Survey Camp Report

RAJALAKSHMI ENGINEERING COLLEGE RAJALAKSHMI NAGAR, THANDALAM – 602105.

DEPARTMENT OF CIVIL ENGINEERING SURVEY CAMP REPORT (11.02.2013 – 16.02.2013) FEBRAURY 2013

NAME REGISTER NO.

: S.NIVETHA : 21110103035

RAJALAKSHMI ENGINEERING COLLEGE RAJALAKSHMI NAGAR, THANDALAM – 602105.

BONAFIDE CERTIFICATE NAME ________________________________________________ ACADEMIC YEAR ________SEMESTER_____ BRANCH______

UNIVERSITY REGISTER NO. ___________________

Certi8fied that this is the bonafide record of work done by the above student in the _________________ Laboratory during the year 2012-2013

Signature of the faculty in charge Submitted for the practical examination held on ______________

Internal examiner

External Examiner

Acknowledgement I would like to acknowledge and extend my heartfelt gratitude to Dr. M. Kaarmegam (Dean, Department of civil engineering) and Dr. A.Geetha Karthi (Head of the Civil Department) for their vital encouragement and support in the completion of this project report. This survey camp meant a lot to me as it gave me a lot of field experience. I would like to thank the faculty in charge, Mr. A.Anbejil and Mr. Gopi (Lab Instructor), who co-operated with me in the matter of guidance and instruments. I would also like to thank all the staff members of civil department for their constant guidance and motivation. Most of all I thank my batch mates, who were very co-operative in the completion of this report. I would also like to thank the chairperson, Dr. (Mrs.) Thangam Meganathan and the principle Dr.G.Thanigaiarasu for giving the perfect opportunity to work within the YMCA camp grounds, Yelagiri.

RAJALAKSHMI ENGINEERING COLLEGE RAJALAKSHMI NAGAR, THANDALAM – 602105.

DEPARTMENT OF CIVIL ENGINEERING SURVEY CAMP REPORT SUBMITTED BY

S.NO.

NAME

REGISTER NO.

1.

NIVETHA.S

21110103035

2.

PRABHAVATHY.S

21110103037

3.

SANJU.S

21110103046

4.

SATHYA.D

21110103047

5.

SHARADHA.S

21110103048

6.

SHOBANA.S

21110103049

7.

SUBHA.S

21110103052

8.

UMA.P

21110103057

9.

SUGANYA.M

21110103053

CONTENTS

S.NO.

DATE

1)

11.02.13

2)

12.02.13

3)

12..02.13

4)

13.02.13

5)

13.02.13

6)

14.02.13

7)

14.02.13

8)

14.02.13

9)

15.02.13

10)

TITLE

PAGE NO.

Preparation of Topographic Map for YMCA CAMPUS Determination of height of base inaccessible object – Single plane method Determination of height of base inaccessible object – Double plane method Determination of height by Stadia method

1 8 10 12 14

15.02.13

Determination of height by Tangential method Determination of area of the site by Triangulation Determination of area of the site by Trilateration Determination of internal angles by traversing method Leveling – Longitudinal and Cross sectional methods Grid contouring

11)

15.02.13

Radial contouring

33

12)

16.02.13

Setting out the curve by Rankine’s method

36

18 21 23 24 31

PREPARATION OF TOPOGRAPHY MAP FOR YMCA SITE TOPOGRAPHY Topography is a field of planetary science comprising the study of surface shape and features of the Earth and other observable astronomical objects including planets, moons, and asteroids. It is also the description of such surface shapes and features (especially their depiction in maps). The topography of an area can also mean the surface shape and features them. In a broader sense, topography is concerned with local detail in general, including not only relief but also natural and artificial features, and even local history and culture. This meaning is less common in America, where topographic maps with elevation contours have made "topography" synonymous with relief. The older sense of topography as the study of place still has currency in Europe.

OBJECTIVES An objective of topography is to determine the position of any feature or more generally any point in terms of both a horizontal coordinate system such as latitude, longitude, and altitude. Identifying features and recognizing typical landform patterns are also part of the field. A topographic study may be made for a variety of reasons: military planning and geological exploration have been primary motivators to start survey programs, but detailed information about terrain and surface features is essential for the planning and construction of any major civil engineering, public works, or reclamation projects.

TECHNIQUES OF TOPOGRAPHY There are a variety of approaches to studying topography. Which method(s) to use depend on the scale and size of the area under study, its accessibility, and the quality of existing surveys.

DIRECT SURVEY Surveying helps determine accurately the terrestrial or three-dimensional space position of points and the distances and angles between them using leveling instruments such as theodolites, dumpy levels and clinometers. Even though remote sensing has greatly sped up the process of gathering information, and has allowed greater accuracy control over long distances, the direct survey still provides the basic control points and framework for all topographic work, whether manual or GIS-based. In areas where there has been an extensive direct survey and mapping program, the compiled data forms the basis of basic digital elevation datasets such as USGS DEM data. This data must often be "cleaned" to eliminate discrepancies

between surveys, but it still forms a valuable set of information for large-scale analysis. The original American topographic surveys (or the British "Ordnance" surveys) involved not only recording of relief, but identification of landmark features and vegetative land cover.

REMOTE SENSING Remote sensing is a general term for geo data collection at a distance from the subject area.

AERIAL AND SATELLITE IMAGERY Besides their role in photogrammetric, aerial and satellite imagery can be used to identify and delineate terrain features and more general land-cover features. Certainly they have become more and more a part of geo visualization, whether maps or GIS systems. False-color and nonvisible spectra imaging can also help determine the lie of the land by delineating vegetation and other land-use information more clearly. Images can be in visible colours and in other spectrum Photogrammetric Photogrammetric is a measurement technique for which the co-ordinates of the points in 3D of an object are determined by the measurements made in two photographic images (or more) taken starting from different positions, usually from different passes of an aerial photography flight. In this technique, the common points are identified on each image. A line of sight (or ray) can be built from the camera location to the point on the object. It is the intersection of its rays (triangulation) which determines the relative three-dimensional position of the point. Known control points can be used to give these relative positions absolute values. More sophisticated algorithms can exploit other information on the scene known a priori (for example, symmetries in certain cases allowing the rebuilding of three-dimensional co-ordinates starting from one only position of the camera).

RADAR AND SONAR Satellite radar mapping is one of the major techniques of generating Digital Elevation Models (see below). Similar techniques are applied in bathymetric surveys using sonar to determine the terrain of the ocean floor. In recent years, LIDAR (Light Detection and Ranging), a remote sensing technique using a laser instead of radio waves, has increasingly been employed for complex mapping needs such as charting canopies and monitoring glaciers.

TOPOGRAPHIC MAP A topographic map is a type of map characterized by large-scale detail and quantitative representation of relief, usually using contour lines in modern mapping, but historically using a variety of methods. Traditional definitions require a topographic map to show both natural and man-made features. A topographic map is typically published as a map series, made up of

two or more map sheets that combine to form the whole map. A contour line is a combination of two line segments that connect but do not intersect; these represent elevation on a topographic map.

