surveying 1 pdf

DEPARTMENT OF TECHNICAL EDUCATION E-CONTENT
Note: This is only Basic Information for students. Please
refer “Reference Books” prescribed as per syllabus
15CE21T- SURVEYING-I

UNIT- 1: INTRODUCTION & CHAIN SURVEYING
1.1 Definition and objectives of surveying
Surveying or land surveying is the technique, profession, and science of determining the
terrestrial or three-dimensional position of points and the distances and angles between
them.
A land surveying professional is called a land surveyor. These points are usually on the
surface of the Earth, and they are often used to establish land maps and boundaries for
ownership, locations like building corners or the surface location of subsurface features, or
other purposes required by government or civil law, such as property sales.
OBJECTS OF SURVEYING :
The primary object of survey is the preparation of plan for building, roads, railways,
pipelines, canals, etc. or to measure area of field, state, and nation.
To determine precise positions on the surface of the earth of widely distant points.
To determine areas, volumes and other related quantities.
1.2 Primary divisions
Based on the considerations and true shape of the earth, surveying is broadly classified into
two types.
(a) Plane surveying :
The surveying in which curvature and spheroidal shape of the earth is neglected and the
surface of the earth is assumed to be flat is called plane surveying. In this type of surveying
all triangles formed by joining survey lines are considered as plane triangles. It is generally
employed for small survey works. This survey is to form on less than 250 sq km.
(b) Geodetic surveying :
In this type of surveying curvature of the earth is taken into account while calculating
reduced levels, angles, bearings and distances. This type of surveying is only employed for
large survey works. Generally the survey works below 260 kilometers radius are treated as
plane and beyond that limit it is treated as geodetic. Thus in this type of surveying
necessary corrections are applied to correct the reduced levels, bearings and other
observations.

1.3 Classifications and Principles
CLASSIFICATIONS OF SURVEYING :
Surveying may be classified on the following basis:
(i) Nature of the survey field
(ii) Object of survey
(iii) Instruments used and
(iv) The methods employed.
(i) Classification Based on Nature of Survey Field : On this basis survey may be classified as
land survey, marine or hydraulic survey and astronomical survey. Land Survey. It involves
measurement of various objects on land. This type of survey may be further classified as
given below:
(a) Topographic Survey: It is meant for plotting natural features like rivers, lakes, forests
and hills as well as man-made features like roads, railways, towns, villages and canals.
(b) Cadestal Survey: It is for marking the boundaries of municipalities, villages, talukas,
districts, states etc. The surveys made to mark properties of individuals also come under this
category.
(c) City Survey: The survey made in connection with the construction of streets, water
supply and sewage lines fall under this category.
(d) Marine or Hydrographic Survey: Survey conducted to find depth of water at various
points in bodies of water like sea, river and lakes fall under this category. Finding depth of
water at specified points is known as sounding.
(e) Astronomical Survey: Observations made to heavenly bodies like sun, stars etc., to
locate absolute positions of points on the earth and for the purpose of calculating local time
is known as astronomical survey.
(ii) Classification Based on Object of Survey : On the basis of object of survey the
classification can be as engineering survey, military survey, mines survey, geological survey
and archaeological survey.
(a) Engineering Survey: The objective of this type of survey is to collect data for designing
civil engineering projects like roads, railways, irrigation, water supply and sewage disposals.
These surveys are further sub-divided into:
Reconnaissance Survey for determining feasibility and estimation of the scheme.
Preliminary Survey for collecting more information to estimate the cost of the project, and
Location Survey to set the work on the ground.

(b) Military Survey: This survey is meant for working out plans of strategic importance.
(c) Mines Survey: This is used for exploring mineral wealth.
(d) Geological Survey: This survey is for finding different strata in the earth’s crust.
(e) Archeological Survey: This survey is for unearthing relics of antiquity.
(iii) Classification Based on Instruments Used : Based on the instruments used, surveying
may be classified as:
(a) Chain survey
(b) Compass survey
(c) Plane table survey
(d) Theodolite survey
(e) Tacheometric survey
(f) Modern survey using electronic distance meters and total station
(g) Photographic and Aerial survey
The survey is taught to students mainly based on this classification.
(iv) Classification Based on Methods Employed : On this basis surveying is classified as
triangulation and traversing.
(a) Triangulation: In this method control points are established through a network of
triangles.
(b) Traversing: In this scheme of establishing control points consists of a series of
connected points established through linear and angular measurements. If the last line
meets the starting point it is called as closed traverse. If it does not meet, it is known as
open traverse.
PRINCIPLES OF SURVEYING :
Following are the two basic principles which are to be observed in surveying
Principle no 1:
The survey work should be carried out from the whole to the part and not from the part to
whole
The main idea of working from whole to part is to localize the errors and prevent their
accumulation. On the contrary if we work from part to whole the errors accumulate and
expand to greater magnitude in the process of expansion of survey and consequently the
survey becomes uncontrollable at the end.

Principle no 2:
The length of the main lines and the positions of important survey stations should be
ascertained by at least two independent measurements.
1.4 Purpose, Accessories
ACESSORIES USED IN CHAIN SURVEYING :
a) SURVEYING CHAINS :
Following are the various types of chain in common use:
Metric chains
Steel band or Band chain
Gunter's chain or surveyors chain
Engineers chain
Revenue chain
1. Metric Chain:
Metric chains are made in lengths 20m and 30m. Tallies are fixed at every five-meter
length and brass rings are provided at every meter length except where tallies are attached.
2. Gunter’s Chain
Length = 66’ (22 yards), No of links = 100, Each link = .66’
Used for measuring distances in miles or furlongs (220 yards), acres (Area).
3. Engineer’s Chain
Length = 100’, No of links = 100, Each link = 1’
Used in all Engineering Surveys.
4. Revenue Chain
Length = 33’, No of links = 16
Commonly used for measuring fields in cadastral Survey.

b) TAPES:
1. Cloth or linen tape :
Used for subsidiary measurements
Very light, easy to handle
May effect by moisture
2. Metric steel tape :
Made of steel
Outer end is provided with a ring for holding
3. Invar tape :
Used for high precision work
Made of alloy steel
4. Synthetic tape :
Made of glass fiber with PVC coating
These are used for short measurements.
c) PEGS :
Pegs are used when certain points on the field require more permanent marking. Pegs are
generally made of wood; sometimes pieces of tree-branches, properly sharpened, are good
enough. The size of the pegs (40 to 60 cm) depends on the type of survey work they are
used for and the type of soil they have to be driven in. The pegs should be driven vertically
into the soil and the top should be clearly visible.
Wooden pegs
d) ARROWS :
These are also known as chaining pins and are used to mark the end of each chain during
the chaining process. These are made of hardened and tempered steel wire 4 mm diameter.
The length of an arrow is kept at 400mm. These are pointed at one end and circular ring at
the other end.

