Levelling

Levelling (Heighting)
 Levelling is the process of determining the
relative differences in heights between two
or more points on the Earth surface.
 If the height of one point above a certain
reference datum is known, then the height
of other points above the same datum can
be determined

Determination of height differences
ABH
ABH
(B.M) A
B
HA
HB
= HB – HA - Height differences
HB = HA +
MSL
ABH

Used terms
 Mean Sea Level (MSL)/Datum
arbitrary surface to which the observed
height of points may be referred.
 Bench Mark (B.M)
A point of known Reduced Level (R.L.).
Usually a permanent stable reference
point.

used terms
 Vertical line
Direction defined by a plumb line under a pull of gravity OR
The direction followed by a freely falling object
 A level surface (line)
This is a surface such that the direction of gravity is
perpendicular to it at all points. Hence it follows the earth
surface curvature
 A horizontal surface (line)
This will form a tangent to the level surface and
perpendicular to a vertical line at one point.
 Line of Collimation
This is the line of sight defined by the optical centre of the
objective lens and the centre of the cross-hair

Definitions
 Back sight (BS)
The first reading taken by an observer
at every instrument station.
 Foresight (FS)
The last reading taken at an instrument
station

TYPE OF LEVELLING
 Trigonometric levelling
 Barometric levelling
 Hydrostatic levelling
 Spirit levelling

Equipments used in Levelling
 A LEVEL: A device that can give us a
truly horizontal line

Equipments used in Levelling
 A LEVELLING STAFF: A suitable
graduated staff for taking vertical
reading:

Level
There are three types of levels:
 dumpy levels
 tilting levels
 automatic levels
‘The differences between the three types being in the
way in which the instruments are designed to be
adjusted to give a horizontal line’

Classes of Level
Levels normally fall into one of three classes.
 Precise
Very accurate instruments for geodetic or any other very precise levelling.
It should be possible to level such an instrument to within +0.1mm.
 Medium Accuracy
These are used for engineering surveys. They may be tilting or
automatic instruments capable of being levelled within the range
of 1 – 5mm.
 Builders
Low accuracy, short range levelling such as setting out on building sites.
The results obtained with this class of instruments will be well within the
tolerances required on the majority of construction sites. (10mm)

Features of conventional level
consists of the followings;
1) Surveying telescope
2) Bubble tube
3) A body to hold the two together plus other
attachment. E.g. tribrach

Surveying telescope
It has four main parts
 Objective lens
 Focusing lens
 Diaphragm
 Eyepiece lens

A surveying optical telescope
eyepiece
object lensobject lensfocusing lensfocusing lens
diaphragm
Typical diaphragms - in different makes of instrument
cross hairs
focusing screw
Focusing
1. Rotate eyepiece to give a sharp,
clear image of the cross hairs
2. Rotate focusing screw to give a
sharp, clear image of the object
being observed.
The aim of focusing is to remove (eliminate) PARALLAX
line of
collimation

Surveying telescope
Objective lens:
 Usually a combination of convex lens
Produce an image of the object sighted

Surveying telescope
Diaphragm/cross-hair:
 Are crossed lines etched on an adjustable
glass disc secured in the telescope
perpendicular to the line of sight

Surveying telescope
Eyepiece lens:
 The magnifying eyepiece facilitates the
viewing of the diaphragm and the image
produced by the objective lens

Surveying telescope
Focusing lens:
 A concave lens which can be moved inside the
telescope by turning the focusing screws
 It alters the focal length of the objective lens
and therefore the position of the image

Parallax
When focussing any optical instrument it is vitally important
that we eliminate Parallax.
Move the eye up and down (or from left to right) over the
eyepiece of the telescope.
If the cross hairs move relative to the object being observed
then Parallax exists and the focussing is not satisfactory.
Parallax. Is the relative motion between cross-hairs and the
image

Bubble tube
Used for levelling the telescope i.e. making the line of
collimation to be horizontal
Two types of bubble exists;
 Tubular bubble
 Circular bubble