MAP CONVENTIONS The various features shown on the map are represented by conventional signs or symbols. For example, colors can be used to indicate a classification of roads. These signs are usually explained in the margin of the map, or on a separately published characteristic sheet. Topographic maps are also commonly called contour maps or topo maps. Topographic maps conventionally show topography, or land contours, by means of contour lines. Contour lines are curves that connect contiguous points of the same altitude (isohypse). In other words, every point on the marked line of 100 m elevation is 100 m above mean sea level. These maps usually show not only the contours, but also any significant streams or other bodies of water, forest cover, built-up areas or individual buildings (depending on scale), and other features and points of interest.

USES OF TOPOGRAPHIC MAPS Topographic maps have multiple uses in the present day: any type of geographic planning or large-scale architecture; earth sciences and many other geographic disciplines; mining and other earth-based endeavors; civil engineering and recreational uses such as hiking and orienteering.

FORMS OF TOPOGRAPHIC DATA Terrain is commonly modeled either using vector (triangulated irregular network or TIN) or gridded (Raster image) mathematical models. In the most applications in environmental sciences, land surface is represented and modeled using gridded models. In civil engineering and entertainment businesses, the most representations of land surface employ some variant of TIN models. In geostatistics, land surface is commonly modeled as a combination of the two signals – the smooth (spatially correlated) and the rough (noise) signal. In practice, surveyors first sample heights in an area, then use these to produce a Digital Land Surface Model (also known as a digital elevation model). The DLSM can then be used to visualize terrain, drape remote sensing images, quantify ecological properties of a surface or extract land surface objects. Note that the contour data or any other sampled elevation datasets are not a DLSM. A DLSM implies that elevation is available continuously at each location in the study area, i.e. that the map represents a complete surface. Digital Land Surface Models should not be confused with Digital Surface Models, which can be surfaces of the canopy, buildings

and similar objects. For example, in the case of surface models produces using the LIDAR technology, one can have several surfaces - starting from the top of the canopy to the actual solid earth. The difference between the two surface models can then be used to derive volumetric measures (height of trees etc.).

RAW SURVEY DATA Topographic survey information is historically based upon the notes of surveyors. They may derive naming and cultural information from other local sources (for example, boundary delineation may be derived from local cadastral mapping. While of historical interest, these field notes inherently include errors and contradictions that later stages in map production resolve.

REMOTE SENSING DATA As with field notes, remote sensing data (aerial and satellite photography, for example), is raw and uninterrupted. It may contain holes (due to cloud cover for example) or inconsistencies (due to the timing of specific image captures). Most modern topographic mapping includes a large component of remotely sensed data in its compilation process.

DIGITAL ELEVATION MODELLING The digital elevation model (DEM) is a raster-based digital dataset of the topography (hypsometry and/or bathymetry) of all or part of the Earth (or a telluric planet). The pixels of the dataset are each assigned an elevation value, and a header portion of the dataset defines the area of coverage, the units each pixel covers, and the units of elevation (and the zero-point). DEMs may be derived from existing paper maps and survey data, or they may be generated from new satellite or other remotely-sensed radar or sonar data.

APPLICATIONS OF TOPOGRAPHY a) It is used to provide highly detailed information about the natural and manmade aspects of the terrain. b) Topography maps are increasingly stored, transmitted and used in digital format. c) Topography maps come in different scales.

 INTRODUCTION TERMINOLOGY 1. SURVEYING The technique and science of accurately determining the terrestrial or three dimensional positions of points and the distances and angles between them. 2. BENCH MARK A survey mark made on a monument having a known location and elevation, serving as a reference point for surveying. 3. TRAVERSING A traverse may be defined as the course taken measuring a connected series of straight lines, each joining two points on the ground; these points are called traverse stations. 4. LEVELLING Levelling is the branch of surveying, which is used to find the elevation of given points with respect to given or assumed datum to establish points at a given elevation or at different elevations with respect to a given or assumed datum. 5. CONTOURING Contour lines are imaginary lines exposing the ground features and joining the points of equal elevations. 6. SIMPLE CIRCULAR CURVE A simple circular curve is the curve, which consists of a singular arc of a circle. It is tangential to both the straight lines. 7. TRANSISTION CURVE A transition curve is a curve of varying radius introduced between a straight line and a circular curve. 8. TRIANGULATION: The process of determining the location of a point by measuring angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly.

9. TRILATERATION

The methods involve the determination of absolute or relative locations of points by measurement of distances, using the geometry of spheres or triangles. In contrast to triangulation it does not involve the measurement of angles. 10. REDUCED LEVEL The vertical distance of a point above or below the datum line is called as reduced level. 11. BACK SIGHT READING This is the first staff reading that is taken in any set of the instrument after the leveling is perfectly done. The point is normally taken on the bench mark. 12. FORESIGHT READING It is the last reading that in any set of instrument and indicates the shifting of the latter. 13. INTERMEDIATE SIGHT READING The staff reading between the back sight and foresight. 14. CROSS LEVELLING: The operation of taking level transverse to the direction of longitudinal leveling. 15. RADIAL CONTOUR: Contour taken over a steep slope 16. GRID CONTOUR Contour taken over a regular (normally rectangular or square) plot

 INSTRUMENTS USED:  TOTAL STATION This survey instrument that combines a theodolite and distance meter.  EDM Electronic Distance Measurement device, the instrument used by modern surveyors that replaces the use of measurement chains. It determines distance by measuring the time it takes for laser light to reflect off a prism on top of a rod at the target location  GUNTER’S CHAIN It is a measuring device used for land survey. It was designed and introduced in 1620 by English CLERGYMAN and mathematician EDMUND GUNTER (1581-1626) long before the development of theodolite



MEASURING TAPE:

It is a flexible form of ruler. It consists of a ribbon of cloth, plastic, fiber glass, or metal strip with linear-measurement markings. It is a common measuring tool  ARROW OR MARKING PINS: They are steel equipment that are used to pin point the point to be used for survey  PEGS: They are made of wood that are used to denote the station or terminal point of a survey line.  RANGING ROD:  These are rod that are painted in black and white or red and white which is used to denote the intermediate points in the survey line.  PLUMB BOB  Equipment that is used to transfer the points from the instrument to the ground or vice versa.  DUMPY LEVEL  This is a type of leveling instrument in which the longitudinal movement of the telescope is arrested.  LEVELLING STAFF  It is a steel rod that is used to measure the vertical distance between the point on the ground and the line of collimation.

