Wednesday 29 October 2014
UNIT 1
Definition of Surveying
Surveying is defined as the science of making measurements of the earth specifically on the
surface of the earth. This is being carried out by finding the spatial location (relative / absolute)
of points on or near the surface of the earth.
Different methods and instruments are being used to facilitate the work of surveying. The
primary aims of field surveying are:
• To measure the Horizontal Distance between points.
• To measure the Vertical elevation between points.
• To find out the Relative direction of lines by measuring horizontal angles with reference to any
arbitrary direction and
• To find out Absolute direction by measuring horizontal angles with reference to a fixed
direction.
These parameters are utilized to find out the relative or absolute coordinates of a point / location.
Importance of Surveying to Civil Engineers
The planning and design of all Civil Engineering projects such as construction of highways,
bridges, tunnels, dams etc are based upon surveying measurements. Moreover, during execution,
project of any magnitude is constructed along the lines and points established by surveying.
Thus, surveying is a basic requirement for all Civil Engineering projects. Other principal works
in which surveying is primarily utilized are:
• To fix the national and state boundaries;
• To chart coastlines, navigable streams and lakes;
• To establish control points;
• To execute hydrographic and oceanographic charting and mapping; and
• To prepare topographic map of land surface of the earth.
Objectives of Surveying
• To collect field data;
• To prepare plan or map of the area surveyed;
• To analyze and to calculate the field parameters for setting out operation of actual engineering
works.
• To set out field parameters at the site for further engineering works.
Level surface: It is a curved surface every point on which is equidistant from the center of the
earth and every surface element is normal to the plumb line.
Mean sea level: A plane surface or ordinary surveying a level surface at any point is assumed to
be at the average sea level known as mean sea level.
Definition of Surveying
Surveying is defined as the science of making measurements of the earth specifically on the
surface of the earth. This is being carried out by finding the spatial location (relative / absolute)
of points on or near the surface of the earth.
Different methods and instruments are being used to facilitate the work of surveying. The
primary aims of field surveying are:
• To measure the Horizontal Distance between points.
• To measure the Vertical elevation between points.
• To find out the Relative direction of lines by measuring horizontal angles with reference to any
arbitrary direction and
• To find out Absolute direction by measuring horizontal angles with reference to a fixed
direction.
These parameters are utilized to find out the relative or absolute coordinates of a point / location.
Importance of Surveying to Civil Engineers
The planning and design of all Civil Engineering projects such as construction of highways,
bridges, tunnels, dams etc are based upon surveying measurements. Moreover, during execution,
project of any magnitude is constructed along the lines and points established by surveying.
Thus, surveying is a basic requirement for all Civil Engineering projects. Other principal works
in which surveying is primarily utilized are:
• To fix the national and state boundaries;
• To chart coastlines, navigable streams and lakes;
• To establish control points;
• To execute hydrographic and oceanographic charting and mapping; and
• To prepare topographic map of land surface of the earth.
Objectives of Surveying
• To collect field data;
• To prepare plan or map of the area surveyed;
• To analyze and to calculate the field parameters for setting out operation of actual engineering
works.
• To set out field parameters at the site for further engineering works.
Level surface: It is a curved surface every point on which is equidistant from the center of the
earth and every surface element is normal to the plumb line.
Mean sea level: A plane surface or ordinary surveying a level surface at any point is assumed to
be at the average sea level known as mean sea level.
Great circle: Imagine a plane passing through the centre of the earth the intersection of such a
plane with the mean sea level surface of the earth is termed as great circle of the earth.
Meridian: It is the line defined by the intersection of an imaginary plane passing through the
poles at any point on the earth level surface.
Plumb line: It is normal drawn to the meridian.
Level line: any portion of the line lying on the great circle of the earth is called as level line. It
may also be defined as the line lying on the level surface & normal to the plumb line at all
points.
Divisions of Surveying
The approximate shape of the earth can best be defined as an oblate tri-axial ovaloid. But, most
of the civil engineering works, concern only with a small portion of the earth which seems to be
a plane surface. Thus, based upon the consideration of the shape of the earth, surveying is
broadly divided into two types. (I) Geodetic Surveying (II) Plane Surveying
Oblate (spheroid): An oblate (spheroid) is a surface of revolution obtained by rotating an ellipse
about its minor axis i.e., having equatorial radius greater than the polar radius.
Ovaloid: A pear shaped figure having dimension of one hemisphere larger than the other for
earth, southern hemisphere is larger than the northern.
Geodetic Surveying
In this branch of surveying, the true shape of the earth is taken into consideration. This type of
surveying is being carried out for highly precise work and is adopted for surveying of large area.
All geodetic survey work includes work of larger magnitude & high degree of precision. The
object of geodetic survey is to determine the precise position on the surface of the earth, of a
system of widely distant points which form control stations to which surveys of less precision
may be referred.
Plane Surveying
In this method of surveying, the mean surface of the earth is considered to be a plane surface.
This type of survey is applicable for small area (less than 200 square kilometer). Thus for most
of the Civil Engineering projects, methods of plane surveying are valid. This course is restricted
to the different aspects of plane surveying. Henceforth, in this course work, the word surveying
implies plane surveying.
Fundamental assumptions in Plane surveying
• All distances and directions are horizontal;
• The direction of the plumb line is same at all points within the limits of the survey;
• All angles (both horizontal and vertical) are plane angles;
• Elevations are with reference to a datum.
Classifications of Surveying
(A) Classification based upon the nature of the field of survey
Land Surveying----
Topographic survey: To prepare a plan/ map of a region this includes natural as well as and manmade
features including elevation.
Cadastral survey: To fix the property line, calculation of land area, to fix the boundaries of
municipalities & of state & federal jurisdictions.
City surveying: they are made in connection with the construction of streets, water supply
systems sewers and other works.
Marine or hydrographic survey: -------
Deals with the bodies of water for purpose of navigation, water supply, harbor works or for the
determination of mean sea level. The work consists in measurement of discharge of streams
making topographic survey of shores & banks taking & locating soundings to determine the
depth of water & observing the fluctuations of the ocean tide.