Arrows
e) RANGING RODS :
Ranging Rods
Used for making the positions of stations and for ranging. They are made of
seasoned timber of teak, blue pine, sisov or deodar. They are circular or octagonal in cross
section of 3 cm diameter. Lower shoe is 15 cm long. They are made in two sizes as 2 meters
and 3 meters and are divided in to equal parts each 0.2 m long. They are painted
alternatively black and white or red and white. Now a day instead of timber, mild steel hallo
pipes are used.
f) RANGING POLES :
Similar to the ranging rods but are heavier, they vary in length from 4 m to 6 m or more.
Used in the case of very long lines.

g) OFFSET RODS :
Similar to the ranging rod, they are usually 3 m long and is divided into parts each 0.2 m
length. Top is an provided with an open ring for puling or pushing the chain through a
hedge. It has two short narrow vertical slots. It is used for aligning short offsets.
Ranging Rod and offset rods
j) PLUMB BOB :
The plumb bob is required when measuring the distance along slopes in order to transfer
points to the ground. It is also used for testing the verticality of ranging poles.
1.5 Principles of chain surveying
Principles of chain surveying :
The main principles of chain surveying are to prepare the frame work or network of triangles
of suitable sides. The triangles plotted should be well conditions triangles so that process of
chain surveying becomes smooth. A well-conditioned or well-proportioned triangle has no
angle greater than 1200 or smaller than 300.As far as possible, the triangles formed should
resemble to the shape of an equilateral triangle.
If however, the conditions are not favourable for forming well-proportioned triangle,
extreme care should be taken in chaining and plotting of the unavoidable ill – proportioned
triangle or ill conditioned triangles. The accuracy of such triangles are obtained with the help
of the check lines.

(a) Main station: Main station is a point in chain survey where the two sides of a traverse
or triangle meet. These stations command the boundaries of the survey and are designated
as capital letters ( A,B,C,D,E) Ref Fig 1.1.
(b)Tie station or subsidiary station:
Tie station is a station on a survey line joining two main stations. These are helpful in
locating the inner details of the area to be surveyed and are designated as small letters such
as a, b, c, etc.
(c )Main survey line:
The chain line joining two main survey stations is called main survey line, AB, BC,
CD,DE,EA and AD (Ref Fig 1.1).are the Main survey line
(d)Tie line or subsidiary line:
The chain line joining two tie stations is called tie line such as ab, cd(Ref Fig 1.1). These
are provided to locate interior details which are far away from the main lines.
(e)Base line:
The longest main survey line on a fairy level ground and passing through the centre of the
area . It is the most important line as the direction of all other survey lines are fixed with
respect with respect to this line.

(f)Check line:
Check line or proof line is a line which is provided to check the accuracy of the field work.
The measured length of the check line and computed one (scaled off the plan) must be the
same. AD is an example of check line.
(g)Off set:
It is the distance of the object from the survey line. It must be perpendicular or oblique.
1.6 Different operations, Ranging
Different operations in Chain Surveying:
Methods of Ranging in Chain Surveying :
In measuring a survey line, the chain has to be laid out on the ground between the stations.
If the line is short, the chain could be put in alignment easily but if it is long or the end
station is not clearly visible, then intermediate points has to be established in line with end
points to know the directions of the line by ranging.
Types of Ranging :
There are two types of ranging:
1. Direct ranging
2. Indirect ranging
(a) Direct ranging :
Direct ranging is possible when the stations are intervisible.
Ranging is done by eye-judgement. Ranging rods are erected vertically beyond each end of
survey line.
The surveyor stands 2m beyond the ranging rod while the assistant folds the ranging rod
vertically in the intermediate stations.
The ranging rod is held roughly in line by the thumb and fore-finger.
The surveyor directs the assistant to move the rod to the left or right until the three ranging
rods appear to be in a straight line.
To avoid errors due to the ranging rods not being vertical, the lower end of the rod are cited
for alignment.

Direct method of Ranging
(b) Indirect Ranging
1. Indirect Ranging is possible when the ends of a line are not inter-visible as in the case
when a hill ground or when the distance between the stations are so large that they are not
clearly inter-visible.
Indirect method of Ranging
Intermediate points are fixed by the process of reciprocal ranging as explained below.
Let A and B be the ends of a survey line to be measured as a rising ground between them.
Two chain men with ranging rods take the positions M1 and N1 such that they are as nearly
in line with A and B as they could judge the chain men at M1 could N1 and B.
And the chain men at N1 could see M1 and A.
First chain men at N1 direct M1 to M2 so that he comes in the line with A and N.
Then the chain man at M2 directs N1 to N2 such that he comes in line with B and M2.
The process is repeated so that they align each other successively directing each other until
they are both finally in the line AB.
LINE RANGER :
It is an optical instrument used for locating a point on a line and hence useful for ranging.
It consists of two isosceless prisms placed one over the other and fixed in an instrument
with handle. The diagonals of the prisms are silvered so as to reflect the rays.

To locate point C on line AB (ref. Fig. 1.9) the surveyor holds the instrument in hand and
stands near the approximate position of C. If he is not exactly on line AB, the ranging rods
at A and B appear separated as shown in Fig. 1.9(b). The surveyor moves to and fro at right
angles to the line AB till the images of ranging rods at A and B appear in a single line as
shown in Fig. 1.9 (c).
It happens only when the optical square is exactly on line AB. Thus the desired point C is
located on the line AB.
Its advantage is it needs only one person to range. The instrument should be occasionally
tested by marking three points in a line and standing on middle point observing the
coincidence of the ranging rods. If the images of the two ranging rods do not appear in the
same line, one of the prism is adjusted by operating the screw provided for it.
Line Ranger
1.7 Cross staff survey, Plotting the chain survey
CROSS STAFF :
Perpendicular Offsets Using Cross Staffs
(a) (b) (c)
Cross staff
Above figure shows 3 different types of cross staffs used for setting perpendicular offsets.
All cross staffs have two perpendicular lines of sights. Cross staffs are mounted on stand.
First line of sight is set along the chain line and without disturbing setting right angle line of