Bubble tube
 Tubular bubble
 The most accurate one and is formed by
taking an arc of circular tube and filling it
with a fluid. E.g. methyl alcohol
 Circular bubble
 Is less accurate than tubular bubble
 Used for rough levelling up of instrument
and also ensuring the verticality of levelling
staff

The levelling Staff
 Nothing than a big ruler
 Used to measure vertical distance
 Staff should be truly vertical
 Graduated such that is possible to read them from over a
long distance.
 The smallest distance graduated on staves is a cm and the
mm are estimated

Reading an E-type levelling staff
Read value at
the
horizontal
cross hair
The value is ?
1.900
1.910
1.920
1.9301.932

Step 1 Staff Slowly Leant
Towards Instrument
Important Note – The person
using the instrument keeps the
staff vertical by use of the
Vertical line in the instrument.
Step 2 Staff Slowly
Tilted away from
Instrument. When
Vertical lowest reading
will be reading recorded
Step 3 Staff Slowly Tilted
away from instrument. Once
past vertical readings will
increase
Removing Staff Reading Errors

Procedure in Levelling
1) Rise and Fall method
2) The height of Instrument method

Rise and Fall method
RL A RL B
A
B
BS FS ABH = BS - FS
Suppose,
If BS > FS, This implies a rise of slope
Suppose,
If BS < FS, This implies there is a fall of slope
consider two points A and B

ABH
ABH
RL A RL B
A
B
BS FS = BS - FS
assuming that, RL A is known,
Then, level at B = Level at A - + Fall/Rise
RL B = RL A +
RL B = RL A - ABH
ABH

The Height of Instrument (HI)
Method
 Line of collimation above the datum is found by
adding the staff reading on a point of known
level
 HI = Known RL + Back Sight

RL A RL B
A
B
C
RL C
BS FS
BS FS
RL A is known
HI =
HI
RL A + BS RL B = HI - FS
(CP)
Now the RL B is known So we can repeat the process
HI =
HI
RL B + BS RL C = HI - FS
Generally : HI = Known RL + Back Sight
Unknown RL = HI - Fore Sight

General Procedures in Levelling
 Consider two distances far apart, AB
How do you do?
Establish change points on the
Line
BS FS
A
B

General procedures in levelling
 Horizontal line generated is more commonly
restricted in slope sites
 We can only measure two points that are below
the line of sight
 To measure height of point above the line of
sight, the instrument has to be moved to
another point or station

 Moving the instrument to another
station
RL A RL B
A
B
C
RL C
BS FS
BS FS

 Movement of the instrument have to be recorded
properly so that when the reduced level (RL) are
calculated they all refer to the same datum.
 This method of levelling is called series levelling.
 The intermediate staff points are called change point
 The intermediate instrument station are called
instrument points

Summary of Levelling Procedure
When the level has been set up we always start with a BS to
a point whose RL is known
- such as an BM
The last reading at any instrument position is always a FS
Either the instrument moves or the staff moves -
never move both
We must always finish levelling at a point of known RL value
- such as an BM
always close your levelling

Procedural Rules
 Always commence and finish a level run on
a Benchmark (B.M. or T.B.M.). The
Benchmark at the start may be different
than that at the finish.
 The length of foresight and backsight
should be as equal as is practical.
 The length of the lines of sight should be
kept less than 50m and more
conventionally 25m.

Procedural Rules
 Staff readings of less than 0.5m should be
avoided to prevent errors due to
atmospheric refraction.
 Change points should be located on suitable
ground, for example the top of a pointed
rock, or a nail placed in a footpath or road.

