pivoting the alidade at a. o The intersection of the three resectors in a point gives the location of the instrument station. MECHANICAL METHOD (TRACING PAPER METHOD) The method involves the use of a tracing paper and is. c is the location of the instrument station. there. A. The following are some of the important methods available for the solution of the problem (a) ) Mechanical Method (Tracing Paper Method) (b) Graphical Method (c) Lehmann‘ s Method (Trial and Error Method) 1. sight B and draw the resector bB to intersect the ray C1a in c.MUKKANNAN M. in three-point problem. In the second method. In the more usual case in which no such ray has been drawn. also known as tracing paper method. c respectively on the plan. on the plan. it is required to orient the table at the station with respect to three visible points already located on the plan. Estimate roughly the position of C on this ray as c1 (3) Shift the table to C and centre it approximately with respect to c.M...E. o Thus.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY (1) Let C be the station to be located on the plan and A and B be two visible points which have been plotted on the sheet as a and b. Resection by Three-point Problem and Two-point Problem Of the two methods described above. o The table is said to be correctly oriented at P when the three resectors through a. b. C be the points which are located as a. (b) Two visible points and their plotted positions (The two point problem). To correct the orientation. A. sight to C. Bessel‟ s Graphical Solution (1) After having set the table at station P. Similarly. the line of sight will pass through C when the alidade is kept on pc. Clamp the table.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY Procedure Let A. L P be the position of the instrument station to be located on the map. The points a. The table is thus oriented. (4) Pivoting the alidade about a. Draw the ray along the edge of the alidade to intersect the ray xy in c‘ Join cc‘ (5) Keep the alidade along C‘ C and rotate the table till C is bisected. sight A. The table is correctly oriented. Clamp the table. The line of sight will not pass through A as the orientation has not yet been corrected.E. keep the alidade on ba and rotate the table so that A is bisected. c and p form a quadrilateral and all the four points lie along the circumference of a circle. C be the known points and a. sight to C and draw the ray xy along the edge of the alidade .I.MUKKANNAN M. Clamp the table. (2) Pivoting the alidade about b. (3) Keep the alidade along ab and rotate the table till B is bisected. If the orientation is correct. p‘ b‘ and p‘ c‘ on the tracing paper. the line of sight will pass through B. and c as the orientation is approximate. (6) Pivoting the alidade about b. Clamp the table. Draw the ray. b.. but the method given by Bessel is more suitable and is described first. Hence. Similarly. draw rays from b and c towards B and C respectively.M. if alidade is pivoted about a and A is sighted. GRAPHICAL METHODS There are several graphical methods available. Transfer p‘ on to the sheet and represent it as p. LEHMANN‟S METHOD Procedure: (1) Set the table at P and orient the table approximately so that ab is parallel to AB. c be their plotted positions. keep the alidade along pb. These lines will not pass through a. (3) Pivoting the alidade at p‘ . the ray will pass through p if the work is accurate. (2) Fix a tracing paper on the sheet and mark on it p‘ as the approximate location of P with the help of plumbing fork. b. b and c respectively. C in turn and draw the corresponding lines p‘ a‘. Similarly. (5) Keep the alidade on pa. (1) Set the table on P. B. loose the clamp and rotate the plane table so that the line of sight pass through A. they will meet in three points forming one small triangle of error. If not. B. 2. Orient the table approximately with eye so that ab is parallel to AB. (2) Keep the alidade pivoted about a and sight A. (6) To test the orientation. Draw the ray to intersect cc‘ in p . DEPARTMENT OF CIVIL ENGINEERING Page 28 . b. If the orientation is correct. p‘ b‘ and p‘ c‘ pass through a. Remove the tracing paper and join pa. this method is known as ― Bessel‘s Method of Inscribed Quadrilateral‖.E. A. pb and pc.. Clamp the table. the three rays will meet at one point. (4) Loose the tracing paper and rotate it on the drawing paper in such a way that the lines p‘ a‘. sight to B. by successive trial and error.E.E. The lines joining A. This will give next approximate orientation (but more accurate than the previous one). Draw the ray to intersect with the ray drawn from D to B in b‘ . to assist the orientation at C. Similarly. the circle passing through A. The whole problem is to orient the table at C. In order that ab and ab‘ may coincide (or may become parallel) keep a pole P in line wih ab‘ and at a A. C or (a. (5) Keep the alidade at b to sight B and draw the ray. Set the table at D in such a way that ab is approximately parallel to AR (either by compass or by eye judgment). (7)The angle between ab and ab‘ is the error in orientation and must be corrected for. sight B. of the station occupied by the plane table by means of observation to two well defined points whose position have been previously plotted on the plan. Transfer the point d to the ground and drive a peg.. (3)Keep the alidade at d and sight C. (4) Keep the alidade along p‘ a and rotate the table to sight A. b. Draw the resector.. A. Thus. orient it (tentatively) by taking backsight to D and centre it with reference to c The orientation is. the degree of accuracy of which depends upon the approximation that has been made in keeping at‘ parallel to AR. the triangle of error can be reduced to a point. b. the same as it was at D. The whole problem.M. c) form a triangle known as the Great Triangle. Similarly. Mark a point c on the ray by estimation to represent the distance DC. To do this. the plotted positions of which are known. Draw the ray to intersect with the previously drawn ray from D in c. c) is known as the Great Circle.MUKKANNAN M. Draw the ray. (4) Shift the table to C. with reference to the approximate orientation made at D. choose the point p‘ as shown. the size of which will be smaller than the previous triangle of error. keep the alidade at c and sight C. (5)Keep the alidade pivoted at a and sight it to A. Clamp the table. giving the point p. Bb and Cc meet in one single point. The final and correct position of the table will be such that the rays Aa. Let C be the point to be plotted. Thus b‘ is the approximate representation of B with respect to the orientation made at D. Draw the ray. c is the point representing the station C. Clamp the table. draw a resector from b and B to intersect the previous one in c The position of d is thus got. thus. C (or a. (6)Pivoting the alidade about c. B.I. The orientation will be correct only when the triangle of error is reduced to one point. involves a fair knowledge of Lehmann‘ s Rules for the approximate fixation of p‘ so that the triangle of error may be reduced to a minimum. These rays will again meet in one triangle. if p‘ has been chosen judiciously keeping in the view the Lehmann‘ s Rules. The approximate choice of the position may be done with the help of Lehmann‘ s Rules described later.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY (3) The triangle of error so formed will give the idea for the further orientation. Procedure (1) Choose an auxiliary point D near C. DEPARTMENT OF CIVIL ENGINEERING Page 29 .‖ Let us take two points A and B. (2) Keep the alidade at a and sight A. TWO-POINT PROBLEM Statement: Location of the position on the plan. B. (6) Thus. thus. Similarly. . (b) Defective sighting The accuracy of plane table mapping depends largely upon the precision with which points are sighted. (e) Inaccurate centring It is very essential to have a proper conception of the extent of error introduced by inaccurate centring. Keeping the alidade along ab. DEPARTMENT OF CIVIL ENGINEERING Page 30 .MUKKANNAN M. Error due to manipulation and sighting. (c) Defective orientation Orientation done with compass is unreliable. Instrumental Errors : Errors due to bad quality of the in strument. ERRORS IN PLANE TABLING The degree of precision to be attained in plane tabling depends upon the character of the survey.E. To reduce the possibility of such movement. 2. These include (a) Non-horizontality of board. as there is every possibility of local attraction. This orientation should be checked at as many stations as possible by sighting distant prominent objects already plotted. draw a resector from a to A and another from b to B. Clamp the table. the quality of the instrument. the intersection of which will give the position C occupied by the table. the clamp should be firmly applied. The plain alidade with open sight is much inferior to the telescopic alidade in the definition of the line of sight. (d) Movement of board between sights Due to carelessness of the observer.M.E.. The various sources of errors may be classified as 1.I. (d) Movement of board between sights. if telescopic alidade is used. the system adopted and upon the degree to which accuracy is deliberately sacrificed for speed.