HEIGHT OF BASE IN-ACCESSIBLE OBJECT - SINGLE PLANE METHOD  AIM: To determine the elevation of the base of an in accessible object by single plane method.  EQUIPMENT REQUIRED: Theodolite with stand, ranging rod, arrow, tape or chain, leveling staff etc  PROCEDURE: 1. Let P and R be the two chosen instrument stations. Q be the elevated object whose elevation is required, R and Q lie in the same vertical plane. 2. Set up the theodolite over the station ‘P’ and level it accurately with respect to the altitude bubble. 3. Take a staff reading on BM with the line of sight horizontal to determine the elevation of instrument axis. Take both face staff readings to get to average. Let it be S1. 4. Direct the telescope with left towards the top of the object Q set ‘Q’ accurately and clamp both plates. Read vernier c and D and determine the vertical angle α 1. 5. Plunge the telescope mark the second station R in the line so that Q1P and R in the same vertical plane. 6. Change the face to right and measure the vertical angle α 1. Obtain the average value of the vertical angle. 7. Shift the instrument to setup and level it with reference to altitude bubble. Repeat step (2) and take the staff readings S2 on B.M. 8. Measure the vertical angle α 2 to Q with both face observations by repeating steps (3),(5). 9. Instruments axes at P and R are at the same level.

 Calculation for Single plane method:

 Tabulation

Inst @ A

B

Sigh t to BM Q

Height (m) 1.20 -

BM Q

1.37 -

Face left A

B

0º0’0” 14º20’20 ” 0º0’0” 14º40’20 ”

0’0” 0º0’0” 14’20” 14º17’20 ” 0’0” 0º0’0” 14’20” 14º26’20 ”

Mean

 Calculation: a) b = 10m ,s =0.170 To find D;

1) D = =

1 º

20

= 1136.68m

2) H= Dtanα1+B.M = 1136.6 tan 14º20’40” 1.37

= 291.87m

3) RL of object = RL of BM + S + H1 = 100 + 0.170 + 291.87 = 392.04m RL of object = 392.04m

 RESULT: R.L of the top of the object = 392.04m

Face Right A B 0º0’0” 14º19’40 ” 0º0’0” 14º40’40 ”

Mean

0’0” 0º0’0” 21’40” 14º20’20 ” 0’0” 0º0’0” 14’20” 14º27’30 ”

Average Value

14º19’30 ” 14º26’55 ”

HEIGHT OF BASE ACCESSIBLE OBJECT- DOUBLE PLANE  AIM: To determine the height of object, when the base is accessible.  Heights and distance or Trigonometrically leveling –Introduction: Trigonometrically leveling is an indirect method of leveling. The relative elevations of various parts are determined from observed vertical angles and horizontal distances by use of certain trigonometrically relations. This method also known as ‘height and distances’ Case1: Base of the object is accessible Case2: Base of the object is inaccessible (i) Single plane method (ii) Double plane method (a) For single object (b) For double object  EQUIPMENT REQUIRED: Transit theodolite, tape or chain, leveling staff, arrows etc  PROCEDURE: Let Q be the top of the object whose elevation is required. The horizontal distance ‘D’ between the object Q and the instrument station ‘P’ can be measured directly using a tape. The following field procedure is used. 1. Set up the theodolite over P and level it accurately with reference to altitude bubble. 2. Take a staff reading over P and level line of sight horizontal to determine the elevation of line of sight. 3. Direct the telescope towards the top of the object Q and observe the vertical angle of elevation α . 4. Let ‘h’—height of the instrument at P h1- QQ’= height of object Q above horizontal line of sight h2 – QQ1- height of object below the horizontal line of sight In the Triangle P’Q’Q h1= D tan α In the Triangle P’Q’Q1

h2= D tan beta

Therefore R.L of the top of object Q= R.L of instrument axis +h1 And R.L of bottom of object Q1=R.L of instrument axis-h2 R.L of instrument axis= R.L of BM +S = R.L of p h’ Hence, Height of object, H= h1+h2 = R.L of tip of the object – R.L of bottom of the object This method is usually employed when the distance ‘D’ is small. However if ‘D’ is large, combined correction for curvature and refraction should be applied for curvature and refraction should be applied to the calculated height. i.e., the combined correction for curvature and refraction , C= 0.06735 D2 where D is the horizontal distance is km. Its sign is positive for angle of elevation and negative for angle of depression. Thus in the figure R.L of Q= R.L of instrument axis +h1+c R.L of Q1= R.L of instrument axis –h2—C

 Calculation for Double plane method:  Tabulation

Instrument @ A B

Sight to BM Q BM Q

Height (m) 1.370 1.420 -

A

Horizontal angle B Mean

0º0’0” 64º20’40” 0º0’0” 18º40’20”

0’0” 20’40” 0’0” 40’20”

0º0’0” 64º20’40” 0º0’0” 18º40’20”

 Calculation: b) b = 2.66m To find D; 4) D = = 5) H1= Dtanα1 = 2.709 tan 14º40’20”

= 7.530m

= 1.971m

6) RL of object = RL of BM + S + H1 = 100 + 1.370 + 1.971 = 103.34 m RL of object = 103.34 m

 RESULT: R.L of top of the object = 103.34m

A

Vertical angle B Mean

0º0’0” 14º40’20” 0º0’0” 14º40’20”

0’0” 14’20” 0’0” 14’20”

0º0’0” 14º26’20” 0º0’0” 14º26’20

Bench Mark

1.370 1.420

DETERMINATION OF HEIGHT OF THE HILL BY STADIA METHOD  AIM: To determine the height of the hill joining the staff stations A and B.  INSTRUMENTS REQUIRED: Theodolite with stand, ranging rod, Leveling staff  GIVEN: Elevation of B.M= 100.000 Target distance = 1m.  PROCEDURE: 1. Set up the instrument approximately between the given objects and do the initial adjustments. 2. Direct the telescope towards object A and find the vertical angles by bisecting the ranging rod at two points having a distance of 1m (given). 3. Note down the vertical angles for the ranging rod at B. 4. Take the horizontal angles also at A and B. 5. When both the observed angles are angles of elevation B.M = 100.000m S=1m = Target distance α1 and α2= Vertical angle to upper and lower targets respectively. In this case, the stadia intercept is maintained a constant and the value of α vary accordingly. h1= Height of lower target above foot of ranging rod h0= Height of instrument above datum line D=horizontal distance between P and A = S/ tanα1 –tan α 2 V= D tanα1 R.L of H.I = R.L of B.M +h0 R.L of A = R.L of H.I + V1-h1 D2 = D12+D22 – 2 D1D2 cosø V0= level difference between A and B Height =V0/D

Tabulation  Horizontal angle :

Inst Sight @ to O A B

FACE LEFT A B MEAN 0 º0’0” 0’0” 0 º0’0” 217º30’0” 0’40” 217 º30’40”

FACE RIGHT C D MEAN 0 º0’0” 0’0” 0 º0’0” 217 º30’0” 0’40” 217 º30’40”

HORIZONTAL ANGLE 217 º30’40”

 Vertical angle : Inst @ O

Sight to A

Stadia 1 2 1 2

B

FACE LEFT C D MEAN 6º0’0” 6’20” 6 º6’20” 7 º40’0” 20’0” 7 º30’10” 9 º0’0” 10’20” 9 º5’20” 5 º0’0” 10’40” 5 º5’20”

FACE RIGHT C D 6º0’0” 6’20” 7 º30’0” 20’0” 9 º0’0” 10’20” 5 º0’0” 10’40”

