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LEVELLING
UNIT 2 SYLLABUS
DEFINITION
• It is a branch of surveying the object of which
is to
– Find the elevation of given points with respect to
a given or assumed datum
– Establish points at a given elevation or different
elevation with respect to a given or assumed
datum
TERMS IN LEVELLING
TERMS IN LEVELLING
• Level Surface
– Curved surface which at
each point is perpendicular
to the direction of gravity at
that point
– The surface of a still water is
a truly level surface
– Any surface parallel to mean
spheroidal surface of the
earth is a level surface
• Level Line
– Line lying in a level surface
– Normal to the plumb line at
all points
TERMS IN LEVELLING
• Horizontal plane
– Horizontal plane through a
point is a plane tangential to
the level surface at that
point
– It is perpendicular to the
plumb line to that point
• Horizontal Line
– It is a straight line tangential
to the level line at a point
– It is also perpendicular to
the plumb line
TERMS IN LEVELLING
• Vertical Line
– It is a line normal to the level
line at a point
– It is commonly considered to
be the line defined by a
plumb line
• Datum
– Datum is any surface to
which elevations are referred
– The mean sea level affords a
convenient datum world over
and elevations are commonly
given as so much above or
below sea level
TERMS IN LEVELLING
• Bench Mark
– Bench mark is a
relatively permanent
point of reference
whose elevation with
respect to some
assumed datum is
known.
– It is used either as a
starting point for
levelling or as point
upon which to close as a
check
LEVELLING INSTRUMENTS
• Instruments used for levelling are
– Level (Dumpy level, Tilting level)
– A levelling staff
TERMS IN LEVELLING
• STATION:-
– In levelling, a station is that point where the levelling
staff is held and not where level is setup.It is the point
whose elevation to be determined.
• HEIGHT OF INSTRUMENT:-
– The height of instrument is the elevation of line of
sight with respect to assumed datum
TERMS IN LEVELLING
• BACK SIGHT (BS):-
– It is the sight taken on a levelling staff held at a point of known elevation
to determine the amount by which the line of sight is above that point
and to obtain the height of instrument
– It is also known as plus sight as the back sight reading is added to the
level of datum to get the height of instrument.
TERMS IN LEVELLING
• FORE SIGHT (FS):-
– Fore sight is a sight taken on a levelling staff held at a point of
unknown elevation to determine the amount by which the point is
below the line of sight and to obtain the elevation of the station.
– It is also known as a minus sight as the fore sight reading is always
subtracted from the height of the instrument to get the elevation of
the point
TERMS IN LEVELLING
• TURNING POINT:-
– Turning point or change point on which both fore sight and back sight
are taken
– Fore sight is taken on the point in one set of instruments to determine
the elevation of the point
– Back sight is taken on the same point in other set of instruments to
establish the new height of the instrument.
TERMS IN LEVELLING
• INTERMEDIATE STATION (IS):-
– Intermediate station is a point, intermediate between
the turning point on which only fore sight is taken to
determine the elevation of the station.
PRINCIPLE OF LEVELLING
BOOKING AND REDUCING LEVELS
• There are two methods of booking and
reducing the elevation of points from the
observed staff readings
– Height of Instrument or Collimation method
– Rise and fall method
RISE AND FALL METHOD
• Backsight – (Intermediate sight or Fore sight) = (+ or -) Rise or
Fall
• Intermediate sight– (Intermediate sight or Fore sight) = (+ or -)
Rise or Fall
• Reduced level of Current station= Reduced level of Previous
station +/- Rise/Fall
• Airthematic Check :-
The following readings were observed
successively with a leveling instrument.
The instrument was shifted after fifth and
eleventh readings. (i) 0.585 (ii) 1.010 (iii)
1.735 (iv) 3.295 (v) 3.775 (vi) 0.350 (vii)
1.300 (viii) 1.795 (ix) 2.575 (x) 3.375 (xi)
3.865 (xii) 1.735 (xiii) 0.635 (xiv) 1.605 m.
