1. Levelling is used to determine the relative or absolute heights of points and is done by measuring vertical angles with a level. 2. The key principles are establishing elevations of unknown points relative to a known benchmark and determining height differences between points. 3. Levelling has many uses including topographic mapping, engineering design, construction, and drainage analysis. Careful instrument setup and line of sight adjustments are needed to get accurate elevation measurements.

1. ORDINARY SPIRIT LEVELLING
Levelling is “an art of determining the relative height of different points
on, above or below the surface”

3. PRINCIPLE OF LEVELLING
• The fundamental principle of leveling lies in finding out
the separation of level lines passing through a point of
known elevation (B.M.) and that through an unknown
point (whose elevation is required to be determined).

5. Objective of Levelling
• To Find the elevation of given point with respect to
some assumed reference line called datum.
• To establish point at required elevation respect to
datum.

6. USES
• To find the elevations of points on the earth’s surface for
topographic maps.
• For design of highways, railways, canals, sewers etc.
• For locating grade lines
• For laying out of construction projects
• For locating excavating levels
• To determine the drainage characteristics of an area
• Determination of volumes of earthwork for roads, railways
etc.

7. TERMS USED IN LEVELLING
• Datum: The level of a point or the surface, with respect to which levels of
other points or planes are calculated, is called a datum or datum surface.
• Reduced level (RL): It is height or depth of any point above or below any
datum. It is denoted as R.L..
• 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 all-important surveys this is used as datum.

8. • Vertical Line: it is the line connecting the point to the
centre of the earth. It is the plumb line at that point.
• Level surface It is the surface parallel to the mean
spheroidal surface of the earth
• Level line - Line lying on level surface.
• Horizontal plane - Horizontal plane through a point is a
plane tangential to level surface.
• Horizontal line- It is a straight line tangential to level
line.

10. • Bench Mark (BM):- B.M. is a fixed reference point of known elevation. 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:
• GTS Bench mark (Geodetic Triangulation Survey):- These benchmarks are established
by national agency. GTS benchmarks are established all over the country with highest
precision survey, the datum being mean sea level. The position of GTS benchmarks
are shown in the topo sheets published.
• Permanent Benchmark: These are the benchmarks established by state government
agencies like water, irrigation etc... They are established with reference to GTS
benchmarks.
• Arbitrary Benchmark: in many engineering projects, the difference in elevations of
neighboring points is more important than their reduced level with respect to mean
sea level. In such cases a relatively permanent point, like corner of a culvert, are taken
as benchmarks, their level assumed arbitrarily such as 100.0 m, 300.0 m, etc.
• 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.

12. • To determine the difference in level between points on the
surface of the ground a 'series' of levels will need to be
carried out; this is called a level traverse or level run
• Line of Collimation: - It is the line joining the intersection
of the cross hair and the optical center of the objective
and its extensions, it is also called line of sight or
collimation.
• Height of Instrument (HI):- The elevation of the line of
sight with respect to assumed datum is known as HI.
• Back sight: (B.S.):- The first sight taken on a levelling staff
held at a point of known elevation. B.S. enables the
surveyor to obtain HI +sight i.e. Height of Instrument or
line of sight.

14. • Fore sight( F.S.) It is the last staff reading taken denoting the
shifting of the instrument.
• Intermediate sight.(I.S.) It is staff reading taken on a point
whose elevation is to be determined. All staff reading
between B.S. and F.S. are Intermediate sight.
• Change Point (T.P) It is a point on which both fore and back
sight are taken.

17. The instrument that provides the horizontal line of sight is
known as level and the graduated staff is called levelling
staff.
A level essentially consists of
1. A telescope to provide the line of sight
2. A level tube to make the line of sight horizontal
3. A levelling head to bring the bubble of the level tube at
the centre of its run
4. A tripod to support the level.
LEVEL

19. 1. Telescope
• A telescope consists of a diaphragm ring and two convex
lenses. The lens near the eye is called eyepiece and that
towards the object is called objective.
• The objective provides a real inverted image in front of the
eyepiece, at a distance lesser than its focal length, and
hence the eyepiece in turn produces a magnified and
vertical image of the object on the same side of eyepiece.