sight is checked to locate the object. With open cross staff (Fig.a) it is only possible to set
perpendicular, whereas with french cross staff (Fig (b)), even 45º angle may be set. Since
there are graduations and upper drum can be rotated over lower drum adjustable cross staff
can be also used to set any angle.
Perpendicular Offsets Using Optical Square and Prism Square :
These instruments are based on the optical principle that if two mirrors are at angle ‘θ’ to
each other, they reflect a ray at angle ‘2θ’. Figure 12.15 shows a typical optical square.
Optical square consists of a metal box about 50 mm in diameter and 125 mm deep. In the
rim of
the box there are three openings:
(i) a pin hole at E
(ii) a small rectangular slot at G, and
(iii) a large rectangular slot at F.
A and B are the two mirrors placed at 45º to each other. Hence the image of an object at F
which falls on A gets reflected and emerges at E which is at right angles to the line FA. The
mirror A which is opposite to the opening at F is fully silvered. It is fitted to a frame which is
attached to the bottom plate. If necessary this mirror can be adjusted by inserting a key on
the top of the cover. The mirror B which is in the line with EG is silvered in the top half and
plain in the bottom half. It is firmly attached to the bottom plate of the box. The ranging rod
at Q is directly sighted by eye at E in the bottom half of the B which is a plain glass. At the
same time in the top half of B, the reflected ray of the object at P is sighted. When the
image of P is in the same vertical line as the object at Q, then the lines PA is at right angles
to the line EB. This instrument can be used for finding foot of the perpendicular or to set a
right angle. In prism square, instead of two mirrors at 45º to each other a prism which has
two faces at 45º to each other is used [Fig. 1.10.]. Its advantage is it will not go out of
adjustment even after long usage.

Optical square
Prism square
CROSS STAFF SURVEY :

Object: – To determine area of field using cross staff survey.
Equipments: –
1. Ranging rod – 7 Nos.
2. 30 m Chain – 1 Nos.
3. Arrow – 5 Nos.
4. Metallic tape (30m) – 1 Nos.
5. Cross staff with stand – 1 Nos.
Procedure: –
1. Field work
2. Classroom work
(1.) Field work
1. First of all first ranging rod is established at point A and makes fixed station taking
measurement revising point A to two permanent structures.
2. Second ranging rod is established at point B and for makes fixed station taking
measurement revising point B to two permanent structures.
3. Established grid line A to B using ranging procedure by judgment of eye and laying chain
on it.
4. Remaining ranging rod established at point P, Q, R, and S, T on right and left side of the
grid line and its may be point of permanent structure at different location.
5. Sight point P perpendicular to grid line using cross staff, let’s meeting point is P’ on grid
line.
6. Measure distance of AP’ and PP’ by chain (on grid line) and metallic tape (between P to
P’).
7. Write all observation in field book or level book immediately.
8. Repeat Sighting procedure using cross staff, let’s meeting point is Q’, R’, S’, and T’ on grid
line.
9. Measure distance of AQ’, AR’, AS’ and AT’ by chain (on grid line) and QQ’, RR’, SS’, TT’
using Metallic tape respectively.
10. Write all observation in field book or level book respectively.
11. When complete all observation removes all ranging rods and packed in its cover.
(2) Classroom work: –
1. Draw a complete figure in field book using field observation.
2. Draw a line meeting point P to S and R to T on field book or level book.
3. Calculate the area of field by subtract out side (remaining) area of meeting line in total
area in field book

Observation table: –
Figure: –
Precautions: –
1. The ranging rod should be established correctly state at all points.
2. The judgment of line should be taking correctly during established ranging rod at a point.
3. Distance between surveyor’s eye and reference station (eg. A, B and C) should be
minimum one meter.
4. The cross staff should be states during sight both station and observations take
accurately.

1.8 Adopting suitable conventions

1.9 Errors & Corrections in chain surveying
Types of Errors occurring in Chain Surveying :
There are two types of Errors that are commonly seen to occur in Chain Surveying. For
students studying the concept of Chain Surveying, study of the occurrence of different types
of Errors in Chain Surveying is important. In this article, we will briefly discuss different
types of Errors in Chain Surveying and the situations in which they occur.
Types of Errors:
1. Cumulative error
2. Compensative error
Cumulative error :
These errors always accumulate in one direction and are serious in nature. They affect the
survey work considerably.
They make measurements too long or too short.
These errors are of two types and are known as systematic errors.
They are classified as follows:
1. Positive error
2. Negative error
Positive errors :
These errors make the measured length more than the actual length which results into
wrong calculations by the Surveyor.
The following are some of the positive errors:
· The length of chain is shorter than the standard length due to bending of links,
removal of connecting rings and knots in links.
· The temperature is lower than at which the tape was calibrated.
· Not applying sag correction.
· Sag takes place due to self-weight of the chain.
· Incorrect alignment
Negative errors :
These errors make the measured length less than the actual length.
Following are some of the negative errors:
Length of chain or tape greater than its standard length due to flattening of rings, opening
of ring joints and temperature being higher than at which it was standardized.

Compensative errors :
These errors occur in either direction and are likely to compensate.
These occur in following situations:
· Incorrect holding of chain
· Displacement of arrows
· Adding or omitting a full length of chain
· Reading wrongly
· Booking wrongly
A practical Example for Calculation of the True Area of the field | Errors in Chain
Surveying
Correction formulas to be kept in mind (for incorrect length of Chain)
True distance = L’/L*measured distance
True area = (L’/L)2*measured area
True Volume = (L’/L)3 * measured volume
Where, L’ = incorrect length of chain
L = correct length of chain
The chain was tested before starting the surveying and was found to be 20m. At the end of
surveying, it was tested again and was found to be 20.12m. The area of the plan of the field
drawn to a scale 1cm = 6m was 50.4sqm. Find the true area of the field in sqcm.
Scale of the plan
1cm = 6m
1cm2 = 36m2
Area of plank = 50.4 cm2
Measured area of field = 50.4 * 36

= 1814.4m2
Incorrect length of chain, L’ = (20+20.12)/2
= 20.06m
L = 20m
True area = (L’/L)2 * measured area
= (20.06/20)2 * 1814.4
= 1825.3m2
1 hectare = 10,000m2
= 0.1825 hectare

1.10 Simple problems

UNIT- 2: COMPASS SURVEYING
2.1 Introduction and purpose
Disadvantage of chain surveying is that, in it only distances are measured and hence area is
to be covered with a network of triangles.
If the length as well as angle of a line can be measured with respect to a known direction
then it is possible to plot a line, independent of length of other lines. Hence, in such cases
there is no compulsion of going for a network of triangles only.
Compass is an instrument which can be used to measure the direction of a survey line with
respect to magnetic north-south. The magnetic north-south direction which is the reference
direction is called meridian (reference direction) and the angle between the line and the
meridian is called bearing.
Use of compass for measuring direction of a line simplifies the surveying to a great extent.
In this chapter construction of different types of compasses, the system of noting bearings
of the lines, some problems associated with measurement with compass are explained and
then field work involved in compass survey is presented.
2.2 Bearing & its type, Problems on bearings
Bearing :
It is an angle made by the survey line with reference to some fixed meridian.
Bearings are classified into three types:
1. True bearing
2. Magnetic bearing
3. Arbitrary Bearing
True bearing
The angle made by a survey line with reference to the meridian is known as true bearing. It
always remains constant.
Magnetic bearing
The angle made by a survey line with respect to magnetic meridian is known as magnetic
bearing. It changes from place to place.

