RAJALAKSHMI ENGINEERING COLLEGE RAJALAKSHMI NAGAR, THANDALAM – 602105.

DEPARTMENT OF CIVIL ENGINEERING

SURVEY CAMP REPORT

(11.02.2013 – 16.02.2013)

FEBRAURY 2013

NAME : S.NIVETHA

REGISTER NO. : 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 TITLE PAGE NO. 1) 11.02.13 Preparation of Topographic Map for

YMCA CAMPUS

1

2) 12.02.13 Determination of height of base

inaccessible object – Single plane method

8

3) 12..02.13 Determination of height of base

inaccessible object – Double plane method

10

4) 13.02.13 Determination of height by Stadia method 12

5) 13.02.13 Determination of height by Tangential

method

14

6) 14.02.13 Determination of area of the site by

Triangulation

18

7) 14.02.13 Determination of area of the site by

Trilateration

21

8) 14.02.13 Determination of internal angles by

traversing method

23

9) 15.02.13 Leveling – Longitudinal and Cross

sectional methods

24

10) 15.02.13 Grid contouring 31

11) 15.02.13 Radial contouring 33

12) 16.02.13 Setting out the curve by Rankine’s method 36

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 non-

visible 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

@

Sigh

t to

Height

(m)

Face left Face Right Average

Value A B Mean A B Mean

A BM 1.20 0º0’0” 0’0” 0º0’0” 0º0’0” 0’0” 0º0’0”

14º19’30

”

Q - 14º20’20

”

14’20” 14º17’20

”

14º19’40

”

21’40” 14º20’20

”

B

BM 1.37 0º0’0” 0’0” 0º0’0” 0º0’0” 0’0” 0º0’0”

14º26’55

”

Q - 14º40’20

”

14’20” 14º26’20

”

14º40’40

”

14’20” 14º27’30

”

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

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

@

Sight

to

Height

(m)

Horizontal angle Vertical angle Bench

Mark A B Mean A B Mean

A

BM 1.370 0º0’0” 0’0” 0º0’0” 0º0’0” 0’0” 0º0’0”

1.370 Q - 64º20’40” 20’40” 64º20’40” 14º40’20” 14’20” 14º26’20”

B

BM 1.420 0º0’0” 0’0” 0º0’0” 0º0’0” 0’0” 0º0’0”

1.420 Q - 18º40’20” 40’20” 18º40’20” 14º40’20” 14’20” 14º26’20

Calculation:

b) b = 2.66m

To find D;

4) D =

=

= 7.530m

5) H1= Dtanα1

= 2.709 tan 14º40’20” = 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

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+D2

2 – 2 D1D2 cosø

V0= level difference between A and B

Height =V0/D

Tabulation

Horizontal angle :

Vertical angle :

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

Inst

@

Sight

to

FACE LEFT FACE RIGHT HORIZONTAL

ANGLE A B MEAN C D MEAN

O A

B

0 º0’0” 0’0” 0 º0’0” 0 º0’0” 0’0” 0 º0’0” 217 º30’40”

217º30’0” 0’40” 217 º30’40” 217 º30’0” 0’40” 217 º30’40”

Inst

@

Sight

to

Stadia FACE LEFT FACE RIGHT VERTICAL

ANGLE C D MEAN C D MEAN

O A

B

1 6º0’0” 6’20” 6 º6’20” 6º0’0” 6’20” 6 º6’20” 6 º6’20”

2 7 º40’0” 20’0” 7 º30’10” 7 º30’0” 20’0” 7 º30’10” 7 º30’10”

1 9 º0’0” 10’20” 9 º5’20” 9 º0’0” 10’20” 9 º5’20” 9 º5’20”

2 5 º0’0” 10’40” 5 º5’20” 5 º0’0” 10’40” 5 º10’20” 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+D2

2 – 2 D1D2 cosø

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

Tabulation

Horizontal : 217 º 30’ 40”

Calculation:

D= KS Cos2ø + C Cos ø

θ1= 5º θ2= 10º

D1= 31.760m D2= 32.010m

AB = √ = 63.770m

VOA = D tanα2 VOB = D tanα2

= 2.778m = 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

Instrument

@ Sight

to

Vertical

angle

Stadia Hair S

(m) Top Middle Bottom

O A 5º 0.650 0.490 0.330 0.320

10º 3.500 3.300 3.170 0.330

B 5º 2.170 2.100 2.020 0.150

10º 0.870 0.840 0.715 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.