 Calculation: D1= 34.120m

D2= 14.120m

AB = √

= 22.26m

Elevation of B = 100+1.440-V-2 = 100+1.440-4.87-2 = 94.57m Elevation of A = 100+1.600-V- 1 = 100+1.600-2.800-1 =96.640m

 RESULT: The height of the object = 96.640m

MEAN 6 º6’20” 7 º30’10” 9 º5’20” 5 º10’20”

VERTICAL ANGLE 6 º6’20” 7 º30’10” 9 º5’20” 5 º10’20”

DETERMINATION OF HEIGHT OF THE HILL BY TANGENTIAL METHOD  AIM: To determine the height of the hill joining the staff stations A and B.  INSTRUMENTS REQUIRED: Theodolite with stand, ranging rod, Leveling staff  GIVEN: Elevation of B.M= 100.000 Target distance = 1m.  PROCEDURE: 1. Set up the instrument approximately between the given objects and do the initial adjustments. 2. Direct the telescope towards object A and find the vertical angles by bisecting the ranging rod at two points having a distance of 1m (given). 3. Note down the vertical angles for the ranging rod at B. 4. Take the horizontal angles also at A and B. When both the observed angles are angles of elevation B.M = 100.000m S=1m = Target distance Α 1 and Α 2= Vertical angle to upper and lower targets respectively. h1= Height of lower target above foot of ranging rod h0= Height of instrument above datum line D=horizontal distance between P and A = S/ tanα 1 –tan α 2 V= D tanα 1 R.L of H.I = R.L of B.M +h0 R.L of A = R.L of H.I + V1-h1 D2 = D12+D22 – 2 D1D2 cosø

V0= level difference between A and height =V0/D

 Tabulation Instrument @

O

Sight to A B

Horizontal

Vertical angle 5º 10º 5º 10º

Top 0.650 3.500 2.170 0.870

Stadia Hair Middle Bottom 0.490 0.330 3.300 3.170 2.100 2.020 0.840 0.715

: 217 º 30’ 40”

 Calculation: D= KS Cos2ø + C Cos ø θ1= 5º θ2= 10º D1= 31.760m D2= 32.010m AB = √ VOA = D tanα2 = 2.778m

= 63.770m VOB = D tanα2 = 2.800m

Elevation of A = 100+1.600-2.778-1 =97.822m Elevation of B = 100+1.440-2.800-1 =96.640m  RESULT: The height of the object = 97.822m

Triangulation and Trilateration

S (m) 0.320 0.330 0.150 0.155

The method of surveying called triangulation is based on the trigonometric proposition that if one side and two angles of a triangle are known, the remaining sides can be computed. The vertices of the triangles are known as triangulation stations. The side of the triangle, whose length is predetermined, is called the base line. A trilateration system also consists of a series of joined or overlapping triangles. However, for trilateration the lengths of all the sides of the triangle are measured and few directions or angles are measured to establish azimuth. Trilateration has become feasible with the development of electronic distance measuring equipment which has made possible the measurement of all lengths with high order of accuracy under almost all field conditions.

Objective of triangulation and trilateration surveys: The main objective of triangulation or trilateration surveys is to provide a number of stations whose relative and absolute positions, horizontal as well as vertical are accurately established. More detailed location or engineering surveys are then carried out from these stations. The triangulation surveys are carried out

1. To establish accurate control for plane and geodetic surveys of large areas, by terrestrial methods, 2. To establish accurate control for photogrammetric surveys of large areas, 3. To assist in the determination of the size and shape of the earth by making observations for latitude, longitude and gravity.  Classification of triangulation and trilateration system 1. First order: Determine the shape and size of the earth or to cover a vast area 2. Second order: This consists of a network within a first order triangulation. 3. Third order: It is a frame work fixed within and connected to a second order triangulation system to immediate control for locating surveys.  Layout for triangulation: The triangles in a triangulation system can be arranged in a number of ways: 1. Single chain of triangles 2. Double chain of triangles 3. Braced quadrilaterals

4. Centered triangles and polygons 1. Single chain of triangles: When the control points are required to be established in a narrow strip of terrain such as a valley between ridges, a layout consisting of single chain of triangles. It does not involve observations of long diagonals. This system does not provide any check on the accuracy of observations. 2. Braced quadrilaterals A triangulation system consisting of figures containing four corner stations and observed diagonals. This system is treated to be the strongest and the best arrangement of triangles, and it provides a mean of computing the lengths of the sides using different combinations of sides and angles. 3. Double chain of triangles: This arrangement is used for covering the larger width of a belt. This system also has disadvantages of single chain of triangles system.

4. Centered triangles and polygons A triangulation system which consists of figures containing interior stations in triangles and polygons is known as centered triangles and polygons Though this system provides checks on the accuracy of the work, generally it is not as strong as the braced quadrilateral arrangement. Moreover, the progress of work is quite slow due to the fact that more settings of the instrument are required.

DETERMINATION OF AREA BY TRIANGULATION METHOD  AIM: To determine the area of the given plot using the method of triangulation

 DESCRIPTION: Triangulation is the process of establishing horizontal control in the surveying. The triangulation system consist of number of inter connected triangles in which the length of base line and the triangle are measured very precisely.  A. B. C. D.

EQUIPMENT NEEDED: Theodolite with tripod stand Ranging rod Tape Arrow

 FORMULA USED: 1) Sine formula: a/sin A= b/sin B= c/sin C  For calculating the sides of a triangle, AB2=AC2+BC2 -2*AC*BC*cos ø ø ---angle between ACB 2) To find area A=(S * (S - a) * (S - b) * (S - c)) S=  PROCEDURE: 1. The base line is selected and marked as I1, I2, I3, I4 and I5 at 60 m distance apart. 2. The other station points namely A, B, C, D and A’, B’, C’, D’ where selected around the base line I1 to I5. 3. Ranging rods are fixed at each point. 4. Now the instrument is placed over the station I1 and all other adjustments were made. 5. Then from I1 the ranging rod at the station I2 is sighted and angles were noted keeping the instrument at face left. 6. Similarly from station I1 all other points were sighted and the angles were measured.

7. After that the angles were noted by changing the face of the instrument to face right. 8. Then the instrument is shifted to station I2 and the initial adjustments are done. 9. Repeat the same procedure carried out at the station I1 and the angles were recorded. 10. Similarly, repeat this procedure for other station points.