Astronomic surveys: --------
To determine the latitude, longitude (of the observation station) and azimuth (of a line through
observation station) from astronomical observation.
(B) Classification based on the object of survey
Engineering survey: To collect requisite data for planning, design and execution of engineering
projects. Three broad steps are
1) Reconnaissance survey: To explore site conditions and availability of infrastructures.
2) Preliminary survey: To collect adequate data to prepare plan / map of area to be used
for planning and design.
3) Location survey: To set out work on the ground for actual construction / execution of
the project.
• Route survey: To plan, design, and laying out of route such as highways, railways,
canals, pipelines, and other linear projects.
• Construction surveys: Surveys which are required for establishment of points, lines,
grades, and for staking out engineering works (after the plans have been prepared and the
structural design has been done).
Mine surveys: To carry out surveying specific for opencast and underground mining purposes.
Military Surveys: This is used for determining points of strategic importance.
Geological survey: This is used for determining different strata in earth’s crust.
Archeological Survey: Unearthing relics of antiquity.
(C) Classification based on instruments used
Chain surveying, compass surveying, plane table surveying, theodolite surveying, tachometric
surveying, triangulation surveying, areal surveying, photogrammetric surveying, total station
surveying.
(D) Classification based on the method employed
Triangulation surveying and traversing surveying
Uses of surveying/ application of surveying:
• By carrying out astronomical survey we can fix up the local and standard time and
movement of planets.
• By preparing the maps dispute between two states can be avoided.
• Natural features can be located by conducting topographical survey.
• Road maps & guide maps helps tourists and travelers.
• For planning & execution of the water supply and sanitary projects.
• To have detailed survey map showing accurate boundary of the area to be covered.
• To enable the project engineer to proceed with the project.
Units of measurement:
In plane surveying the following two types of measurements are taken:
1) Linear measurements
2) Angular measurements
Linear measurements: The linear measurements can be sub divided into two categories namely
horizontal distances and vertical distances.
In surveying all the measurements represent the horizontal distances only because plotting on
plan or map is made for horizontal distances only irrespective of difference in elevation between
the two points. In certain unavoidable cases if the inclined measurements are taken they are
converted suitably to represent the corresponding horizontal distance.
When the distance between two points is measured in a vertical plane it is known as the vertical
distance.
Angular measurements: The angular measurements can also be sub divided into two categories
namely horizontal angle and vertical angles.
The horizontal angle represents the angles between two intersecting lines in a horizontal plane.
The vertical angle represents the angle between horizontal line and the line of sight inclined to
that point in vertical plane.
Basic units of measurement
No Item Basic unit
1 Length 10 millimeters(mm)= 1 centimeter (cm)
10 centimeter (cm) = 1 decimeter (dm)
10 dm = 1 meter (m)
UNIT 1 INTRODUCTION
DEPT. OF CIVIL ENGG. GNDECB Page 5
10 m = 1 decameter (D)
10 D = 1 hectometer (hm)
10 hm = 1 kilometer (km)
1000 meters = 1 km
1852 meters = 1 nautical mile
2 Area 100 mm2 = 1 cm2
100 cm2 = 1 dm2
100 dm2 = 1 m2
100 m2 = 1 are or sq decameter
100 ares (a) = 1 hectare (ha) or 1 sq hectometer
100 hectares = 1 sq kilometer (km2) or 106 sq meters
3 Volume 1000 mm3 = 1 cm3
1000 cm3 = 1 dm3
1000 dm3 = 1 m3
The angular measurements are taken in degrees, minutes and seconds & radians having the
following relations:
Ð/2 radians = 90 degrees = 1 right angle
Ð/180 radian = 1 degree = 60 minutes
Ð/10800 radian = 1 minute = 60 seconds
The radian is the unit of plane angle & it is defined as the angle between two radii of a circle
which cut off on the circumference an arc equal in length to the radius or in other words it is the
angle subtended at the centre of a circle by an arc equal to the length of the radius of that circle.
Plans and maps:
A map is a graphical representation of large area work with smaller scale. Plan is a graphical
representation of small area work with larger scale.
Scale: the distance measured on ground are plotted on paper in such a way that a fixed ratio is
maintained between the distances on ground to corresponding distance on paper. This ratio is
known as scale. (Engineer’s scale, graphical scale, representative fraction scale)
Map classification:
Large scale map: 1 cm= 10m or less than 10m
Medium scale map: 1 cm = 10m to 100m
Small scale map: 1 cm = 100m or more than 100m
Type of map Representative factor Scale
Geographical map 1:16000000 1cm = 160km
Topographical map 1: 250000 1cm = 2.5km
Location map 1: 500 to 2500 1 cm = 5m to 25m
Forest map 1: 2500 1cm = 0.25km
Cadastral map 1: 1000 to 5000 1cm = 10m to 50m
UNIT 1 INTRODUCTION
DEPT. OF CIVIL ENGG. GNDECB Page 6
Town planning map 1: 5000 to 1000 1 cm = 50m to 10m
Building map 1: 1000 1 cm= 10m
Mines map 1: 1000 to 25000 1 cm = 10m to 250m
Preliminary survey of rail & road 1: 1000 to 6000 1 cm = 10m to 60m
Indian Topographic Maps
Topographic maps provide the graphical portrayal of objects present on the surface of the earth.
These maps provide the preliminary information about a terrain and thus very useful for
engineering works. For most part of India, topographic maps are available which are prepared by
the Survey of India. To identify a map of a particular area, a map numbering system has been
adopted by Survey of India. The system of identification is as follows:
An International Series (within 4° N to 40° N Latitude and 44° E to 124° E Longitude) at the
scale of 1: 1,000,000 is being considered as base map. The base map is divided into sections of
4° latitude x 4° longitude and designated from 1 (at the extreme north-west) to 136, covering
only land areas and leaving any 4° square if it falls completely in the sea.
