Levelling
Principle
operation required in the determination of
heights of points on the surface of the Earth
Elementary Land Surveying
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Equipment
1. Level with tripod (device
to gives a truly
horizontal line)
2. Levelling staff (a suitably
graduated staff for
reading vertical heights)
3. Chain/Tape (to enable
the points leveled to be
located relative to each
other on a map)
4. Change plate (staff base
plate)
5. Staff bubble
Elementary Land Surveying
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1
Elements of Surveyor’s Level
1. Telescope
Diaphragm – plane glass on
which a series of line is
etched (cross-hairs)
Parallax – in focusing the real
image formed by the
objective lens is made to lie in
the same plane as diaphragm
Procedure of focusing:
a) Adjusting eyepiece to bring
diaphragm into sharp focus
b) Adjust focusing screw until no
parallax
Elementary Land Surveying
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Elements of Surveyor’s Level
2. Compensating Device in
Automatic Level
The telescope need only
be approximately
levelled and then a
compensating device
corrects for the residual
mislevelment
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2
Levelling Staff
1. Sectional and assembled
by slotting onto one
another vertically
2. Made of aluminium alloy
3. E-shaped graduation
(reading to 1mm for
ordinary levelling)
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Precision Levelling Staff
1. Used for more
accurate work
(accuracy to 0.1mm in
use with precise level)
2. Spring-mounted at the
top
3. Made of invar alloy
(iron + nickel) which
has a lower coefficient
of expansion –
unaffected by
temperature effects
Elementary Land Surveying
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3
Levelling Terminology
1. Level line is a surface
which is at a constant
height relative to Mean
Sea Level (MSL) and is a
curved line
2. Horizontal line is
tangential to the level
line at any particular
point and is
perpendicular to the
direction of gravity.
Over short distance, the 2
lines are taken to
coincide
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Levelling Terminology (con’t)
3. Datum
A level line is chosen in which the elevation of
all points is referred
a) Mean Sea Level (MSL) is the mean of tidal
height over a period of time (> 19 years)
b) Principal Datum Hong Kong (PDHK) – most of
the works in HK refer to this. It is 1.230m
below MSL (revised in June 1984)
c) Chart Datum (CD) is a tidal datum for marine
works and navigation
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4
Relationship among different datums
(Source: Lands Department, No Date)
Elementary Land Surveying
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Levelling Terminology (con’t)
4) Bench Marks
Points of known
elevation above PDHK
a) Bench Mark (BM) –
established on vertical
surfaces such as walls
of buildings or
substantial structures
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5
Levelling Terminology (con’t)
4. Bench Marks (con’t)
b) Temporary Bench Marks
(TBM) – constructed at
locations on site or off
site, where the level of
the mark is calculated
from PDHK
5. Reduced Level (RL) –
the height of a point
relative to PDHK
6. Height of Collimation is
the height of collimation
above PDHK
+5.00
TBM
+10.00
Elementary Land Surveying
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Levelling Terminology (con’t)
7. Backsight (BS) – 1st sight taken after the level has been set up. It is
also a sight taken to a point whose height above HKPD is known
8. Foresight (FS) – last sight taken before moving the level. It is also a
sight taken to a point whose height is required to carry on the line
of levels
9. Intermediate Sight (IS) – other staff readings taken between BS and
FS
10. Change Point (CP) – the staff position at which a FS and then a BS
readings are taken
BS
FS
IS
CP
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6
Levelling Terminology (con’t)
FS
BS
FS
IS
IS
BS
Elementary Land Surveying
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Field Procedure
1. The level is set up at P where BM may be observed and
readings taken at points A, B, C and D
a) The 1st reading (BS) made with the staff on a point of known
RL
b) The staff is now held at points A, B and C (ISs) in turn, and
record the readings
c) A change point (CP) is chosen at D, owing to the nature of the
ground and take the reading (FS)
Elementary Land Surveying
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7
Field Procedure (con’t)
2. The staff remains at point D. The level is moved to Q, set up and
levelled
a) Taking the reading on the staff at the change point D (BS)
b) Followed by IS with the staff on E, F and G until a further change
becomes necessary
3. This procedure is repeated until all the required levels have been
obtained
4. The final staff position is at a point of known RL
Elementary Land Surveying
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Procedure in Levelling
1. Height of Collimation Method
¾ 1st find the height of the line of collimation above the datum