 Tabulation : Instrument at

Sight to E B H C A E F H I F G D B I J G C J

A

B

C

D

31 87 36 71 61 25 32 36 63 39 23 70 74 56 39 23 84 42

Horizontal Angle A B ‘ “ “ 25 25 24 25 0 5 0 5 0 25 0 25 10 5 10 5 20 0 20 5 15 0 15 0 29 25 20 25 0 0 0 0 30 5 29 5 25 40 25 40 29 20 20 20 5 5 5 5 20 10 20 10 20 20 20 20 25 20 24 20 29 20 20 20 15 10 15 10 0 5 0 5

Mean

31 87 36 71 61 25 32 36 63 32 23 70 74 56 39 23 84 42

‘ 49 0 0 20 40 30 39 0 59 50 39 10 40 40 49 39 30 0

“ 50 5 50 10 5 0 50 0 10 40 40 10 20 40 40 40 20 5

 Calculation: 

IN TRIANGLE FBC:

FBC= 0 0”, BCF=71 20’10” BFC=180-( =

= =

= ; b=28.12m, s=36.88

S= a=√

= 223.49m²

 IN TRIANGLE BIC: IBC= 72 16.2/sin 63

, ICB=44 = BI/sin

, BIC=

d1 =16.2m ; C=28.44m

BI =12.523

=

; CI =17.14m

S= Area = √ = 96.42m². TOTAL AREA =223.49+96.42+179.04+363.511+336.80+178.6+141.56+186.869+401.54+286.26 /10 = 2623.6m².

 RESULT: The total area of the given land area by triangulation method is: 2623.6m2

DETERMINATION OF AREA BY TRILATERATION METHOD  AIM:

To determine the distance between the given station points using the method of trilateration and area enclosed by the station points  DESCRIPTION: Trilateration is the method of calculating the distance between the station points by running a closed traverse.  EQUIPMENT REQUIRED: 1. Theodolite 2. Ranging rod 3. Leveling staff 4. Cross staff 5. Arrows 6. Pegs  FORMULA USED: 1) HORIZONTAL DISTANCE: D= KS Cos2ø + C Cos ø K=multiplicative constants=100 S= Staff intercepts (Top hair- bottom hair) C= additive constants=0 2) AREA OF TRIANGLE: A= S *(S - a) * (S - b) * (S - c) S=  PROCEDURE: 1) Mark the given points A, B, C, D, and E … by using peg or arrows in such a way that it is possible to see those points from any point 2) Then the instrument is placed in such a way that it is center to all the points and also visible from the selected point. 3) The initial adjustment are done for accuracy in the survey 4) Then the point A is focused, and then the vertical angle and the top, middle and top hair reading are taken by placing the leveling staff at point A. 5) The vertical angle and the top, middle and top hair reading are taken for all the given points 6) Then the instrument is set any point and the point and the distance and vertical angle between the adjacent points are taken. 7) Thus we get a polygon whose sides are known or multiple triangles whose sides are known. By using the given dimensions and by using the triangle formulas the area can be calculated.  Tabulation

Instrument @ O

A C E G

Sight to A B C D E F G G B B D D F F A

 Calculation : Consider ∆OAG; OA = 34.95 m (a) OG = 22.96 m (b) AG = 16.49 m (c) S=

Vertical angle 2 º10’7.5” 0º0’20” 0º20’20” 3º20’5” 3º24’20” 6º12’10” 0º40’3.5” 0º20’10” 0º20’15” 1º40’0” 0º1 ’20” 0º20’10” 0º0’0” 0º40’2.5” 1º40’15”

TOP 1.720 1.780 1.300 1.480 0.980 3.060 2.020 1.315 0.765 2.210 0.870 1.630 1.760 1.250 1.820

Staff Reading MIDDLE BOTTOM 1.635 1.370 1.605 1.435 1.360 0.830 0.270 1.070 0.815 0.660 2.910 2.750 1.940 1.790 1.475 1.150 0.920 0.595 2.350 2.070 0.910 0.850 1.460 1.300 1.320 0.920 1.090 0.930 1.645 1.495

S (m) 0.350 0.345 0.470 0.410 0.320 0.310 0.230 0.165 0.170 0.140 0.020 0.330 0.840 0.320 0.325

= 37.208 m

Area of triangle OAG √ = (37.208 (37.208-34.95) (37.208-22.96) (37.208-16.49)) ½ = 157.403 m2 Similarly for other triangles; AOB = 286.95m2 BOC =125.87m2 COD =114.68m2 DOE =514.74m2 EOF =423.46m2 GOF =335.95m2 Total area of the triangles: 1958.15m2  RESULT: Thus the area of the given land is found out by using trilateration.

THEODOLITE TRAVERSING  AIM:

Distance (m) 34.949 34.499 46.998 40.862 31.887 30.638 22.997 16.499 16.999 13.988 1.999 32.998 84.000 31.995 32.472

To determine the individual angle for closed traverse.  INSTRUMENT REQUIRED: 1. Theodolite 2. Chain or tape 3. Ranging rod 4. Peg etc…  PROCEDURE: 1. ABCDE is a closed traverse whose included angle can be calculated as follows. 2. Setup the theodolite exactly over the station A and level it accurately. 3. Fix the tabular compass or through compass to the theodolite. 4. Set the vernier A reads to zero degree and loosen the lower clamp and direct the telescope towards north through tabular compass bisect it accurately using lower clamp and tangent screw. 5. Loosen the upper clamp and direct the telescope towards B and bisect it accurately note down the reading in the horizontal circle which gives the fore bearing of line AB. 6. Determine the included angle A. 7. Shift the theodolite to the station B and do all temporary adjustments. 8. With vernier reads to zero, direct the telescope towards A and bisect it accurately using lower clamp and tangent screw. INS. @A

SIGHT TO

A

E B

B

A C

C

D B

D

E C

E

A D

FACE LEFT SWING RIGHT VER. VER. B MEAN HORI. A ANGLE 0˚0’0” 0’0” 0’0” 134˚40’4” 134˚20 20’4” 134˚20’4 ’4” ” 0˚0’0” 0’0” 0’0” 100˚40’0” 100˚40 40’0” 100˚40’0 ’0” ” 0˚0’0” 0’0” 0’0” 10 ˚20’5” 10 ˚20 20’5 10 ˚20’5 ’5” ” 0˚0’0” 0’0” 0’0” 109˚20’5” 109˚20 20’5” 109˚20’5 ’5” ” 0˚0’0” 0’0” 0’0” 7˚40’15” 7˚40’ 40’15” 7˚40’15 15” ”

FACE RIGHT SWING LEFT VER. VER. B MEAN HORI. A ANGLE 0˚0’0” 0’0” 0˚0’0” 134˚0’5 ” 134˚0’5 20’4” 134˚0’5 ” ” 0˚0’0” 0’0” 0˚0’0” 100˚20’ 0” 101˚20’ 40’0” 100˚20’ 0” 0” 0˚0’0” 0’0” 0˚0’0” 10 ˚40’ 5” 10 ˚40’ 20’5 10 ˚40’ 5” 5” 0˚0’0” 0’0” 0˚0’0” 109˚20’ 5” 109˚20’ 20’5 109˚20’ 5” 5” 0˚0’0” 0’0” 0˚0’0” 7˚0’15 ” 7˚0’15 40’15” 7˚0’15 ” ”

AVG. ANGLE 134˚20’ 5” 100˚20’ 0” 10 ˚30’ 5” 109˚20’ 5” 7˚29’4 5”

 RESULT: Thus a closed traverse is plotted and the angles are taken.