21. • Eye Piece: It comprises of a magnifying glass and is
primarily used by the observer.
• Objective Piece: it is placed at the farther end of eyepiece.
It comprises a convex lens and a concave lens.
• Diaphragm: Provided in the outline of the eyepiece with
the cross of dark metal. They are provided to bisect object.
• Focusing Screw: They are meant to align the focus and
image clarity of the object.
• Ray Shade: Prevents sunlight from entering the objective
lens.
Parts of the Telescope

22. 2. Levelling Head
• It is generally a conical socket attached with a triangular base
called tribrach having three or four levelling screws.
• Two level tubes are provided over it. The screws are adjusted
by turning them until the bubble remains in the centre of the
tube for a complete revolution of the telescope.

23. 3. Level Tube
• A level tube is also known as a bubble tube or spirit level or level
vial.
• It is a glass tube, sealed at both the ends, the inside of which is
ground to a circular curve longitudinally, and nearly filled with a
sensitive liquid such as alcohol, leaving enough space to form a
bubble.
• The liquid must be quick acting, non-freezing and stable under
normal temperature variations. Purified synthetic alcohol is the best
• The level is provided with a scale having uniform graduations
(generally of 2 mm length) etched on the exterior surface of the
tube to show the exact position of the bubble.

25. Types of levels

26. 1. Dumpy level
• It consists of a telescope which is rigidly fixed to its support.
• It can neither be rotated about its longitudinal axis nor can it
be removed from its support.
• It is very advantageous when several observations are to be
made with one set up of the instrument.

27. 2. Tilting Level
• The telescope can be rotated about a horizontal axis.
• It enables the observer to quickly centre the bubble and
thus bring the line of sight into the horizontal plane.
• The telescope can be tilted by 4° in a vertical plane with the
help of a tilting screw

28. 3. Automatic or Adjusting Level
• For accurate levelling, a stabilizer or compensator is fitted
inside the telescope, which automatically levels the
instrument.
• Whatever may be the type of automatic level used, it must be
levelled within approximately 15 - 30’ of the vertical, to allow
the compensator to work.
• This is usually achieved by using a three foot screw
arrangement in conjunction with a small circular level
(sometimes called a pond bubble) which is mounted
somewhere on the level.

30. 4. Digital Level
• The digital level can be used for any type of levelling in the
same way as an optical level but has the advantage of being
able to measure and record the observations electronically.
• A digital level uses electronic image-processing techniques
and interrogates a specially made bar-coded staff in order to
obtain readings.

31. 5. Wye-level
• This is similar to the dumpy level except that the telescope in
this is supported by two Y-shaped uprights fixed to a
horizontal bar and attached to the vertical spindle about
which the instrument rotates.
• The telescope can be lifted clear of the Y-supports by
releasing the two clamping collars which fit across the tops of
the Y-supports.

33. 6. Cooke’s reversible level
• It combines the good features of both the dumpy and wye-
levels. It may be rotated about its line of sight giving a
bubble left and bubble right reading.
• Thus, the collimation error is eliminated. It also permits an
easy permanent adjustment.

35. 7. Cushing’s level
• In Cushing’s level, the telescope can neither be revolved
about its longitudinal axis nor can it be removed from its
socket.
• However, the object glass and the eyepiece along with the
diaphragm ring are reversible and can be interchanged.
8. Hand level
• The hand level, as its name implies, is a small level. It is held
in the hand while in use and is adjusted by hand alone.
• A hand level is recommended for short sights and when high
accuracy is not required, e.g., for preliminary surveys. It is
very useful in contouring hilly areas.

37. Levelling Staff
• A levelling staff is a straight, rectangular
rod graduated into metres and smaller
divisions.
• The reading given by the line of sight on
a levelling staff is the height of the line
of collimation from the point on which
the staff is held vertically.
• Levelling staff may be divided into two
groups:
• Self-reading staff
• Target staff.

39. • This staff reading is directly read by the instrument man
through telescope. In a metric system staff, one metre 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.
• The following three types of self-reading staffs are available
a. Self-reading staff

40. I. Telescopic staff
A staff of 3 or more 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.

41. II. Solid staff
It is usually a single piece of 3 m. Invar precision levelling staff
used for precise levelling work is a good example

42. III. Folding staff
A staff of two pieces each of 2 m, which can be, folded one
over the other. It is hinged in the middle so that top half
can be folded over to lie against the lower half

43. b. Target Staff
• If the sighting distance is more, it is 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.
• It is fitted with a Vernier at the centre. The observer directs
the person holding target staff to move the target, till its
centre is in the horizontal line of sight. Then target person
reads the target and is recorded.

