Surveying Complete Notes PDF

LEARNING RESOURCE MATERIAL ON SURVEY-I (Th-3) Code:CET303 UNDER EDUSAT PROGRAMME SCTE&VT, ODISHA BHUBANESWAR  CONTENTS Chapter Topic Name Page No. Prepared by No. 01 INTRODUCTION 01-04 Dr.P.K...

LEARNING RESOURCE MATERIAL ON SURVEY-I (Th-3) Code:CET303 UNDER EDUSAT PROGRAMME SCTE&VT, ODISHA BHUBANESWAR  CONTENTS Chapter Topic Name Page No. Prepared by No. 01 INTRODUCTION 01-04 Dr.P.K. Muduli, Sr. Lecturer (Civil) GP Kendrapara 02 LINEAR MEASUREMENTS 05-16 03 CHAINING 17-27 Sri E. Ekka, Sr. Lecturer (Civil) 28-38 04 CHAIN SURVEYING GP, Berhampur Sri D. Khura 05 ANGULAR MEASUREMENT Sr. Lecturer (Civil) JES, Jharsuguda 06 CHAIN AND COMPASS SURVEYING Sri D.K Mohapatra, 07 COMPUTATION OF AREA Lect.(Civil) ITT,Choudwar 08 PLANE TABLE SURVEYING  CHAPTER-1 INTRODUCTION 1.1. SURVEYING- Surveying is the art of determining the relative position of different objects on the surface of the earth by means of measurements of distances, directions and elevations and then, preparing a map to any suitable scale. TECHNICAL TERMS: (i) Plan: A plan is a geographical representation of the features on the earth surface or below the earth surface as projected on horizontal plane. This may not necessarily show its geographical position on the globe. On a plan horizontal distances and directions are shown. (ii) Map: The representation of earth surface on a small scale is called a map. The map must show its geographical position on the globe. (iii) Topographical map: The maps which are on sufficiently large scale to enable the individual features shown on the map to be identified on the ground by their shapes and positions are called topographical map. (iv) Geographical map: The maps which are on such a small scale that the features shown on the map are suitably generalized and the map gives a picture of the country as a whole and not a strict representation of its individual features, are called geographical maps. 1.2. AIM AND OBJECTIVES OF SURVEYING- The aim of surveying is to prepare a map to show the relative positions, horizontal distances, and elevation of the objects on the surface of the earth. The map is drawn to some suitable scale. It shows the natural features of a country, such as towns , villages , roads , railways , river etc. The objectives of surveying can be stated as follows. (i) Collect and record data on the relative positions of points on the surface of the earth. (ii) Compute areas and volumes using this data,required for various purposes. (iii) Prepare the plans and maps required for various activities.  (iv) Lay out, using survey data, the various engineering works in correct positions. (v) Check the accuracy of laid out lines, built of structure. 1.3 CLASIFICATION OF SURVAYING- (1) PRIMARY CLASSIFICATION Surveying is primarily classified as: (i) Plane surveying (ii) Geodetic surveying (i) PLANE SURVEYING: In plane surveying the curvature of the earth is not taken into consideration. This is because surveying is carried out over a small area so the surface of the earth is consider as plane.Plane surveying is done on an area of less than 250 km2. (ii) GEODETIC SURVEYING: In geodetic surveying the curvature of the earth is taken into consideration. It is extended over a large area. It is carried out over an area exceeding 250 km2. (2) SECONDARY CLASSIFICATION (i) Chain surveying (ii) Compass surveying (iii)Plane table surveying (iv) Thedolite surveying (v) Tachometric surveying 1.4 GENERAL PRINCIPLE OF SURVEYING- The two basic principles of surveying need to be followed for accurately locating points on earth. (i) To work from the whole to part: The main principle of surveying is to work from whole to part whether it is plane or geodetic surveying. To achieve this in actual practice, a sufficient number of primary control points are established with higher precision in and around the area to be detail  surveyed. Minor control points in between the primary control points are then established with less precise method. Further details are surveyed with the help of these minor control points by adopting any of the survey methods. The main idea of working from whole to part is to prevent accumulation of errors and localize minor errors within the frame work of control points. On the other hand if survey is carried out from part to whole, the errors would expand to greater magnitudes and the scale of the survey will be distorted beyond control. In general practice the area is divided into a number of large triangles and the positions of their vertices are surveyed with greater accuracy, using sophisticated instruments. These triangles are further divided into smaller triangles and their vertices surveyed with less accuracy. (ii) To locate a new station by at least two measurements from fixed reference