LONGITUDINAL AND CROSS SECTIONAL SECTIONING SURVEY  AIM:

To plot the longitudinal section and cross section of the given and using the method of fly leveling.  1. 2. 3. 4. 5. 6. 7. 8.

EQUIPMENT REQUIRED: Leveling staff Levelling instrument Ranging rods Cross staff Chain Tape Peg Arrow

 FORMULA: Arithmetic check: ∑Back sight –∑ fore sight = last reduced level-first reduced level LONGITUDINAL SECTIONING: The operation of taking level along the centre lines if any augments at regular intervals is known as longitudinal leveling. Back sight, intermediate sight, fore sight are taken at regular intervals at every set up of the instrument to the nature of the ground surface. CROSS SECTIONING: The operation of taking levels along the transverse direction to the direction of the longitudinal leveling. The cross section is taken at regular interval along the augment.  PROCEDURE: 1. The instruments were setup along the side of the road and the necessary adjustments were made. 2. Then the bench mark is fixed by sighting the instrument on any permanent structures. 3. The width of the road is measured and the staff is held at the midway of the proposed road. 4. The central hair reading is noted down, then staff is shifted to the right and the left side and the reading is recorded. 5. Similarly, the same procedure is carried out by keeping the staff at regular intervals. 6. Then the reduced levels of the offsets were calculated and the profile is shown in the graph.

 LONGITUDINAL LEVELLING (L.S) Station

H.DISTANCE B.S

I.S

F.S

RISE

FALL

R.L

Remarks

A

B C

D

E

F

G

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 205 210 215 220 225

1.485 1.55 1.89 2.175 2.61 2.845 3.075 3.74 4.32 4.235 0.620

0.065 0.340 0.285 0.015 0.685 0.230 0.665 0.580 0.580 0.570 1.350 0.395 0.215 0.425 0.505 0.580 0.40

4.900 4.805 1.97 2.365 2.58 3.005 3.51 4.09

1.00

4.49 0.7 1.3 2.005 2.64 3.29 4.02

1.23

0.300

4.63 1.13 1.42 2.13 2.735 3.10 3.35 3.83

0.3

0.100

4.17 0.93 1.23 1.43 1.605 1.74 1.94 2.10 2.17 2.24 2.38 2.45

1.34

0.600 0.705 0.635 0.650 0.730 0.610

2.600

0.320 0.710 0.005 0.965 0.250 0.480 0.340 0.630 0.300 0.200 0.175 0.135 0.200 0.160 0.070 0.070 0.140 0.070 0.150

101.550 101.485 101.145 100.860 100.875 100.190 99.960 99.295 98.715 98.135 97.565 96.215 95.820 95.605 95.180 94.675 94.095 93.695 93.995 93.395 92.690 92.055 91.405 90.675 90.065 90.195 89.875 89.165 89.160 88.195 87.945 87.465 87.125 86.496 86.195 85.995 85.820 85.685 85.485 85.325 85.255 85.185 85.015 84.945 84.795

BM

Station1 Station2

Station3

Station4

Station5

Station6

230 235 240 245 250

2.12 2.25 2.42 2.51

0.780 0.130 0.170 0.090 0.090

2.600

 Last R.L – First R.L 18.015

= =

84.015 83.885 83.715 83.625 83.535

∑Rise - ∑ Fall 18.015

 TABULATION (CROSS SECTION – LEFT) Station H.DISTANCE 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155

B.S 1.485

I.S

F.S

RISE

1.55 1.865 2.115 2.62 2.790 3.060 3.75 4.325 4.75

0.065 0.315 0.250 0.505 0.170 0.270 0.690 0.575 0.625

4.95 4.22

0.63

0.53 4.76

0.540 1.44 0.305 0.265 0.46 0.43 0.58 0.19 0.18

2.07 2.375 2.64 3.10 3.53 4.11 4.30 1.07

4.48 0.82 1.22 2.075 2.67 3.29 4.07

1.130

0.25

4.57 1.45 2.085 2.775 3.00

FALL

0.400 0.855 0.595 0.620 0.780 0.500 0.32 0.635 0.69 0.225

R.L 101.550 101.485 101.170 100.920 100.415 100.245 99.975 99.285 98.710 98.085 98.615 98.075 96.635 96.330 96.065 95.605 95.175 94.595 94.405 94.225 94.475 94.075 93.220 92.625 92.005 91.225 90.725 90.405 89.770 89.080 88.855

160 165 170 175 180 185 190 195 200 205 210 215 220 225 230 235 240 245 250

3.33 3.81 0.3

0.33 0.48 0.31 0.595 0.34 0.195 0.190 0.110 0.240 0.110 0.080 0.020

4.12 0.895 1.235 1.43 1.62 1.73 1.97 2.08 2.16 2.18

0.920

∑RISE - ∑FALL 16.956

2.13

0.050

1.126 1.320 1.580 1.742 1.988

0.206 0.194 0.260 0.162 0.246 0.279

2.267 = =

88.525 88.045 87.735 87.140 86.800 86.605 86.415 86.305 86.101 85.991 85.911 85.891 85.941 85.735 85.541 85.281 85.119 84.873 84.594

LAST R.L - FIRST R.L 16.956

 TABULATION (CROSS SECTION- RIGHT) H.DISTANCE B.S I.S F.S 5 1.39 10 1.63 15 1.87 20 2.27 25 2.63 30 2.815 35 3.13 40 3.78 45 4.33 50 4.76 4.88 55 4.235 60 0.69 4.3 65 1.745 70 2.05 75 2.4 80 2.61 85 3.003 90 3.47 95 4.08

RISE

FALL 0.240 0.240 0.400 0.360 0.185 0.315 0.650 0.550 0.550

0.525 0.065 1.055 0.305 0.350 0.210 0.393 0.467 0.610

R.L 101.550 101.310 101.710 100.670 100.310 100.125 99.810 99.160 98.610 98.060 98.585 98.520 97.465 97.160 96.810 96.600 96.207 95.740 95.130

100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 205 210 215 220 225 230 235 240 245 250

1.05

4.5

0.420

0.84 1.44 2.09 2.66 3.34 4.06 1.09

0.21 0.600 0.650 0.570 0.680 0.720 0.590 0.340 0.680 0.565 0.125 0.520 0.480 0.350 0.650 0.360 0.120 0.180 0.110 0.230 0.120 0.070 0.060

4.65 1.43 2.11 2.675 2.8 3.32 3.8

0.3

4.15 0.95 1.31 1.43 1.61 1.72 1.95 2.07 2.14 2.20

0.930

2.19

0.100

1.129 1.322 1.575 1.745 1.982

0.199 0.193 0.253 0.170 0.237 0.279

2.261  Last R.L - First R.L 16.631

= =

94.710 94.920 94.320 93.670 93.100 92.420 91.700 91.110 90.770 90.090 89.525 89.400 88.880 88.400 88.050 87.400 87.040 86.920 86.740 86.630 86.400 86.280 86.210 86.150 86.250 86.051 85.858 85.605 85.435 85.198 84.919

∑Rise - ∑ Fall 16.631

 RESULT: The R.L of various points along the cross section and longitudinal section are determined and the graph is plotted to scale.