EQUIPMENT NEEDED:

A. Theodolite with tripod stand

B. Ranging rod

C. Tape

D. Arrow

FORMULA USED:

1) Sine formula:

a/sin A= b/sin B= c/sin C

For calculating the sides of a triangle,

AB2=AC

2+BC

2 -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

Horizontal Angle Mean

A B

‘ “ “ ‘ “

A

E 31 25 25 24 25 31 49 50

B 87 0 5 0 5 87 0 5

H 36 0 25 0 25 36 0 50

B

C 71 10 5 10 5 71 20 10

A 61 20 0 20 5 61 40 5

E 25 15 0 15 0 25 30 0

F 32 29 25 20 25 32 39 50

H 36 0 0 0 0 36 0 0

I 63 30 5 29 5 63 59 10

C

F 39 25 40 25 40 32 50 40

G 23 29 20 20 20 23 39 40

D 70 5 5 5 5 70 10 10

B 74 20 10 20 10 74 40 20

I 56 20 20 20 20 56 40 40

J 39 25 20 24 20 39 49 40

D

G 23 29 20 20 20 23 39 40

C 84 15 10 15 10 84 30 20

J 42 0 5 0 5 42 0 5

Calculation: IN TRIANGLE FBC:

FBC= 0 0”, BCF=71 20’10”

BFC=180-( = d1 =16.2m

=

=

; C=28.44m

=

; b=28.12m, s=36.88

S =

a = √ = 223.49m²

IN TRIANGLE BIC:

IBC= 72 , ICB=44 , BIC= 16.2/sin 63 = BI/sin

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

Calculation :

Consider ∆OAG;

OA = 34.95 m (a)

OG = 22.96 m (b)

AG = 16.49 m (c)

S =

= 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:

Instrument

@

Sight to Vertical

angle

Staff Reading S

(m)

Distance

(m) TOP MIDDLE BOTTOM

O A 2 º10’7.5” 1.720 1.635 1.370 0.350 34.949

B 0º0’20” 1.780 1.605 1.435 0.345 34.499

C 0º20’20” 1.300 1.360 0.830 0.470 46.998

D 3º20’5” 1.480 0.270 1.070 0.410 40.862

E 3º24’20” 0.980 0.815 0.660 0.320 31.887

F 6º12’10” 3.060 2.910 2.750 0.310 30.638

G 0º40’3.5” 2.020 1.940 1.790 0.230 22.997

A G 0º20’10” 1.315 1.475 1.150 0.165 16.499

B 0º20’15” 0.765 0.920 0.595 0.170 16.999

C B 1º40’0” 2.210 2.350 2.070 0.140 13.988

D 0º1 ’20” 0.870 0.910 0.850 0.020 1.999

E D 0º20’10” 1.630 1.460 1.300 0.330 32.998

F 0º0’0” 1.760 1.320 0.920 0.840 84.000

G F 0º40’2.5” 1.250 1.090 0.930 0.320 31.995

A 1º40’15” 1.820 1.645 1.495 0.325 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

FACE LEFT SWING RIGHT FACE RIGHT SWING LEFT AVG.

ANGLE VER.

A

VER. B MEAN HORI.

ANGLE

VER.

A

VER. B MEAN HORI.

