Everything You Need to Know About Levelling in Surveying

What is Levelling?
 The art of determining relative altitudes of points on
surface of earth r beneath surface of earth is called
levelling.
 This is branch of surveying which deals with
measurement in vertical planes only.
 For execution of any engineering project like
highways, railways, canals, dams, building, water
supply and sanitary scheme it is very necessary to
determine elevations of different points along the
alignments of proposed projects.

 Levelling is employed to provide accurate network of
heights, covering entire area of project.
 Levelling is of prime importance to the engineers, both
in acquiring necessary data for design of project and
also during its execution.
 Principle of Levelling The principle of levelling is
to obtain horizontal line of sight with respect to
which vertical distances of the points above or
below this line of sight are found.

Objects of levelling
 Levelling is done for following purposes.
 To prepare a contour map for fixing sites for
reservoirs, dams, barrages etc, and to fix alignment of
roads, railways, irrigation canal etc.
 To determine the altitudes of different important points
on hill or to know reduce level of different points on
surface , above or below surface of earth.
 To prepare longitudinal section or cross section of
projects in order to determine volume of earth work.
 To prepare layout map for water supply , sanitary or
drainage.

Uses of Levelling.
 1. To establish bench mark as vertical control points which
serve as references for other levelling.
2. To enable surveyor calculate whether two points are
intervisible from each other on the ground surface.
3. To enable surveyor measurements to be reduced to the
horizontal at sea level.
4. To enable drainage works to be surveyed so that water
way flow in the desired direction.
5. To provide information for scientists about the shape and
structure of the earth and its movement.

Terms used in leveling
 (1)Level surface : A surface parallel to the mean spheroidal
surface of the earth is called a level surface. Such surface is
a curved surface. Water surface of still lake is considered as
level surface.
 The line drawn on the level surface is known as a level line.
This line is normal to plumb line. Hence all points lying on
a level surface are equidistant from the centre of the earth.
 (2)Horizontal Surface: A surface tangential to level
surface at a given point is called horizontal surface at that
point. Hence a horizontal line is at right angles to the plumb
line at that point, which indicates direction of gravity

 . Any line lying on horizontal plane is called horizontal
line it is tangential to level line.
 3)Vertical Line. The direction indicated by plumb line
is called vertical line, which is perpendicular to
horizontal line.
 Vertical plane: any plane passing through the vertical
line is called vertical plane.
 4)Datum surface or line: This is an imaginary level
surface or line with the reference of which vertical
distance of different points above or below of this line
is measured. in Pakistan datum adopted for GTS is
mean sea level Karachi.

 5)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 making hourly
observations of tides and by averaging tide heights
over a long period of at least 19 years. In India and
Pakistan MSL used is that established at Karachi,
presently, in Pakistan. In all important surveys this is
used as datum.
 6)Reduced Levels (RL): The height or depth of a
point taken as height above or below the datum surface
is known as RL of that point. It is also called elevation
of a point.
 Elevation of any object below MSL is called negative
elevation.

 7)LINE OF COLLIMATION- - the line which
passes through the Intersection of the cross hairs of
the eye piece and optical centre of the objective
and its continuation is called as line of collimation.
This is also known as line of sight.
 Axis of the Telescope : This axis is an
imaginary line passing through the optical center
of the object glass and the optical centre of the eye
piece.

 8)BENCH MARK – (BM) – B.M. is a fixed reference
point of known elevation with reference to datum line.
They survey as reference points for finding RL of new
points or for conducting levelling operations in project
involving roads and railways.
 It may be of the following types.
i) GTS Bench mark (Great Trigonometrically
Survey) :
These Bench marks are established by national agency
like Survey of Pakistan. They are established with
highest precision at an interval of 100 km all over
country . Their position and elevation above MSL is
given in a special catalogue known as GTS Maps.

 ii) Permanent Bench Mark : They are fixed
points of reference establish with reference to GTS
Bench mark by other government agencies like
PWD , Railways, irrigation etc, and are kept on
permanent points like culvert, kilometer stones,
railway platforms, pillars etc.

 iii) Arbitrary Bench mark : These are reference
points whose elevations are arbitrarily assumed.
These are adopted for small work, when only
undulation of ground is important to be
determined.
 (iv) Temporary B.M: when the B.Ms are
established temporarily at the end of day’s work,
they are said to be temporary Bench Mark. They
are generally made on root of tree, parapet of
nearby culvert etc.