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY great distance. (8) After having oriented the table as above. as it avoids unnecessary waste of time in setting up the table by repeated trials. (a) Non-horizontality of board The effect of non-horizontality of board is more severe when the difference in elevation between the points sighted is more. Errors of plotting. rotate the table till P is bisected. It is always advisable to check the orientation at the end of the observation from a station. This includes all errors described for theodolite. (b) Defective sighting. (c) ) Defective orientation. the table may be disturbed between any two sights resulting in the disturbance of orientation. The table is thus correctly oriented. Erroneous orientation contribute to wards distortion of the survey. A. 3. A. (e) ) Defective or inaccurate centring. SDA 260° 290° 30‘ 110° 10‘ BC => 130° 30‘ ~ 311° 35‘ = 181° 5‘ DA => 290° 30‘ ~ 110° 10‘ = 180° 20‘ Magnetic error 1° 30‘ w 9. BC 130° 30‘ 311° 35‘ 3. BC 3. Both the bearings expressed in whole circle bearing deter each other by 180°. DEPARTMENT OF CIVIL ENGINEERING Page 31 . A. Station F. AB 2.79° 15‘ = 29° 25‘ B = 258° 30‘ . CD 4.. Compute the included angles. PROBLEMS Compute magnetic declination for the following observations.I.E.129° =129° 30‘ C = 310° 5‘ .No. Station 1. S.M.E. AB => 260° . AB 80° 45‘ 2.B 1.MUKKANNAN M. CD 240° 15‘ 60° 15‘ 4.289° = 129° 45‘ Sum of included angles = 360° A.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY Fore and Back bearing: A line may be expressed by two bearings observed from the either end of the line.B B.No. The bearing of the line in the direction of progress of survey is called fore or Forward bearing while the bearing opposite to the direction of the progress of survey is known as reverse of Back bearing.. DA = 179° 15‘ Fore bearing Back bearing Inc Angle 258° 30‘ 29° 25‘ 310° 5‘ 129° 30‘ 79° 15‘ 129° 238° 45‘ 58° 45‘ 108° 40‘ 289° 71° 20‘ 129° 45‘ A = 108° 40‘ .238° 45‘ = 71° 20 D = ( 360° +58° 45‘) .80° 45‘ S. and a graduated leveling staff provides the vertical height of a station with reference to the level line..I. SPECIAL TERM AND THEIR ABBREVIATIONS USED IN LEVELING INSTRUMENT STATION:A point where instrument is set up for observations is called instrument station. Sources of errors in leveling Errors in leveling may be categorized into  Personal error  Errors due to natural factors and  Instrumental error PRINCIPLE OF LEVELLING:The principle of level lies in furnishing a horizontal line of sight and finds the vertical distance of the points above or below the line of site. A line of sight is provided with a level. DEPARTMENT OF CIVIL ENGINEERING Page 32 .E. (i) Centering of bubble to align the line of sight horizontal using foot screws. By setting the level midway the error due to the curvature and refraction and also the collimation error is eliminated.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY UNIT – III LEVELLING LEVELLING The principle of level lies in furnishing a horizontal line of sight and finds the vertical distance of the points above or below the line of site.E. and a graduated leveling staff provides the vertical height of a station with reference to the level line.MUKKANNAN M. A line of sight is provided with a level.M. (ii) Focusing of telescope to a distant object (iii) Adjustment of eye piece to have a clear view of the cross hairs Reciprocal leveling A method of differential leveling is based on the fact the instrument kept equidistant from the back and forward station. A. The difference in elevation of two stations is equal to the difference of the staff readings. A. TEMPORARY ADJUSTMENTS OF A LEVEL Temporary adjustments are done before the beginning of the survey and after each shifting of the instrument.. This should be checked often since slight disturbance of the instrument affects the line of sight to a large extent. M. It ascertains the amount by which the line of sight is above or below the elevation of the point.MUKKANNAN M. ADJUSTMENT OF LEVEL:A leveling instrument needs two types of adjustment.. FORE SIGHT (F. Back site enable the surveyor to obtain the height of instrument.S) A first site taken on a level staff held at position of known elevation is called back site. A.S) The site on a level staff held at a point of unknown elevation to ascertain by what extent the point is above or below the line of site is called fore site. The change point is always selected on a relatively permanent point.S taken on a level staff held at points between two turning points to determine the elevation of points is known as intermediate sight. It does not mean the height of telescope above the ground level were the level is setup. DEPARTMENT OF CIVIL ENGINEERING Page 33 . Sights are taken from two different instrument station a fore sight ascertains the elevation of point to establish the height of instrument at the new instrument station.P): The point at which both a fore sight and back sight are taken during the operation of levelling is called a change point.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY HEIGHT OF INSTRUMENT (Hi) The elevation of line of site with respect to assumed datum is known as height of instrument. (i) Centering of bubble to align the line of sight horizontal using foot screws.I.E. CHANGE POINT OR TURNING POINT (C. A.P OR T. It may be noted that for one setting of the level there will be only a back sight and fore sight but there can be a number of intermediate sights. BACK SIGHT (B. This should be checked often since slight disturbance of the instrument affects the line of sight to a large extent. Fore site enables surveyor to obtain the elevation of the point.. (1) Temporary adjustment (2) Permanent adjustment Temporary adjustments are done before the beginning of the survey and after each shifting of the instrument. INTERMEDIATE SIGHT:The F.E. 0..570 – 9.330 2.600 RECIPROCAL LEVELLING: A method of differential leveling is based on the fact the instrument kept equidistant from the back and forward station.430 81. 0. Station A B C D E F G H I J K L SUM B.E.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY (ii) Focusing of telescope to a distant object (iii) Adjustment of eye piece to have a clear view of the cross hairs Permanent adjustments include orientation of bubble tube axis parallel to line of sight of the telescope.455 74.C 81.400 76. 1. A.400 R.680.430 81.530 2. 3.750m rule out a page of level book an enter above readings carry out reduction of height by collimation method and apply arithmetic checks.S F.330. A.455. The difference in elevation of two stations is equal to the difference of the staff readings.570 H.6. 1.100 78.975 79.430 79.105 79.600 = . this ensures that if the bubble tube is centered the line of sight is perfectly horizontal.L of starting point was 80.105 79.860 2. DEPARTMENT OF CIVIL ENGINEERING Page 34 .870 74.750 79.S 1.860.250 9.150 – 80.945 1.170 = 74.250 The R.855.855. 2.575 79.400 76.430 81.840 75.855 2.540. 1. 2.565 75.430 81.170 2.265 0.855 1.835.055 3.050 77.380. A following readings are taken with the level with a 4m leveling staff on a continuously slope ground at 30m interval.M.575 78.945.455 1. 0.245 76.380 1.6.835 3. Determine gradient of the line joining 1st and last point. 1. 2.680 I.265.E.105 76.L 80.430 81.150 Arithmetic check BS - FS = RL of last point – RL of first point 2.055.S 0..750 .540 0.I. 1.530 & 2. 3.MUKKANNAN M. take reading on the staff held at A & B. (ii) Let the staff readings are A & B be a1 and b1. When it is not possible to set up the level midway between two points as in the case of leveling across large water bodies the reciprocal leveling is employed to carry forward a levels on the other side of the obstruction. A true difference in elevation between A & B is equal to the mean of the two apparent difference of levels.I. A.E. (iii) Transfer instrument to B and set it very near to B when the bubble is centered observe the readings at A & B as a2 and b2.m 2 H = Different in elevation. Let A & B be two points on opposite banks of the lake the differents of level of A & B may be determine as follows: (i) Set up the level very near to A Keeping the bubble of the level tube centre . DEPARTMENT OF CIVIL ENGINEERING Page 35 . PROCEDURE: (b1 – a1) + (b2 – a2) h = ----------------------------.0785d² A.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY By setting the level midway the error due to the curvature and refraction and also the collimation error is eliminated. CC = 0. Difference in elevation between A and B is (b1 – a1) + (b2 + a2) h = ----------------------------2 CURVATURE CORRECTION:A line of sight is the straight line Assumed to be free from effect of curvature a level live is a curve line having its concave surface towards the earth. A pencil may be pointed on the staff till it is see through the telescope a connect reading is noted.E...MUKKANNAN M. Due to curvature of the earth reading taken on a leveling staff held vertically is always more than what these would have been if the earth has a plan surface.M.Readings as A is usually taken through the objective as a field of view is very small. The points so obtained are joining to get the desired sectional elevation. A convenient scale is assumed and the difference of elevation of each point and the datum are plotted along the perpendicular. atmospheric condition also cause on error in sighting. In order to minimize the error due to the curvature of line of sight a correction is applied. It may be noted that the elevation of cross datum lines for different section may be different to have the ordinates fairly short.