ANGLE

A E 0˚0’0” 0’0” 0’0” 134˚40’4” 0˚0’0” 0’0” 0˚0’0” 134˚0’5

”

134˚20’

5” B 134˚20

’4”

20’4” 134˚20’4

”

134˚0’5

”

20’4” 134˚0’5

”

B A 0˚0’0” 0’0” 0’0” 100˚40’0” 0˚0’0” 0’0” 0˚0’0” 100˚20’

0”

100˚20’

0” C 100˚40

’0”

40’0” 100˚40’0

”

101˚20’

0”

40’0” 100˚20’

0”

C D 0˚0’0” 0’0” 0’0” 10 ˚20’5” 0˚0’0” 0’0” 0˚0’0” 10 ˚40’

5”

10 ˚30’

5” B 10 ˚20

’5”

20’5 10 ˚20’5

”

10 ˚40’

5”

20’5 10 ˚40’

5”

D E 0˚0’0” 0’0” 0’0” 109˚20’5” 0˚0’0” 0’0” 0˚0’0” 109˚20’

5”

109˚20’

5” C 109˚20

’5”

20’5” 109˚20’5

”

109˚20’

5”

20’5 109˚20’

5”

E A 0˚0’0” 0’0” 0’0” 7˚40’15” 0˚0’0” 0’0” 0˚0’0” 7˚0’15

”

7˚29’4

5” D 7˚40’

15”

40’15” 7˚40’15

”

7˚0’15

”

40’15” 7˚0’15

”

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.

EQUIPMENT REQUIRED:

1. Leveling staff

2. Levelling instrument

3. Ranging rods

4. Cross staff

5. Chain

6. Tape

7. Peg

8. 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 5 1.485 101.550 BM

10 1.55 0.065 101.485

15 1.89 0.340 101.145

20 2.175 0.285 100.860

25 2.61 0.015 100.875

30 2.845 0.685 100.190

35 3.075 0.230 99.960

40 3.74 0.665 99.295

45 4.32 0.580 98.715

B 50 4.235 4.900 0.580 98.135 Station1

C 55 0.620 4.805 0.570 97.565 Station2

60 1.97 1.350 96.215

65 2.365 0.395 95.820

70 2.58 0.215 95.605

75 3.005 0.425 95.180

80 3.51 0.505 94.675

85 4.09 0.580 94.095

D 90 1.00 4.49 0.40 93.695 Station3

95 0.7 0.300 93.995

100 1.3 0.600 93.395

105 2.005 0.705 92.690

110 2.64 0.635 92.055

115 3.29 0.650 91.405

120 4.02 0.730 90.675

E 125 1.23 4.63 0.610 90.065 Station4

130 1.13 0.100 90.195

135 1.42 0.320 89.875

140 2.13 0.710 89.165

145 2.735 0.005 89.160

150 3.10 0.965 88.195

155 3.35 0.250 87.945

160 3.83 0.480 87.465

F 165 0.3 4.17 0.340 87.125 Station5

170 0.93 0.630 86.496

175 1.23 0.300 86.195

180 1.43 0.200 85.995

185 1.605 0.175 85.820

190 1.74 0.135 85.685

195 1.94 0.200 85.485

200 2.10 0.160 85.325

205 2.17 0.070 85.255

210 2.24 0.070 85.185

215 2.38 0.140 85.015

220 2.45 0.070 84.945

G 225 1.34 2.600 0.150 84.795 Station6

230 2.12 0.780 84.015

235 2.25 0.130 83.885

240 2.42 0.170 83.715

245 2.51 0.090 83.625

250 2.600 0.090 83.535

Last R.L – First R.L = ∑Rise - ∑ Fall

18.015 = 18.015

TABULATION (CROSS SECTION – LEFT)