points / control points. The reference points / control points are selected in the area and distance between them, is measured accurately. The line is then plotted to a convenient scale on a drawing sheet. In case, the control points are co-ordinated, their locations may be plotted with the system of coordinates (Cartesian or spherical). The location of the required point may then be plotted by making two measurements from the given control points as explained below. Let P and Q be two given control points. Any other point R can be located with reference to these points, by any of the following methods. P P P P R R R R Q Q Q Q (a) (b) (c) (d) Fig.1 (i) By measuring distances PR and QR:- The distances PR and QR may be measured and the location of R may be plotted by drawing arcs to the same scale to which line PQ has been drawn as shown in Fig 1 (a). (ii) By dropping a perpendicular from R on PQ:- A perpendicular RT may be dropped on the line PQ. Distances PT, TQ and RT are measured and the location of R may be plotted by drawing the perpendicular RT to the same scale to which line PQ has been drawn (Fig. 1 (b)). The above two principles are generally used in “Chain surveying”. (iii) By measuring the distance QR and angle PQR:- The distance QR and the angle PQR equal to α are measured and location of R may be plotted either by means of a protractor or trigonometrically (Fig 1 (c)), This principle is used in “Theodolite traversing”. (iv) By measuring the interior angles of the triangle PQR:- The interior angles P,Q and R of the triangle PQR are measured with an angle measuring instrument such as theodolites. The length of sides PR and QR are calculated by solving the triangle PQR and coordinates of R are calculated in the same terms as those of P and Q. Even without calculating the co-ordinates, or sides the location of R can be obtained by plotting the angles PQR and QPR (Fig 1(d). This principle is used in the method of ‘Triangulation’.  CHAPTER- 2 LINEAR MEASUREMENTS 2.1 INTRODUCTION There are two main methods of determining the distances between points on the surface of earth: (i) Direct Measurement: In this method, distances are actually measured on the earth surface by means of chains, tapes etc. (ii) Computative Measurement: In this method distances are determined by calculation as in tachometry and triangulation. 2.2 INSTRUMENTS FOR MEASURING DISTANCES (i) Tapes (ii) Steel Bands (iii) Chains (iv) Arrows (v) Pegs (vi) Ranging Rods (vii) Ranging Poles (viii)Offset Rods (ix)Plumb Bobs 2.3 TAPES: Depending upon the material tapes are classified as (i) Cloth or linen tape (ii) Metallic tape (iii)Steel tape (iv) Invar tape (i) Cloth or linen tape: Linen tapes are closely woven linen and varnished to resist moisture. They are generally 10 metres to 30 metres in length and 12mm to 15 mm in width. Cloth tapes are generally used for measuring offset measurements only due to following reasons : (i) It is easily affected by moisture and shrunk.  (ii) Its length gets altered by stretching. (iii) It is likely to twist and tangle. (iv) It is not strong as a chain or steel tape. (v) It is light and flexible and it does not remain straight in strong wind. (vi) Due to continuous use, its figures get in-distinct. (ii) Metallic Tape: A linen tape reinforced with brass or copper wires to prevent stretching or twisting of fibers is called a metallic tape. As the wires are interwoven and the tape is varnished, these wires are not visible to naked eyes. These tapes are available in different lengths but tapes of 20m and 30m lengths are very common. These are supplied in leather case with winding machine. Each metre is divided into decimeters and each decimeter is sub-divided into centimeters. (iii) Steel Tape: Steel tapes are available with different accuracy of graduation. Steel tapes are available in different lengths but 10m, 20m, 30m and 50m tapes are widely used in survey measurements. At the end of the tape a brass ring is provided. The length of metal ring is included in the length of tape. A steel tape of lowest degree of accuracy is generally superior to a metallic or cloth tape for linear measurements. (iv) Invar Tape: Invar tapes are made of an alloy of nickel (36%) and steel (64%) having very low co-efficient of thermal expansion (0.000000122 per 1ºC). These are 6mm wide and are available in length of 30m, 50m and 100m. These tapes are used for high degree of precision required for base measurements. 