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY REFRACTION CORRECTION As line sight passes through the atmosphere it passes through regions of different density.Instrumental error PERSONAL ERROR:Personal error include the following (i) Error in sighting: This is caused when it is difficult to see the exact coincide of the crosshairs and the staff graduation. The error is more for long sights & less for short sights. To avoid the error the observer should develop the habit of checking the bubble before and after taking reading. This error is accidental and may be classified as compensative. (ii) Error in manipulation:- This is due to careless setting up of the level neither the telescope nor the tripod should be disturbed while taking readings. In the sectioning profile a Horizontal & vertical scales are generally kept the same. This may be either due to long sights or due to poor focusing of the crosshair.E.M. ERRORS IN LEVELLING:Errors in leveling may be categorized into 1.I. If the bubble is not centered a Horizontal axis telescope gets inclined affecting the staff readings. Errors due to natural factors 3.E. The corrector of refraction is always add to the staff reading. A. A. Take care that the bubble is centre when the readings are observed. This causes the line of sight to bend instead of traveling straight.MUKKANNAN M... The instrument should be set up on a firm ground and carefully leveled. DEPARTMENT OF CIVIL ENGINEERING Page 36 . Some times atmospheric air.Personal error 2. PLOTTING OF CROSS SECTION:A Horizontal line is draw and different cross section are plotted on a convenient Scale keeping the central peg of the profile in the centre. DEPARTMENT OF CIVIL ENGINEERING Page 37 .MUKKANNAN M. The staff should be held vertical using a plumb bob. Refraction rise the elevation of the station on the error is also professional to the square of the horizontal distance of the station from the level. The correction of the curvature has to be subtracted from the observe staff reading to get correct reading. (iii) Concentrating the attention on decimal part of reading and entering the whole value wrongly.S reading in the I. (ii) Reading top or bottom hair instead of center hair. A. (iv) Adding the F.. The wind is also responsible for small disturbance in the instrument level.M. (iii) Omitting on entry. (iii) Error due to wind & sun:Due to strong winds it is always difficult to hold the staff vertical due to non-verticality of the staff the observed reading is higher. Errors due to natural causes :Errors due to curvature :The curvature of the earth surface lowers the elevation of the station and it is directly proportional to the square of the horizontal distance between the staff position and the point of observation. In case of ordinary leveling error due to curvature in negligible that is only 0.I. (iv) Reading the inverted staff as a vertically held staff.S or F. This is negligible for short sites and it‘s generally ignored in ordinary leveling.E. A.S reading instead of adding.S reading instead of subtracting with and subtracting a B.. In strong winds it‘s always advisable to suspend the work. (ii) Recording the reading with digits inter change.S column.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY (iii) Non Vertically of staff: If the staff is not held vertical during observation of the staff reading the observed value will be higher than the actual value.E.003m for a sight of 300 m length. (ii) Error due to refraction:The effect of refraction on the observe readings is opposite to that of the curvature. Error is recording & computation:Common errors is recording are (i) Entering the reading in the wrong column that is B. Error is reading the staff : These error generally committed are (i) Reading the staff upside down. When adjustment is not perfect the line of collimation is either inclined upwards or downwards or observed reading are either more a less.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY The sun causes a considerable trouble. It will remain centre even if the bubble axis is not horizontal or on the other hand if its two sensitive a reasonable time is spent to bring a bubble centre. If the B.S distance are kept equal as in the case of the leveling. (v) Smoothness of the internal surface A. Irregularly of curvature of the tube is also a series defect. Instrumental error:(i) Imperfect adjustment of level: . In case of leveling an steep slopes. (iv) The viscosity and the surface tension of the bubble also affect sensitiveness of the level tube. (iii) The length of the vapor bubble that is greater the length of the bubble more is the sensitivity of the tube. The effect of sun in also cause’s elongation of the staff due to increased temperature but in ordinary leveling the changing in length is negligible. But in the case of inter mediate site the distance reading are thrown into error by a different amount. Sensitiveness of a l e v e l tube is either expressed in terms of minimum angle required by t h e bubble to move the smallest division on the angled scale..E. SENSITIVITY OF LEVEL TUBE:The ability of level tube to express small deviation from the horizontal axis is termed as sensitivity of level tube. It‘s recommended to protect the objective by an umbrella. DEPARTMENT OF CIVIL ENGINEERING Page 38 ..In a perfected adjusted level a line of collimation remains horizontal when the bubble of the level tube occupies the central position. (ii) Defecting level tube: . A. The sensitivity of the level tube depends on (i) The radius of curvature of the internal surface that is higher the radius greater the sensitivity of the tube.M. The effect of deflective level tube also gets neutralized if the sights are of equal length.If the bubble of level tube is sluggish.MUKKANNAN M. Such errors get compensative. (ii) The diameter of the level tube that is larger the diameter greater is the sensitivity of the level tube.E.S & F.I. L. BOOKING AND REDUCING LEVELS methods of booking and reducing the elevation of points from the observed staff readings (1) Collimation or Height of Instrument method (2) Rise and Fall method.L.L. (2) To establish points at a given elevation or at different elevations With respect to a given or assumed datum.I. as the case may be. the R. RISE AND FALL METHOD In rise and fall method..MUKKANNAN M. DEPARTMENT OF CIVIL ENGINEERING Page 39 . I to its R.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY UNIT-IV LEVELLING AND APPLICATIONS LEVELLING Levelling is a branch of surveying the object of which is : (1) To find the elevations of given points with respect to a given or assumed datum. the H is obtained by adding the B. If there are some intermediate points.M. normal to the plumb line at all points. It is. The process continues till the R. Level Line A level line is a line lying in a level surface. For the next setting of the instrument.E. and if the level of any one point is known the level of the next will be obtained by adding its rise or subtracting its fall. therefore.L. A.L. The figures for ‗ rise‘ and ‗ fall‘ worked out thus for all the points give the vertical distance of each point above or below the preceding one. Horizontal Line It is straight line tangential to the level line at a point. of last and first point. the height of the instrument (Hi) is calculated for each setting of the instrument by adding back sight (plus sight) to the elevation of the B. The difference between their stall readings indicates a rise or fall according as the staff reading at the point is smaller or greater than that at the preceding point.S taken on T. Example: Arithmetic Check: The difference between the sum of back sights and sum of fore sights should be equal to the difference between the sum of rise and the sum of fall and should also be equal to the difference between the R. of those points is calculated by subtracting the intermediate sight (minus sight) from the height of the instrument for that setting. the height of instrument is not at all calculated but the difference of level between consecutive points is found by comparing the staff readings on the two points for the same setting of the instrument. It is also perpendicular to the line defined by a plumb line. The elevation of reduced level of the turning point is then calculated by subtracting from Hi the fore sight (minus sight).E. of the last point (a fore sight) is obtained by subtracting the staff reading from height of the last setting of the instrument. Example: Arithmetic check: The difference between the sum of back sights and the sum of fore sights should be equal to the difference between the last and the first R.M (First point).. HEIGHT OF INSTRUMENT METHOD In this method.F. A. Contour lines of different elevations can unite to form one line only in the case of a vertical cliff. a single contour cannot split into two lines.