 CONTOURING

A contour line is a curve along which the function has a constant value. In cartography, a contour line (Often just called a “contour”) joins points of equal elevation (height) above a given level, such as mean sea level. A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness of slopes.  CONTOUR- INTERVAL: The vertical distances between two consecutive contours are called as contour interval. The contour interval is kept constant for a contour plan, otherwise the general appearance of the map will be misreading. 1. Nature of the ground 2. The scale of the map 3. Purpose and extend of the survey 4. Time and expense of field and office work.  Characteristics of contour: The following characteristics features may be used while plotting or reading a contour plan or topographic map.  Two contour lines of different elevations cannot cross each other.  Contour lines of different elevations can write to from one line only in the case of a vertical cliff.  Contour lines close together indicate steep slope. They indicate a gentle slope if they are far apart.  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 and it represents a hill.  Two contour lines having the same elevation cannot write and continue split into two lines.  A contour line must close upon itself, not necessarily within the limits of the map.  Contour lines cross a watershed or ridge line at right angles.  Contour lines close a valley line of right angles.  Methods of locating Contours: The method may be divided into two classes; (a) The direct method (b) The indirect method

(a)The direct method

As in the indirect method, each contour is located by determining the positions of a series of points through which the contour passes. The operation is also sometimes called tracing out contours. The field work is two –fold. 1. Vertical control: Location of points on contour 2. Horizontal control: Survey of those points (b)The indirect method In this method, some guide points are selected along a system of straight lines and their elevations are found. The points are taken plotted and contours are drawn by interpolation. These guide points are not except by coincidence. The following are some of the indirect method of locating the ground points. 1. By squares 2. By cross sections 3. Tachometric method

GRID CONTOURING

 AIM: To draw the block of given plot  DESCRIPTION: A map without relief representation is simply a plan on which relative positions of details are only shown in horizontal phase. Relative heights of various points on the map may be represented by one of the methods of contour.  SQUARE METHOD: It is the indirect method of contouring. Here the entire area is divided into number of square sides which may vary from 4m-48m, depending upon nature of the ground, the contour interval and the scale of the plan.  EQUIPMENT REQUIRED: 1. Theodolite with tripod stand 2. Ranging rod 3. Levelling staff 4. Arrows 5. Cross staff  1. 2. 3. 4. 5. 6. 7. 8.

PROCEDURE The site for block contouring is selected by through study. The dimensions of block contour size are selected accordingly. Then the area is divided into blocks of the size 3mx3m by using cross staff, chain and ranging rod. The instrument is placed in such a place where maximum reading can be taken on the intersection points. Readings taken at the intersection points are entered in the field book. Change points are provided wherever needed. After taking the readings, the R.L of the each point is calculated by height of collimation method or by rise and fall method. All reduced levels are plotted in A2 drawing sheet of suitable scale. The points having same reduced levels are connected and finally we observe a contour map. The contour of the desired values is interpolated.

 Tabulation :

S.no

X

Y

Back sight

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

0

0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30

1.15

5

10

15

20

25

Intermediate sight

Fore sight

1.78 1.88 2.25 2.53 2.70 2.805 2.84 2.15 2.52 2.805 3.03 3.17 3.25 1.975 2.395 2.62 2.97 3.15 3.34 3.54 2.28 2.62 2.925 3.18 3.925 3.34 3.42 3.50 2.25 2.78 2.98 3.23 3.50 3.59 3.64 2.84 3.10 3.22 3.36 3.55 3.65

Height of Reduced the level instrument 101.15 99.73 99.63 99.26 98.98 98.81 98.705 98.67 99.36 98.99 98.705 98.48 98.34 98.26 99.535 99.115 99.89 98.54 98.36 98.17 97.97 99.23 98.89 98.585 98.33 98.215 98.17 98.09 98.01 99.26 98.73 98.53 98.28 98.01 97.92 97.87 98.09 98.41 98.29 98.15 97.96 97.86

 RESULT: The contour map of plotted for the given area.

RADIAL CONTOURING

 AIM: To prepare contour map for the given area.  1. 2. 3. 4. 5.

INSTRUMENTS REQUIRED Theodolite Ranging rod Chains Arrows Pegs

 PRINCIPLE: This method is suitable for contouring the area of long strip undulations where direct chaining is difficult.  1. 2. 3. 4. 5. 6. 7.

PROCEDURE: Range out the radial line from a common centre at known angular intervals. Fix arrows on the radial lines at equal distances of 3m or 5m. Set up the instrument at any convenient place to cover the maximum points. Hold the leveling staff in the place of arrows. Note down the vertical angles and the hair readings and enter it correctly. Repeat the same procedure for other radial lines. Similarly shift the instrument station to other convenient place and over the entire area.

 CALCULATION: 1. Calculate the reduced level and horizontal distance of instrument station using tacheometric formulae. 2. Plot the radial lines and positions of the points on the desired scale and enter spot levels. 3. Calculate the reduced level for the intermediate points using interpolation.  RADIAL CONTOURING BM= 100m Instrument station ‘O’ Height of Instrument= 1.60 m Staff reading for BM=1.34 m R.L of ‘O’ = 100 1.34-1.60=99.74m R.L of horizontal sight=100+1.34=101.34m

 Tabulation :

S.no 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

Staff Horizontal station angle A1 A2 A3 A4 A5 B1 B2 B3 B4 B5 C1 C2 C3 C4 C5 D1 D2 D3 D4 D5 E1 E2 E3 E4 E5 F1 F2 F3 F4 F5 G1 G2 G3 G4 G5 H1 H2 H3 H4 H5 I1 I2

0˚

30˚

60˚

90˚

120˚

150˚ ˚

1 0˚

210˚

240˚

Stadia reading Top 1.4 1.29 1.15 1.03 0.69 1.415 1.335 1.21 1.025 0.82 1.44 1.39 1.29 1.15 0.89 1.5 1.435 1.395 1.43 1.115 1.52 1.55 1.55 1.105 2.23 1.57 1.63 1.62 2.235 2.71 1.575 1.7 1.96 2.63 3.21 1.54 1.75 2.46 2.695 3.75 1.495 1.475

Middle Bottom 1.39 1.37 1.275 1.24 1.11 1.065 0.975 0.91 0.6 0.52 1.40 1.39 1.31 1.28 1.16 1.12 0.965 0.91 0.775 0.745 1.43 1.41 1.36 1.33 1.25 1.20 1.10 1.04 0.81 0.74 1.45 1.47 1.41 1.38 1.35 1.305 1.375 1.315 1.65 1.565 1.52 1.49 1.525 1.5 1.515 1.47 1.045 0.98 2.17 2.09 1.56 1.545 1.60 1.57 1.58 1.535 2.165 2.160 2.64 2.56 1.56 1.55 1.67 1.64 1.92 1.875 2.575 2.515 3.14 3.05 1.53 1.52 1.72 1.69 2.415 2.37 2.64 2.58 3.3 2.94 1.48 1.47 1.45 1.415