2.4 Chains: The different types of chains are used in surveying and are given below. (1) Gunter’s chain: It is 66ft. long and divided into 100 links. Each link measures 0.66 ft. (2) Engineer’s chain: It is 100ft. long and divided into 100 links. Each link measures 1 ft. Fig. 2.1  (3) Metric Chain: A metric chain is prepared with 100 or 150 pieces/ links of galvanized mild steel wire of diameter 4mm. The ends of the pieces are bent to form loops and connected together by means of three oval shaped rings which gives flexibility to the chain. Two brass handles are provided at the two ends of the chain with swivel joints so that chain can be turned round without twisting. The outside of the handle is the zero point or the end point of the chain. The length of the chain is measured from the outside of one handle to the outside of the other. The length of a link is the distance between the centres of the two consecutive middle rings as shown in the Fig. 2.1. The end links include the length of handle. Tallies are provided for marking 5m, 10m, etc are marked with letter “m” to distinguish the metric chain from non-metric chain. The length of chain whether 20m 0r 30m is indicated on the handle for easy identification. Suitability of Chains: The chains are suitable for the following cases. (i) It is suitable for ordinary or preliminary works as its length alters due to continuous use. (ii) Its length gets shortened due to bending of links and gets lengthened by flattening of the rings. (iii) Being heavier, a chain gets sagged considerably when suspended at the ends. (iv) It can be easily repaired in the field. (v) Measurement readings can be taken very easily. (vi) It is only suitable for rough works. Merits of Chains: (i) They can be read easily and quickly (ii) They can withstand wear and tear (iii)They can be easily repaired or rectified in the field. Demerits of Chains: (i) They are heavy and take too much time to open or fold. (ii) They become longer or shorter due to continuous use. (iii)When the measurement is taken in suspension the chain sags excessively giving incorrect measurements. ARROWS: Arrow are made of tempered steel wire of diameter 4mm.One end of the arrow is bent into a ring of diameter 50 mm and the other end is pointed. Its overall length is 400mm. Arrows are used for counting the number of chains while measuring a chain line. Generally 10 arrows accompany a chain. RANGING RODS: Rods, which are used for ranging a line are known as ranging rod. Such rods are made of seasoned timber or seasoned bamboo. Sometimes GI pipes of 25mm/ 30mm diameter are also used as ranging rods. They are generally circular in section of diameter 25mm/30mm and length 2m / 3m.The rod is divided into equal parts of 20cm each and the divisions are painted black and white or red and white alternatively so that the rod is visible from a long distance. The lower end of the rod is pointed or provided with an iron shoe. RANGING POLES: These are similar to ranging rods except that they are heavier in section of length 4m to 6m. They are used for ranging very long lines in undulating ground. OFFSET RODS: These are similar to ranging rods and o 3m long. The top is provided with an open hook for pulling or pushing a chain through obstruction like bushes etc.It is used for aligning the offset line and measuring short offsets. PLUMB BOB: It is used to transfer the end points of the chain onto ground while measuring distances in hilly terrain. It is also used for testing verticality of ranging poles, ranging rods. PEGS: Wooden pegs usually 2.5cm square and 15cm deep are used to mark the position of survey stations. ADJUSTMENT OF CHAIN: Chains are adjusted in the following ways- (1) When the chain is too long, it is adjusted by (a) Closing up the joints of the rings (b) Hammering the elongated rings (c) Replacing some old rings by new rings (2) When the chain is too short, it is adjusted by (a) Straightening the bent links (b) Opening the joints of the rings  (c) Replacing the old rings by some larger rings 2.5 ERRORS IN LINEAR MEASUREMENTS / CHAINING Errors in chaining may be caused due to variation in temperature and pull, defects in instruments etc. They may be classified into two catagories. (i) Compensating errors (ii) Cumulative error (i) COMPENSATING ERRORS: Errors, which may occur in both directions (that is both positive and negative) and which finally tend to compensate are known as compensating errors. (ii) CUMULATIVE ERRORS: Errors, which may occur in the same direction and which finally tend to accumulate are said to be cumulative. They seriously affect the accuracy of the work and are proportional to the length of the line (L).The errors may be positive or negative. I. Positive Cumulative Error: The error, which make the measured length more than the actual is known as positive cumulative error. Sources: (a) The length of chain / tape is shorter than its standard length due to
Bending of links
Removal of too many rings due to adjustment of its length.
Knots in connecting links.
The field temperature is lower than that at which the tape was calibrated.