45. Temporary Adjustments
The temporary adjustment of a dumpy level consists of Setting,
Leveling and Focusing (elimination of parallax)
1. Setting up
While locating the level, the ground point should be so chosen
that
a) the instrument is not too low or too high to facilitate
reading on a bench mark
b) the length of the back sight should preferably be not more
than 98.0 m
c) the back sight distance and the foresight distance should be
equal, and the foresight should be so located that it
advances the line of levels.

46. • The tripod stand is set up at a convenient height having its
head horizontal (through eye estimation).
• The instrument is then fixed on the head by rotating the
lower part of the instrument with right hand and holding
firmly the upper part with left hand.
• Before fixing, the leveling screws are required to be brought
in between the tribrach and trivet.
• The bull's eye bubble (circular bubble), if present, is then
brought to the centre by adjusting the tripod legs.

47. 2. Levelling up
1. The clamp is loosened and the upper plate is turned until the
longitudinal axis of the plate level is parallel to a line joining
any two levelling screws, say A and B.
2. The two foot screws are turned uniformly towards each other
or away from each other until the plate bubble is central (a).
3. The telescope is swing through 90° so that it lies over the third
foot screw (b).
4. The third screw is turned until the plate bubble is central.
5. The telescope is swing again through 90° to its original position
and the above procedure is repeated till the bubble remains
central in both the positions.
6. The telescope is now swing through 180°. The bubble should
remain central if the instrument is in proper adjustment.

49. 3. Elimination of parallax
It consists of focusing the eyepiece and objective of the level
Focusing the eyepiece - This operation is done to make the cross-hairs
appear distinct and clearly visible. The following steps are involved:
a) The telescope is directed skywards or a sheet of white paper is
held in front of the objective.
b) The eyepiece is moved in or out till the cross-hair appear distinct.
Focusing the objective -This operation is done to bring the image of
the object in the plane of the cross-hairs. The following steps are
involved:
a) The telescope is directed towards the staff.
b) The focusing screw is turned until the image appears clear and
sharp.

50. Permanent Adjustments
• These are the adjustments that are done to set the essential parts
of the instrument in their true positions relative to each other
• The testing of the level is based on the principle of reversal which
states that if there exists any error in a certain part, it gets doubled
by reversing, i.e., revolving the position of that part through 180°.
• The fundamental lines of a level are the axis of the bubble tube,
the vertical axis, the axis of the telescope, and the line of
collimation.
• These relationships generally get disturbed because of mishandling
of the level during its usage in the field and need frequent
adjustment.

52. The desired relationship of the fundamental lines are
1. The vertical axis of the level should be perpendicular
to the axis of the plate bubble tube.
2. The line of collimation should be perpendicular to the
vertical axis.
3. The axis of the telescope and the line of collimation
should coincide.

54. Two adjustment are required in the dumpy level
1. To make the vertical axis of the level perpendicular to the
axis of the plate bubble tube.
Test
a) The instrument is levelled as described under temporary
adjustments.
b) Swing the telescope through 180°. If the bubble runs out of
the bubble tube centre, the adjustment is not in order.
c) If it is so, count the number of graduations on the bubble
tube by which the bubble has run out of its central position.

56. Adjustment
a) Bring the bubble halfway back to a central position by using
the two foot screws. This makes the vertical axis truly vertical.
b) Bring the bubble to the centre of its run by means of the
capstan screw provided at one of the ends of the bubble
tube. This makes the axis of the bubble tube truly horizontal.

57. 2. To make the line of sight perpendicular to the vertical axis (or
parallel to the axis of the bubble) when the instruments is truly
levelled

58. Test
1. This test is known as the two-peg test.
2. Choose two suitable points A and B about 60 m apart and
place the level mid-way at C
3. Level the instrument and read the staff at A and B. Calculate
the difference in elevation between A and B. The difference
will be correct even if the line of sight is not parallel to the axis
of the bubble tube as the error resulting from the line of sight
being inclined is directly proportional to the length of sight.

59. 4. Choose another point D in line with A and B about 15 m
ahead of B.
5. Level the instrument at D and again take the observations at
A and B.
6. Calculate the difference in elevations. If it is same as
calculated before (step 3), the adjustment is correct.
7. If not, the reading at A will have a bigger error than that at
B, since the error is proportional to sight distance.