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY LONGITUDINAL SECTIONING PROCEDURE Profile levelling. intermediate sights should be taken after the foresight on the next turning station has been taken. A.M. The position of the intermediate points on the profile are simultaneously located by chaining a along the profile and noting their distances from the point of commencement. For each set up.E. They provide the data for estimating quantities of earth work and for other purposes. Plotting the profile Contouring A contour is an imaginary line on the ground joining the points of equal elevation. otherwise. indicate a knife-edge ridge or depression which does not occur in nature. It is a line in which the surface of ground is intersected by a level surface. like differential levelling.I. A contour passing through any point is perpendicular to the line of steepest slope at that point.. A closed contour line with one or more higher ones inside It. two different contours of the same elevation may approach very near to each other. CROSS SECTIONING Cross sections are run at right angles to the longitudinal profile and o either side of it for the purpose of lateral outline of the ground Surface.MUKKANNAN M. A. when the vertical profile of the ground is regular or gradually curving. DEPARTMENT OF CIVIL ENGINEERING Page 40 . any number of intermediate sights may be obtained on points along the line from each set up of the instrument It is generally best to set up the level to one side of the profile line to avoid too short sights on the points near the instrument. similarly. The length of cross-section depends the nature of work. However. Characteristics of contours Two contour lines of different elevations cannot cross each other. represents a hill. Similarly.. the crossstaff or the optical square and the distances are measured left and right from the centre peg Cross-section be taken at each chain.E. Contour lines close together indicate steep slope. They indicate a gentle slope if they are far apart. The level is then set up in an advanced position and a back is taken on that turning point. levels are taken on points at equal-distances apart and generally at intervals of a chain length. The cross-sections are numbered consecutively from the commencement of the centre line and are set out at right angles to the main line of section with the chain and tape. a closed contour line With one or more lower ones inside it indicates a depression without an outlet To contour lines having the same elevation cannot unite and continue as one line. Contour lines of different elevation intersect only in case of overhanging cliff or a cave. requires the establishment of turning points on which both back and foresights are taken. This is evident because the single line would. In addition. Indirect method Direct method: The field work is of two-fold Vertical control Horizontal control Vertical control The points on the contours are traced either with the help of a level and staff or with a help of a hand level.8m means the staff reading will be 1. they are to be surveyed with a survey control system. The contour lines may then be drawn by interpolation. A. They form sharp curves of V-shape across it with convex side of the curve towards the higher ground If there is a stream.. Horizontal control After having located the points on various contours. may disappear in coincidence with the edge of the stream and cross underneath the water surface.M. Direct method 2. The same contour appears on either sides of a ridge or valley. Calculate the staff reading For example if height of the instrument is 101. A. In a work of a larger nature a traverse may be used. though not necessarily within the limits of the map.80m Taking one contour at a time the staff man is directed to keep the staff on the point on contour so that readings of 1. Contour lines cross a watershed or ridge line at right angles. for the highest horizontal plane that intersects the ridge must cut it on both sides.80m are obtained every time. turning upstream. The size of the square may vary from 5 to 20 m depending upon the nature of the contour and contour interval. The elevations of the corners of the square are then determined by means of a level and a staff. the contour on either side.E.. The same is true of the lower horizontal plane that cuts a valley.E. METHODS OF CONTOURING 1. DEPARTMENT OF CIVIL ENGINEERING Page 41 . the same size.By tacheometric method By square The method is used when the area to be surveyed is small and the ground is not very much undulating.M. The staff is kept on the B. The area is divided into a number of squares.By cross-section iii. and the height of the instrument is determined. INDIRECT METHOD The following are some of the indirect methods: i. It is not necessary that the squares may be of. They form curves of Vshape round it with the concave side of the curve towards the higher ground Contour lines cross a valley line at right angles.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY A contour line must close upon itself.I. For small area chain survey may be used and points may be located by offsets.MUKKANNAN M.By square ii. .. guide points in addition to those at corners may also be used. DEPARTMENT OF CIVIL ENGINEERING Page 42 . The staff intercept s is then obtained by taking the difference between the readings against the top and bottom wires. A. The contour lines are interpolated on the assumption that there is uniform slope between two points on two adjacent contours. The method is most suitable for railway route surveys. The line of sight can make any inclination with the horizontal the range of instrument observations. When there are appreciable breaks in the surface between corners. the points marked with dots are the points actually surveyed in the field while the points marked with x on the first cross-section are the points interpolated on contours. The squares should be as long as practicable. rectangles are also used in place of squares. The method is also known as spot leveillng.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY Sometimes. The cross-section and the points can then be plotted and the elevation of each point is marked. The horizontal distances need not be measured since the tacheometer provides both horizontal as well as vertical control. cross-sections are run transverse to the centre line of a road.M. yet small enough to conform to the inequalities of the ground and to the accuracy required. Thus. as in ravines or on spurs.E.MUKKANNAN M. A. Thus if ɵ is the inclination of the line of sight with horizontal the horizontal distance (D) between the instrument axis and the point in which the line of sight against the central wire intersects the staff are given by: D=K1s cos2ɵ + K2 cos2ɵ V= D tan ɵ K1 & K2 are instrumental constants. railway or canal etc.E. By Cross Section In this method. The cross-sections should be more closely spaced where the contours curve abruptly. By tacheometric method In the case of hilly terrain the tacheometric method may be used with advantage. A tacheometer is a theodolite fitted with stadia diaphragm so that staff readings against all the three hairs may be taken.I.  The index arm is centered on the trunnion axis in front of the vertical circle and remains fixed  When the telescope is moved in the vertical plane. A. however. The Vertical Circle  The vertical circle is a circular graduated arc attached to the trunnion axis of the te1escope consequently the graduated arc rotates with the telescope when the latter is turned about the horizontal axis. establishing grades.  A long sensitive bubble tube. A. the vertical circle moves relative to the verniers with the help of which reading can be taken. Transit theodolite It is the one in which the line of sight can be reversed by revolving the telescope through 180º in the vertical plane..  For adjustment purposes.E.M.MUKKANNAN M. prolonging survey lines.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY UNIT V THEODOLITE SURVEYING The Theodolite The measurement of horizontal and vertical angles and it is the most precise instrument designed for points on line.  At the two extremities of the index arm are fitted two verniers to read the vertical circle. the index arm can be rotated slightly with the help of a clip screw fitted to the clipping arm at its lower end. Theodolites may be classified as  Transit theodolite. The Index Frame (or T-Frame or Vernier Frame)  The index frame is a 1-shaped frame consisting of a vertical leg known as clipping arm and a horizontal bar known as vernier arm or index arm. Non-transit theodolite It may be either plain theodolites or Y-theodolites in which the telescope cannot be transited.  By means of vertical circle clamp and its corresponding slow motion or tangent screw the telescope can be set accurately at any desired position in vertical plane. THE ESSENTIALS OF THE TRANSIT THEODOLITE The Telescope  The telescope is an integral part of the theodolite and is mounted on a spindle known as horizontal axis or trunnion axis  The telescope may be internal focusing type or external focusing type. determining difference in elevation. setting out curves etc. DEPARTMENT OF CIVIL ENGINEERING Page 43 . sometimes known as the altitude bubble is placed on the top of the index frame..  Glass magnifiers are placed in front of each vernier to magnify the reading .  Non-transit theodolite.E.I. The Levelling Head.  The levelling head usually consists of two parallel triangular plates known as tribrach plates.E.  The upper tribrach has three arms each carrying a levelling screw  The lower tribrach plate or foot plate has a circular hole through which a plumb bob may be suspended.I.  