 Station: A point where the levelling staff is
kept.
 Back sight : (B.S.) - The first sight taken on
a levelling staff held at a point of known
elevation (BM) is called Back sight. B.S.
enables the surveyor to obtain Height of
Instrument or elevation of line of sight.

 Fore Sight : (F.S.) – It is the last staff reading taken
from a setting of the level. It is also termed as minus
sight.
 Fore sight is the sight taken on a levelling staff held at
a point of unknown elevation to ascertain the amount
by which the point is above or below the line of sight.
This is also called minus sight as the foresight reading
is always subtracted from height of Instrument.
 Intermediate Sight (IS) :
The foresight taken on a levelling staff held at a point
between two turning points, or taken on points
between BS and Fs , to determine the elevation of that
point, is known as intermediate sight.

 Height of Instrument (HI) : The elevation of the
line of sight with respect to assumed datum is
known as HI. This is obtained by adding Back
sight to RL of B.M or change point.
 Change Point (CP) : The point on which both the
foresight and back sight are taken during the
operation of levelling is called change point.

 Parallax: if the image formed by objective does not lie
in the plane of cross hairs , there will be shift in image
due to shift of the eye. Such displacement of image is
called parallax.
 For accurate sighting , the parallax is eliminated in two
steps.
 (a) Focussing eye piece for distinct vision of cross hairs.
 (b) Focussing objective so that the image is formed in
plane of cross hairs.

 Focussing the eye-piece – a piece of white paper
is held in front of the object glass and the eye
piece is moved in or out by turning it clockwise
or anticlockwise until the cross hairs can be seen
clearly.
 Focussing the object glass – telescope directed
toward the levelling staff. Looking through the
eye piece, the focusing screw is turned clockwise
or antilock wise until the graduation of staff is
visible.

Types of Levelling Equipments
 i) Dumpy level
ii) Tilting level
iii) Automatic level
iv) Digital Auto level
v)Y level
vi)Cooke’s reversible level

Dumpy Level
 Dumpy level is the most commonly used instrument in
leveling. In this level the telescope is restricted against
movement in its horizontal plane and telescope is fixed
to its support. A bubble tube is provided on the top of
the telescope.
 But however, the leveling head can be rotated in
horizontal plane with the telescope.

Tilting Level
Tilting level consist a telescope which enabled for the
horizontal rotation as well as rotation about 4 degree in
its vertical plane. Centering of bubble can be easily
done in this type of level. But, for every setup bubble is
to be centered with the help of tilting screw.
The main advantage of tilting level is it is useful when
the few observations are to be taken with one setup of
level.

The Automatic level: Automatic level is like the dumpy
level. In this case the telescope is fixed to its supports.
Circular spirit can be attached to the side of the telescope
for approximate leveling. For more accurate leveling,
compensator is attached inside the telescope.

 Compensator can help the
instrument to level automatically.
Compensator is also called as
stabilizer. Now days it is most
commonly used in every type of
work.

Advantage of automatic level
Much simpler to use
High precision : Mean elevation error on staff
graduated to 5mm division varies between +0.5 to 0.8
mm per km of forward and backward levelling.
High speed : In fly levelling the progress achieved by
various level-wise compared.

Wye (Y) Level
 Y level or Wye-level consists y-shaped frames which
supports the telescope. Telescope cane be removed
from the y-shaped supports by releasing clamp screws
provided. These y-shaped frames are arranged to
vertical spindle which helps to cause the rotation of
telescope.

 Cooke’s Reversible Level
 Cooke’s reversible level is the combination of dumpy
level and y-level. In this instrument, the telescope can
be reversed without rotation the instrument.
Collimation error can be eliminated in this case
because of bubble left and bubble right reading of
telescope.

Diaphram : A frame carrying cross hairs usually made of either
silk thread or platinum wire and placed at the plane at which
vertical image of the object is formed by the objective.
Vertical hair of the diaphram enables the surveyor to check the
verticality of levelling staff whereas horizontal hairs are used to
read the staff graduations.

Components of Dumpy level :
1.Tripod – The tripod stand consist of three legs which may
be solid or framed to support the above three parts of the level.
2.Levelling head : Levelling head generally consists of two
parallel plates with 3 foot screws. Upper plate is known as
Tribrach and lower plate is trivet which can be screwed on to
the tripod. Levelling head has to perform 3 distant functions :
i) to support the telescope
ii) to attach the level to the tripod
iii) to provide a means for level (foot screws)
to bring the bubble of tube level at the centre of its run.