60. Alternatively, the adjustment can be made as follows
1. Workout the reading that should be obtained at A from D, to
make the line of sight horizontal.
Let, reading at A from C – reading at B from C = h1
and, reading at A from D – reading at B from D = h2
Required increase in the reading at A = (h1 – h2 ) (DA/BA)
2. Correct the staff reading at A.
3. Keep the staff at A and take the observation from D.
4. Diaphragm capstan screws are turned to get the same staff
reading as calculated above (step 1).

61. TWO-PEG TEST

62. Methods of Levelling
1. Direct levelling
• It is also known as spirit levelling. Because a spirit level is
mounted on the telescope of the levelling instrument which is
used to make the line of sight horizontal.
• The vertical distances are measured with respect to this horizontal
line of sight and are used to compute the difference in elevations
of various points.

63. 2. Trigonometric levelling
• It is also known as indirect levelling. Because the elevations are
determined indirectly from the horizontal distances and vertical
angle measured at the point.
• As trigonometric relations are used to determine the elevations,
it is called trigonometric levelling.
• This is generally used when direct levelling becomes difficult,
such as at the elevations of inaccessible points like mountain
peaks or top of towers etc.

65. 3. Barometric levelling
• The elevations are determined indirectly from the changes in
atmospheric pressure.
• The atmospheric pressure decreases with an increase in
elevation.
• Examples are the aneroid barometer, which can be used for
determining the changes in atmospheric pressure.
• Also called the altimeter, it is quite light, sturdy and convenient
compared to the mercury barometer, but not as accurate. It is
quick method of levelling with accuracy to the nearest 1 -2
meters.

66. 4. Hypsometric levelling
• In this method the difference of elevations is obtained by noting
down the temperature at which water starts boiling.
• This is because, the boiling point of water decreases with
increase in altitude.
• The altitudes of various points may be determined by using
hypsometer, also called as thermo-barometer.

67. 5. Stadia Leveling
• It is a modified form of trigonometric leveling in which
Tacheometer principle is used to determine the elevation of
point.
• In this case the line of sight is inclined from the horizontal.
• It is more accurate and suitable for surveying in hilly terrains.

68. Classification of Direct Levelling
a. Simple levelling
• This is the easiest type of direct levelling because it only
needs one set up of the levelling instruments.
• This is commonly adopted for determining the difference in
elevations of 2 points visible from a single position of the
instrument.

70. b. Differential levelling/Compound levelling
• This type of levelling needs more than one set up of the
levelling instrument.
• This is used to find the difference of elevations of two
points which are situated at a large distance apart or the
difference in elevations of the two points is large.

72. c. Check Levelling
• This type of levelling is adopted for the purpose of checking a
series of levels previously fixed.
• This is often done at the end of a day to check the accuracy of
the work by returning to the starting point of the day.

74. d. Profile levelling
• This is used for determining the elevations of points at
known distances which are apart, along a given line to get an
accurate outline of the whole surface of the ground.
• This also called as longitudinal levelling or sectioning.
• Profile levelling is done along the center line of the proposed
route (road, canal, railway line, sewer line etc.)
• It is used for plotting the longitudinal section, which is useful
for fixing the gradients and for determining the earthwork
quantities.

76. e. Cross-section Levelling
• This type of levelling is done to determine the difference of
elevations of the ground surface lying along the perpendicular
to the center line of a proposed road, canal etc.
• The cross-section levelling is required to determine the
configuration across the alignment.
• Cross-section of a plot is helpful for determining the quantities
of earthwork.

78. f. Precise Leveling
• Precise leveling is similar to differential leveling but in this case
higher precise is wanted.
• To achieve high precise, serious observation procedure is
performed. The accuracy of 1 mm per 1 km is achieved.
• The instruments and methods used are of high precision and
due to that this is a costly method.

79. g. Reciprocal Levelling
• In this method of levelling in which the difference in elevations
between two points is accurately determined by two sets of
observations where it is not possible to set up the levelling
instrument midway.

81. Booking and Reducing Levels
The observations are recorded in a level book.
There are two methods of booking and reducing the levels of
the points from the observed staff readings and they are-
1. Rise and Fall Method
2. Height of Collimation Method

82. Height of Instrument Method
• This method consist of finding H.I. for every setup of instrument,
and then obtaining the R.L. of point of reference with respect to
H.I
• The reduced level of plane of collimation is also known as height
of instrument (H.I.).

83. • The elevation of the plane of collimation for the first set up of
the level is determined by adding back sight to the reduced
level of a B.M.
• The reduced levels of the intermediate points and the first
change point are obtained by subtracting the staff readings
taken on these points, i.e., by subtracting successively (one by
one) I.S. and F.S. from the H.I.
• The instrument is then shifted to the second position and a
new plane of collimation is set up by taking a B.S. on the
change point.