In some instruments.MUKKANNAN M.E.M. A.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY The Standards (or A-Frame)  Two standards resembling the letter A are mounted on the upper plates  The trunnion axis of the telescope is supported on these. A..  The T-frame and the arm of vertical circle clamp are also attached to the A frame. DEPARTMENT OF CIVIL ENGINEERING Page 44 . for levelling screws are provided between two parallel plates.. .  On clamping the upper and unclamping the lower clamp.E. however.  When the clamp is tightened.  The lower plate carries a lower clamp screw and a corresponding slow motion or tangent screw with the help of which it can be fixed accurately in any desired position.  The upper plate supports the standards it carries an upper clamp screw and a corresponding tangent screw for purpose of accurately fixing it to the lower plate. the instrument can rotate on its outer axis without any relative motion between the two plates.  Both the axes have a common axis which forms the vertical axis of the instrument. the lower plate can be rotated slightly. the lower plate is fixed to the upper tribrach of the levelling head.MUKKANNAN M. also.  One of the plate level is kept parallel to the trunnion axis. A.  The plate level can be centred with the help of foot screws A. The Upper Plate (or Vernier Plate)  The upper plate or vernier plate is attached to the inner axis and carries two verniers with magnifiers at two extremities diametrically opposite. therefore. The Two Spindles  The inner spindle or axis is solid and conical and fits into the outer spindle which is hollow and ground conical in the interior.  For using any tangent screw.  The inner spindle is also called the upper axis since it carries the vernier or upper plate  The outer spindle carries the scale or lower plate and is. (b) To attach the theodolite to the tripod. the lower clamp is clamped and upper clamp unclamped.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY A levelling head has three distinctive functions: (a) To support the main part of the instrument.  If.E.M. (c) To provide a mean for levelling the theodolite.  The lower plate carries a horizontal circle at its levellel edge and is. The Lower Plate (or Scale Plate)  The lower plate is attached to the outer spindle. the upper plate and the instrument can rotate on the inner axis with a relative motion between the vernier and the scale.. its corresponding clamp screw must be tightened.I.  In some theodotites only one plate level is provided.  On turning the tangent screw. known as the lower axis. The Plate Levels  The upper plate carries two plate levels placed at right angles to each other. DEPARTMENT OF CIVIL ENGINEERING Page 45 . also known as the scale plate. therefore. .  Small flat curve scales of only a few degrees are provided on each side of the trough.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY Tripod  When in use.  At the lower ends.E. The Compass  Theodolites are provided with a compass which can be either tubular type or trough type. Striding Level  Some theodolites are fitted with a striding level. it is know as the left swing. it is also known as plunging or reversing. Centring.. Swinging the telescope.  It is used to test the horizontality of the transit axis or trunnion axis.hairs and the optical centre of the object glass and its continuation. the legs are provided with pointed steel shoes. Since the line of sight is reversed in this operation. The process of setting the theodolite exactly over the station mark is known as centring. The axis of level tube The axis of the level tube or the bubble line is a straight line tangential to the longitudinal curve of the level tube at its centre.. A. Transiting. DEPARTMENT OF CIVIL ENGINEERING Page 46 . If telescope is rotated in the anti-clockwise direction. The line of sight or line of collimation It is the line passing through the intersection of the horizontal and vertical cross. The horizontal or trunnion axis is the axis about which the telescope and the vertical circle rotate in vertical plane.I. A. it is known as right swing.E. The horizontal axis. The tripod head carries at its upper surface an external screw to which the foot plate of the levelling head can be screwed. This is the axis about which the lower and upper plates rotate. DEFINITIONS The vertical axis The vertical axis is the axis about which the instrument can be rotated in a horizontal plane. It is the process of turning the telescope in vertical plane through 1800 about the trunnion axis. the theodolite is supported on a tripod which consists of three solid or framed legs.M. It is the process of turning the telescope in horizontal plane. The Plumb pob  A plumb bob is suspended from the hook fitted to the bottom of the inner axis to centre the instrument exactly over the station mark.  A trough compass consists of a long narrow rectangular box along the longitudinal axis of which is provided a needle balanced upon a steel pivot. If the telescope is rotated in clock-wise direction.MUKKANNAN M. The axis of the level-tube is horizontal when the bubble is central. I. the plumb bob is shifted in the direction of the leg while by moving the leg circumferentially or sideways considerable change in the inclination is effected without disturbing the plumb bob.  The purpose of the levelling is to make the vertical axis truly vertical. Changing face It is an operation of bringing the face of the telescope from left to right and vice versa. (2) levelling up (3) Elimination parallax. Three Screw Head. SETTING UP The operation of setting up includes Centring  Centering of the instrument over the station mark by a plumb bob or by optical plummet.  By moving the leg radially.E. therefore.  The second movement is.  Some instruments are provided with shifting head with the help of which accurate centring can be done easily.  Turn the upper plate until the longitudinal axis of the plate level is roughly parallel to a line joining any two of the levelling screws A.M. the observation of the angle (horizontal or vertical) is known as face left observation. Telescope inverted A telescope is said to inverted or reversed when of the vertical circle is to the right and the ―bubble down‖.. and Approximate levelling with the help of tripod legs. Levelling up  After having centred and approximately levelled the instrument. effective in the approximate levelling of the instrument.MUKKANNAN M. DEPARTMENT OF CIVIL ENGINEERING Page 47 . Telescope normal A telescope is said to be normal or direct when the face of the vertical circle is to the left and the ―bubble (of the telescope) up‖. accurate levelling is done with the help of foot screws and with reference to the plate levels. TEMPORARY ADJUSTMENTS Temporary adjustments or station adjustments are those which are made at every instrument setting and preparatory to taking observation with the instrument.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY Face left observation. The temporary adjustments are : (1) Setting over the station. If the face of the vertical circle is to the left of the observer.. the observation is known as face right observation.E.  The manner of levelling the instrument by the plate levels depends upon whether there are three levelling screws or four levelling screws. Face Right Observation If the face of the vertical circle is to the right of the observer.  The approximate levelling is done either with reference to a small circular bubble provided on tribrach or is done by eye judgment. A. Four Screw Head  Turn the upper plate until the longitudinal axis of the plate level is roughly parallel to the line joining two diagonally opposite screws (such as D and B)  Bring the bubble central exactly in the same manner as described in step (2) above. ELIMINATION OF PARALLAX  Parallax is a condition arising when the image formed by the objective is not in the plane of the cross-hairs.M.I. provided it is in correct adjustment. as for the three screw instrument. until the axis of the level passes over the position of the third levelling screw C  Turn this levelling screw until the bubble is central. A.  Turn the upper plate through 90 degree until the spirit level axis is parallel to the other two diagonally opposite screws (such as A and C)  Centre the bubble as before.  It should be noted that the bubble will move in the direction of movement of the left thumb  Turn the upper plate through 90 degree.E.  Turn back again through 90 degree and repeat step (4).  Repeat the above steps till the bubble is central in both the positions.  The bubble should remain in the centre of its run.  Return the upper plate through 90 degree to its original position and repeat step (2) till the bubble is central.  Turn through 180 degree to check the permanent adjustment.. Parallax can be eliminated in two steps: A.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY  Hold these two levelling screws between the thumb and first finger of each hand and turn them uniformly so that the thumbs move either towards each other or away from each other until the bubble is central.  Now rotate the instrument through 180 degree.  Unless parallax is eliminated..  Repeat steps (2) and (4) till the bubble is central in both the positions.MUKKANNAN M. DEPARTMENT OF CIVIL ENGINEERING Page 48 .E. accurate sighting is impossible.  