3. Foot screws : Three foot screws are provided between
the trivet & tribrach. By turning the foot screws the tribrach can
be raised or lowered to bring the bubble to the centre of its run.
4. Telescope : Telescope is an optical instrument used for
magnifying and viewing the images of distant objects. It
consists of two lenses. The lens fitted near the eye is called the
eye piece and the other fitted at the end near to the object is
called the objective lens.
5.Level Tube : Also known as Bubble Tube.

Points to be remembered by Staff man
The staff should be made vertical by holding it with both
arms while standing behind it.
The staff should be held on firm ground.
When the telescopic staff is to be extended, care should
be taken so that it is perfectly stretched and properly
fixed on the spring catcher.
The bottom of the staff should be kept clean.

Points to be remembered by Level man
The Levelling instrument should be placed at a position suitable
for the greatest no. of observation to be taken.
The instrument should not be too high or too low.
The Levelling should be done perfectly.
The Levelling instrument should not be placed on the profile line
(i.e. the center line of the project).
The eye-piece should be focused by holding a sheet of white
paper in front of the telescope.

 The objective should be focused by pointing the telescope
towards the staff.
 The parallax should be eliminated.
 The verticality of the staff should be verified by observing
the two vertical hairs & by noting the minimum reading on
the staff when it is moved along the line of sight.

After taking the staff reading, the position of the bubble
should be verified. If it is disturbed, the reading should be
taken again.

Temporary Adjustment of Level
1. Selection of suitable position
2. Fixing level with tripod stand
3. Approximate levelling by legs of tripod stand
4. Perfect levelling by foot screws
5. Focussing the eye-piece
6. Focussing the object glass
7. Taking the staff readings

 Selection of suitable position - A sutaible position is
selected for setting the level . From this position , it
should be possible to take the greatest number of
observation without difficulty.
 Fixing level with tripod stand – the tripod stand is
placed at the required position with its legs well apart,
and pressed firmly into the ground. The level is fixed
on the tripod stand according to the fixing
arrangement provided.

 Approximate levelling by legs of tripod stand-
the foot screws are brought to the center of their
run. Two legs of the tripod stand are firmly fixed
into the ground. Then the third leg is moved to the
left or right , in or until the bubble is
approximately at the centre of its run.

 Perfect levelling by foot screws – longitudinal bubble
on the top of the telescope.
 Bubble brought to the center by turning the foot
screw equally either both inward or outward.
 Then telescope turned through 90 degree. And
brought over the third foot screw , and the bubble
is brought to the center by turning this foot screw
clockwise and anticlockwise.
 The telescope again brought to its original
position. And bubble to the centered the process
repeated several times until bubble remain its
central position.

 Focussing the eye-piece – a piece of white paper is held
in front of the object glass and the eye piece is moved in or
out by turning it clockwise or anticlockwise until the cross
hairs can be seen clearly.
 Focussing the object glass – telescope directed toward
the levelling staff. Looking through the eye piece, the
focusing screw is turned clockwise or antilock wise until the
graduation of staff is visible.
 Taking the staff readings- finally the leveling of the
instrument is verified by turning the telescope in any
direction. When the bubble remain in the central position for
any direction of the telescope.

Levelling Staff
 Rod which helps in taking reading for determining RL
of different points is called levelling rod or staff rod.
 Levelling Staff are of two types
 (i) Self reading staff (ii) Target staff.
 (i) Self reading staff: This staff reading is directly read
by the instrument man through telescope.
In a metric system staff, one meter length is divided into
200 subdivisions, each of uniform thickness of 5 mm.
All divisions are marked with black in a white
background. Meters and decimeters are written in red
color.

 Self reading staff are further divided in
 (a) Solid staff: It is a single piece of 3 m
 (b)Folding staff: A staff of two pieces each of 2 m
which can be folded one over the other
 (c)Telescopic staff: A staff of 3 pieces with upper
one solid and lower two hollow. The upper part can
slide into the central one and the central part can
go into the lower part.
Each length can be pulled up and held in position
by means of brass spring. The total length may be
4 m. Top and central portion are of 1.25m and
bottom portion is 1.5m.

 ii) Target staff: If the sighting distance is more,
instrument man finds it difficult to read self reading
staff. In such case a target staff may be used. Target
staff is similar to self reading staff, but provided with a
movable target. Target is a circular or oval shape,
painted red and white in alternate quadrant.

