2. Levelling
• It is a branch of surveying the object of which is:
– To find the elevations of given points with respect to a
given or assumed datum
– To establish points at a given elevation or at different
elevations with respect to a given or assumed datum
• First operation – enable the works to be designed
• Second operation – required in the setting out of all
kinds of engineering works
• Measurements in a vertical plane
4. Levelling terminology
• Level surface: A surface parallel to the mean spheroidal
surface of the earth, Eg: a still lake
• Level line: It is a line lying on a level surface. It is normal to
the plumb line at all the points
• Horizontal plane: It is a plane tangential to the level surface
at the point under consideration. It is perpendicular to the
plumb line
• Vertical line: It is a line from any point on the earth’s
surface to the centre of the earth. It is the line defined by a
plumb line
5. Levelling terminology
• Datum surface: It is an arbitrarily assumed level surface
from which vertical distances are measured. The mean sea
level at Karachi is taken as the datum surface for India
• Reduced Level: It is the vertical distance of a point
measured above or below the datum. Also called as
elevation of a point
• Back sight: It is a staff reading taken on a point of known
elevation (plus sight - reading is added to the RL of the
bench mark)
• Fore sight: It is a staff reading taken on a point whose
elevation is to be determined (minus sight - reading is
subtracted from RL of collimation plane to get RL of point)
6. Levelling terminology
• Intermediate sight: It is a staff reading taken on a point of
unknown elevation between back sight and fore sight (also
called minus sight – the reading is subtracted from the RL of
collimation plane to get the RL of the point)
• Change point or turning point: It is a point on which fore
sight and back sight readings are taken. It indicates the
shifting of the level
• Height of instrument: It is the elevation of the plane of
collimation when the instrument is levelled.
7.
8.
9. Levelling terminology
• Bench mark: It 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
closing point as a check
• Mean sea level: It is the average height of the sea for all
stages of tides. At any particular place it is derived by
averaging the hourly tide heights over a long period of 19
years
• Vertical angle: It is an angle between two intersecting lines
in a vertical plane. One of these lines is horizontal
10. Levelling instruments
• Level
– The purpose of level is to provide a horizontal line of
sight
– Parts: Telescope, Level tube, Levelling head and Tripod
– Types of levels: Dumpy level, Wye (or Y) level, Reversible
level and Tilting level
• Levelling staff
– It is straight rectangular rod having graduations, the foot
of the staff representing zero reading
– Types: Self reading staff and Target staff
16. Methods of levelling
• Differential levelling: To determine the difference in
elevation of two points regardless of the horizontal positions
of the points with respect to each other (fly levelling)
• Profile levelling: It is the method of levelling in which the
elevations of points are determined along some fixed line at
some common interval (also called as longitudinal
sectioning)
• Cross-sectioning: This is the process of taking levels on each
side of a main line at right angles to that line, in order to
determine the vertical c/s of the ground surface
17. Methods of levelling
• Check levelling: The levelling is carried out to check the
reduced levels of points which have been already fixed
(usually carried out at the end of day)
• Reciprocal levelling: when it is not possible to set up the
levelling instrument mid-way between the two points, the
difference in RL’s between the two points is accurately
found out by two sets of observations
• Barometric levelling: This method makes use of phenomenon
that difference in elevation between two points is
proportional to the difference in atmospheric pressures at
these points. These are obtained with the help of barometer
18. Differential levelling
• To determine the elevation of points at some distance
apart
• If two points are not in the range of level at the same
time, the difference in elevation can find by using
turning points
• Methods of differential levelling
– Collimation or height of instrument method
– Rise and fall method
19. Differential levelling – Height of
Instrument method
• In this method, height of instrument is calculated for each
setting of the instrument by adding back sight to the
elevation of the B.M.
• The elevation of reduced level of the turning point is then
calculated by subtracting from H.I. the fore sight
• For the next setting of the instrument, the H.I. is obtained
by adding the B.S. taken on Turning point to its R.L.
• Check: ∑B.S. - ∑F.S. = Last R.L. – First R.L.
20. Differential levelling – Rise and fall method
• H.I. is not required
• In this method, the difference of level between consecutive
points is found by comparing the staff readings on the two
points for the same setting of the instrument
• The difference between their staff readings indicates a rise
or fall according as the staff reading at the point is smaller
or greater than the preceding point
• Check: ∑B.S.- ∑F.S. = ∑Rise - ∑Fall =
Last R.L.– First R.L.
21. Examples
• The following staff readings were observed 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, 2.684 metres. Enter the above
readings in a page of a level book and calculate the R.L. of
points if the first reading was taken with a staff held on a
bench mark of 432.384 m
22. Profile levelling
• The process of determining elevations of points at short
measured intervals along a fixed line
• The fixed line can be the centre line of a railway,
highway, canal or sewer
• The fixed line may be a single straight line or
succession of straight lines or series of straight lines
connected by curves
• Also known as longitudinal sectioning
24. Cross sectioning
• Cross sections are run at right angles to the
longitudinal profile and on either side of it for the
purpose of lateral outline of the ground surface
• The point along the longitudinal section is plotted at
the centre of the horizontal axis
• The points to the left of centre point are plotted to the
left and those to the right are plotted to the right
26. Curvature and Refraction
• The effect of curvature is that the objects sighted
appear lower than they actually are.
• The effect of refraction is to make the objects sighted
appear higher than they actually are.
• Correction for curvature (Cc) is negative
• Correction for refraction is positive
• Curvature correction (m) = [d2/2R] where, R = 6370 km
• Refraction correction (m) = [1/7] Cc where, d is in km
• Combined correction = [6/7] Cc
27.
28. Examples
• Find the correction for curvature and for refraction for
a distance of (a) 1200 metres (b) 2.48 km. Also find the
combined correction for curvature and refraction
• An observer standing on the deck of a ship just sees a
light house. The top of the light house is 42 metres
above the sea level and the height of the observer’s eye
is 6 metres above the sea level. Find the distance of the
observer from the light house.
29. Reciprocal levelling
• It is a method used to determine the difference of elevation
correctly between two points spaced at a long distance
apart and when the level cannot be set up midway between
the two points
• This situation arises when two points whose difference of
elevation is to be found out are located on opposite banks of
a river or valley
• The error due to curvature and refraction and line of
collimation not remaining parallel to the bubble line can be
eliminated by this levelling
30. Reciprocal levelling
• True difference in elevation is equal to mean of the two
apparent differences in elevations obtained by reciprocal
observations: H = ½ {(ha – hb) + (ha’ – hb’)}
31. Examples
• In levelling between two points A and B on opposite banks of a
river, the level was set up near A, and the staff readings on A
and B were 1.285 and 2.860 m respectively. The level was
then moved and set up near B and the respective readings on
A and B were 0.860 and 2.220. find the true difference of
level between A and B.
• Two points A and B are 1530 m apart across a wide river. The
following reciprocal levels are taken with one level. The error
in the collimation adjustment of the
level is -0.004 m in 100 m. Calculate
the true difference of level between
A and B and the refraction.
Level at Readings on
A B
A 2.165 3.810
B 0.910 2.355
32. Errors in levelling
• Instrumental
– Error due to imperfect adjustment, sluggish bubble,
movement of objective slide, defective joint and rod not
of standard length
• Natural
– Earth’s curvature, atmospheric refraction, variations in
temperature, settlement of tripod or turning points, wind
vibrations
• Personal
– Mistakes in manipulation, rod handling, reading the rod,
errors in sighting, mistakes in recording
