Surveying
Chapter–3
Levelling
Levelling
➢ Levelling is an operation in surveying performed to
determine the difference in levels of two points.
➢By this operation the height of a point from a
datum, known as elevation, is determined.
➢A datum is a reference surface of constant
potential, called as a level surface of the earth’s
gravity field, for measuring the elevations of the
points.
Datum
➢ One of such surfaces is the mean sea level surface
and is considered as a standard datum.
➢ Also an arbitrary surface may be adopted as a
datum.
➢Level line is a line lying in a level surface.
➢ It is thus a curved line
Level Line
➢A level in proper adjustment, and correctly set up,
➢produces a horizontal line of sight which is at right
angles to the direction of gravity and tangential to
the level line at the instrument height.
• It follows a constant height above mean sea level
and hence is a curved line, as shown in Fig.1 below
Line of Sight
•
Level surface
▪ A level surface is the
equipotential surface of the
earth’s gravity field.
▪ It is a curved surface and every
element of which is normal to
the plumb line
DIRECT DIFFERENTIAL
OR SPIRIT LEVELLING
•Differential levelling or spirit levelling is
the most accurate simple direct method
of determining the difference of level
between two points using an instrument
known as level with a levelling staff.
Differential Levelling
• A level establishes a horizontal line of sight
• The difference in the level of the line of sight and
the point over which the levelling staff is held, is
measured through the levelling staff.
• A levelling staff is usually 3m , 4.5m, 5m
graduated staff placed at different stations
Levelling
➢Fig.2 below shows the
principle of determining
the difference in
level Δh between two
points A and B,
➢The elevation of one of
them can be determined if
the elevation of the other
one is known.
Levelling
▪From the figure, we find that
▪ If SB < SA, the point B is higher than point A.
▪ If SB > SA, the point B is lower than point A.
▪To determine the difference of level, the
elevation of ground point at which the level is
set up, is not required.
Levelling
Keyterms associated with differential levelling
▪ Station: a station is the point where the levelling staff is held. (Points A, a,
b, B, c, and C as shown in Fig. )
▪ Height of instrument (H.I.) or height of collimation: For any set up of
the level, the elevation of the line of sight is the height of instrument. (H.I.
= hA + SA in Fig. 2.)
▪ Back sight (B.S.): It is the first reading taken on the staff after setting up
the level usually to determine the height of instrument.
Levelling
▪ It is usually made to some form of a bench mark (B.M.)
or to the points whose elevations have already been
determined.
▪ When the instrument position has to be changed, the
first sight taken in the next section is also a back sight.
(Staff readings S1 and S5 in Fig. 3
Levelling
▪ Fore sight (F.S.): It is the last reading from an instrument
position on to a staff held at a point.
▪ It is thus the last reading taken within a section of levels
before shifting the instrument to the next section,
▪ It is also the last reading taken over the whole series of
levels.
▪ (Staff readings S4 and S7 in Fig. 3 are fore sight readings
Levelling
▪ Change point (C.P.) or turning point: A change point or
turning point is the point where both the fore sight and
back sight are made on a staff held at that point.
▪ A change point is required before moving the level from
one section to another section.
▪ By taking the fore sight the elevation of the change point is
determined and by taking the back sight the height of
instrument is determined.
▪ The change points relate the various sections by making
fore sight and back sight at the same point.(Point B in Fig.
3
Levelling
▪Intermediate sight (I.S.): ‘intermediate sight’
covers all sightings readings made between back
sight and fore sight within each section.
▪Thus, intermediate sight station is neither the change
point nor the last point. (Points a, b, and c in Fig. 3.)
▪Balancing of sights: when the distances of the
stations where back sight and fore sight are taken
from the instrument station are kept approximately
equal
Levelling
❑Reduced level (R.L.): Reduced level of a point is its height
or depth above or below the assumed datum. It is the
elevation of the point.
❑Rise and fall: The difference of level between two
consecutive points indicates a rise or a fall between the two
points. In Fig. 3.3, if (SA – SB) is positive, it is a rise and if
negative, it is a fall.
❑Rise and fall are determined for the points lying within a
section.
❑Section: A section comprises of one back sight, one fore
sight and all the intermediate sights taken from one
instrument set up within that section.
❑Thus , the number of sections is equal to the number of set
ups of the instrument.
Levelling
For booking and reducing the levels of points,
there are two systems, namely
▪ The height of instrument or height of
collimation method and
▪ Rise and fall method.
▪ To explain the booking and reducing levels, the
levelling operation from stations A to C shown
in Fig. 3, has been presented in Tables 1 and 2
for both the methods.
Levelling
Height of Instrument Method
Levelling
Rise and Fall Method
Click to add text
I
Levelling
The following rules are used in the two methods of
reduction of levels.
1) For the height of instrument method
(i) Σ B.S. – Σ F.S. = Last R.L. – First R.L.
(ii) Σ [H.I. × (No. of I.S.’s + 1)] – Σ I.S. – Σ F.S. = Σ R.L. –
First R.L.
2) For the rise and fall method
Σ B.S. – Σ F.S. = Σ Rise – Σ Fall = Last R.L. – First R.L.
Example - 1
➢ The following readings were taken with a
level and 4 m staff. Draw up a level book
page and reduce the levels by the height of
instrument method. 0.578 B.M.(= 58.250
m), 0.933, 1.768, 2.450, (2.005 and 0.567)
C.P., 1.888, 1.181, (3.679 and 0.612) C.P.,
0.705, 1.810
….continue