Draw up a page of level book and
determine the R.L of various point on
which the first reading was taken is
136.440. Use Rise and Fall method
(Nov/Dec 2018) (13 marks)
STATION BACK
SIGHT
INTERMEDIATE
SIGHT
FORE SIGHT HEIGHT OF
INSTRUME
NT
REDUCE
D LEVEL
REMARKS
A 0.585 136.440 Benchmark
B 1.010 136.015
C 1.735 135.29
D 3.295 133.73
E 0.350 3.775 133.25 Change point 1
F 1.300 132.30
G 1.795 131.805
H 2.575 131.025
I 3.375 130.225
J 1.75 3.865 129.735 Change point 2
K 0.635 130.835
L 1.605 129.865
The following consecutive readings
were taken with a dumpy level. 6.210,
6.920, 7.120, 8.420, 9.810, 6.630, 7.90,
8.26, 9.710 and 10.210. The level was
shifted after 5th reading. The R.L at
first point was 100 m. Calculate the
R.L of the points and apply the
arithmetic check. (Nov/Dec 2016) (13
marks)
The following readings were taken
with a dumpy level. 1.904, 2.653,
3.906, 4.026, 1.964, 1.702, 1.592,
1.261, 2.542, 2.006, 3.145. The
instrument was moved after fourth
and seventh readings, the first reading
was taken on the staff held on the
B.M of R.L 100m. Calculate the R.L of
the points and apply the arithmetical
check. (Apr/May 2018) (13 marks)
The following readings were taken with a
dumpy level. 0.875, 1.235, 2.310, 1.385,
2.930, 3.125, 4.125, 0.120, 1.875, 2.030,
3.765. The instrument was moved after
second, fourth and eighth readings. The
first reading was taken on the staff held
on the B.M of R.L 132.135m. Calculate the
R.L of the points and apply the
arithmetical check. (Apr/May 2017) (13
marks)
The following staff readings were
obsereved successively with a level,
the instrument having been moved
after third, sixth and eighth readings,
2.228, 1.606, 0.988, 2.090, 2.864,
1.262, 0.602, 1.982, 1.044, and 2.684.
Enter the above readings in a page of a
level book and calculate RL of points if
the first reading was taken with a staff
held on a benchmark of 432.384 m.
Following readings were observed
successively with a levelling
instrument. The instrument was
shifted after 5th and 11th readings
0.585, 1.010, 1.735, 3.295, 3.775,
0.350, 1.300, 1.795, 2.575, 3.375,
3.895, 1.745, 0.635, and 1.605. Draw
up a page of level book and determine
the RL of various points, if the RL of
first point is 134.00 m (Nov/Dec 2013)
(13 marks)
The following staff readings were observed
successively with a level. The instrument
having been moved after the second, fifth
and eighth readings 0.675, 1.230, 0.750,
2.565, 2.225, 1.935, 1.835, 3.220, 3.115,
and 2.875. The first staff reading was taken
with a staff held on a bench mark of
reduced level +100.00. Enter the readings
in the level book form and find the reduced
levels of all the points (Nov/Dec 2012) (13
marks)
The following consecutive readings were taken
from a dumpy level and 4m levelling staff on a
continuously sloping ground at 30 m intervals
0.680, 1.455, 1.855, 2.330, 2.885, 3.380, 1.055,
1.860, 2.265, 3.540, 0.835, 0.945, 1.530, and
2.250. R.L of the starting point was 80.750 m.
Rule out a page of a level book and enter the
above readings. Determine the RL of various
staff stations. Estimate average gradient of
ground measured (Apr/May 2010) (13 marks)
The following consecutive readings
were taken with a levelling staff at an
interval of 20m. The readings are
2.375, 1.730, 0.615, 3.450, 2.835,
2.070, 1.835, 0.435, 1.630, 2.255, and
3.630m. The instrument was shifted
after fourth and eigth readings. The
last reading was taken on a B.M of R.L
110.200 m. Calculate the R.L of all the
points. (Apr/May 2019) (13 marks)
The following consecutive readings
were taken with a levelling staff at an
interval of 20m. The readings are
2.375, 1.730, 0.615, 3.450, 2.835,
2.070, 1.835, 0.435, 1.630, 2.255, and
3.630m. The instrument was shifted
after fourth and eigth readings. The
last reading was taken on a B.M of R.L
110.200 m. Calculate the R.L of all the
points. (Apr/May 2019) (13 marks)
The following consecutive readings were
taken along AB with a 4m levelling staff
on a continuously sloping ground at a
interval of 20m 0.345 on A, 2.630, 3.875,
0.665, 1.745, 2.965, 3.945, 1.125, 2.475,
3.885 on B. The first reading was taken on
the staff held on the B.M of R.L
60.350m.Calculate the R.L of the points
and also find the gradients of line AB.