The image so formed is in the plane of cross-hairs.  Read both verniers. Turn the upper and lower plates in opposite directions till the zero of one of the vernier (say A) is against the zero of the scale and the vertical circle is to the left.. MEASUREMENT OF HORIZONTAL ANGLES To measure the horizontal angle PQR  Set up the instrument at Q and level it accurately. the full reading of vernier A (i.  The reading on vernier B will be 180 degree. point the telescope towards the sky or hold a sheet of white paper in front of the objective and move eye-piece in or out till the cross-hairs are seen sharp and distinct.  Bisect point F accurately by using lower tangent screw.  Unclamp the upper clamp and rotate the instrument clockwise about the inner axis to bisect the point R. A. the instrument will rotate about the outer axis.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY By Focusing The Eye-Piece  To focus the eye-piece for distinct vision of the cross-hairs.E. graduations are provided at the eye-piece end so that one can always remember the particular graduation position to suit his eyes.  Clamp both the plates together by upper clamp and lower clamp and bring the two zeros into exact coincidence by turning the upper tangent screw.I.M.  Loose the lower clamp and turn the instrument towards the signal at F.  While entering the reading. By Focusing the objective.MUKKANNAN M. minutes and seconds) should be entered  while only minutes and seconds of the vernier B are entered. DEPARTMENT OF CIVIL ENGINEERING Page 49 .  The mean of the two such vernier readings gives angle with one face.  Clamp the upper clamp and bisect R accurately by using upper tangent screw. The reading of vernier A gives the angle PQR directly while the vernier B gives by deducting 180 degree. if there is no instrumental error.  Take both vernier readings. Check the readings of verniers A and B.  Change the face by transiting the telescope and repeat the whole process. degrees.  In some telescopes.  There should be no change in the previous reading.  Since both the plates are clamped together.E. A.e...  Release all clamps.  The telescope is now directed to wards the object to be sighted and the focusing screw is turned till the image appears clear and sharp.  The average angle with face left will be equal to final reading divided by three. A.  Note the reading of verniers A and B to get the approximate value of the angle PQR.  The final value of the angle will be obtained by taking the mean of the values obtained by different sets.Obtain the second value of the angle by dividing the final reading by 6. Obtain the first value of the angle by dividing the final reading by 6.  The average horizontal angle is then obtained by taking the average of the two angles obtained with face left and face right. set 00 reading on vernier A. measure the angle clockwise by 6 repetitions.  Take the mean of the first and second values to get the average value of the angle by first set. Clamp the lower clamp and bisect point P accurately by lower tangent screw.. Clamp the upper clamp and bisect R accurately with the upper tangent screw.  Loose the lower clamp and direct the telescope towards the point P. To measure the angle PQR  Set the instrument at Q and level it. by dividing the final reading by three.  Unclamp the upper clamp.I.  For first order work. „Sets‟ by Method of Repetition for High Precision First Method  Keeping the telescope normal throughout.  Repeat the process until the angle is repeated the required number of times.  Invert the telescope and measure the angle counter-clockwise by 6 repetitions . Bisect R accurately by upper tangent screw.  Note the reading of vernier B.MUKKANNAN M.  Unclamp the lower clamp and turn the telescope clockwise to sight P again.  Unclamp the upper clamp and turn the instrument clockwise about the inner axis towards R.E.  The average horizontal angle is then obtained by dividing the final reading by the number of repetitions.  Change face and make three more repetitions as described above. Bisect P accurately by using the lower tangent screw.  Find the average angle with face right. turn the telescope clockwise and sight R. A. five or six sets are usually required. DEPARTMENT OF CIVIL ENGINEERING Page 50 .AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY REPETITION METHOD  It is used to measure a horizontal angle to a finer degree of accuracy than that obtainable with the least count of the vernier.  Thus an angle reading is mechanically added several times depending upon the number of repetitions.  Take as many sets in this way as may be desired. With the help of upper clamp and tangent screw..E.  An angle is measured two or more times by allowing the vernier to remain clamped each time at the end of each measurement instead of setting it back at zero when sighting at the previous station.M. the measurement of an angle is ordinarily reached after the fifth or sixth repetition. operations such as sighting and clamping are multiplied and hence opportunities for error are multiplied.  Loose the upper clamp and turn the telescope clockwise to point B.E. are not eliminated since they are all cumulative. may be to some extent counter-balanced in different observations. Read both the verniers.  If not. The following errors are eliminated by method of repetition:  Errors due to eccentricity of verniers and centres are eliminated by taking both vernier readings.... however.M.  Errors due to in adjustments of line of collimation and the trunnion axis are eliminated by taking both face readings. A. that in repeating angles. the first three with the telescope normal and the last three with the telescope inverted.MUKKANNAN M.  The limit of precision in.  The result is the corrected value of the angle by the first set  Take as many sets as are desired and find the average angle.  Without altering the reading obtained in the sixth repetition. by reiteration. COD etc. and want of verticality of the vertical axis etc. note the error and distribute half the error to the first value of the angle. the initial reading at the beginning of each set may not be set to zero but to two different values..AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY Second Method  Measure the angle clockwise by six repetitions.I. DIRECTION METHOD (OR REITERATION METHOD) To measure the angles AOB.  Take the reading which should theoretically by equal to zero (or the initi l value).  The error due to inaccurate graduations are eliminated by taking the readings at different pans of the circle. BOC. Set one vernier to zero and bisect point A (or any other reference object) accurately.E. Bisect B accurately using the upper tangent screw.  Errors due to inaccurate bisection of the object.  It should be noted.. eccentric centring etc. measure the explement of the angle clockwise by six repetitions. displacement of station signals. DEPARTMENT OF CIVIL ENGINEERING Page 51 . A.  Errors due to slip.  For more accurate work. Find the first value of the angle by dividing the final by six. proceed as follows Set the instrument over 0 and level it. the first three with telescope inverted and the last three with telescope normal. The mean of the vernier readings will give the angles AOB. Measure clockwise the angles AOB.. C. Procedure  Set the instrument at P and level it accurately. each included angle is obtained by taking the difference between two con secutive readings. thus closing the circle. Read both the verniers at each bisection. MEASUREMENT OF VERTICAL ANGLES  Vertical angle is the angle which the inclined line of sight to an object makes with the horizontal.  The sum of all the average angles so found should be 360°.  Keep the altitude level parallel to any two foot screws and bring the bubble central. distribute it equally to all angles. Loose the lower clamp. A. A.M. Do not distribute the error. the theodolite should be provided with either a tubular compass or trough compass.e.  Repeat the procedure till the bubble is central in both the positions.  Several such sets may be taken by setting the initial angle on the vernier to different values.  Loose the vertical circle clamp and rotate the telescope in vertical plane to sight the object. Clamp the lower clamp. C.MUKKANNAN M.  Use vertical circle tangent screw for accurate bisection.  Two values of each of the angles are obtained.  In the case of discrepancy. repeat the procedure and take a fresh set of readings. the reading of the vernier should be the same as the original setting.E. DOA.  Rotate the telescope through 90° till the altitude bubble is on the third screw.  Reverse the telescope. etc. Similar observation may be made with another face. COD.E.  Bring the bubble to the centre with the third food screw. unclamp the lower clamp and back Sigh on A.. bisect successively. C and D) of vertical circle. DOC. Take reading and foresight on D.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY  Similarly. the error (if small) may be distributed equally to all the angles.  Release the needle of the compass.  The values so obtained are the corrected values for the first set. B and A.  The mean of the two is taken as the average value of each of the uncorrected angles.. The procedure for each set is as follows  Set zero reading on one vernier and take a back sight on A.  