Survey Camp Report
description
Transcript of 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 : 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.