(Apr/May 2017) (13 marks)
Following are the successive staff readings
taken in a leveling continuously on sloping
ground at common interval of 25 m.
0.605, 1.235, 1.860, 2.575, 0.735, 1.430,
1.955, 2.875, 0.875, 1.825, 2.720. Reduced
levels of the first point is 160.00 m. Rule
out a level book page and enter the above
readings. Calculate the reduced levels of
the points and also the gradient of the
line joining the first point and last point.
CURVATURE AND REFRACTURE
CORRECTION
CURVATURE AND REFRACTURE
CORRECTION
CURVATURE AND REFRACTURE
CORRECTION
CURVATURE AND REFRACTURE
CORRECTION
CURVATURE AND REFRACTURE
CORRECTION
CURVATURE AND REFRACTURE
CORRECTION
Find the combined correction for curvature and refraction for
a distance of a
3400 m
1.29 km (Apr/May 2019)
CURVATURE AND REFRACTURE
CORRECTION
CURVATURE AND REFRACTURE
CORRECTION
• A level was set up at a point ‘O’ and
the distance to two staff stations A
and B were 60m and 200m. The
observed staff readings, on A and B
were 2.25 and 1.815. Find the
correct difference of levels between
stations A and B. (Nov/Dec 2017)
(13 marks)
CURVATURE AND REFRACTURE
CORRECTION
CURVATURE AND REFRACTURE
CORRECTION
RECIPROCAL LEVELLING
• When it is necessary to carry levelling across a
river, special method i.e. reciprocal levelling
must be used to obtain accuracy and to
eliminate the following
– Error in instrument adjustment
– Combined effect of earth’s curvature and
refraction
– Variations in the average variation
RECIPROCAL LEVELLING
RECIPROCAL LEVELLING
RECIPROCAL LEVELLING
RECIPROCAL LEVELLING
A dumpy level was set up with its eye-piece
vertically over a peg C. The height from the top of
C to the centre of its eyepiece was measured and
found to be 1.578 m. The reading on the staff
held on the peg D was 1.008. The level was then
moved and setup likewise at the peg D. The
height of eyepiece above D was 1.258 m and the
reading on the staff held on the peg C was 1.812.
Determine the true reduced level of peg D, if that
of peg C was 163.373 (Apr/May 2018) (13 marks)

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Levelling - Rise and fall - Height of instrument method

  • 3. DEFINITION • It is a branch of surveying the object of which is to – Find the elevation of given points with respect to a given or assumed datum – Establish points at a given elevation or different elevation with respect to a given or assumed datum
  • 5. TERMS IN LEVELLING • Level Surface – Curved surface which at each point is perpendicular to the direction of gravity at that point – The surface of a still water is a truly level surface – Any surface parallel to mean spheroidal surface of the earth is a level surface • Level Line – Line lying in a level surface – Normal to the plumb line at all points
  • 6. TERMS IN LEVELLING • Horizontal plane – Horizontal plane through a point is a plane tangential to the level surface at that point – It is perpendicular to the plumb line to that point • Horizontal Line – It is a straight line tangential to the level line at a point – It is also perpendicular to the plumb line
  • 7. TERMS IN LEVELLING • Vertical Line – It is a line normal to the level line at a point – It is commonly considered to be the line defined by a plumb line • Datum – Datum is any surface to which elevations are referred – The mean sea level affords a convenient datum world over and elevations are commonly given as so much above or below sea level
  • 8. TERMS IN LEVELLING • Bench Mark – Bench mark is a relatively permanent point of reference whose elevation with respect to some assumed datum is known. – It is used either as a starting point for levelling or as point upon which to close as a check
  • 9. LEVELLING INSTRUMENTS • Instruments used for levelling are – Level (Dumpy level, Tilting level) – A levelling staff
  • 10. TERMS IN LEVELLING • STATION:- – In levelling, a station is that point where the levelling staff is held and not where level is setup.It is the point whose elevation to be determined. • HEIGHT OF INSTRUMENT:- – The height of instrument is the elevation of line of sight with respect to assumed datum
  • 11. TERMS IN LEVELLING • BACK SIGHT (BS):- – It is the sight taken on a levelling staff held at a point of known elevation to determine the amount by which the line of sight is above that point and to obtain the height of instrument – It is also known as plus sight as the back sight reading is added to the level of datum to get the height of instrument.