Repeat steps 2 to 4 with the other face.  The mean of the two gives the vertical circle. DEPARTMENT OF CIVIL ENGINEERING Page 52 . COB and BOA. and if the error is small.  It may be an angle of elevation or angle of depression depending upon whether the object is above or below the horizontal plane passing through the trunnion axis of the instrument. It not. etc. OPERATIONS WITH THEODOLITE TO MEASURE MAGNETICBEARING OF A LINE  To measure the magnetic bearing of a line. D. Since the graduated circle remains in a fixed position throughout the entire process. in counter Clockwise direction and measure angles AOD. BOC. Rotate the instrument about its outer axis till the magnetic needle roughly points to north...  Read both verniers (i. The procedure is as follows  Level the instrument with reference to the plate level.I.  On final sight to A.. The average of the two will give the required angle. note the reading and find the error due to slips etc. If large. Set accurately the vernier A to zero. exactly in the same manner as explained above and close the horizon.  The line of sight will also be in the magnetic meridian those the upper clamp and point the telescope towards Q.M.. Bisect R accurately using the upper tangent screw. bring the needle exactly against the mark so that it is in magnetic meridian. Read verniers A and B.E.I. LPQR will then be obtained by dividing the final reading by two. TO MEASURE DEFLECTION ANGLES A deflection angle i  It is the angle which a survey line makes with the prolongation of the preceeding line. DEPARTMENT OF CIVIL ENGINEERING Page 53 . Read the verniers.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY  Using the lower tangent screw. next) line. A.. Bisect it accurately using the lower tangent screw.  Unclamp the lower clamp and direct the telescope to P. It is designated as Right (R) or Left (L) according as it is measured to the clockwise or to anticlockwise from the prolongation of the previous line. Read both verniers. The average of the two will give the correct bearing of the line PQ.  Plunge the telescope. To measure the angle PQR  Set the theodolite at Q and level it accurately. 3 and 4.MUKKANNAN M.  Unclamp the upper clamp and swing telescope clockwise and sight R. Reading on the vernier will be the same as in step  Unclamp the upper clamp and bisect R again. set the reading on vernier A to zero. A. Bisect Q accurately using the upper tangent screw. unclamp the tower clamp and take backsight on P.  Change the face and repeat steps 2.E. The reading will be equal to twice the angle. With face left.e. TO MEASURE DIRECT ANGLES Direct angles are the angles measured clockwise from the preceding line to the following (i. and  Natural. P and Q being their projection on a horizontal trace Let the line of sight AP make an angle 1 with horizontal. INSTRUMENTAL ERRORS The instrumental errors are due to  imperfect adjustment of the instrument. Read both verniers.  The error can be eliminated only by careful levelling with respect to the altitude bubble if it is in adjustment. When the telescope is lowered after sighting P. Thus.E. SOURCES OF ERROR IN THEODOLITE WORK  Instrumental  Personal.  imperfections due to wear. take back sight on P.  The vertical angles measured will also be incorrect. the line of sight will move in an inclined plane when the telescope is raised or lowered. Let P and Q be the two points to be observed.  structural defects in the instrument. one-half of the final reading gives the deflection angle at Q. The errors cannot be eliminated by double sighting. Error due to the vertical axis to horizontal axis not being perpendicular If the horizontal axis is not perpendicular to the vertical axis. A. Plunge the telescope..M. Error due to imperfect adjustment of plate levels  If the upper and lower plates are not horizontal when the bubbles in the plate levels are centred. it will move in an inclined plane APP2 and not in the vertical plane APPI.  The error may be serious in observing the points the difference in elevation of which is considerable. The horizontal angle measured will now be with reference to AP2 and not with AP1 If is the instrumental error and e is the resulting error.I. we get Since e and will be usually small.. Thus the line of sight is in the direction PQ produced when the reading on vernier A is 0°.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY Set the instrument at Q and level it.  With both plates clamped at 0°. The verniers still read the same reading as in (4).E.  Unclamp the upper clamp and turn the telescope clockwise to take the foresight on R.  Plunge the telescope. Read both the verniers. we get A. the vertical axis of the instrument will not be truly vertical  The horizontal angles will be measured in an inclined plane and not in a horizontal plane.  Unclamp the lower clamp and turn the telescope to sight P again.MUKKANNAN M.  Unclamp the upper clamp and turn the telescope to sight R. the horizontal and vertical angles measured will be incorrect. DEPARTMENT OF CIVIL ENGINEERING Page 54 .  Since the deflection angle is doubled by taking both face readings. The error can be eliminated by focusing the eye-piece and objective.  It will also be a source of error when the transit is used as a level. the vertical angles measured will be incorrect. Error due to eccentricity of verniers  The error is introduced when the zeros of the vernier are not at the ends of the same diameter. DEPARTMENT OF CIVIL ENGINEERING Page 55 . accurate bisection is not possible.M. Error due to imperfact adjustment of the vertical circle vernier  If the vertical circle verniers do not read zero when the line of sight is horizontal. Mistakes  Mistakes in setting the vernier.E.MUKKANNAN M. Error due to imperfect graduations  The error due to defective graduations in the measurement of an angle may be eliminated by taking the mean of the several readings distributed over different portions of the graduated circle. but the error due to the latter cannot be detected. A..AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY Error due to non-parallelism of the axis of telescope level and line of collimation  If the line of sight is not parallel to the axis of telescope level.  Thus.  The error can be eliminated by reading both the verniers and taking the mean of the two.  The error due to the former can be easily detected by checking the vernier reading after the back sight point is sighted. A.  It should always be remembered to use lower tangent screw while taking a back sighting and to use upper tangent screw while taking the foresight reading.  The error varies inversely as the length of the line of sight.. the difference between the two vernier readings will not be 180°. Errors in sighting and reading Inaccurate Bisection Of Points Observed  The observed angles will be incorrect if the station mark is not bisected accurately due to some obstacles etc. The error can be eliminated by taking both face observations.E. If the ranging rod put at the station mark is not held vertical.  The error is known as the index error and can be eliminated either by applying index correction or by taking both face observations. taking the reading and wrong booking of the readings. the error e is given By Parallax  Due to parallax.  Care should be always be taken to intersect the lowest point of a ranging rod or an arrow placed at the station mark if the latter is not distinctly visible. the measured vertical angles will be incorrect since the zero line of the vertical verniers will not be a true line of reference. Manipulating wrong tangent screw  The error is introduced by using the upper tangent screw while taking the back sight or by using the lower tangent screw while taking a foresight.I. but there will be a constant difference of other than 180. AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY NATURAL ERRORS Sources of natural errors are  Unequal atmospheric refraction due to high temperature.  Object The object of the adjustment is to make the vertical axis truly vertical . adjustment is correct. level the instrument with to the altitude bubble till it remains central in two position right angles to each other.  Swing the telescope through 180 degree . swing it through 180 degree. A. bring it back halfway with the levelling screw with the clip screw. If the bubble remains central. A.  Unequal settlement of tripod.. Object  The object of the adjustment is to place the intersection of the cross-hair in the optical axis. ADJUSTMENT OF LINE OF SIGHT Desired Relation  The line of sight should coincide with the optical axis of the telescope..  When the telescope is on the third foot screw.E. The vertical axis is now truly vertical.  Repeat till the altitude bubble remains central in all positions. DEPARTMENT OF CIVIL ENGINEERING Page 56 .MUKKANNAN M.  Unequal expansion of parts of telescope and circles due to temperature changes.M.  centralize the plate levels(s) of the horizontal plate with capstan headed screw. If the bubble moves from its centre.E. ADJUSTMENT OF PLATE LEVEL Desired Relation  The axis of the plate bubble should be perpendicular to the vertical axis when the bubble is central.  