Shrinkage of tape when moist
Clogging of rings with mud. (b) The slope correction is ignored while measuring along slopping ground. (c) The sag correction, if not applied when chain / tape is suspended at its ends. (d) Incorrect alignment. II. Negative Cumulative Error: The error, which make the measured length less than the actual is known as negative cumulative error. Sources: (a) The length of chain / tape is longer than its standard length due to 
Flattening of connecting rings.
Opening of the ring joints.
The field temperature is higher than that at which the tape was calibrated. MISTAKES: Errors occurring due to the carelessness of the chainman are called mistakes. Following are a few common mistakes: (1) Once an arrow is withdrawn from the ground during chaining it may not be replaced in proper position, if required due to some reason. (2) A full chain length may be omitted or added. This happen when arrows are lost or wrongly counted. (3)The number may be read from the wrong direction; for instance a 6 may be read as a 9. (4) Some number may be called wrongly. For example 50.2 may be called as fifty two without the decimal point being mentioned. PRECAUTIONS AGAINST ERRORS AND MISTAKES: (1) The point where the arrow is fixed on the ground should be marked with a cross(×). (2) The zero end of the chain or tape should be properly held. (3) During chaining the number of arrows carried by the follower and leader should always tally with the total number of arrows taken. (4) The chainman should call the measurement loudly and distinctly and the surveyor should repeat them while booking. (5) Ranging should be done accurately. (6) No measurement should be taken with the chain in suspension. ERRORS IN MEASUREMENT DUE TO INCORRECT CHAIN / TAPE LENGTH: Due to usage of chain over rough ground, its oval shaped rings get elongated and thus the length of chain gets increased. On the other hand, sometimes some of the links get bent and consequently the length of the chain gets decreased. Thus, the lengths obtained by chaining with a faulty chain are either too long or too short than the length which would be obtained with a chain of standard length. If the chain is too long the measured distance will be less and if the chain is too short the measured distance will be more. Let L be the true length of chain and L’ be the faulty length of chain.  L' Then, the true length of a line = × measured length L 2.6 CORRECTIONS IN LINEAR MEASUREMENTS (i) Correction for standard length (ii) Correction for alignment (iii) Correction for slope (iv) Correction for tension (v) Correction for temperature (vi) Correction for sag (i) Correction for standard length: Before using a tape, its actual length is ascertained by comparing it with a standard tape of known length. The designated nominal length of a tape is its designated length e.g. 30m or 100m. The absolute length of a tape is its actual length under specified conditions. Let L= measured length of a line Ca = correction for absolute length l = nominal designated length of tape C = correction be applied the tape L.C Then, Ca = l The sign of the correction Ca will be the same as that of C. (ii) Correction for alignment: Generally a survey line is set out in a continuous straight line. Sometimes, it becomes necessary, due to obstruction to follow a bent line which may be composed of two or more straight portions subtending an angle other than 180º as shown in Fig.2.2. A B ϴ1 ϴ2 α C  Fig.2.3. Correction for alignment Let AC=l1; CB= l2 Angle BAC = ϴ1; Angle BAC = ϴ2 Length AB= l1 cos ϴ1 + l2 cos ϴ2 The required correction = (l1+ l2)-( l1 cos ϴ1 + l2 cos ϴ2) (iii) Correction for slope: The distance measured along the slope between two stations is always greater than the horizontal distance between them. The difference in slope distance and horizontal distance is known as slope correction which is always substractive. Fig. 2.4 Slope Correction Let L = slope distance AB D = horizontal distance AC h=difference in reduced levels of A and B D= (L 2 − h2 ) h2 Slope Correction = L – D = 2L (iv) Correction for pull/ tension (CP): During measurement the applied pull may be either more or less than the pull at which the chain or tape was standardized. Due to the elastic property of materials the strain will vary according to the variation of applied pull and hence necessary correction should be applied. This correction is given by the expression CP =((P-P0)xL)/(AxE)  where, P= Pull or tension applied during measurement in Newtons A= Cross-sectional area of the tape in square cm. L= Length of the measured line P0 = Standard pull E = Modulus of Elasticity of the tape If the applied pull is more, tension correction is positive, and if it is less, the correction is negative. (v) Temperature correction (Ct): This correction is necessary because the length of the tape or chain may be increased or decreased due to rise or fall of temperature during measurement. The correction is given by the expression as mentioned below. Ct = α(Tm-T0)L where Ct = correction for temperature α=coefficient of thermal expansion Tm=temperature during measurement in degrees centigrade T0=temperature at which the tape was standardized in degrees centigrade L=length of tape (vi) Correction for sag (Cs) This correction is necessary when the measurement is taken with the tape in suspension. It is given by the expression as mentioned below. 