various terms that are used in the levelling. Methods of levelling - Rise and fall method, Height of instrument method.

1. LEVELLING

2. UNIT 2 SYLLABUS

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

4. TERMS IN LEVELLING

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.

15. PRINCIPLE OF LEVELLING

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 :-

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.

34. CURVATURE AND REFRACTURE
CORRECTION

35. CURVATURE AND REFRACTURE
CORRECTION

36. CURVATURE AND REFRACTURE
CORRECTION

37. CURVATURE AND REFRACTURE
CORRECTION

38. CURVATURE AND REFRACTURE
CORRECTION

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)

40. CURVATURE AND REFRACTURE
CORRECTION

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)

42. CURVATURE AND REFRACTURE
CORRECTION

43. CURVATURE AND REFRACTURE
CORRECTION

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

45. RECIPROCAL LEVELLING

46. RECIPROCAL LEVELLING

47. RECIPROCAL LEVELLING

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)