Arbitrary Bearing
The angle made by the survey line with reference to arbitrary meridian is known as Arbitrary
Bearing.
Designation of Bearings
1. Whole circle bearing
2. Reduced Bearing (RB) or quadrantal bearing (QB)
3. Fore Bearing (FB) or forward bearing (FB)
4. Back bearing or Backward bearing (BB)
5. Calculated bearing
In whole circle bearing (WCB) the bearing of a line at any point is measured with respect to
a meridian. Its value varies from zero to 360°, increasing in clockwise direction. Zero is
north direction, 90° is east, 180° is south and 270° is west (Ref. Fig. 13.2). This type of
bearing is used in prismatic compass.
In reduced bearing (RB) system, bearings are measured from north or south direction
towards east or west. Hence, angles are from 0 to 90° as shown in Fig. 13.3. This system of
measuring bearings is used in Surveyor’s compass and it is also known as Quadrantal
Bearing (QB). The bearing measured is designated with letter N or S in the beginning to
indicate whether it is from north or south. The letter E or W written after the angle indicates
whether the bearing read is towards east or west, respectively.
The conversion of the bearing from one system to the other system can be easily carried out
by drawing a sketch to indicate WCB or RB as shown in Fig. It may be observed that
conversion table is as given below:

2.3 Compass and its types
The types of compass that are used commonly are:
(i) Prismatic compass and
(ii) Surveyor compass
The essential parts of both type are:
(i) a magnetic needle,
(ii) a graduated circle,
(iii) a line of sight, and
(iv) a box to house them.
There are some differences in the essential parts of the two type of compass. The
construction of the two types of compass is explained and the difference in them is pointed
out in this article.
Prismatic Compass :
Figure shows the cross-section of a typical prismatic compass". A magnetic needle of broad
form (1) is balanced on a hard and pointed steel pivot (2). The top of the pointed pivot is
protected with agate cap (3).
An aluminium graduated disk (4) is fixed to the top of the needle. The graduations are from
zero to 360° in clockwise direction when read from top. The direction of north is treated as
zero degrees, east as 90°, south as 180° and west as 270°. However, while taking the
readings observations are at the other end of line of sight. Hence, the readings are shifted

by 180° and graduations are marked as shown in fig. The graduations are marked inverted
because they are read through a prism.
The line of sight consists of object unit and the reading unit.
Object unit consists of a slit metal frame (5) hinged to the box.
In the centre the slit is provided with a horse hair or a fine wire or thread (6).
The metal frame is provided with a hinged mirror (7), which can be placed upward or
downward on the frame.
It can be slided along the frame.
The mirror can be adjusted to view objects too high or too low from the position of
compass. Reading unit is provided at diametrically opposite edge.
It consists of a prism (8) with a sighting eye vane (9). The prism magnifies the readings on
the graduation disk just below it. For focusing, the prism is lowered or raised on the frame
carrying it and then fixed with the stud (10). Dark sunglasses (11) provided near the line of
sight can be interposed if the object to be sighted is bright (e.g., sun).The bottom of the
box (12) which is about 85 mm to 110 mm supports the pivot of needle firmlyat its centre.
The object vane and the prism are supported on the sides of the box. The box is provided
with a glass (13) lid which protects the graduation disc at the same time permit the direct
reading from the top. When the object vane is folded on the glass top it presses a lifting pin
(14) which activates lifting lever (15) lifts the needle off the pivot. Thus, it prevents undue
wear of pivot point. While taking reading, if graduation disc vibrates, it can be dampened
with a spring (16). For pressing spring a knob or brake pin (17) is provided on the box.
When not in use prism can be folded over the edge of the box.
The box is provided with a lid to close it when the compass is not in use. The box is
provided with a socket to fit it on the top of a tripod.

Surveyors Compass :
In this type of compass graduation disc is fixed to the box and magnetic needle is free to
rotate above it. There is no prism provided at viewing end, but has a narrow slit. After fixing
the line of sight, the reading is directly taken from the top of the glass cover. Hence,
graduations are written directly (not inverted). In this compass graduations are from zero to
90°, zero being to north or south and 90° being to east and west. An angle of 20° to north
direction to the east is written as N 20° E, and an angle of 40° to east from south is written
as S 40° E. Always first direction indicated is north or south and the last letter indicates east
or west direction. In this system graduated circle rotates with line of sight and magnetic
needle is always towards north. The reading is taken at the tip of needle. Hence, on the
compass east and west are marked interchanged and marked.
Difference Between Prismatic Compass and Surveyors Compass

2.4 Dip and declination, Simple problems
Magnetic Dip :
A perfectly balanced, freely suspended magnetic needle dips towards its northern end in
northern hemisphere and towards its southern end in southern hemisphere. If it is at north
pole, the needle takes vertical position. The vertical angle between the horizontal and the
direction shown by a perfectly balanced and freely suspended needle is known as the
magnetic dip at that place. Its value is 0° at equator and 90° at magnetic poles. To
counteract the dip, a sliding rider (weight) is provided on the needle.
Magnetic Declination :
The magnetic meridian and the true meridian may not coincide with each other in a place.
The horizontal angle between these two meridians is known as magnetic declination. The
magnetic north at a place may be towards east or west of true north. If it is towards east, it
is known as eastern or +ve declination. Western declination is known as –ve declination.
Eastern declination is to be added to observed magnetic bearings to get true meridian. To
find magnetic declination at a point true meridian should be established from astronomical
observations and magnetic meridian by a compass. Maps are made with respect to true
meridian.
Magnetic declination varies from time to time and also from place to place. In the noon sun
is exactly on the geographical meridian. In India, ‘Survey of India’ department conducts
astronomical survey and publishes Isogonic Charts from which magnetic declinations at any
point can be found.
The lines joining the points at which declination is the same at the given time are called
‘Isogonic Lines’. Lines joining points of zero declinations are called ‘Agonic Lines’. The
isogonic lines are quite irregular near geographic poles. The isogonic charts show lines of
equal annual change in declination.
2.5 Local attraction
Local Attraction :
A freely suspended and properly balanced magnetic needle is expected to show magnetic
meridian.
However, local objects like electric wires and objects of steel attract magnetic needle
towards themselves.
Thus, needle is forced to show slightly different direction. This disturbance is called local
attraction.