2 L W  Cs =   24  P  where W= total wt of the tape; L= horizontal distance between the supports P = pull applied during measurement Problem 1. The length of a survey line measured with a 30m chain was found to be 631.5m. When the chain was compared with a standard chain, it was found to be 0.1m too long. Find the true length of the survey line. Solution L' The true length of a line = × measured length L L’ = 30.1m. L = 30m and measured length of the survey line = 631.5m 30.1 Thus, true length of the survey line = × 631.5 = 633.603 m. Ans. 30 Problem 2. A 20m chain was found to be 4 cm too long after chaining 1400m. It was 8 cm too long at the end of day’s work after chaining a total distance of 2420m. If the chain was correct before commencement of the work, find the true distance. Solution The correct length of the at commencement = 20m The length of the chain after chaining 1400m = 20.04 m. The mean length of the chain while measuring = (20+20.04)/2 = 20.02m The true distance for the wrong chainage of 1400m = (20.02/20)x1400 = 1401.4 m The remaining distance = 2420-1400 = 1020m The mean length of chain while measuring the remaining distance = (20.08+20.04)/2 = 20.06m The true length of remaining 1020m = (20.06/20)x 1020 =1023.06m Hence, the total true distance = 1401.4 + 1023. 06 = 2424.46 m Ans. Problem No.3. A line was measured with a steel tape which was exactly 30 meters at 20℃ at a pull of 100N (or 10kgf), the measured length being 1650.00 meters. The temperature during measurement was 30° C and the pull applied was 150N (or 15kgf). Find the length of the line, if the cross-sectional area of the tape was 0.025 sq.cm. The co-efficient of expansion of the material of the tape per 1 ºC =3.5x10 and the modulus of elasticity of the material of the tape=2.1x10 N/m (2.1x10 kg/c ). Solution: (i) Correction of temperature per tape length = −  = 0.0000035 30 − 20 30 = 0.00105m (+ve) (ii) Correction for pull per tape length  = CP =((P-P0)xL)/(AxE)=((150-100)x30)/(2.5x2.1x10  =0.00286m (+ve) Combined correction = 0.00105+0.00286=0.00391m True length of the tape = 30+0.0039=30.0039m True length of the line = (30.0039x1650.00)/30 =1650.21m. Ans. EXERCISE 1. A distance of 2000m was measured by a 30m chain. Later on, it was detected that the chain was 0.1 m too long. Another 500 m (i.e. total 2500 m) was measured and it was detected that the chain was 0.15 m too long. If the length of the chain in the initial stage was quite correct, determine the exact length that was measured. 2. To measure a base line a steel tape 30m long standardized at 15 C with apull of 100N was used. Find the correction per tape length if the temperature at the time of measurement was 20ºC and the pull exerted was 160N, weight of 1 cubic cm of steel is 0.0786N, weight of the tape = 8N. E = 2.1 x 105 kg/sq.cm, Co-efficient of expansion of the tape per 1ºC = 7.1x 10-7. 3. A tape 100m long, 6.35mm wide, 0.5 mm thick was used to measure a line, the apparent length of which was found to be 1986.96m. The tape was standardized under a pull of 67.5 N, but after the line was measured, it was found that the pull actually used during the measurement was 77.5 N. What was the true length of the line if the tape was standardized? Take E = 200000 N/mm2.  3.0 CHAINING(Chapter-3) In addition to chain or tape, several other auxiliary equipment are required in a chain surveying These are listed in subsequent paragraphs. Arrows Arrows or chain pins, as these are called sometime, are made of stout steel wire 4 mm in diameter, 400 to 450 mm long and black enameled. These are used to mark the end of each chain length as shown in Figure (a). Wooden Pegs These are made of stout timber generally 25 to 30 mm square or circular size and 150 mm long as shown in Figure (b). Wooden pegs are normally used to mark station position on ground on a quasi-permanent state. These are tapered at one end so that they can be driven in the ground with a hammer. These are kept at about 40 mm (minimum) projecting above the ground. Ranging Rods These are octagonal or circular in plan normally 25 to 30 mm diameter straight timber or tubular steel rods, 3 m in length and provided with an iron shoe at lower end as shown in Figure (c). These are painted in black and white alternate bands and normally have a flag at the top for easy recognition and identification from a distance. If the ranging roads are graduated in meters and one tenth of a meter, they are called offset rods and are used for measurement of short offsets. Plumb Bob It is usually heavy spherical or conical ball, as shown in Figure (d), of metal and is used to transfer points on ground by suspending it with the help of a strong thread. It is used in measuring distances on sloping ground by stepping. Compass, Dumpy levels and. Theodolites are also positioned over the station point accurately with the help of plumb bobs. Line Ranger A line ranger consists