Booking of Levelling Observation
 Readings observed are booked in a level
book/form
 Reduction of these readings is carried
out in the same book/form
 The two methods are:
 Rise and Fall
 Height of Instrument

The Height of Instrument Method
of Booking
 The procedure is as follows;
BM
B
E
2.20
A
C
D
1.05
2.30 1.15
0.75
2.50
1.00
X
Y
Z

Note
 The First entry is the RL of the BM which is
60.50m
 The 2nd entry is the reading of the staff placed
on BM, booked under column of BS.
 To get the HI, we add the RL of the BM to the
observed BS.
 The staff is moved to A, which is an IS, and
read as 2.05

Note
 To get the RL of A, we deduce 2.05 from
the HI.
 The staff is moved to B, the last
observing station from instrument point
x, i.e. station B. The reading is called
the FS and booked in the same line as
B.

Note
 We can now calculate the RL of
station B as HI – FS = RLB
 The instrument is moved to Y, but the
staff remain on B. the first reading
taken is the BS to B, entered in the
same line to B.

Note
 A new HI is computed as RLB + BSB
= HIY and this is entered on the line
B. this HI is used to calculate the RL
of the IS points and for the change
point D through the FS. The process
is continued until the RL of the last
point is computed

Note
 Finally, the calculation are checked by
adding all the entries in the BS and FS
column and compare the differences
between them with the differences
between the first RL and the Last RL

Carry out Calculation Checks
 BS -  FS = Last RL - First RL
Simple Calculation Check:

Site: …………………………………. Instrument: ………………………………….
Date: …………………………………. Observer: ………………………………….
Weather: …………………………………. Booker: ………………………………….
Burnaby Building L 52
07/10/98 M.A.R.
Good M.A.R.
BS IS FS HPC RL Corr Corr RL Remarks
Top Struct. Lab Door-2.420 13.822
TBM 10.00m AAD1.546 10.00011.546
C.P.1.562 9.9841.418 11.402
Point 11.390 10.012
GL Struct. Lab Door1.281 10.121
CP1.321 10.0811.011 11.092
TBM 9.09m AAD2.009 9.083
This Simple Check does not check the calculations for RL values calculated from IS
NOT
CHECKED
NOT
CHECKED
G
 3.975 4.892
STN
A
B
C
D
E
F

BS IS FS HPC RL Corr Corr RL Remarks
Top Struct. Lab Door-2.420 13.822
TBM 10.00m AAD1.546 10.00011.546
C.P.1.562 9.9841.418 11.402
Point 11.390 10.012
GL Struct. Lab Door1.281 10.121
CP1.321 10.0811.011 11.092
TBM 9.09m AAD2.009 9.083
Now we can look at the magnitude of the misclosure
We have already seen that the
Actual misclosure = 9.083 - 9.09 = -0.007m Is this acceptable ?
Rule of Thumb:
Allowable misclosure = ± 5 N mm Where N is the Number of Instrument Positions
which is the same as Number of BS readings
Therefore our Allowable misclosure = ± 5 3 mm = ± 8.66 say ± 9mm
Therefore Actual < Allowable Therefore our Fieldwork is OK

The Rise and Fall method
 The procedure is as follows;
3.80
A
C
D
2.50
0.60
3.50
1.10
2.45
X Y
Z
BM
B
E
F
G HQ
1.40 0.75
1.65 1.30

 First entry is the RL of BM
 Second entry is the BS taken on B.M, third
entry is the IS at A
 To get the rise of fall between BM and A,
we subtract the reading at A from that of
B.M. since it is positive, means a rise, and
so is booked under column of rise.

 5th entry is the FS at B, to get the slope
between A and B, we subtract IS – FS, it
is positive means a rise
 B is a change point, the BS is taken to B
from instrument station Y. this is booked
under BS column

 From the same instrument station, a FS
to C is taken, the slope is obtained as
BS – FS. It is negative, means a fall,
and is booked under Fall column
 The process is continued to all other
staff positions. When all the Rise and
Falls have been calculated, then we
check by; BS -  FS =  RISE -  FALL

 To get RL of the station, we start with the RL of
the B.M and add the Rise or subtract the Fall of
station below to get the RL of that station.
 A final check is applied by finding the
difference between the RL of last station with
the RL of the first station. This should check
with the value obtained above by
 BS -  FS =  RISE -  FALL = Last RL - First RL