For Indian Topographic maps, each section is further divided into 16 sections (4 rows by 4
columns), each of 1° latitude x 1° longitude (1:250,000), staring from a letter A (North-West
corner) and ending on P, column-wise. These degree sheets are designated by a number and an
alphabet such as 53 C.
These degree sheets are further sub-divided in the following ways:
Each sheet is divided into four parts (2 rows by 2 columns), each of 30' latitude x 30' longitude
(1:100,000) designating them by cardinal directions NW, NE, SW, and SE. Such sheets are
identified as 53 M/SE.
Degree sheets have also been divided into 16 sheets (4 rows by 4 columns), each 15' latitude x
15' longitude (1:50,000) and numbered from 1 (at the north-west corner of the particular degree
sheet) to 16 column wise and are identified as 53 B/3
Each 1:50,000 scale sheet contains four (2 rows by 2 columns) 1:25,000 sheet ( 7' 1/2 latitude x
7' 1/2 longitude ) which are numbered NW, NE, SW, and SE. Such sheets are identified as 53
O/14/NE.
In this way, the topographic map of most of the area of India may be acquired at the scale
available and subsequently can be updated and upgraded as required for a particular project. For
large scale maps, further surveying needs to carry out.
Principles of Surveying
1. Location of a point by measurement from two points of reference
The relative positions of the points to be surveyed should be located by measurement from at
least two points of reference the positions of which have already been fixed. Let P & Q be the
reference line on the ground. The distance PQ can be measured accurately & the relative
positions of P and Q can be plotted on the sheet to some scale. Thus P & Q will serve as
reference points for fixing the relative positions of other points. Any other such as R can be
located by any of the following direct methods.
a) Distances PR & QR can be measured & the point R can be plotted by swinging the two arcs
to the same scale to which PQ has been plotted. The principle is very much used in chain
surveying.
b) A perpendicular RS can be dropped on the reference line PQ & the lengths PS & SR are
measured. The point R can be plotted using set square. This principle is used for defining
details.
c) The distance QR & the angle PQR can be measured & point R is plotted either by means of a
protractor or trigonometrically. This principle is used in traversing.
d) In this method the distances PR & QR are not measured but angle RPQ & angle RQP are
measured with an angle measuring instrument. Knowing the distance PQ point R is plotted
either by means of a protractor or by solution of triangle PQR. This principle is very much
used in triangulation & the method is used for very extensive work.
e) Angle RQP & distance PR are measured & point R is plotted either by protracting an angle &
swinging an arc from P or plotted trigonometrically. This principle is used in traversing, is
of minor utility.
2. Working from whole to part but from part to whole
The fundamental principles upon which the surveying is being carried out are working from
whole to part. After deciding the position of any point, its reference must be kept from at least
two permanent objects or stations whose position has already been well defined. The purpose of
working from whole to part is to localize the errors and to control the accumulation of errors.
This is being achieved by establishing a hierarchy of networks of control points. The less precise
networks are established within the higher precise network and thus restrict the errors. To
minimize the error limit, highest precise network (primary network) Figure 1.1 of control points
are established using the most accurate / precise instruments for collection of data and rigorous
methods of analysis are employed to find network parameters. This also involves most skilled
manpower and costly resources which are rare and cost intensive.
Errors
State of being wrong in judgment is defined as error (or) the difference between a measured and
its true value is called the measurement error.
Error in Measurement
In case of repeated observation of any parameter, usually it has been found to have variations,
however small, in the resulting measurement. Moreover, there is nothing definite in the amount
UNIT 1 INTRODUCTION
DEPT. OF CIVIL ENGG. GNDECB Page 10
of variation i.e., variations are random in nature. Thus, a measurement usually differs from its
true value. The difference between a measured and its true value is called the measurement error.
Thus, if x is a given measurement and x t is the true value, then the error e is given by
e = x - x t error = measured value – true value.
If an estimated value of xt is usually known and is denoted by x1. Then, an estimate of error for a
measurement value x of the parameter is obtained as e1 = x - x1
However, correction is the term more popularly being used to define the magnitude of error but
opposite in sign. Thus, rearranging the error relation, correction = (-e1) = x1 – x or, correction =
(estimated / designated) true value - measured value.
Sources of Errors in Measurement
Depending on sources of origin, errors in measurements fall into three classes. They are
Natural Errors
Instrumental Errors
Personal Errors
Natural Errors
These are caused due to variations in nature i.e., variations in wind, temperature, humidity,
refraction, gravity and magnetic field of the earth.
Instrumental Errors
These result from imperfection in the construction or adjustment of surveying instruments, and
movement of their individual parts.
Personal Errors
These arise from limitations of the human senses of sight, touch and hearing.
Types (or) classification of Errors
Errors are traditionally been classified into three types.
Gross Error
Systematic Error
Random Error
Gross Error
Gross errors, also known as blunders or mistakes, are results from Carelessness on the part of
observer in taking or recording reading; Faults in equipments; Adoption of wrong technique.
Miss interpretation.
The blunders or mistakes result into large errors and thus can easily be detected by comparing
with other types of errors (generally small in value). The maximum permissible error in an
observation is ± 3.29 s (where s is the standard deviation of sample distribution) and is used to
separate mistakes or blunders from the random errors. If any error deviates from the mean by
more than the maximum permissible error, it is considered as a gross error and the measurement
is rejected.
After mistakes have been detected and eliminated from the measurements, the remaining errors
are usually classified either as systematic or random error depending on the characteristics of
errors.
Systematic Error
Systematic errors occur according to a system. These errors follow a definite pattern. Thus, if an
experiment is repeated, under the same conditions, same pattern of systematic errors reoccur.
These errors are dependent on the observer, the instrument used, and on the physical
environment of the experiment. Any change in one or more of the elements of the system will
cause a change in the character of the systematic error. Depending on the value and sign of errors
in successive observation, systematic errors are divided into two types.
Cumulative Error and Compensating Error
Cumulative Error
If the sign in error remains the same throughout the measuring process, the error will go on
accumulating all throughout the process. This type of systematic error is termed as cumulative
error.
Compensating Error
If the sign of the systematic error changes, the resulting systematic error is termed as
compensating error.