Thus. to ensure that. provided both of these are perpendicular to the vertical axis.I. once the instrument is levelled up. Level the instrument in the two positions at right angles to each other 3 in temporary adjustment. Necessity Horizontal hair  The adjustment is of importance only in the case of external focusing telescope in which the direction of line of sight will change while focusing if the horizontal hair does not intersect the vertical hair in the same point in which the optical axis docs. Adjustment  If not. Test  Set the instrument on firm ground. both horizontal as well as vertical hair are to be adjusted. the bubble will remain central for all directions of sighting Necessity  Once the requirement is accomplished the horizontal circle and also the horizontal axis of the telescope will be truly horizontal. ( Wind producing vibrations) PERMANENT ADJUSTMENTS OF THEODOLITE The permanent adjustments of a transit are as follows  Adjustment of plate level  Adjustment of line of sight  Adjustment of the horizontal axis  Adjustment of altitude bubble and vertical index frame. the horizontal hair is in adjustment.  To see this. A. TACHOMETRY SURVEY :Tachometry is a branch of angular surveying in which A horizontal & vertical distance is of points are obtain by optical means as suppose to ordinary slow process of measure by tape chain. DEPARTMENT OF CIVIL ENGINEERING Page 57 . Test for horizontality and verticality of hairs. transit the telescope and set it through 180 degree .  Repeat the test till the adjustment is corrected Adjustment of Vertical hair Set the instrument on a level ground) so that a length of about 100 in is available to either side of it.E. All though the accuracy of tachometry is low it is best adopted in obstructed such as steep & broken ground stretches of water etc which make drawn age difficult.I. suspend a plumb to at some distance and sight it through the telescope by careful using. the latter is vertical. adjust the horizontal hair by top and bottom capstan screws of the diaphragm until the reading on the staff is the mean of the two. the line of collimation will be perpendicular to the horizontal axis and hence the line of sight will sweep out a plane when the telescope is plunged. Adjustment of Horizontal Hair  Level the instrument carefully with all clamps fixed. If the same reading is obtained..E. Level it. They primary object of tachometry is the preparation of contour maps are plans required with both horizontal & vertical measurements also accuracy improvement it provides at check an distance measure with tape.  Take a reading on a staff placed some distance apart  Unclamp the lower clamp. This methods is very rapid & convenient.  If the image of the plumb bob string is parallel to the vertical hair.MUKKANNAN M. A. Adjustment  If not. Set the same reading on the vertical circle and see the staff.  If not.. level the instrument carefully. loose the capstan screws the diaphragm and rotate it till the vertical hair coincides with the image of the string.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY Vertical hair  If the adjustment is accomplished.M. Telescope is used in stadia surveying are of 3 types :(i) Simple external focusing telescope (ii) External focusing analytic (iii) Internal focusing telescope Different system of Tachometry measurements : Fixed hair method (or) stadia method  Movable hair method (or) substance Fixed hair method :In method observation are made with stadia diaphragm having stadia wires at fixed (a) constant distance occur.M.005m.I. A. They stadia being taken against the horizontal hair as against any two point on the staff on their corresponding vertical angles are measured.E.distance between the stadia hair so as to said them against the two targets on the staff kept at a point and observation this in this case the staff intercept that is the distance between the two forgets is kept fixed while the stadia interval that is the distance between the stadia hair is carrying as is the case of fixed hair method inclined site they out show be taken the tangential method. DEPARTMENT OF CIVIL ENGINEERING Page 58 . Subtense method :This method is similar to fixed hair method except the stadia internal is varying table arrangement is may to --.. Staff in theodalite normal mean by perpendicular. They reading an the staff corresponding to all three wires are taken.MUKKANNAN M. This measurement of vertical angles tube for one single observation.E. For inclined said reading may be taken by keeping the staff either vertical a normal to the line of site.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY At the instruments a normally transit theodalite pitted with stadia diaphragm is generally used for tachometry survey. Least count of staff 0. A stadia diaphragm essentially consist of one stadia hair above on the other an equal distance below the horizontal cross hair.. The staff intercept that is the differents of reading corresponding to top & bottom stadia wires will depend on the distance of the staff from the instrument when the staff intercept is more than the length of the staff only ½ interne of real. A. l take multiplying as 100 assume h to be 1 m RL of A = 10.M. DEPARTMENT OF CIVIL ENGINEERING Page 59 .I.s.H reading 1.855 sin²30° / 2 = 48.855 cos²30° / 2 reduce level Q= 57.000 + 48.930 m elevation of point A is 10m above m.855 m & C. A.260m Horizontal distance : D = MS cos²θ + cosθ = 100 x 3.19m reduce level of Q = 10.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY Held staff vertical :Horizontal D = MS cos²θ + cos θ Vertical V = MS sin²θ / 2 + C sin θ H = height of instruct R = observe staff reading Staff normal to lined site : Find the elevation & horizontal distance of point Q view from A is than angle of 30° above horizontal with staff intercept with staff held vertically occur 3..E.190 – 1.930 = 57.MUKKANNAN M..000 + 1.E.260m A.000 m RL of Q = RL of A + height of instrument + v – r V = MS sin²θ / 2 + c sinθ = 100 x 3. .805 D = 93.650.r cosθ S = 1m R = 2.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY 2.461m RL of θ = 0 + 0.E.MUKKANNAN M.650 Assume m = 100 RL of θ = RL of A + h – v. DEPARTMENT OF CIVIL ENGINEERING Page 60 ..8m above A clip of 22° to a staff held normal to the line of site at B.E.8 – 37.M.993 = 38.150 r cosθ = 1.150. d tan²θ D = ------------------tanθ1 – tan θ2 h = D tanθ1 A. Find vertical & horizontal distance between point A & B. A.461 – 1. 2.51m 3. If the instrument located 0. 2.993 V = (ms + c) sinθ = (100 x 1) sin 22° = 37.I.654m horizontal distance D D = (ms + c) cosθ + r sinθ = (100) cos 22° + 0. To determine distance between two points with base of one point is axiable and instrument station in the same vertical plane as the elevated object. The staff read 1. .E.M.s cot θ2 ) tanθ2 D = --------------------------tanθ1 – tan θ2 ( 4 – 0..AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY Instrument with two different Axis :(d + s cot θ2 ) tanθ2 D = --------------------------tanθ1 – tan θ2 (d + s cot θ2 ) sinθ1 sinθ2 h = ----------------------------------sin (θ1 – θ2 ) h2 = h1 + s use positive sign with s cot θ2 when instrument a axis a Q is lower & negative sign when it‘s height the instrument axis at P. DEPARTMENT OF CIVIL ENGINEERING Page 61 .310m and 1.98) sin 11°15‘ sin 9°30‘ h2 = --------------------------------------------------sin (11°15‘ – 9°30‘ ) A.164 = ---------- tan 11°15‘ – tan 9°30‘ D = 5.M having elevation 2650.E.505 x 5.815m respectively. 1.13m (4 – 0.21m 0.I. Find the RL of Q = θ1 = 9°30‘ θ2 = 11°15‘ (d .38m are 1. An instrument was setup at station P and the angle of elevated to an objective was 9°30‘ the same object was focus from a point 4m away the first one angle was 11° 150‘ the staff reading s from a B.MUKKANNAN M. A.535 ( d 9°30‘) tan 9°30‘ = ----------------------------------------- 0.0315 = -204. 0673 x 3² = 0. A instrument was setup a P and angle of depression to a plane 2m above the fast of the staff held at Q was 5° 36‘ H.38 + 1.505 = 39.69m RL of Q = RL of instrument axis + Ccr + V – h = 2650.0673 x 2000² Ccr = 0. An instrument was setup a P and the angle of elevation to a volume 4m above the focus of the staff held at Q was 9°30‘.E.E.673 x 2 = 0...175 = 2612. d between P & Q was 3000m determine RL of staff station Q given the staff readings as a B.68 + 0.310 – 39.27m V = D tanθ = 2000 x tan 9°30‘ = 334.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY = 39.6057 V = 3000 x tan 5°36‘ = 294.0673 d² 0.52m 2.L of D² + S² = 2650. DEPARTMENT OF CIVIL ENGINEERING Page 62 .38 + 0.MUKKANNAN M. A.I.34m 3.050m was 2.175 RL of stadia = R.27 + 334.865m Cn = 0. A horizontal distance Pl was known 2000m determine the RL of staff station Q given RL of instrument axis was 2650.68m h2 = h1 + s = 39.15m A.M.69 – 4 = 2981.M of elevation 436.38m 0. 15 = 142.AKSHAYA COLLEGE OF ENGINEERING AND TECHNOLOGY RL of Q = BM + cn – V – n + instrument = 436.865 – 0. (iii) Clamp vertical axis tightly while observing the horizontal angles.6057 – 294.MUKKANNAN M.16m Measurement of horizontal angles :(i) Direct method (ii) Method of Repetition (iii) Method of Reiteration Precaution to be taken theodolite observation:(i) Turn the theodolite by the standards and not by using telescope ensuring slow & smooth movement.. DEPARTMENT OF CIVIL ENGINEERING Page 63 .E.I. (ii) Done force the foot screws & tangent screws to heart.E. Sources of errors in theodolite:(i) Instrumental Error (ii) Personal Error (iii) National Error A.M. A..050 + 2.