Types of Levelling operation
1. Simple levelling
2. Differential Levelling
3. Fly Levelling
4. Longitudinal or Profile Levelling
5. Cross-sectional Levelling
6. Check Levelling

Simple levelling : When the difference of level
between two points is determined by setting the
levelling instrument midway between the points, the
process is known as simple levelling.

Differential levelling :
i) If the difference in elevation between them is too
great.
ii) If there are obstacles intervening. In such case it is
necessary to set up the level in several positions and to
work in series of stages.

Differential levelling
This method is also known as compound levelling or
continuous levelling.
Suppose it is required to know the difference of level
between A & B. the level is set up at point O1, O2, O3
etc after temporary adjustment staff reading are taken at
every set up . The point C1, C2, C3 are known as change
points then difference of level between the A & B is
found out.

Fly levelling
When Differential levelling is done in order to connect
a bench mark to the starting point of the alignment of
any project, it is called fly levelling.
Fly levelling is also done to connect the BM to any
intermediate point of the alignment for checking the
accuracy of the work.

Longitudinal or profile levelling
The operation of taking levels along the centre line of
any alignment (road, railway, etc.) at regular intervals is
known as longitudinal levelling. This operation is
undertaken in order to determine the undulations of the
ground surface along the profile line.

Cross Sectional levelling
The operation of taking levels transverse to the
direction of longitudinal levelling is known as cross
sectional levelling. This operation is undertaken in
order to know the nature of the ground across the
centre line of any alignment.

Check levelling
The fly levelling done at end of the day’s work to connect the
finishing point with the starting point on the particular day is
known as check levelling. It is undertaken in order to check the
accuracy of the day’s work.

Reciprocal Levelling
 In this levelling set up on both banks of the river or
valley and two set of staff reading are taken by
holding the staff on the both banks.
 Procedure – Suppose A& B are two points on the
opposite back of river. The level is set up very near A
and after proper temporary adjustment , staff reading
are taken at A & B . Suppose the readings are a1 &b2
 The level is shifted and set up very near B and after
proper adjustment , staff reading are taken at A & B .
Suppose the reading are a2 & b2.

h= true difference between point A & B
 In the first case
correct staff reading at A= a1
correct staff reading at B= b1 – e
True difference of level between A & B
h = a1 – (b1 – e ) …………………(1)
 In second case
Correct staff reading at B = b2
Correct staff reading at A = a2 – e
True difference in level
h =(a2 -e) –b2 ……………(2)
From (1)&(2)
2h = a1 – (b1 - e) + (a2 - e) – b2
= a1 – b1 +e +a2 – e – b2
= (a1 – b1) +(a2 – b2)
h = (a1-b1) + (a2 – b2) / 2

Difficulties faced in levelling
1. When the staff is too near the instrument
2. Levelling across a large pond or lake
3. Levelling across a river

Levelling across a large pond or lake
 We know that the water surface of still lake or
pond is considered to be level.
 Therefore all points on the a water surface have
the same R.L. Two peg A &B fix on opposite bank
of the lake or pond.
 The top of the pegs are just flush with the water
surface. The level is set up at O1 and RL of A is
determined by taking FS on A. the RL of B is
assume to be equal to that of A .
 Now the level is shifted and set up at O2 . Then by
taking a BS on peg B, levelling is continued.

Levelling across a river
 In case of flowing water , the surface cannot be
considered level, the water level on the opposite
edges will be different. In such case the method of
reciprocal levelling is adopted. Two peg A &B are
driven in opposite bank of river.

4. Levelling across a solid wall
Two peg A &B are driven on either side of wall, just touching
it. The level is set up at O1 and a staff reading is taken on A.
let this reading be AC. Then then the height of wall is
measured by staff . Let the height be AE. The HI is found out
by taking a BS on any BM or CP
RL of A = HI – AC
RL of E = RL of A + AE = RL of F
RL of B = RL of F – BF
HI at O2 = RL of B + BD

 5. When BM is above line of collimation
this happens when the BM is at the bottom of the bridge
girder or bottom surface of the culvert. And that it is
required to find out RL of A. the level is set up at O and
staff is held inverted on the BM. The staff readig taken
and noted with negative sign. Let BS & FS reading be –
1.5 and 2.250 respectively.
HI of instrument = 100 – 1.5 = 98.5
RL of A = 98.5 – 2.250 = 95.250

 6. Levelling across a rising ground or depression
while levelling across high ground, the level should not be
placed on the top of the ground , but on side so that the line
of collimation just passes through the apex.
While levelling across a depression the level should be set
up on one side and not at the bottom of the depression.