Station H.DISTANCE B.S I.S F.S RISE FALL R.L

5 1.485 101.550

10 1.55 0.065 101.485

15 1.865 0.315 101.170

20 2.115 0.250 100.920

25 2.62 0.505 100.415

30 2.790 0.170 100.245

35 3.060 0.270 99.975

40 3.75 0.690 99.285

45 4.325 0.575 98.710

50 4.75 4.95 0.625 98.085

55 4.22 0.53 98.615

60 0.63 4.76 0.540 98.075

65 2.07 1.44 96.635

70 2.375 0.305 96.330

75 2.64 0.265 96.065

80 3.10 0.46 95.605

85 3.53 0.43 95.175

90 4.11 0.58 94.595

95 4.30 0.19 94.405

100 1.07 4.48 0.18 94.225

105 0.82 0.25 94.475

110 1.22 0.400 94.075

115 2.075 0.855 93.220

120 2.67 0.595 92.625

125 3.29 0.620 92.005

130 4.07 0.780 91.225

135 1.130 4.57 0.500 90.725

140 1.45 0.32 90.405

145 2.085 0.635 89.770

150 2.775 0.69 89.080

155 3.00 0.225 88.855

160 3.33 0.33 88.525

165 3.81 0.48 88.045

170 0.3 4.12 0.31 87.735

175 0.895 0.595 87.140

180 1.235 0.34 86.800

185 1.43 0.195 86.605

190 1.62 0.190 86.415

195 1.73 0.110 86.305

200 1.97 0.240 86.101

205 2.08 0.110 85.991

210 2.16 0.080 85.911

215 2.18 0.020 85.891

220 0.920 2.13 0.050 85.941

225 1.126 0.206 85.735

230 1.320 0.194 85.541

235 1.580 0.260 85.281

240 1.742 0.162 85.119

245 1.988 0.246 84.873

250 2.267 0.279 84.594

∑RISE - ∑FALL = LAST R.L - FIRST R.L

16.956 = 16.956

TABULATION (CROSS SECTION- RIGHT)

H.DISTANCE B.S I.S F.S RISE FALL R.L

5 1.39 101.550

10 1.63 0.240 101.310

15 1.87 0.240 101.710

20 2.27 0.400 100.670

25 2.63 0.360 100.310

30 2.815 0.185 100.125

35 3.13 0.315 99.810

40 3.78 0.650 99.160

45 4.33 0.550 98.610

50 4.76 4.88 0.550 98.060

55 4.235 0.525 98.585

60 0.69 4.3 0.065 98.520

65 1.745 1.055 97.465

70 2.05 0.305 97.160

75 2.4 0.350 96.810

80 2.61 0.210 96.600

85 3.003 0.393 96.207

90 3.47 0.467 95.740

95 4.08 0.610 95.130

100 1.05 4.5 0.420 94.710

105 0.84 0.21 94.920

110 1.44 0.600 94.320

115 2.09 0.650 93.670

120 2.66 0.570 93.100

125 3.34 0.680 92.420

130 4.06 0.720 91.700

135 1.09 4.65 0.590 91.110

140 1.43 0.340 90.770

145 2.11 0.680 90.090

150 2.675 0.565 89.525

155 2.8 0.125 89.400

160 3.32 0.520 88.880

165 3.8 0.480 88.400

170 0.3 4.15 0.350 88.050

175 0.95 0.650 87.400

180 1.31 0.360 87.040

185 1.43 0.120 86.920

190 1.61 0.180 86.740

195 1.72 0.110 86.630

200 1.95 0.230 86.400

205 2.07 0.120 86.280

210 2.14 0.070 86.210

215 2.20 0.060 86.150

220 0.930 2.19 0.100 86.250

225 1.129 0.199 86.051

230 1.322 0.193 85.858

235 1.575 0.253 85.605

240 1.745 0.170 85.435

245 1.982 0.237 85.198

250 2.261 0.279 84.919

Last R.L - First R.L = ∑Rise - ∑ Fall

16.631 = 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

PROCEDURE

1. The site for block contouring is selected by through study.

2. The dimensions of block contour size are selected accordingly.

3. Then the area is divided into blocks of the size 3mx3m by using cross staff, chain and

ranging rod.

4. The instrument is placed in such a place where maximum reading can be taken on the

intersection points.

5. Readings taken at the intersection points are entered in the field book.

6. Change points are provided wherever needed.

7. After taking the readings, the R.L of the each point is calculated by height of collimation

method or by rise and fall method.