Systematic errors are dealt with mathematically using functional relationships or models.
Propagation of Error
Measurements are used for calculation of different parameters. As the measurements are fraught
with errors, it is important to know how these errors combine in various mathematical
operations.
Accuracy and precision
Accuracy: The term accuracy is used to denote the closeness or nearness of a measurement to its
true value. The measured value is said to be accurate if it is very near to its true value. Thus the
accuracy reflects the degree of perfection achieved in the measurement.
Precision: The term precision of a measurement is used to denote its closeness or nearness to
another measurement of the same quantity. For instance if a particular quantity is measured
several times & the values obtained are very close to one another it is said that the precision is
high. It thus indicates the degree of agreement between several measurements of the same
quantity & it depends on the degree of perfection used in the observation, the instruments & the
methods.
It should be remembered that the high precision does not necessarily mean that the accuracy is
high because the values though close to one another may not be close to the true value.
A precise measurement will represent an accurate measurement only if it contains no error. It is
advisable for a good surveyor to achieve both precision & accuracy. It can be done by using the
precise instruments, by adopting the correct methods of surveying & by eliminating or
minimizing the possible error & mistakes.
Operations in Surveying
Operations in surveying consist of:
1. Planning
2. Field Observation
3. Office Works
4. Setting out Works
Planning
To decide
• The methods to be adopted for surveying;
• The resources (instruments & personnel) to be used;
• The control points / stations to be used (those already available and/ or to set up).
The planning operation needs a-priori field visit and this is known as reconnaissance.
Field Observation
It involves
• Collection of field data by making necessary measurements;
• Recording of observed data in a systematic manner.
Before starting any field observation, the permanent adjustments of all the instruments need to be
checked thoroughly by trained personnel and if required, it must be adjusted.
Office Work
It involves
• Processing, analyzing and calculation of observed data;
• Preparation of necessary data (for making plan or map of the area);
• Making of a plan or map of the area;
• Computation of relevant field parameters as per design for setting out engineering works at site.
Setting out Works
To locate and establish different parameters / dimensions at the site as per design for further
engineering works.
Mapping Fundamentals
The data collected through field surveying are presented in the form of a plan or a map. Since,
the actual surface of the earth is curved, and the surface of the map is flat, a method of projection
is usually used to fit a curved surface of earth into a plane surface of paper. However, no map
can represent a terrain without some distortion. To minimize the effect of distortion, conformal
projections are generally employed.
To prepare a map, first a grid of meridians and parallels of latitude is being prepared to provide a
framework of map. Control points are then plotted by their spherical coordinates (latitude,
longitude). A plane coordinate system is then used to plot other points accurately in orthogonal
coordinate system obviating direct use of spherical coordinates.
In case of plane surveying, the earth's surface is regarded as plane and thus, a map is constructed
by orthographic projection. Points are being plotted by their rectangular coordinates, angles and
distances as horizontal.
During the preparation of maps, the factors which need important considerations are:
• Scales
• Conventional symbols
• Generalization of details
• Plotting accuracy
• Rectangular Coordinates
Examples
Ex2-1 In a plan, a 10 cm scale drawn shrunk to 9.7 cm. If the scale of the given plan is written as
1:250, determine the actual length of a line which at present shows 10 cm.
Solution:
Present representative fraction (R.F.) =
Therefore Actual distance = = 25.77 m
Overview of Land Surveying
The fundamental objective of land surveying is to prepare a plan or map of an area. The map
thus prepared serves as the primary source of information about the surface of the earth for
further engineering works. The data required for making of a map gets collected through field
surveying. To start field surveying, it is required to know very accurately, the geographical
coordinates (latitude, longitude) of at least one point, known as control point and the length as
well as azimuth of a line, known as baseline. The Latitude of the point and the azimuth of the
line are determined through astronomical survey and longitude from time measurement. The
length of the line is measured with a distance measuring instrument.
From the control point in association with the base line, a number of inter visible points are
selected such that on joining these points well shaped triangles are required to be formed. These
triangles carry forward points whose geographical positions are calculated from the
measurements (horizontal distance, horizontal angles) taken from the network of triangles. The
calculated parameters undergo further adjustment by satisfying the geometrical conditions
associated with the parameters as well as with figures. This helps in minimization of errors
which may creep in further surveying operation. Inside the big triangles formed by widely
spaced control points, network of smaller triangles get established. This process gets repeated
materializing the basic principle of surveying "to work from whole to part". Thus the entire area
to be surveyed gets covered with network of triangles.
The detail surveying is then carried out within the smallest triangle. During surveying,
measurements (distance, direction, angles, height etc.) for important objects/ points are taken.
The measurements are then used for necessary calculations and adjustments resulting in
identification and finding positions (with respect to standard reference) of salient objects.
To prepare map, first a grid of medians and parallels of latitudes is being prepared to provide a
frame work of map. Control points are then plotted by their spherical coordinates.
Then objects are graphically represented in a rectangular coordinate system for depicting
planimetric position. Terrain height is depicted by using contours at regular interval. The
identification of objects is depicted using conventional symbols and colors.
To prepare map of the area, first the surveying measurements and plotting are being carried out
for plot number 1.
Next, detail surveying and plotting are being carried out for plot number 2 and subsequently
detail mapping is carried out for plot number 3 and plot number 4. Then, a final map of the
whole area is being prepared by mosaicing the component maps
Definition of Surveying
Surveying is defined as the science of making measurements of the earth specifically on the
surface of the earth. This is being carried out by finding the spatial location (relative / absolute)
of points on or near the surface of the earth.
Different methods and instruments are being used to facilitate the work of surveying. The
primary aims of field surveying are:
• To measure the Horizontal Distance between points.
• To measure the Vertical elevation between points.
• To find out the Relative direction of lines by measuring horizontal angles with reference to any
arbitrary direction and
• To find out Absolute direction by measuring horizontal angles with reference to a fixed
direction.
These parameters are utilized to find out the relative or absolute coordinates of a point / location.