of either two plane mirrors or two right angled isosceles prisms placed one above the other as depicted in Figure (e). The diagonals of both the prisms are silvered so as to reflect the incident rays. Line rangers are provided with a handle to hold the instrument. A line ranger can also be used to draw offset on a chain line. Use of chain Unfolding Of Chain: To open a chain the strap is unfastened and the two brass handles are held in the left hand and the bunch is thrown forward with the right hand. Then on chainman stands at the starting station by holding one handle and another moves forward by holding the other handle until the chain is completely extended. Folding of Chain : After the completion of the work the chain should be folded in to a bundle and fastened with a leather strap. To do this the handles of the chain should be brought together by pulling the chain at the middle. Commencing from the middle, take two pairs of link at a time with the right hand and place them obliquely across the other in the left hand. When the chain is collected in a bundle, it is tied with a leather strap. This process is called the folding of chain. Reading a chain : A survey chain is generally composed of 100 or 150 links formed by pieces of galvanised mild steel wire of 4 mm diameter. The ends of each link are looped and connected together by means of three circular or oval shaped wire rings to provide flexibility to chain. The length of each link is measured as the distance between the centres of two consecutive middle rings. The ends of chain are provided with brass handles with swivel joints. The end link length includes the length of handle and is measured from the outside of the handle, which is considered as zero point or the chain end. Tallies, which are metallic tags of different patterns, are provided at suitably specified points in the chain to facilitate quick and easy reading. A semi-circular grove is provided in the centre on the outer periphery of handle of chain for fixing the mild steel arrow at the end of one chain length. The number of links in a chain could be 100 in a 20 m chain and 150 in a 30 m chain. The details of a metric chain are as shown in Figure Testing of a chain : Due to continuous use, a chain may be elongated or shortened. So, the chain should be tested and adjusted accordingly. If full adjustment is not possible, then the amount of shortening ( known as ‘too short’ ) and elongation ( known as ‘too long’ ) should be noted clearly for necessary correction applicable to the chain. For testing the chain, a test gauge is established on a level platform with the help of standard steel tape. The steel tape is standardised at 200C and under a tension of 8 kg. The test gauge consist of two pegs having nails at the top and fixed on a level platform a required distance apart ( say 20 or 30m ). The incorrect chain is fully stretched by pulling it under normal tension along the test gauge. If the length of the chain does not tally with standard length, then the attempt should be made to rectify the error. Finally the amount of elongation or shortening should be noted. The allowable error is about 2mm per 1m length of the chain. The overall length of the chain should be within the following permissible limit : 20 m chain : ± 5mm 30m chain : ± 8mm Adjustment of a chain : Chains are adjusted in the following ways :  When the chain is too long, it is adjusted by : Closing the opened joints of the rings. Reshaping the elongated rings. Removing one or more circular rings. Replacing the worn-out rings.  When the ring is too short, it is adjusted by: Straightening the bent links. Flattening the circular rings. Inserting the new rings where necessary. Replacing the old rings by some larger rings. Ranging : The process of establishing intermediate points on a straight line between two end points is known as ranging. Purpose of ranging : The purpose of ranging is to mark a number of intermediate points on a survey line joining two stations in the field so that the length between them may be measured correctly. If the line is short or its end station is clearly visible, the chain may be laid in true alignment. But if the line is long or its end station is not visible due to undulation ground, it is required to mark a number of points with ranging rods. Code of Signals for Ranging Sl.No. Signal by the Surveyor Action by the Assistant 1 Rapid sweep with right hand Move considerably to the right 2 Slow sweep with right hand Move slowly to the right 3 Right arm extended Continue to move to the right 4 Right arm up and moved to the right Plumb the rod to the right 5 Rapid sweep with left hand Move considerably to the left 6 Slow sweep with left hand Move slowly to the left 7 Left arm extended Continue to move to the left 8 Left arm up and moved to the left Plumb the rod to the left 9 Both hands above head and then brought down Correct 10 Both arms extended forward horizontally and the Fix the rod hands depressed briskly Direct ranging : When intermediate ranging rods are fixed along the chain line, by direct observation from either end station, the process is known as “Direct