The list of materials which cause local attraction are:
(i) magnetic rock or iron ore,
(ii) steel structures, iron poles, rails, electric poles and wires,
(iii) key bunch, knife, iron buttons, steel rimmed spectacles, and
(iv) chain, arrows, hammer, clearing axe etc.
Surveyor is expected to take care to avoid local attractions listed in (iii) and (iv) above.
Detecting Local Attraction :
For detecting local attraction it is necessary to take both fore bearing and back bearing for
each line. If the difference is exactly 180°, the two stations may be considered as not
affected by local attraction. If difference is not 180°, better to go back to the previous
station and check the fore bearing. If that reading is same as earlier, it may be concluded
that there is local attraction at one or both stations.
Correcting Observed Bearings :
If local attraction is detected in a compass survey observed bearings may be corrected by
any one of the following two methods:
Method I: It may be noted that the included angle is not influenced by local attraction as
both readings are equally affected. Hence, first calculate included angles at each station,
commencing from the unaffected line and using included angles, the corrected bearings of
all lines may be calculated.
Method II: In this method, errors due to local attraction at each of the affected station is
found starting from the bearing of a unaffected local attraction, the bearing of the
successive lines are adjusted.
2.6 Open and closed traverse, checks, Errors.
TRAVERSE :
A traverse is a series of connected lines whose lengths and directions are measured in the
field work. The lengths are measured with tape or chain and directions are measured with a
compass or theodolite. The ends of traverse line are called traverse station.

Types of Traverse :
Open traverse
Closed traverse
Open traverse :
An open traverse is a traverse in which the traverse line starts from one point and ends
somewhere else. The open traverse is suitable for surveying a long narrow strip of land i.e.
railway line, road, canal or pipe line etc.
Closed traverse :
When the traverse line from a circuit which ends at the starting point, it is known as closed
traverse. It is suitable for locating the boundaries of lakes, forests etc & survey lines of large
areas.
CHECK ON CLOSED TRAVERSE :
Check on angular measurements
(a) The sum of the measured interior angles should be equal to (2N – 4) x 900 where N is
the number of sides of the traverse.
(b) The sum of the measured exterior angles should be equal to (2N + 4) x 900.
(c) The algebraic sum of the deflection angles should be equal to 3600.
Right-hand deflection is considered positive and left-hand deflection negative.

Check on linear measurement
(a) The lines should be measurement once each on two different days (along opposite
directions). Both measurements should tally.
(b) Linear measurements should also be taken by the stadia method. The measurements by
chaining and by the stadia method should tally.
CHECK ON OPEN TRAVERSE :
In open traverse, the measurements cannot be checked directly. But some field
measurements can be taken to check the accuracy of the work. The methods are discussed
below.
Taking cut-off lines Cut-off lines are taken between some intermediate stations of the open
traverse. Suppose ABCDEF represents an open traverse. Let AD and DG be the cut-off lines.
The lengths and magnetic bearings of the cut-off lines are measured accurately. After
plotting the traverse, the distances and bearings are noted from the map. These distances
and bearings should tally with the actual records from the field
Taking an auxiliary point Suppose ABCDEF is an open traverse. A permanent point P is
selected on one side of it. The magnetic bearings of this point are taken from the traverse
stations A,B,C,D, etc. If the survey is carried out accurately and so is the plotting, all the
measured bearings of P when plotted should meet at the point P. The permanent point P is
known as the ‘auxiliary point’

UNIT – 3: LEVELLING
3.1 Terms used in levelling
INTRODUCTION:
The art of determining relative altitudes of points on the surface of the earth is
called levelling. This branch deals with the measurements in vertical planes.
TERMS USED IN LEVELLING:
1. LEVEL SURFACE: The surface which is parallel to the mean spheroidal
surface of the earth is known as level surface. Every point on level surface will be
equidistant from the centre of the earth.
2. LEVEL LINE: The line lying on the level surface is known as level line. Every
point of level line is equidistant from the centre of the earth.
3. HORIZONTAL SURFACE: The surface tangential to the level surface at any
point is known as horizontal surface.
4. HORIZONTAL LINE: The line lying on the horizontal surface is known as
horizontal line.
5. VERTICAL LINE: A line perpendicular to the level line is called vertical line.
6. VERTICAL PLANE: The plane which contains the vertical line at a place is
called vertical plane.

7. DATUM : The imaginary level surface with respect to which vertical distances
of the points (above or below) are measured or calculated is called a datum or
datum surface.
8. MEAN SEA LEVEL(MSL) : MSL is the average height of the sea for all
stages of the tides. At any particular place MSL is established by finding the mean
sea level (free of tides) after averaging tide heights over a long period of at least 19
years. In India MSL used is that established at Karachi, presently, in Pakistan. In all
important surveys this is used as datum.
9. REDUCED LEVELS (RL) : The level of a point taken as height above or
below the datum surface is known as RL of that point.
10. LINE OF SIGHT : The line passing through the optical centre of the objective
is known as line of sight.
11. LINE OF COLLIMATION : The line passing through the optical centre of the
objective and the point of intersection of the cross hairs is known as line of
collimation.
12. BEBENCH MARK (BM) : A benchmark is a relatively permanent reference
point, the elevation of which is known (assumed or known w.r.t. MSL). It is used as
a starting point for levelling or as a point upon which to close for a check.
13. INSTRUMENT STATION : The point where instrument is set up for
observations is called instrument stations.
14. HEIGHT OF INSTRUMENT (HI) : The elevation of line of sight wrt the
assumed datum is known as height of instrument.
HI = BS + RL OF THE BM