Importance of Surveying to Civil Engineers
The planning and design of all Civil Engineering projects such as construction of highways,
bridges, tunnels, dams etc are based upon surveying measurements. Moreover, during execution,
project of any magnitude is constructed along the lines and points established by surveying.
Thus, surveying is a basic requirement for all Civil Engineering projects. Other principal works
in which surveying is primarily utilized are:
• To fix the national and state boundaries;
• To chart coastlines, navigable streams and lakes;
• To establish control points;
• To execute hydrographic and oceanographic charting and mapping; and
• To prepare topographic map of land surface of the earth.
Objectives of Surveying
• To collect field data;
• To prepare plan or map of the area surveyed;
• To analyze and to calculate the field parameters for setting out operation of actual engineering
works.
• To set out field parameters at the site for further engineering works.
Level surface: It is a curved surface every point on which is equidistant from the center of the
earth and every surface element is normal to the plumb line.
Mean sea level: A plane surface or ordinary surveying a level surface at any point is assumed to
be at the average sea level known as mean sea level.
Great circle: Imagine a plane passing through the centre of the earth the intersection of such a
plane with the mean sea level surface of the earth is termed as great circle of the earth.
Meridian: It is the line defined by the intersection of an imaginary plane passing through the
poles at any point on the earth level surface.
Plumb line: It is normal drawn to the meridian.
Level line: any portion of the line lying on the great circle of the earth is called as level line. It
may also be defined as the line lying on the level surface & normal to the plumb line at all
points.
Divisions of Surveying
The approximate shape of the earth can best be defined as an oblate tri-axial ovaloid. But, most
of the civil engineering works, concern only with a small portion of the earth which seems to be
a plane surface. Thus, based upon the consideration of the shape of the earth, surveying is
broadly divided into two types. (I) Geodetic Surveying (II) Plane Surveying
Oblate (spheroid): An oblate (spheroid) is a surface of revolution obtained by rotating an ellipse
about its minor axis i.e., having equatorial radius greater than the polar radius.
Ovaloid: A pear shaped figure having dimension of one hemisphere larger than the other for
earth, southern hemisphere is larger than the northern.
Geodetic Surveying
In this branch of surveying, the true shape of the earth is taken into consideration. This type of
surveying is being carried out for highly precise work and is adopted for surveying of large area.
All geodetic survey work includes work of larger magnitude & high degree of precision. The
object of geodetic survey is to determine the precise position on the surface of the earth, of a
system of widely distant points which form control stations to which surveys of less precision
may be referred.
Plane Surveying
In this method of surveying, the mean surface of the earth is considered to be a plane surface.
This type of survey is applicable for small area (less than 200 square kilometer). Thus for most
of the Civil Engineering projects, methods of plane surveying are valid. This course is restricted
to the different aspects of plane surveying. Henceforth, in this course work, the word surveying
implies plane surveying.
Fundamental assumptions in Plane surveying
• All distances and directions are horizontal;
• The direction of the plumb line is same at all points within the limits of the survey;
• All angles (both horizontal and vertical) are plane angles;
• Elevations are with reference to a datum.
Classifications of Surveying
(A) Classification based upon the nature of the field of survey
Land Surveying----
Topographic survey: To prepare a plan/ map of a region this includes natural as well as and manmade
features including elevation.
Cadastral survey: To fix the property line, calculation of land area, to fix the boundaries of
municipalities & of state & federal jurisdictions.
City surveying: they are made in connection with the construction of streets, water supply
systems sewers and other works.
Marine or hydrographic survey: -------
Deals with the bodies of water for purpose of navigation, water supply, harbor works or for the
determination of mean sea level. The work consists in measurement of discharge of streams
making topographic survey of shores & banks taking & locating soundings to determine the
depth of water & observing the fluctuations of the ocean tide.
Astronomic surveys: --------
To determine the latitude, longitude (of the observation station) and azimuth (of a line through
observation station) from astronomical observation.
(B) Classification based on the object of survey
Engineering survey: To collect requisite data for planning, design and execution of engineering
projects. Three broad steps are
1) Reconnaissance survey: To explore site conditions and availability of infrastructures.
2) Preliminary survey: To collect adequate data to prepare plan / map of area to be used
for planning and design.
3) Location survey: To set out work on the ground for actual construction / execution of
the project.
• Route survey: To plan, design, and laying out of route such as highways, railways,
canals, pipelines, and other linear projects.
• Construction surveys: Surveys which are required for establishment of points, lines,
grades, and for staking out engineering works (after the plans have been prepared and the
structural design has been done).
Mine surveys: To carry out surveying specific for opencast and underground mining purposes.
Military Surveys: This is used for determining points of strategic importance.
Geological survey: This is used for determining different strata in earth’s crust.
Archeological Survey: Unearthing relics of antiquity.
(C) Classification based on instruments used
Chain surveying, compass surveying, plane table surveying, theodolite surveying, tachometric
surveying, triangulation surveying, areal surveying, photogrammetric surveying, total station
surveying.
(D) Classification based on the method employed
Triangulation surveying and traversing surveying
Uses of surveying/ application of surveying:
• By carrying out astronomical survey we can fix up the local and standard time and
movement of planets.
• By preparing the maps dispute between two states can be avoided.
• Natural features can be located by conducting topographical survey.
• Road maps & guide maps helps tourists and travelers.
• For planning & execution of the water supply and sanitary projects.
• To have detailed survey map showing accurate boundary of the area to be covered.
• To enable the project engineer to proceed with the project.
Units of measurement:
In plane surveying the following two types of measurements are taken:
1) Linear measurements
2) Angular measurements
Linear measurements: The linear measurements can be sub divided into two categories namely
horizontal distances and vertical distances.
In surveying all the measurements represent the horizontal distances only because plotting on
plan or map is made for horizontal distances only irrespective of difference in elevation between
the two points. In certain unavoidable cases if the inclined measurements are taken they are
converted suitably to represent the corresponding horizontal distance.
When the distance between two points is measured in a vertical plane it is known as the vertical
distance.