Ranging”. Direct ranging is possible when the end stations are inter visible. The following procedure is adopted for direct ranging : Erect ranging rods or poles vertically behind each end of the line. Stand about 2m behind the ranging rod at the beginning of the line. Direct the assistant to hold a ranging rod vertically at arm’s length at the point where the intermediate station is to be established. Direct the assistant to move the rod to the right or left , until the ranging rods appear to be exactly in a straight line. Stoop down and check the position of the rod by sighting over their lower ends in order to avoid error to non-vertically of the ranging rods. After ascertaining that the ranging rods are in a straight line, signal the assistant to fix the ranging rod. Indirect ranging : When the end stations are not inter visible due to there being high ground between them, intermediate ranging rods are fixed on the line in an indirect way. This method is known, as indirect ranging or reciprocal ranging. The following procedure is adopted for indirect ranging. Suppose A and B are two end stations which are not intervisible due to high ground existing between them. Suppose it is required to fix intermediate points between A and B. Two chain men take up positions at R1 and S1 with ranging rods in their hands. The chainman at R1 stands with his face towards B so that he can see the ranging rods at S1 and B. Again the chainman at S1 stands with his face towards A so that he can see the ranging rods at R1 and A. Then the chainmen proceed to range the line by directing each other alternately. The chainman at R1 direct the chainman at S1 to come to position S2 so that R1 , S2 and B are in the same straight line. Again the chainman at S2 directs the chainman at R1 to move the position at R2 so that S2 , R2 and A are in the same straight line. By directing each other alternately in this manner, they change their positions every time until they finally come to the positions R and S,which are in the straight line AB. This means the points A, R, S and B are in the same straight line. Role of Leader and Follower : The chainman at forward end of the chain, who drag the chain forward, is known as leader. The duties of the leader are as follows: a. To drag the chain forward with some arrows and a ranging rod. b. To fix arrows on the ground at the end of every chain. c. To obey the instructions of the follower. The chainman at the rear end of the chain, who holds the zero end of the chain at the station, is known as the follower. The duties of the follower are : a. To direct the leader at the time of ranging. b. To carry the rear handle of the chain. c. To pick up the arrows inserted by the leader. Chaining on Level Ground : Before starting the chaining operation two ranging rods should be fixed on the chain line, at the end stations. The other ranging rods, should be fixed near the end of each chain length, during the ranging operation. To chain the line, the leader moves forward by dragging the chain and by taking with him a ranging rod and 10 arrows. The follower stands at the starting station by holding the other end of chain. When the chain is fully extended , the leader holds the ranging rod vertically at arm’s length. The follower directs the leader to move his rod to the left or right until the ranging rod is exactly in line. Then the follower holds the zero end of the chain by touching the station peg. The leader stretches the chain by moving it up and down with both hands, and finally places it on the line. He then inserts an arrow on the ground at the end of the chain and marks with a cross ( X ). Again, the leader moves forward by dragging the chain with nine arrows and the ranging rod. At the end of the chain, he fixes another arrow as before. As the leader moves further, the follower picks up the arrows which were inserted by the leader. During chaining the surveyor or an assistant should conduct the ranging operation. In this way, chaining is continued. When all the arrows have been inserted and the leader has none left with him, the follower hands them over to the leader; this should be noted by the surveyor. To measure the remaining fractional length, the leader should drag the chain beyond the station and the follower should hold the zero end of the chain at the last arrow. Then the odd links should be counted. Chaining on Sloping Ground: Chaining on the surface of a sloping ground gives the sloping distance. For plotting the surveys, horizontal distances are required. It is therefore, necessary either to reduce the sloping distance to horizontal equivalent or to measure the horizontal distances between the stations directly. The following are the different methods that are generally employed. a) Direct Method or Stepping Method b) Indirect Method Direct Method: This method is applied when slope of the ground is very steep. In this method, the sloping ground is divided in to a number of horizontal and vertical strips, like steps. So, this method is also known as stepping method. The length of the horizontal portions are measured and added to get the total horizontal distance