8. 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

Intermediate

sight

Fore

sight

Height of

the

instrument

Reduced

level

1 0

0 1.15 101.15

2 5 1.78 99.73

3 10 1.88 99.63

4 15 2.25 99.26

5 20 2.53 98.98

6 25 2.70 98.81

7 30 2.805 98.705

8 5

0 2.84 98.67

9 5 2.15 99.36

10 10 2.52 98.99

11 15 2.805 98.705

12 20 3.03 98.48

13 25 3.17 98.34

14 30 3.25 98.26

15 10 0 1.975 99.535

16 5 2.395 99.115

17 10 2.62 99.89

18 15 2.97 98.54

19 20 3.15 98.36

20 25 3.34 98.17

21 30 3.54 97.97

22 15

0 2.28 99.23

23 5 2.62 98.89

24 10 2.925 98.585

25 15 3.18 98.33

26 20 3.925 98.215

27 25 3.34 98.17

28 30 3.42 98.09

29 20

0 3.50 98.01

30 5 2.25 99.26

31 10 2.78 98.73

32 15 2.98 98.53

33 20 3.23 98.28

34 25 3.50 98.01

35 30 3.59 97.92

36 25

0 3.64 97.87

37 5 2.84 98.09

38 10 3.10 98.41

39 15 3.22 98.29

40 20 3.36 98.15

41 25 3.55 97.96

42 30 3.65 97.86

RESULT:

The contour map of plotted for the given area.

RADIAL CONTOURING

AIM:

To prepare contour map for the given area.

INSTRUMENTS REQUIRED

1. Theodolite

2. Ranging rod

3. Chains

4. Arrows

5. Pegs

PRINCIPLE:

This method is suitable for contouring the area of long strip undulations where direct

chaining is difficult.

PROCEDURE:

1. Range out the radial line from a common centre at known angular intervals.

2. Fix arrows on the radial lines at equal distances of 3m or 5m.

3. Set up the instrument at any convenient place to cover the maximum points.

4. Hold the leveling staff in the place of arrows.

5. Note down the vertical angles and the hair readings and enter it correctly.

6. Repeat the same procedure for other radial lines.

7. 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 Staff

station

Horizontal

angle

Stadia reading Stadia

intercept

Horizontal

distance

Reduced

level Top Middle Bottom

1 A1 0˚

1.4 1.39 1.37 0.03 3 100.05

2 A2 1.29 1.275 1.24 0.05 6 100.165

3 A3 1.15 1.11 1.065 0.085 9 100.83

4 A4 1.03 0.975 0.91 0.12 12 100.465

5 A5 0.69 0.6 0.52 0.17 15 100.84

6 B1 30˚

1.415 1.40 1.39 0.025 3 100.04

7 B2 1.335 1.31 1.28 0.055 6 101.385

8 B3 1.21 1.16 1.12 0.09 9 100.28

9 B4 1.025 0.965 0.91 0.115 12 100.475

10 B5 0.82 0.775 0.745 0.075 15 100.665

11 C1 60˚

1.44 1.43 1.41 0.03 3 100.01

12 C2 1.39 1.36 1.33 0.06 6 100.08

13 C3 1.29 1.25 1.20 0.09 9 100.19

14 C4 1.15 1.10 1.04 0.11 12 100.34

15 C5 0.89 0.81 0.74 0.15 15 100.63

16 D1 90˚

1.5 1.45 1.47 0.03 3 99.955

17 D2 1.435 1.41 1.38 0.055 6 100.03

18 D3 1.395 1.35 1.305 0.09 9 100.09

19 D4 1.43 1.375 1.315 0.115 12 100.065

20 D5 1.115 1.65 1.565 0.15 15 99.79

21 E1 120˚

1.52 1.52 1.49 0.03 3 99.935

22 E2 1.55 1.525 1.5 0.05 6 99.915

23 E3 1.55 1.515 1.47 0.08 9 99.925

24 E4 1.105 1.045 0.98 0.125 12 100.315

25 E5 2.23 2.17 2.09 0.14 15 99.27

26 F1 150˚

˚

1.57 1.56 1.545 0.025 3 99.88

27 F2 1.63 1.60 1.57 0.06 6 99.84

28 F3 1.62 1.58 1.535 0.085 9 99.86

29 F4 2.235 2.165 2.160 0.075 12 99.275

30 F5 2.71 2.64 2.56 0.15 15 98.8

31 G1 1 0˚

1.575 1.56 1.55 0.025 3 99.88

32 G2 1.7 1.67 1.64 0.06 6 99.77

33 G3 1.96 1.92 1.875 0.085 9 99.52

34 G4 2.63 2.575 2.515 0.175 12 98.865

35 G5 3.21 3.14 3.05 0.16 15 98.5

36 H1 210˚

1.54 1.53 1.52 0.02 3 99.91

37 H2 1.75 1.72 1.69 0.06 6 99.72

38 H3 2.46 2.415 2.37 0.09 9 99.025

39 H4 2.695 2.64 2.58 0.105 12 98.8

40 H5 3.75 3.3 2.94 0.11 15 98.14

41 I1 240˚

1.495 1.48 1.47 0.025 3 99.96

42 I2 1.475 1.45 1.415 0.06 6 99.99

43 I3 1.635 1.595 1.55 0.085 0 99.845

44 I4 2.0 1.945 1.885 0.115 12 99.495

45 I5 2.06 1.915 1.9 0.16 15 99.525

46 J1 270˚

1.47 1.455 1.4 0.07 3 99.985

47 J2 1.11 1.08 1.05 0.06 6 100.36

48 J3 1.15 1.11 1.08 0.07 9 100.33

49 J4 1.20 1.14 1.085 0.115 12 100.3

50 J5 1.57 1.50 1.42 0.15 15 99.94

51 K1 300˚

1.43 1.42 1.40 0.03 3 100.4

52 K2 1.34 1.315 1.29 0.05 6 100.125

53 K3 1.19 1.15 1.10 0.09 9 100.29

54 K4 1.035 0.98 0.92 0.115 12 100.46

55 K5 1.16 0.98 0.92 0.24 15 100.46

56 L1 330˚

1.38 1.37 1.36 0.02 3 100.07

57 L2 1.385 1.36 1.33 0.055 6 100.08

58 L3 1.28 1.24 1.14 0.09 9 100.2

59 L4 0.91 0.86 0.79 0.12 12 100.58

60 L5 0.81 0.74 0.63 0.18 15 100.7

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.

EQUIPMENT REQUIRED:

1. Theodolite

2. Ranging rod

3. Thread

4. Mallet

5. Tape

6. Pegs

7. 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”) 0˚10’39”

= 24˚59’46” = 25˚

So, the calculated deflection angles are correct

Field check:

Apex distance= R (sec ø)

= 50 (sec25˚-1) = 5.168m

TABULATION:

POINT CHAINAGE CHORD

LENGTH

(m)

DEFLECTION

ANGLE FOR

CHORD

TOTAL

DEFLECTION

ANGLE (ð)

Angle to

be set

T1 976.68 - - - -

P1 980 1˚54’07” 1˚54’07” 1˚54’07” 1˚54’07”

P2 984 2˚17’30” 4˚11’37” 4˚11’37” 4˚11’37”

P3 988 2˚17’30” 6˚2 ’40” 6˚2 ’40” 6˚2 ’40”

P4 992 2˚17’30” 8˚46’10” 8˚46’10” 8˚46’10”

P5 996 2˚17’30” 11˚30’40” 11˚30’40” 11˚30’40”

P6 1000 2˚17’30” 13˚21’10” 13˚21’10” 13˚21’10”

P7 1004 2˚17’30” 15˚3 ’40” 15˚3 ’40” 15˚3 ’40”

P8 1008 2˚17’30” 17˚56’10” 17˚56’10” 17˚56’10”

P9 1012 2˚17’30” 20˚13’40” 20˚13’40” 20˚13’40”

P10 1016 2˚17’30” 22˚31’10” 22˚31’10” 22˚31’10”

T2 1020.31 0˚10’39” 24˚4 ’40” 24˚4 ’40” 24˚4 ’40”

RESULT:

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