Angular measurements: The angular measurements can also be sub divided into two categories
namely horizontal angle and vertical angles.
The horizontal angle represents the angles between two intersecting lines in a horizontal plane.
The vertical angle represents the angle between horizontal line and the line of sight inclined to
that point in vertical plane.
Basic units of measurement
No Item Basic unit
1 Length 10 millimeters(mm)= 1 centimeter (cm)
10 centimeter (cm) = 1 decimeter (dm)
10 dm = 1 meter (m)
UNIT 1 INTRODUCTION
DEPT. OF CIVIL ENGG. GNDECB Page 5
10 m = 1 decameter (D)
10 D = 1 hectometer (hm)
10 hm = 1 kilometer (km)
1000 meters = 1 km
1852 meters = 1 nautical mile
2 Area 100 mm2 = 1 cm2
100 cm2 = 1 dm2
100 dm2 = 1 m2
100 m2 = 1 are or sq decameter
100 ares (a) = 1 hectare (ha) or 1 sq hectometer
100 hectares = 1 sq kilometer (km2) or 106 sq meters
3 Volume 1000 mm3 = 1 cm3
1000 cm3 = 1 dm3
1000 dm3 = 1 m3
The angular measurements are taken in degrees, minutes and seconds & radians having the
following relations:
Ð/2 radians = 90 degrees = 1 right angle
Ð/180 radian = 1 degree = 60 minutes
Ð/10800 radian = 1 minute = 60 seconds
The radian is the unit of plane angle & it is defined as the angle between two radii of a circle
which cut off on the circumference an arc equal in length to the radius or in other words it is the
angle subtended at the centre of a circle by an arc equal to the length of the radius of that circle.
Plans and maps:
A map is a graphical representation of large area work with smaller scale. Plan is a graphical
representation of small area work with larger scale.
Scale: the distance measured on ground are plotted on paper in such a way that a fixed ratio is
maintained between the distances on ground to corresponding distance on paper. This ratio is
known as scale. (Engineer’s scale, graphical scale, representative fraction scale)
Map classification:
Large scale map: 1 cm= 10m or less than 10m
Medium scale map: 1 cm = 10m to 100m
Small scale map: 1 cm = 100m or more than 100m
Type of map Representative factor Scale
Geographical map 1:16000000 1cm = 160km
Topographical map 1: 250000 1cm = 2.5km
Location map 1: 500 to 2500 1 cm = 5m to 25m
Forest map 1: 2500 1cm = 0.25km
Cadastral map 1: 1000 to 5000 1cm = 10m to 50m
UNIT 1 INTRODUCTION
DEPT. OF CIVIL ENGG. GNDECB Page 6
Town planning map 1: 5000 to 1000 1 cm = 50m to 10m
Building map 1: 1000 1 cm= 10m
Mines map 1: 1000 to 25000 1 cm = 10m to 250m
Preliminary survey of rail & road 1: 1000 to 6000 1 cm = 10m to 60m
Indian Topographic Maps
Topographic maps provide the graphical portrayal of objects present on the surface of the earth.
These maps provide the preliminary information about a terrain and thus very useful for
engineering works. For most part of India, topographic maps are available which are prepared by
the Survey of India. To identify a map of a particular area, a map numbering system has been
adopted by Survey of India. The system of identification is as follows:
An International Series (within 4° N to 40° N Latitude and 44° E to 124° E Longitude) at the
scale of 1: 1,000,000 is being considered as base map. The base map is divided into sections of
4° latitude x 4° longitude and designated from 1 (at the extreme north-west) to 136, covering
only land areas and leaving any 4° square if it falls completely in the sea.
For Indian Topographic maps, each section is further divided into 16 sections (4 rows by 4
columns), each of 1° latitude x 1° longitude (1:250,000), staring from a letter A (North-West
corner) and ending on P, column-wise. These degree sheets are designated by a number and an
alphabet such as 53 C.
These degree sheets are further sub-divided in the following ways:
Each sheet is divided into four parts (2 rows by 2 columns), each of 30' latitude x 30' longitude
(1:100,000) designating them by cardinal directions NW, NE, SW, and SE. Such sheets are
identified as 53 M/SE.
Degree sheets have also been divided into 16 sheets (4 rows by 4 columns), each 15' latitude x
15' longitude (1:50,000) and numbered from 1 (at the north-west corner of the particular degree
sheet) to 16 column wise and are identified as 53 B/3
Each 1:50,000 scale sheet contains four (2 rows by 2 columns) 1:25,000 sheet ( 7' 1/2 latitude x
7' 1/2 longitude ) which are numbered NW, NE, SW, and SE. Such sheets are identified as 53
O/14/NE.
In this way, the topographic map of most of the area of India may be acquired at the scale
available and subsequently can be updated and upgraded as required for a particular project. For
large scale maps, further surveying needs to carry out.
Principles of Surveying
1. Location of a point by measurement from two points of reference
The relative positions of the points to be surveyed should be located by measurement from at
least two points of reference the positions of which have already been fixed. Let P & Q be the
reference line on the ground. The distance PQ can be measured accurately & the relative
positions of P and Q can be plotted on the sheet to some scale. Thus P & Q will serve as
reference points for fixing the relative positions of other points. Any other such as R can be
located by any of the following direct methods.
a) Distances PR & QR can be measured & the point R can be plotted by swinging the two arcs
to the same scale to which PQ has been plotted. The principle is very much used in chain
surveying.
b) A perpendicular RS can be dropped on the reference line PQ & the lengths PS & SR are
measured. The point R can be plotted using set square. This principle is used for defining
details.
c) The distance QR & the angle PQR can be measured & point R is plotted either by means of a
protractor or trigonometrically. This principle is used in traversing.
d) In this method the distances PR & QR are not measured but angle RPQ & angle RQP are
measured with an angle measuring instrument. Knowing the distance PQ point R is plotted
either by means of a protractor or by solution of triangle PQR. This principle is very much
used in triangulation & the method is used for very extensive work.
e) Angle RQP & distance PR are measured & point R is plotted either by protracting an angle &
swinging an arc from P or plotted trigonometrically. This principle is used in traversing, is
of minor utility.