Comparison of the methods
 Rise and Fall method
 Has more arithmetic checks
 Intermediate sight are checked also
 The rise and fall column gives an
impression of the topography along the
line of levels

 Rise and Fall method
 The method is slow, involves a lot of calculations
and is not suitable for job involving intermediate
sights os setting out
 The method is preferred in precise levelling of
establishing the benchmarks because of
complete arithmetic checks it have

 The Height of Instrument Method
 Has less arithmetic check
 Intermediate sights are not checked
 Method is faster, involve less calculations and is
suitable for jobs involving setting out
 Is not preferred in precise levelling for
establishing other benchmarks because of lack
of the complete arithmetic checks

Source of Errors in Levelling
 Can be grouped in three category
1) Instrument Errors
2) Error in handling the instrument
3) Error from natural sources

Instrument Error
a) Collimation error
 Line of sight not horizontal
 The error can either be negative or
positive
 The magnitude depends upon the
distance between the instrument and
the staff

Instrument error
Collimation error
Collimation Error - Line of sight not horizontal
Correct
reading
Actual
reading

Instrument Error
Elimination of Collimation error
 Making the BS and FS distance equal
 Results in error of equal magnitude in both
the BS and FS reading.
 The difference between them to get H
will result in error canceling out

Error in handling the Instrument
a) parallax
 Eliminated by perfect focusing of the telescope
 Focus of Cross Hairs to a sharp setting
:Note: every users parallax focus is different.
 Refocus on Target and check for parallax

 Bubble not exactly centred
 Eliminated by ensuring the bubble is centred
before and after taking the reading
b) Non – verticality of staff
 Eliminated by using a staff fitted with a circular
bubble

c) Error due to displacement of the
instrument
 When tripod is set up on soft ground it may
settle during observations and alter the HI
 Watch out for soft ground under tripod or staff
 Don’t touch (or kick!) tripod

d) Error due to staff movement during the
change of instrument station
 Eliminated by using a foot plate
e) Error in reading the staff and booking the
readings
 Reading the staff against a stadia line
 Omitting a zero, e.g. reading 3.09 instead of
3.009

 Booking reading with number interchanged, e.g. 1.145
instead of 1.415
 Entering reading in a wrong column
 Forgetting to book a reading
 All are eliminated by careful reading on the staff and
booking
 Also help if a booker repeats the readings to the
observer after booking

Natural Causes of Errors
a) Wind
 Cause swinging of the staff
 Vibration of the instrument
 Cause vibration of tripod
Precautions
 Shorten the length of sight
 Stop observation all together

b) Sun
 Cause differential expansion of the Instrument
due to heating up
 Affecting the bubble making it go off centre
 Sighting is impossible when sun shines into the
objective lens
 Cause shimmering of the image due to
overheated ground causing different air masses
convection.

b) Sun
Precautions:
 Shading of the instrument using Umbrella
 Reduce a length of sight
 Avoid sighting to close to the ground, less than
30cm
 Avoid observing when the sun is too hot especially
mid day

c) Curvature of the Earth and Refraction
Curvature of the Earth”
 Line of sight is not a level line but a horizontal
line tangential to a level line
 When sights are long, the deviation of tangent
from a circle becomes appreciable
 Hence, correction must be applied when sights
are long

Curvature of the Earth
 Due to the curvature of the Earth, the line of
sight at the instrument will deviate from a
horizontal line as one moves away from the
level

Correction of Curvature Error
 For a sight length of 100m the effect is
only 1mm.
 Keep Sight lengths under 50m
 the effect is eliminated by using equal
sight lengths for fore- and back sights.

Refraction
 The variable density of the Earth's
atmosphere causes a bending of the ray
from the staff to the level.
 May also be caused by heat emitted by
plant
 The effect of refraction is 1/7 that of
curvature of the earth and acting in
opposite direction.

Levelling

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