Stadia Horizontal Reduced intercept distance level 0.03 0.05 0.085 0.12 0.17 0.025 0.055 0.09 0.115 0.075 0.03 0.06 0.09 0.11 0.15 0.03 0.055 0.09 0.115 0.15 0.03 0.05 0.08 0.125 0.14 0.025 0.06 0.085 0.075 0.15 0.025 0.06 0.085 0.175 0.16 0.02 0.06 0.09 0.105 0.11 0.025 0.06

3 6 9 12 15 3 6 9 12 15 3 6 9 12 15 3 6 9 12 15 3 6 9 12 15 3 6 9 12 15 3 6 9 12 15 3 6 9 12 15 3 6

100.05 100.165 100.83 100.465 100.84 100.04 101.385 100.28 100.475 100.665 100.01 100.08 100.19 100.34 100.63 99.955 100.03 100.09 100.065 99.79 99.935 99.915 99.925 100.315 99.27 99.88 99.84 99.86 99.275 98.8 99.88 99.77 99.52 98.865 98.5 99.91 99.72 99.025 98.8 98.14 99.96 99.99

43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

I3 I4 I5 J1 J2 J3 J4 J5 K1 K2 K3 K4 K5 L1 L2 L3 L4 L5

270˚

300˚

330˚

1.635 2.0 2.06 1.47 1.11 1.15 1.20 1.57 1.43 1.34 1.19 1.035 1.16 1.38 1.385 1.28 0.91 0.81

1.595 1.945 1.915 1.455 1.08 1.11 1.14 1.50 1.42 1.315 1.15 0.98 0.98 1.37 1.36 1.24 0.86 0.74

1.55 1.885 1.9 1.4 1.05 1.08 1.085 1.42 1.40 1.29 1.10 0.92 0.92 1.36 1.33 1.14 0.79 0.63

0.085 0.115 0.16 0.07 0.06 0.07 0.115 0.15 0.03 0.05 0.09 0.115 0.24 0.02 0.055 0.09 0.12 0.18

0 12 15 3 6 9 12 15 3 6 9 12 15 3 6 9 12 15

99.845 99.495 99.525 99.985 100.36 100.33 100.3 99.94 100.4 100.125 100.29 100.46 100.46 100.07 100.08 100.2 100.58 100.7

 RESULT: The contour map of plotted for the given area.

SETTING OUT OF A CURVE USING SINGLE THEODOLITE BY RANKINE’S DEFLECTION ANGLE METHOD

 AIM: To set the horizontal curve by deflection curve by deflection angle method using single theodolite.  1. 2. 3. 4. 5. 6. 7.

EQUIPMENT REQUIRED: Theodolite Ranging rod Thread Mallet Tape Pegs Lime powder

 PROPERTIES OF A CURVE:

 PROCEDURE: 1. A theodolite is set up at the point of curvature T1, and is temporarily adjusted. 2. The vernier A is set to Zero and the upper plate is clamped. Then the lower plate main screw gets tightened and get the point B bisected exactly using the lower plate tangent screw. Now the line of sight is in the direction of the rear tangent T1B and the vernier A reads zero. 3. Open the upper plate main screw, and set the vernier A to the deflection angle. The line of sight is now directed along the chord T1 A. Clamp the upper plate. 4. Hold the zero end of the steel tape at T1. Note a mark equal to the first chord length P1 on the tape and swing an arrow pointed at the mark around A till it is bisected along the line of sight. 5. Unclamp the vernier plate and set the vernier A to the deflection angle. The line of sight is now directed along T1B.

6. With the zero end of the tape at A and an arrow on the mark on the tape equal to the normal chord length P, swing the tape around B until the arrow is bisected along the line of sight. Fix the second peg at the point B at the arrow point. 7. It may be noted that the deflection angles are measured from the tangent point T1 but the chord lengths are measured from the preceding point ‘r’. Thus the deflection angles are cumulative in nature but the chord lengths are not cumulative. 8. Repeat steps 5 and 6 till the last point is reached. The last point so located must coincide with the tangent point T2 already fixed from point of intersection.  CALCULATION AND OBSERVATION: 1. Radius = 50m 2. Deflection angle = 50˚ 3. Chord length = 4m 4. Long chord length = 2R sin Ø/2 5. Tangent length

= =

R tan ø/2 50 X tan 25˚ = 23.32m 6. Curve Length = πRØ/1 0˚ = 43.630m 7. Chainage of the first tangent pointT1 = 1000 – Tangent length = 1000 – 23.32 = 976.68m 8. Chainage of the second tangent point T2 = T1 + curve length = 976.68 + 43.63 = 1020.31m 9. Length of the initial sub chord (l) = 980 - 976.68 = 3.32m 10. Number of full chord length (4m) = 43.63/4 = 24.10m 11. Chainage covered = 980 + (4 X 10) = 1020m 12. Length of final sub chord = 1020.31 – 1020 = 0.31m 13. Deflection angle for initial sub-chord (D1) = (1718.9 X 3.32)/50 = 114.13= 1˚54’07” 14. Deflection angle for full chord D2 to D11 = (1718.9 X 4)/50 = 137.512 = 2˚17’30” 15. Angle for final sub-chord D12 = (1718.9 X 0.31)/50 = 10.657 = 0˚10’39” Arithmetic check: Total deflection angle (ð) = D1 + 10 x D + D n Ø/2 = 50/2 = 25˚ (ð) = 1˚54’07” + (10 x 2˚17’30”) = 24˚59’46” = 25˚ So, the calculated deflection angles are correct

0˚10’39”

Field check: Apex distance= R (sec ø) = 50 (sec25˚-1) = 5.168m  TABULATION: POINT

T1 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 T2

CHAINAGE

976.68 980 984 988 992 996 1000 1004 1008 1012 1016 1020.31

CHORD LENGTH (m) 1˚54’07” 2˚17’30” 2˚17’30” 2˚17’30” 2˚17’30” 2˚17’30” 2˚17’30” 2˚17’30” 2˚17’30” 2˚17’30” 0˚10’39”

DEFLECTION ANGLE FOR CHORD 1˚54’07” 4˚11’37” 6˚2 ’40” 8˚46’10” 11˚30’40” 13˚21’10” 15˚3 ’40” 17˚56’10” 20˚13’40” 22˚31’10” 24˚4 ’40”

TOTAL DEFLECTION ANGLE (ð) 1˚54’07” 4˚11’37” 6˚2 ’40” 8˚46’10” 11˚30’40” 13˚21’10” 15˚3 ’40” 17˚56’10” 20˚13’40” 22˚31’10” 24˚4 ’40”

Angle to be set 1˚54’07” 4˚11’37” 6˚2 ’40” 8˚46’10” 11˚30’40” 13˚21’10” 15˚3 ’40” 17˚56’10” 20˚13’40” 22˚31’10” 24˚4 ’40”

 RESULT: The curve was plotted in the ground by Rankine’s method and marked with chalk powder.