2. Working from whole to part but from part to whole
The fundamental principles upon which the surveying is being carried out are working from
whole to part. After deciding the position of any point, its reference must be kept from at least
two permanent objects or stations whose position has already been well defined. The purpose of
working from whole to part is to localize the errors and to control the accumulation of errors.
This is being achieved by establishing a hierarchy of networks of control points. The less precise
networks are established within the higher precise network and thus restrict the errors. To
minimize the error limit, highest precise network (primary network) Figure 1.1 of control points
are established using the most accurate / precise instruments for collection of data and rigorous
methods of analysis are employed to find network parameters. This also involves most skilled
manpower and costly resources which are rare and cost intensive.
Errors
State of being wrong in judgment is defined as error (or) the difference between a measured and
its true value is called the measurement error.
Error in Measurement
In case of repeated observation of any parameter, usually it has been found to have variations,
however small, in the resulting measurement. Moreover, there is nothing definite in the amount
UNIT 1 INTRODUCTION
DEPT. OF CIVIL ENGG. GNDECB Page 10
of variation i.e., variations are random in nature. Thus, a measurement usually differs from its
true value. The difference between a measured and its true value is called the measurement error.
Thus, if x is a given measurement and x t is the true value, then the error e is given by
e = x - x t error = measured value – true value.
If an estimated value of xt is usually known and is denoted by x1. Then, an estimate of error for a
measurement value x of the parameter is obtained as e1 = x - x1
However, correction is the term more popularly being used to define the magnitude of error but
opposite in sign. Thus, rearranging the error relation, correction = (-e1) = x1 – x or, correction =
(estimated / designated) true value - measured value.
Sources of Errors in Measurement
Depending on sources of origin, errors in measurements fall into three classes. They are
Natural Errors
Instrumental Errors
Personal Errors
Natural Errors
These are caused due to variations in nature i.e., variations in wind, temperature, humidity,
refraction, gravity and magnetic field of the earth.
Instrumental Errors
These result from imperfection in the construction or adjustment of surveying instruments, and
movement of their individual parts.
Personal Errors
These arise from limitations of the human senses of sight, touch and hearing.
Types (or) classification of Errors
Errors are traditionally been classified into three types.
Gross Error
Systematic Error
Random Error
Gross Error
Gross errors, also known as blunders or mistakes, are results from Carelessness on the part of
observer in taking or recording reading; Faults in equipments; Adoption of wrong technique.
Miss interpretation.
The blunders or mistakes result into large errors and thus can easily be detected by comparing
with other types of errors (generally small in value). The maximum permissible error in an
observation is ± 3.29 s (where s is the standard deviation of sample distribution) and is used to
separate mistakes or blunders from the random errors. If any error deviates from the mean by
more than the maximum permissible error, it is considered as a gross error and the measurement
is rejected.
After mistakes have been detected and eliminated from the measurements, the remaining errors
are usually classified either as systematic or random error depending on the characteristics of
errors.
Systematic Error
Systematic errors occur according to a system. These errors follow a definite pattern. Thus, if an
experiment is repeated, under the same conditions, same pattern of systematic errors reoccur.
These errors are dependent on the observer, the instrument used, and on the physical
environment of the experiment. Any change in one or more of the elements of the system will
cause a change in the character of the systematic error. Depending on the value and sign of errors
in successive observation, systematic errors are divided into two types.
Cumulative Error and Compensating Error
Cumulative Error
If the sign in error remains the same throughout the measuring process, the error will go on
accumulating all throughout the process. This type of systematic error is termed as cumulative
error.
Compensating Error
If the sign of the systematic error changes, the resulting systematic error is termed as
compensating error.
Systematic errors are dealt with mathematically using functional relationships or models.
Propagation of Error
Measurements are used for calculation of different parameters. As the measurements are fraught
with errors, it is important to know how these errors combine in various mathematical
operations.
Accuracy and precision
Accuracy: The term accuracy is used to denote the closeness or nearness of a measurement to its
true value. The measured value is said to be accurate if it is very near to its true value. Thus the
accuracy reflects the degree of perfection achieved in the measurement.
Precision: The term precision of a measurement is used to denote its closeness or nearness to
another measurement of the same quantity. For instance if a particular quantity is measured
several times & the values obtained are very close to one another it is said that the precision is
high. It thus indicates the degree of agreement between several measurements of the same
quantity & it depends on the degree of perfection used in the observation, the instruments & the
methods.
It should be remembered that the high precision does not necessarily mean that the accuracy is
high because the values though close to one another may not be close to the true value.
A precise measurement will represent an accurate measurement only if it contains no error. It is
advisable for a good surveyor to achieve both precision & accuracy. It can be done by using the
precise instruments, by adopting the correct methods of surveying & by eliminating or
minimizing the possible error & mistakes.
Operations in Surveying
Operations in surveying consist of:
1. Planning
2. Field Observation
3. Office Works
4. Setting out Works
Planning
To decide
• The methods to be adopted for surveying;
• The resources (instruments & personnel) to be used;
• The control points / stations to be used (those already available and/ or to set up).
The planning operation needs a-priori field visit and this is known as reconnaissance.
Field Observation
It involves
• Collection of field data by making necessary measurements;
• Recording of observed data in a systematic manner.
Before starting any field observation, the permanent adjustments of all the instruments need to be
checked thoroughly by trained personnel and if required, it must be adjusted.
Office Work
It involves
• Processing, analyzing and calculation of observed data;
• Preparation of necessary data (for making plan or map of the area);
• Making of a plan or map of the area;
• Computation of relevant field parameters as per design for setting out engineering works at site.
Setting out Works
To locate and establish different parameters / dimensions at the site as per design for further
engineering works.
Mapping Fundamentals
The data collected through field surveying are presented in the form of a plan or a map. Since,
the actual surface of the earth is curved, and the surface of the map is flat, a method of projection
is usually used to fit a curved surface of earth into a plane surface of paper. However, no map
can represent a terrain without some distortion. To minimize the effect of distortion, conformal
projections are generally employed.