Sources of Errors in levelling
Instrumental errors
Personal errors
Errors due to natural causes

Instrumental errors
 The permanent adjustment of the instrument may
not be perfect. i.e. the line of collimation may not
be parallel to the axis of the bubble tube.
 The internal arrangement of the focusing tube is
not perfect.
 The graduation of the levelling staff may not be
perfect.

Personal errors
a) The instrument may not be levelled perfectly.
b) The focusing of the eye-piece & object glass may not be perfect & the
parallax may not be eliminated.
c) The position of the staff may be displaced at the change point at the time of
taking FS & BS readings.
d) The staff may appear inverted when viewed through the telescope. By
mistake, the staff readings may be taken upwards instead of downwards.
e) The reading of the stadia hair rather than the central collimation hair may be
taken by mistake.
f) A wrong entry may be made in the level book.
g) The staff may not be properly & fully extended.

Errors due to natural causes
 When the distance of sight is long, the
curvature of the earth may affect the staff
reading.
 The effect of refraction may cause a wrong staff
reading to be taken.
 The effect of high winds & a shining sun may
result in a wrong staff reading.

Curvature Correction
 For long sights , the curvature of earth effects staff
readings.
 The line of sight is horizontal , but level line is curved
and parallel to mean spheroidal surface of earth, that’s
why horizontal line do not coincides with level line.
 The vertical distance between line of sight and level
line at particular place is called curvature correction.
 This correction is negative as object appears lower
than they really are.
 CC= 0.0785 D2 ( where Distance is in km)

Refraction correction
 Error due to refraction can be understood easily once you
understand the phenomenon which takes place when light
passes from one density system to another density system.
 Refraction is nothing but the phenomenon by which when
light travels from a denser media to the lighter media, it
deflects away from the normal to the plane of the media.
 Refraction correction value is always positive and is one-
seventh part of Curvature Correction.
 Cr= 0.0785 D2/7 = 0.0112 D2
 Combined curvature and refraction effect is = 0.0112 D2
+(- 0.0785 D2 )= - 0.0673 D2 ( always negative)

Methods of Determining RLs
 1. Collimation Method: It consist of finding the
elevation of the plane of collimation ( H.I.) for every
set up of the instrument, and then obtaining the
reduced level of point with reference to the respec
 1. Elevation of plane of collimation for the first set of
the level determined by adding back side to R.L. of
B.M.
 2. The R.L. of intermediate point and first change point
are then obtained by subtracting the staff reading taken
on respective point (IS & FS) from the elevation of the
plane collimation. [H.I.].

 3. When the instrument is shifted to the second position a new
plane collimation is set up.
 The elevation of this plane is obtained by adding B.S. taken on
the C.P. And adding RL of C.P.
 The R.L. of successive point and second C.P. are found by
subtract these staff reading from the elevation of second plane
of collimation
 Arithmetical check
 Sum of B.S – sum of F.S. = last R.L. – First R.L.
 This method is simple and easy.
 Reduction of levels is easy.
 There is no check for intermediate sight readings
 This method is generally used where more number of readings
can be taken with less number of change points for
constructional work and profile leveling.

 2.Rise and Fall Method: It consists of determining the
difference of elevation between consecutive points by
comparing each point after the first that immediately
preceding it. The difference between there staff reading
indicates a riseor fall according to the staff reading at the
point. The R.L is then found adding the rise to, or
subtracting the fall from the reduced level of preceding
point.
 Arithmetic check
 Sum of B.. – sum of F. S. = sum of rise – sum of fall = last
R. L. – first R.L

 This method is complicated and is not easy to carry
out.
 Reduction of levels takes more time.
 Complete check is there for all readings ( BS, IS and
FS).
 This method is preferable for check levelling where
number of change points are more.

References
 Surveying and Levelling: N N Basak, Tata McGraw Hill,
New Delhi.
 Surveying: R. Agor, Khanna Publishers.
 http://nptel.iitm.ac.in/courses-contents/IIT Kanpur and IIT
Madras.
 http://www.slideshare.net
 www.scribd.com

Everything You Need to Know About Levelling in Surveying

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Everything You Need to Know About Levelling in Surveying