15. BACK SIGHT (BS) : The first sight taken on a levelling staff held at point of
known elevation is called as Back sight. Back sight enables the surveyor to obtain
the height of the instrument.
16. FORE SIGHT (FS) : It is the last sight taken from the instrument station. It is
generally known as minus sight as it is always subtracted from the height of the
instrument to obtain the elevation.
17. CHANGE POINT (CP) : The point on which both fore sight and back sight are
taken during levelling operation is called change point.
18. INTERMEDIATE SIGHT (IS) : The fore sight taken on a levelling staff held at
a point between two turning points (BS and FS) to determine the elevation of those
points is known as intermediate sight.
3.2 Types of levels, Bench marks, Temporary adjustments of level
BENCHMARKS : A benchmark is a relatively permanent reference point, the
elevation of which is known (assumed or known wrt MSL). It is used as a starting
point for levelling or as a point upon which to close for a check.
The following are the different types of benchmarks used in surveying:
(a) GTS benchmarks
(b) Permanent benchmarks
(c) Arbitrary benchmarks and
(d) Temporary benchmarks.
(a) GTS Benchmark: The long form of GTS benchmark is Great Trigonometrically
Survey benchmark. These benchmarks are established by national agency. In India,
the department of Survey of India is entrusted with such works. GTS benchmarks
are established all over the country with highest precision survey, the datum being
mean sea level.
(b) Permanent Benchmark: These are the benchmarks established by state
government agencies like PWD. They are established with reference to GTS
benchmarks. They are usually on the corner of plinth of public buildings.

(c) Arbitrary Benchmark: In many engineering projects the difference in
elevations of neighbouring points is more important than their reduced level with
respect to mean sea level. In such cases a relatively permanent point, like plinth of a
building or corner of a culvert, are taken as benchmarks, their level assumed
arbitrarily such as 100.0 m, 300.0 m, etc.
(d) Temporary Benchmark: This type of benchmark is established at the end of
the day’s work, so that the next day work may be continued from that point. Such
point should be on a permanent object so that next day it is easily identified.
The adjustments to be made at every setting of the instrument are called temporary
adjustments.
TEMPORARY ADJUSTMENTS OF LEVEL :
The following three adjustments are required for the instrument whenever set over a
new point before taking a reading:
(i) Setting
(ii) Levelling
(iii) Focusing and Elimination of parallax
Setting :
Tripod stand is set on the ground firmly so that its top is at a convenient height.
Then the level is fixed on its top. By turning tripod legs radially or circumferentially,
the instrument is approximately levelled.
Some instruments are provided with a less sensitive circular bubble on tribrach for
this purpose.
Levelling : The procedure of accurate levelling with three levelling screw is as given
below:
(i) Loosen the clamp and turn the telescope until the bubble axis is parallel to the
line joining any two screws [Ref. Fig. (a)].

(ii) Turn the two screws inward or outward equally and simultaneously till bubble is
centred.
(iii) Turn the telescope by 90° so that it lies over the third screw [Fig. (b)] and level
the instrument by operating the third screw.
(iv) Turn back the telescope to its original position [Fig.(a)] and check the bubble.
Repeat steps (ii) to (iv) till bubble is centred for both positions of the telescope.
(v) Rotate the instrument by 180°. Check the levelling.
Focussing :
Focussing is necessary to eliminate parallax while taking reading on the staff. The
following two steps are required in focussing:
(i) Focussing the eyepiece: For this, hold a sheet of white paper in front of telescope
and rotate eyepiece in or out till the cross hairs are seen sharp and distinct.
(ii) Focussing the objective: For this telescope is directed towards the staff and the
focussing screw is turned till the reading appears clear and sharp.
3.3 Concept of B.S, I.S, F.S, C.P, H.I and remarks
BACK SIGHT (BS) : The first sight taken on a levelling staff held at point of known
elevation is called as Back sight. Back sight enables the surveyor to obtain the height
of the instrument.
INTERMEDIATE SIGHT (IS) : The fore sight taken on a levelling staff held at a point
between two turning points (BS and FS) to determine the elevation of those points is
known as intermediate sight.
FORE SIGHT (FS) : It is the last sight taken from the instrument station. It is
generally known as minus sight as it is always subtracted from the height of the
instrument to obtain the elevation.
CHANGE POINT (CP) : The point on which both fore sight and back sight are taken
during levelling operation is called change point.
HEIGHT OF INSTRUMENT (HI) : The elevation of line of sight wrt the assumed
datum is known as height of instrument.
HI = BS + RL OF THE BM

3.4 Simple levelling and differential levelling
SIMPLE LEVELLING
a) Simple levelling: The operation of levelling for determining the difference in
elevation, if not too great between two points visible from single position of the level
is known as simple levelling.
A level is set up approximately midway between the benchmark and the point of
which the elevation is to be determined by direct levelling. A back sight is taken on
the rod held at the benchmark, then HI = RL OF BENCHMARK + BACK SIGHT
Turning the telescope to bring into view the rod held on point B, the fore sight is
taken, then
RL OF B = HI – FS
DIFFERNTIAL LEVELLING :
The operation of levelling to determine the elevation of points at some distance
apart is called differential levelling. When two points are at such a distance from
each other they cannot both be within the range of level at the same time, the
difference in elevation is not found by single setting but the distance between the
points is divided in two stages by turning points on which the staff is held and the
difference in elevation of each of succeeding pair of such turning points is found by
setting of the levels.

3.5 Reduction of levels i) Plane of collimation method ii) Rise and fall
methods
REDUCTION OF LEVELS :
There are two methods of booking and reducing the elevation of points from the
observed staff readings.
Plane of collimation or height of instrument method:
In this method, height of instrument (HI) is calculated for each setting of instrument
by adding back sight to the elevation of the bench mark. Then obtain the reduced
level of points with reference to the respective plane of collimation.
The reduced level of intermediate points and change point are then obtained by
subtracting the staff readings taken on these points from the height of instrument.
When the instrument is shifted to the next position, the new plane of collimation is
set up.
Rise and Fall Method :
In rise and fall method the height of instrument is not calculated but difference in
level between consecutive points is found by comparing the staff readings on two
points for the same setting of instrument. The difference between staff readings
indicate rise or fall according as the staff reading at the point is smaller or greater
than that at the preceding point. If the level of any one point is known the level of
the next will be obtained by adding its rise or subtracting its fall.