  • 12. TERMS IN LEVELLING • FORE SIGHT (FS):- – Fore sight is a sight taken on a levelling staff held at a point of unknown elevation to determine the amount by which the point is below the line of sight and to obtain the elevation of the station. – It is also known as a minus sight as the fore sight reading is always subtracted from the height of the instrument to get the elevation of the point
  • 13. TERMS IN LEVELLING • TURNING POINT:- – Turning point or change point on which both fore sight and back sight are taken – Fore sight is taken on the point in one set of instruments to determine the elevation of the point – Back sight is taken on the same point in other set of instruments to establish the new height of the instrument.
  • 14. TERMS IN LEVELLING • INTERMEDIATE STATION (IS):- – Intermediate station is a point, intermediate between the turning point on which only fore sight is taken to determine the elevation of the station.
  • 16. BOOKING AND REDUCING LEVELS • There are two methods of booking and reducing the elevation of points from the observed staff readings – Height of Instrument or Collimation method – Rise and fall method
  • 17. RISE AND FALL METHOD • Backsight – (Intermediate sight or Fore sight) = (+ or -) Rise or Fall • Intermediate sight– (Intermediate sight or Fore sight) = (+ or -) Rise or Fall • Reduced level of Current station= Reduced level of Previous station +/- Rise/Fall • Airthematic Check :-
  • 18.
  • 19. The following readings were observed successively with a leveling instrument. The instrument was shifted after fifth and eleventh readings. (i) 0.585 (ii) 1.010 (iii) 1.735 (iv) 3.295 (v) 3.775 (vi) 0.350 (vii) 1.300 (viii) 1.795 (ix) 2.575 (x) 3.375 (xi) 3.865 (xii) 1.735 (xiii) 0.635 (xiv) 1.605 m. Draw up a page of level book and determine the R.L of various point on which the first reading was taken is 136.440. Use Rise and Fall method (Nov/Dec 2018) (13 marks)
  • 20. STATION BACK SIGHT INTERMEDIATE SIGHT FORE SIGHT HEIGHT OF INSTRUME NT REDUCE D LEVEL REMARKS A 0.585 136.440 Benchmark B 1.010 136.015 C 1.735 135.29 D 3.295 133.73 E 0.350 3.775 133.25 Change point 1 F 1.300 132.30 G 1.795 131.805 H 2.575 131.025 I 3.375 130.225 J 1.75 3.865 129.735 Change point 2 K 0.635 130.835 L 1.605 129.865
  • 21. The following consecutive readings were taken with a dumpy level. 6.210, 6.920, 7.120, 8.420, 9.810, 6.630, 7.90, 8.26, 9.710 and 10.210. The level was shifted after 5th reading. The R.L at first point was 100 m. Calculate the R.L of the points and apply the arithmetic check. (Nov/Dec 2016) (13 marks)
  • 22. The following readings were taken with a dumpy level. 1.904, 2.653, 3.906, 4.026, 1.964, 1.702, 1.592, 1.261, 2.542, 2.006, 3.145. The instrument was moved after fourth and seventh readings, the first reading was taken on the staff held on the B.M of R.L 100m. Calculate the R.L of the points and apply the arithmetical check. (Apr/May 2018) (13 marks)
  • 23. The following readings were taken with a dumpy level. 0.875, 1.235, 2.310, 1.385, 2.930, 3.125, 4.125, 0.120, 1.875, 2.030, 3.765. The instrument was moved after second, fourth and eighth readings. The first reading was taken on the staff held on the B.M of R.L 132.135m. Calculate the R.L of the points and apply the arithmetical check. (Apr/May 2017) (13 marks)
  • 24. The following staff readings were obsereved successively with a level, the instrument having been moved after third, sixth and eighth readings, 2.228, 1.606, 0.988, 2.090, 2.864, 1.262, 0.602, 1.982, 1.044, and 2.684. Enter the above readings in a page of a level book and calculate RL of points if the first reading was taken with a staff held on a benchmark of 432.384 m.