84. • By means of back sight and foresight taken on the change point,
the levels of the two planes of collimation are correlated.
• The elevations of the new plane of collimation is obtained by
adding the back sight, taken on the change point from the second
position of the level, to the reduced level of the first change
point.
• Then the reduced level of successive points and the second
change point is obtained by subtracting their staff readings from
the elevation of the new plane of collimation.

86. Exercise

87. Rise and Fall Method
• It consists of determining the difference of levels between
the consecutive points by comparing their staff readings.
• The rise or fall is obtained by calculating the difference
between the consecutive staff readings.
• A rise is indicated if the backsight is more than the foresight,
and a fall if the backsight is less than the foresight.
• Then the reduced level of each point is obtained by adding
the rise to, or by subtracting the fall from the reduced level of
the preceding point.

89. Exercise

91. Use of Inverted Staff
• When the point, whose elevation is to be found, is much
above the line of sight (e.g., projection from the face of a
building, underside of beams, girders and arches, etc.), the
staff is placed inverted with its zero end touching the point.
• The reading on the staff is taken in the usual manner.
• Such an observation is entered in the level page book with a
minus sign, for convenience.
• For instance, in a levelling operation, the inverted sights were
taken at B, C, D and E.
• The levels of these points can be obtained by simply adding
the staff readings to the height of the instrument.

94. Adjusting the Closing Error
• If the last foresight is taken on the starting point and if it is
subtracted from the current height of the instrument, the
result should be the elevation of the starting point.
• If this is achieved, it provides a complete verification of both
the field observations and the arithmetic ones.
• The amount of error of closure is proportional to the length
of line of levels or to the number of times the level is set up.
It can be computed by the formula:

97. Curvature and Refraction
• Curvature and refraction effects should be accounted for in
precise levelling work and also if the sights are too long.
• The effect of curvature is to cause the objects sighted, to
appear lower than they really are.
• The effect of refraction is to make the objects appear higher
than they really are.

98. Curvature
• In case of a long sight the horizontal line is not a level line
due to curvature of the earth.
• The vertical distance between a horizontal line and the
level line represents the effect of curvature of the earth.

99. • Let ABD be a level line through A, and O be the centre of the
earth. A is the instrument position.
• AC, the line of collimation, will be a horizontal line. R is the
radius of the earth.

101. Refraction
• Refraction of the ray passing through the atmosphere from
the signal to the observer is the main source of external error.
• The rays of light while passing through layers of air of
different densities refract or bend down.
• These densities depend upon the temperature and pressure
at all points along the track of the rays.

102. • Consequently, ray from a staff follows a curved path, say AE
• CE is the amount of refraction correction and varies considerably with climatic
conditions.
• The average refraction correction can, however, be taken as 1/7th of the
curvature correction.

103. Combined Correction
• Since, the effect of curvature and refraction, when
combined, is to make the objects sighted appear low, the
overall correction is subtractive.
• Error due to curvature and refraction can be eliminated by
equalizing F.S. and B.S. distances or by reciprocal levelling

104. Example
In order to find the difference in elevation between two
points A and B, a level was set up on the line AB, 50 m
from A and 1300 m from B. A and B being on the same
side of the instrument. The readings obtained on staff
held at A and B were 0.435 m and 3.950 m, respectively.
Find the true difference in elevation between A and B.
Take radius of earth = 6370

105. Reciprocal levelling
• The difference in elevation between two points is accurately
determined by two sets of reciprocal observations
• Useful when:
• The instrument cannot be set up between the two points due to an
obstruction such as a valley, river, etc., and
• if the sights are much longer than are ordinarily permissible
• Collimation error, Earth curvature and refraction affect the
longer sight much more than the shorter one.

106. Procedure
• The instrument is set up near one point say A, on one side on
the valley, and a reading is taken on the staff held at A near the
instrument and on the staff at B on the other side of the valley
• Let these readings be a and b, respectively. The near reading a
is without error, whereas the reading b would have an error e
due to curvature, refraction and collimation.
• The instrument is then shifted near to B on the other side of
the valley and the reading is taken on the staff held at B and
that on A. Let these readings be c and d
• The near reading c is without error, whereas reading d would
contain an error e

107. Let h be the
true difference
of elevation
between A and
B.