3.6 Problems on reduction of levels.

UNIT – 4 : LEVELLING – APPLICATION
INTRODUCTION:
· Knowing the topography of an area.
· Aligning highways, railways, canals, sewers etc.
· Laying out construction projects.
· Locating the gradient lines for drainage.
· Calculating the volume of earth work.
DIFFERENT TYPES OF LEVELLING:
Levelling is classified into different types:
· Simple Levelling
· Differential or fly levelling
· Check levelling
· Profile levelling
· Cross-section levelling
· Reciprocal levelling
· Precise levelling
· Barometric levelling
· Hypsometry levelling
· Trigonometrical levelling
FLY LEVELLING:
It is differential levelling that is done to connect benchmark to the starting point of the
survey. In this levelling only foresight and back sight readings are taken and no distances
are measured.

CHECK LEVELLING:
It is carried out for the purpose of checking of elevations which have already been
determined. Generally check levelling is done at the end of each day’s work from the last
station to the starting station.
PROFILE LEVELLING:
It is also a differential levelling done for the purpose of determining the elevation of the
ground surface along the fixed line at regular interval. The fixed line is generally the centre
line of the proposed route levels as road, canal, railway line etc. The profile levelling is also
known as longitudinal levelling.
CROSS SECTION LEVELLING:
It is done to determine the difference of elevations of the ground surface on each side of
the centre line that is right angle to the main line in order to determine the vertical cross
section of the ground and estimation of quantities of the earth work. It is also known as
cross levelling.
4.2 Plotting of longitudinal and cross section
PLOTTING OF PROFILE OR LONGITUDINAL SECTION:
The profile is plotted after the staff readings obtained in the field are reduced and checked.
The vertical scale is conveniently taken as 10 times the horizontal scale so that undulations
in the ground may be shown clearly.
Procedure:
Select suitable scales for plotting horizontal and vertical distance. Eg: horizontal
scale is 1:1000 (1cm = 10m) and vertical scale is 1:100 (1cm = 1m).
A horizontal line is drawn as the datum line. The RL of the datum line is assumed in
such a way that ground surface can be shown above the datum.
Mark the chainages of various points of the profile along the datum line to the
selected horizontal scale.
Write RL of each profile point below datum line.
Then the ordinates (perpendicular lines) are drawn at each of the chainage points.
Vertical distance (RL of GL – RL of Datum) are plotted along the ordinates according
to the vertical scale.
Join the plotted points by straight line to obtain the outline of existing ground
surface.

PLOTTING OF CROSS SECTION:
Procedure:
Cross sections are plotted almost in the same manner as the longitudinal section
except that in this case, both the scales are kept equal.
The point along the longitudinal section is plotted at the centre of longitudinal axis.
The points to the left of centre point are plotted to the left and those to the right are
plotted to the right.
The points so obtained are joined by straight line.
4.3 Errors in levelling and precautions
ERRORS IN LEVELLING:
All levelling measurements are subject to three principle sources of errors:
INSTRUMENTAL ERRORS
a. Errors due to imperfect adjustment
b. Errors due to sluggish bubble
c. Errors due to movement of objective slide
d. Rod not of standard length
e. Errors due to defective joint
NATURAL ERRORS
a. Earth’s curvature
b. Atmospheric refraction
c. Variations in temperature
d. Settlement of tripod or turning points
e. Wind vibrations

PERSONAL ERRORS
a. Mistakes in manipulation
b. Rod handling
c. Mistake in reading the rod
d. Errors in sighting
e. Mistakes in recording
PRECAUTIONS IN SETTING:
The adjustments of the level are carefully tested.
The bubble is very carefully centred and kept under observation at the time of reading
the staff.
The level should be protected from the sun or wind by a screen.
The level should be secured on the hard firm ground.
Lengths of sight are limited to about 100m.
Change points are taken on a steel pin or foot plate.
The back sights and the following sights are taken in quick succession to eliminate errors
due to settlement of the tripod and the staff.
The levelling is carried during favourable atmospheric conditions of light and
temperature.
Check levels are taken in the opposite direction by different surveyor on different days
and with different change points.
4.4 Setting grade stakes and setting out grades for sewers and problems on it.
SETTING GRADE STAKES:
Grade setting is a process of fixing stakes or pegs at given elevation to indicate the depth of
fill or cut to make ground surface to a given gradient.
The staff reading required to fix a grade stake is obtained by subtracting the FL from the HI.
And this staff reading is known as grade-rod.
GRADE SETTING FOR SEWERS:
Sight rails are basically horizontal rails set a specific distance apart and to a specific level
which is at the required gradient. Thus they are used to control trench excavation and pipe
gradient without the need of constant professional supervision.

The bottom of the inside surface of the sewer/pipeline is known as invert. The inverts of
sewers are set out to a required gradient using cross heads and boning rods.
Cross heads: consists of two vertical posts and a horizontal sight rail nailed across. The
vertical posts are 1m or 1.5m long and 100mmx100mm in cross section.
Sight rail: It is a horizontal strip of wood 150mm wide and 50mm thick.
Boning rod: It is also known as travelling rod which is T-shaped strip of wood. It consists of
cross-piece wood 100mm x 30mm and 400mm long joints to a long piece of same cross-
section. The length of long piece may be 3m, 4m or 5m. The boning rods are painted white
and blackened at the top. The boning rod length is constant for any one section, but may
vary for different sections.
Field procedure:
 Peg out centre line of sewer/pipe-line at 20m interval.
 One side of this line, a parallel is set out at such a distance apart that it will not be
disturbed by the excavation and it is then marked at 20m interval.
 The sight rails are placed across the trench at 30m interval and at each change of
gradient and direction.
 The top of each sight rail is usually set by a level at a fixed height say 3m, 4m, 5m
above the invert of the sewer and a boning rod of same length is prepared.
 The top edge of each sight rail is set truly horizontal with a carpenter level.
 The nail is driven at the top edge of the each sight rail at the centre to define the
line.
 The line joining the top edges of the two consecutive sight rails should have exactly
the same gradient as that of the invert of the sewer.
 The setting of the sight rails is commenced from the lower end of the sewer.
 Pipe lines are laid in the same manner but the intervals between the sight rails may
be greater.