  • 25. Following readings were observed successively with a levelling instrument. The instrument was shifted after 5th and 11th readings 0.585, 1.010, 1.735, 3.295, 3.775, 0.350, 1.300, 1.795, 2.575, 3.375, 3.895, 1.745, 0.635, and 1.605. Draw up a page of level book and determine the RL of various points, if the RL of first point is 134.00 m (Nov/Dec 2013) (13 marks)
  • 26. The following staff readings were observed successively with a level. The instrument having been moved after the second, fifth and eighth readings 0.675, 1.230, 0.750, 2.565, 2.225, 1.935, 1.835, 3.220, 3.115, and 2.875. The first staff reading was taken with a staff held on a bench mark of reduced level +100.00. Enter the readings in the level book form and find the reduced levels of all the points (Nov/Dec 2012) (13 marks)
  • 27. The following consecutive readings were taken from a dumpy level and 4m levelling staff on a continuously sloping ground at 30 m intervals 0.680, 1.455, 1.855, 2.330, 2.885, 3.380, 1.055, 1.860, 2.265, 3.540, 0.835, 0.945, 1.530, and 2.250. R.L of the starting point was 80.750 m. Rule out a page of a level book and enter the above readings. Determine the RL of various staff stations. Estimate average gradient of ground measured (Apr/May 2010) (13 marks)
  • 28. The following consecutive readings were taken with a levelling staff at an interval of 20m. The readings are 2.375, 1.730, 0.615, 3.450, 2.835, 2.070, 1.835, 0.435, 1.630, 2.255, and 3.630m. The instrument was shifted after fourth and eigth readings. The last reading was taken on a B.M of R.L 110.200 m. Calculate the R.L of all the points. (Apr/May 2019) (13 marks)
  • 29. The following consecutive readings were taken with a levelling staff at an interval of 20m. The readings are 2.375, 1.730, 0.615, 3.450, 2.835, 2.070, 1.835, 0.435, 1.630, 2.255, and 3.630m. The instrument was shifted after fourth and eigth readings. The last reading was taken on a B.M of R.L 110.200 m. Calculate the R.L of all the points. (Apr/May 2019) (13 marks)
  • 30. The following consecutive readings were taken along AB with a 4m levelling staff on a continuously sloping ground at a interval of 20m 0.345 on A, 2.630, 3.875, 0.665, 1.745, 2.965, 3.945, 1.125, 2.475, 3.885 on B. The first reading was taken on the staff held on the B.M of R.L 60.350m.Calculate the R.L of the points and also find the gradients of line AB. (Apr/May 2017) (13 marks)
  • 31. Following are the successive staff readings taken in a leveling continuously on sloping ground at common interval of 25 m. 0.605, 1.235, 1.860, 2.575, 0.735, 1.430, 1.955, 2.875, 0.875, 1.825, 2.720. Reduced levels of the first point is 160.00 m. Rule out a level book page and enter the above readings. Calculate the reduced levels of the points and also the gradient of the line joining the first point and last point.
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  • 39. CURVATURE AND REFRACTURE CORRECTION Find the combined correction for curvature and refraction for a distance of a 3400 m 1.29 km (Apr/May 2019)
  • 41. CURVATURE AND REFRACTURE CORRECTION • A level was set up at a point ‘O’ and the distance to two staff stations A and B were 60m and 200m. The observed staff readings, on A and B were 2.25 and 1.815. Find the correct difference of levels between stations A and B. (Nov/Dec 2017) (13 marks)
  • 44. RECIPROCAL LEVELLING • When it is necessary to carry levelling across a river, special method i.e. reciprocal levelling must be used to obtain accuracy and to eliminate the following – Error in instrument adjustment – Combined effect of earth’s curvature and refraction – Variations in the average variation
  • 48. RECIPROCAL LEVELLING A dumpy level was set up with its eye-piece vertically over a peg C. The height from the top of C to the centre of its eyepiece was measured and found to be 1.578 m. The reading on the staff held on the peg D was 1.008. The level was then moved and setup likewise at the peg D. The height of eyepiece above D was 1.258 m and the reading on the staff held on the peg C was 1.812. Determine the true reduced level of peg D, if that of peg C was 163.373 (Apr/May 2018) (13 marks)