To prepare a map, first a grid of meridians and parallels of latitude is being prepared to provide a
framework of map. Control points are then plotted by their spherical coordinates (latitude,
longitude). A plane coordinate system is then used to plot other points accurately in orthogonal
coordinate system obviating direct use of spherical coordinates.
In case of plane surveying, the earth's surface is regarded as plane and thus, a map is constructed
by orthographic projection. Points are being plotted by their rectangular coordinates, angles and
distances as horizontal.
During the preparation of maps, the factors which need important considerations are:
• Scales
• Conventional symbols
• Generalization of details
• Plotting accuracy
• Rectangular Coordinates
Examples
Ex2-1 In a plan, a 10 cm scale drawn shrunk to 9.7 cm. If the scale of the given plan is written as
1:250, determine the actual length of a line which at present shows 10 cm.
Solution:
Present representative fraction (R.F.) =
Therefore Actual distance = = 25.77 m
Overview of Land Surveying
The fundamental objective of land surveying is to prepare a plan or map of an area. The map
thus prepared serves as the primary source of information about the surface of the earth for
further engineering works. The data required for making of a map gets collected through field
surveying. To start field surveying, it is required to know very accurately, the geographical
coordinates (latitude, longitude) of at least one point, known as control point and the length as
well as azimuth of a line, known as baseline. The Latitude of the point and the azimuth of the
line are determined through astronomical survey and longitude from time measurement. The
length of the line is measured with a distance measuring instrument.
From the control point in association with the base line, a number of inter visible points are
selected such that on joining these points well shaped triangles are required to be formed. These
triangles carry forward points whose geographical positions are calculated from the
measurements (horizontal distance, horizontal angles) taken from the network of triangles. The
calculated parameters undergo further adjustment by satisfying the geometrical conditions
associated with the parameters as well as with figures. This helps in minimization of errors
which may creep in further surveying operation. Inside the big triangles formed by widely
spaced control points, network of smaller triangles get established. This process gets repeated
materializing the basic principle of surveying "to work from whole to part". Thus the entire area
to be surveyed gets covered with network of triangles.
The detail surveying is then carried out within the smallest triangle. During surveying,
measurements (distance, direction, angles, height etc.) for important objects/ points are taken.
The measurements are then used for necessary calculations and adjustments resulting in
identification and finding positions (with respect to standard reference) of salient objects.
To prepare map, first a grid of medians and parallels of latitudes is being prepared to provide a
frame work of map. Control points are then plotted by their spherical coordinates.
Then objects are graphically represented in a rectangular coordinate system for depicting
planimetric position. Terrain height is depicted by using contours at regular interval. The
identification of objects is depicted using conventional symbols and colors.
To prepare map of the area, first the surveying measurements and plotting are being carried out
for plot number 1.
Next, detail surveying and plotting are being carried out for plot number 2 and subsequently
detail mapping is carried out for plot number 3 and plot number 4. Then, a final map of the
whole area is being prepared by mosaicing the component maps
PLANE TABLE SURVEYING
Introduction
A plane table surveying is a graphical method of surveying. In this method of surveying, field
observation and plotting are done simultaneously helping the surveyor to compare the plotted
details with actual features of the ground.
Advantages of Plane Table Survey
It is suitable for location of details as well as contouring for large scale maps directly in
the field.
As surveying and plotting are done simultaneously in the field, chances of getting
omission of any detail get less.
The plotting details can immediately get compared with the actual objects present in the
field. Thus errors as well as accuracy of the plot can be ascertained as the work
progresses in the field.
Contours and specific features can be represented and checked conveniently as the whole
area is in view at the time of plotting.
Only relevant details are located because the map is drawn as the survey progresses.
Irrelevant details get omitted in the field itself.
The plane table survey is generally more rapid and less costly than most other types of
survey.
As the instruments used are simple, not much skill for operation of instruments is
required. This method of survey requires no field book.
Disadvantages of Plane Table Survey
The plane table survey is not possible in unfavorable climates such as rain, fog etc.
This method of survey is not very accurate and thus unsuitable for large scale or precise
work.
As no field book is maintained, plotting at different scale require full exercise.
The method requires large amount of time to be spent in the field.
Quality of the final map depends largely on the drafting capability of the surveyor.
This method is effective in relatively open country where stations can be sighted easily.
Instruments
A plane table mounted on a tripod stand and a number of accessories are used during plane table
survey. The accessories consist of alidade, spirit level, trough compass, plumbing fork, plumb
bob, drawing sheet.
Introduction
A plane table surveying is a graphical method of surveying. In this method of surveying, field
observation and plotting are done simultaneously helping the surveyor to compare the plotted
details with actual features of the ground.
Advantages of Plane Table Survey
It is suitable for location of details as well as contouring for large scale maps directly in
the field.
As surveying and plotting are done simultaneously in the field, chances of getting
omission of any detail get less.
The plotting details can immediately get compared with the actual objects present in the
field. Thus errors as well as accuracy of the plot can be ascertained as the work
progresses in the field.
Contours and specific features can be represented and checked conveniently as the whole
area is in view at the time of plotting.
Only relevant details are located because the map is drawn as the survey progresses.
Irrelevant details get omitted in the field itself.
The plane table survey is generally more rapid and less costly than most other types of
survey.
As the instruments used are simple, not much skill for operation of instruments is
required. This method of survey requires no field book.
Disadvantages of Plane Table Survey
The plane table survey is not possible in unfavorable climates such as rain, fog etc.
This method of survey is not very accurate and thus unsuitable for large scale or precise
work.
As no field book is maintained, plotting at different scale require full exercise.
The method requires large amount of time to be spent in the field.
Quality of the final map depends largely on the drafting capability of the surveyor.
This method is effective in relatively open country where stations can be sighted easily.
Instruments
A plane table mounted on a tripod stand and a number of accessories are used during plane table
survey. The accessories consist of alidade, spirit level, trough compass, plumbing fork, plumb
bob, drawing sheet.
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