between the points. The steps may not be uniform, and would depend on the nature of the ground. Procedure: Suppose the horizontal distance between points A and B is to be measured. The line AB is first ranged properly. Then, the follower holds the zero end of the tape at A. The leader selects a suitable length AP1 so that P1 is at chest height and AP1 is just horizontal. The horizontal is maintained by eye estimation, by tri-square or by wooden set-square. The point P2 is marked on the ground by plumb-bob so that P1 is just over P2. The horizontal length AP1 is noted then the follower moves to the position P2 and holds the zero end of the tape at that point. Again the leader selects a suitable length P2P3 in such a way that P2P3 is horizontal and P3P4 vertical. Then the horizontal lengths P2P3 and P4P5 are measured. So the total horizontal length, AB = AP1 + P2P3 + P4P5 Indirect Method :  When the slope of the ground surface is long and gentle, the stepping method is not suitable. In such a case, the horizontal distance may be obtained by the indirect methods. Those are of following types. a. By measuring the slope with clinometers. b. By applying hypotenusal allowance c. By knowing the difference of level between the points. a. Measuring slope with a clinometer : A clinometers is a graduated semicircular protractor. It consists of two pins P1 and P2 for sighting the object. A plum bob is suspended from point O with a thread. When the straight edge is just horizontal, the thread passes through 0. When the straight edge is tilted, the thread remains vertical, but passes through a graduation on the arc which shows the angle of slope. Suppose C and D are two points on sloping ground. Two ranging rods are fixed at these points. Then two other points C1 and D1 are marked on the ranging rods so that CC1 = DD1 The clinometers is placed in such a way that its centre just touches the mark C1. The clinometers is then inclined gradually until the points P1, P2, and D1 are in the same straight line. At this position the thread of the clinometers will show an angle which is the angle of slope of the ground. Suppose this angle is α. The sloping distance CD is also measured. The required horizontal distance = CB = lcosα  b. Applying hypotenusal allowance In this method , the slope of the ground is first out by using the clinometers. Hypotenusal allowance is then made for each tape length. Let = angle of slope measured by clinometers AB = AB1 = 20m = 100 links AC = AB sec = 100 sec  B1C = AC – AB1 = 100 sec  - 100 = 100 (sec − 1) Obstacle: A chain line may be interrupted the following situations: 1. When chaining is free, but vision is obstructed. 2. When chaining is obstructed, but vision is free, and 3. When chaining and vision are both obstructed 1. Chaining free but vision obstructed: Such a problem arises when a rising ground or a jungle area interrupts the chain line. Here the end stations are not inter-visible. Case – I The end stations may be visible from some intermediate points on the rising ground. In this case, reciprocal ranging is resorted to, and the chaining is done by stepping method. Case – II The end stations are not visible from intermediate points when jungle are comes across the chain line. Let AB line be the actual chain line which can not be ranged and extended because of interruption by a jungle. Let line extended up to R. A point P is selected on the chain line and a random line PT is taken in a suitable direction. Points C, D and E are selected on the random line and perpendiculars are projected from them. The perpendicular at C meets the line at  Theoretically, ! ##! " = "# ##! $$% = "# x PD …………… ………. …………… (1) Again from triangle &''% and &((% ))! ##! ") = "# ##! ''% = "# x PE …………… ………. …………… (2) From eq 1 and 2, the lengths ** and ++ are calculated. The distance is measured along the perpendiculars at D and E. Points * and + should lie in the chain line AB Distance ,+ = -,+. + ++. 2. Chaining obstructed but vision free: Such a problem arises when a pond or river comes across the chain line. The stations may be tackled in the following ways. Case – I When a pond interrupts the chain line, it is possible to go around the obstruction. CD = EF CD = √'$ + ('  3. Chaining and vision both obstructed : Such a problem arises when a building comes across the chain line. It is solved in the following manner. Suppose AB is the chain line. Two points C and D are selected on it at one side of the building. Equal perpendiculars CC1 and DD1 are erected. The line C1D1 is extended until the building is crossed. On the extended line, two points E1 and F1 are selected. Then perpendiculars E1E and F1F are so erected that E1E = F1F = D1D = C1C Thus, the points C, D, E and F will lie on the same straight line AB Here, DE = D1E1 The distance D1E1 is measured , and is equal to the required distance DE. Problem : A chain line ABC crosses a river, B and C being on the near and distant banks respectively. The line BM of length 75 m is set out at right angles to the chain line at B. If the bearings of BM and MC are 2870 15’ and 620 15’ respectively, find the width of the river. Solution :