UNIT – 5: CONTOURING
5.1 Concepts of contour and terms used in contouring
Concepts of contouring :
On any plan only the horizontal dimensions of the objects surveyed can be shown.
For showing vertical dimensions, certain conventions must be adopted. The vertical
dimensions should be represented on the plan as accurately and clearly as the horizontal
distances. For this the reduced levels of the points with reference to the known datum shall
be shown as spot levels. But these spot levels convey a vague idea of the form of the
ground. Therefore contour lines are used which are nothing but the arranged spot levels in
such a manner that the form of the surface can be readily and easily interpreted.
A contour may be defined as the line of intersection of a level surface with the
surface of the ground. All the points on any one contour have the same elevation above the
datum surface.
Terms used in contouring :
 Contouring: The process of plotting the reduced levels of points & arranging in
such a way that the surface slopes can be easily read by studying the plan.
 Contour line: It may be defined as an imaginary line which joins the points of
equal elevation on the ground.
 Contour interval: It is the vertical distance between any two consecutive
 Horizontal equivalent : It is the horizontal distance between any two
consecutive contours.
For a given contour interval the horizontal equivalent depends upon the steepness of the
ground. The contour interval depends upon a) the nature of the ground, b)the purpose
and extent of the survey, c) the scale of the map and d)the time and expense required in its
determination. In general if the ground is flat, a small contour interval will be suitable, on
the other hand a grater contour interval will be suitable for the steep terrain or mountainous
area. It should also be noted that, the contour interval is inversely proportional to the scale
of the map.

5.2 Characteristics of contour
Characteristics of contour lines :
 Closer contours indicate steep ground & contours wide apart indicate flat ground.
 A uniformly paced contour lines indicate a uniform slope of the ground. A plane
surface is indicated when contours are straight and equally spaced.
 Contour lines and cross ridge lines or valley lines are at right angles. A ridge line is
shown when higher values are inside the loop or bend in the contour, while lower
values inside the loop appear in case of valley line.
 Contour lines cannot merge or cross one another on the map except in the case of
an overhanging cliff. In case of vertical cliff horizontal equivalent is zero and several
contours coincide.
 Contour lines cannot end anywhere but close on themselves either within or without
the limits of the map.
 A series of closed contours on the map indicates a depression or a summit, according
as the lower or higher values are inside them.

5.3 Uses of contours
Uses of Contours:
 By inspection of a contour map, the characteristics of the terrain of the country
whether it is flat, mountainous or undulating is obtained.
 Quantities of earthwork required for construction may be computed using contour
maps.
 Contour maps may be used for the selection of site for the constructions such as
road, sewer, railway, reservoir etc.,
 The sections may be obtained along any direction as shown in the following figure.
 Indivisibility of two given points can be ascertained from the map.
 A route of a given grade line can be traced on the map.
5.4 Methods of contouring
Methods of location of contours
The methods of locating contours can be divided into the following two categories.
1. Direct method
2. Indirect method

1. Direct method :
In this method, the points for a particular contour are located on the ground with the help of
a level and marked. The marked points are then surveyed to get their positions on the plan.
To begin with, level is set up in a commanding position and accurately levelled. The height
of the instrument(HI) is determined by taking a backsight on the bench mark and adding it
to the RL of the benchmark. From the known elevation of the contour, and the H I , the
required staff reading to fix point on the contour line is obtained as follows.
Required staff reading=H I-elevation of the contour.
For example if the HI is 100.5 and the elevation of the contour is 99.0, then the staff
reading from the instrument station is 100.5-99=1.5m. Similarly for contours of elevations
98 and 97, the staff readings from the station shall be 2.5m & 3.5m respectively.
The staff is held vertically on an estimated position of a point and is then staff is moved up
or down the slope until the desired staff reading is obtained. Several points are thus
obtained and marked on each contour within the sighting length of the instrument. Having
fixed the contours within the range of the instrument, the level is shifted to a new
commanding position to fix other points. The new H I & staff readings are then calculated in
a similar manner and the process is repeated. The positions of contour points can be located
by a compass, theodolite or plane table survey. The points are then plotted on the plan and
contours are drawn by joining them by curved lines.
2. Indirect method :
The indirect method is cheaper, quicker and less laborious than the direct method. In this
method the spot levels (RL’s on the surface of the ground) are taken along series of lines
laid out over the area. Their positions are then plotted on the map and the contours are
then drawn by interpolation.
The following are the indirect methods of locating the ground points.
i. By cross sections:
This method may be used for route surveys such as canal, road, railway etc.,. the cross
sections are laid transverse to the alignment at any angle to the alignment. The spacing of
sections depends upon the character of the ground, lesser for steep terrain to wider interval
for flat country. The reduced levels of the various points along the section lines are plotted
on the plan and the contours are then interpolated.

ii. By Squares:
In this method the area is divided into a series of squares of size 2m to 5m and the corners
of the square are marked with pegs. This method is suitable for small areas. The elevations
of the ground at the corners of the squares are determined with a level. The reduced levels
at any intermediate points may also be taken if required. The system of squares is plotted
and near each corner its elevation is written. The contour lines are then interpolated using
any of the conventional method.

iii. By Tacheometric method:
This method is suitable when contour map of hill is required. In this method a number of
lines are set out radiating at a given angular interval from each of traversing stations and
elevations of various points along the radiating lines are taken using tacheometer. The
distance measurement is not required as would be known by tacheomeric calculations. The
contours are then drawn by interpolation.
5.5 Interpolation by arithmetical method
Interpolation of contours by arithmetic calculation:
This method is used where greater accuracy is required.
Illustration: Suppose A & B are the two ground points 5m apart and of elevations 99.0
and 100.25 respectively. To locate the contour of elevation 99.5 , its distance from A is
calculated as follows.
Difference in elevations(RL’s) between A & B=100.25-99=1.25m.
Difference in elevations between 99.5 contour & point A=99.5-99.0=0.5m.
The distance of 99.5 contour from point A=(5x0.5)/1.25=2 m.
5.6 Calculation of capacity of the reservoir
Calculation of reservoir capacity:
The capacity of a reservoir can be calculated using contour plan as follows.
The area enclosed by each contour is to be determined using planimeter & let them be A1,
A2, A3…
If H is the contour interval & V is the total volume or capacity of the reservoir, then V may
be computed using either Tapezoidal formula or Prismoidal formula as follows.
Trapezoidal Formula:
V=H((A1+An)/2)+A2+A3+………………………..+An-1)
Prismoidal formula :
V=H/3(A1+4(A2+A4+A6+…………….+ An-1)+2(A3+A5+A7+…………….+ An-2)+An)

It should be noted that n should be odd for Prismoidal formula. If n is to be even, the
Prismoidal formula is applied upto the last but one contour and the volume of the last
contour is worked out separately and then it is added to get the total volume.

UNIT – 6: AREAS & VOLUMES
6.1 Computation of Area of Irregular figures using Trapezoidal & Simpson's rule -
problems.

6.2 Volumes of Irregular solids- using Trapezoidal &Prismoidal Rule - Problems
on Embankment & Cutting

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