Height of collimation (HC) = 128.480 + 3.222 = 131.702m PD
a) level at B (rise from A to B)
= height of collimation – reading at B = 131.702 – 1.414
= 130.288m PD
b) level at B (rise from A to B)
= height of collimation – reading at B = 131.702 – 3.484
= 128.218m PD
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8
Procedure in Levelling
2. Rise and Fall Method
¾ Rise – 2nd reading < 1st reading
¾ Fall - 2nd reading > 1st reading
b) from A to B
a) from A to B
1st reading – 2nd reading
= 3.222 – 1.414 = 1.808 (rise)
level at B (rise from A to B)
= level at A + rise
= 128.480 + 1.808
= 130.288mPD
1st reading – 2nd reading
= 3.222 – 3.484 = -0.262 (fall)
level at B (fall from A to B)
= level at A - fall
= 128.480 + 0.262
= 128.218mPD
Elementary Land Surveying
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Booking and Calculation
1) Rise and Fall Method – each reading is entered on a different line in the
appropriate column, except at a change point, where a FS and BS occupy the
same line. To check, ΣBS - ΣFS = ΣRise - ΣFall = Last RL – First RL
BS
IS
FS
Rise
Fall
RL
Remarks
98.760
BM
1.283
97.477
A
98.415
B
0.145
98.270
C
0.432
97.838
D (CP)
0.663
1.946
1.008
0.938
1.153
2.787
1.585
2.270
0.517
98.355
E
1.218
1.052
99.407
F
0.646
0.572
99.979
G
2.231
3.079
3.450
1.860
99.979
2.231
1.860
98.760
1.219
1.219
1.219
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9
Booking and Calculation (con’t)
2) Height of Collimation Method – the collimation height is obtained by
adding the staff reading, which must be a BS, to the known RL of the point on
which the staff stands. To check, ΣBS - ΣFS = Last RL – First RL
BS
IS
FS
Collimation
RL
Remarks
99.423
98.760
BM
1.946
97.477
A
1.008
98.415
B
1.153
98.270
C
97.838
D (CP)
98.355
E
0.663
2.787
1.585
100.625
2.270
1.218
3.450
99.407
F
0.646
99.979
G
2.231
99.979
2.231
98.760
1.219
1.219
Elementary Land Surveying
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Comparison
Rise and Fall Method
¾ More accurate
¾ More calculation
¾ Intermediate RLs are known
Height of Collimation Method
¾ Quicker
¾ Good for a lot of ISs
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10
Accuracy in Levelling
For normal engineering works and site surveys
Allowable misclosure = ± 5 √ n mm
where n = no. of instrument positions
OR
Allowable misclosure = ± 12 √ k mm
where k = length of levelling circuit in km
If actual misclosure > allowable misclosure,
levelling should be repeated
If actual misclosure < allowable misclosure,
misclosure should be equally distributed equally
between the instrument positions
Elementary Land Surveying
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Summary of Levelling Fieldwork
For levelling fieldwork, the following practice should be
adhered to in order to improve the accuracy of the
levelling works.
1. Levelling should always start and finish at points of
known RL so that misclosure can be detected
2. Where possible, all sight lengths should be below 60 m
3. The staff must be held vertically by suitable use of a
bracket bubble
4. BS ≅ FS Lengths
5. Reading should be booked immediately after they
are observed. Important readings, particularly readings
at change points, should be checked
6. The rise and fall method of reduction should be used if
possible, especially for control works
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11
Collimation Error
if level is set up, levelled and the line of sight or
collimation is not truly horizontal, it will sweep out a
cone as it is rotated.
this cone will be either above or below the horizontal
plane
Staff
Horizontal Line
Level
Line of Sight
Elementary Land Surveying
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Permanent Adjustment – Two Peg Test
1. On fairly level ground, set 2 points A and B, a maximum of 60m
apart. Let this distance be L metres
2. Set up the level exactly midway between the points at point C and
level carefully
3. Place a levelling staff at each peg in turn and obtain readings S1
and S2
S1 – S2 = (S1’ + x ) – (S2’ + x) = S1’ – S2’
= true difference on height between A and B
X is the error due to collimation error (inclination of the collimation line by
angle α
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12
Permanent Adjustment – Two Peg Test
4. Move the level so that it is L/10 metres from point B at
D. Take readings S3 and S4
Apparent difference in height between A and B = S3 – S4
If there is any difference between the apparent and true value,
e = (S1 – S2) – (S3 – S4) m per L metres
(e should be less than ±0.5mm per 10 m for average precision)
Elementary Land Surveying
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Permanent Adjustment – Two Peg Test
5. Any error e of the level should be adjusted using the
adjusting screw with the collimation line altered to the
correct staff reading
For example, to adjust the level with instrument at D
and staff at A,
S4’ = S4 – e(L/10 + L) / L
6. The test should be repeated to ensure that the
adjustment has been successful
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13
Two Peg Test - Example
The reading obtained from a two-peg test
carried out on an automatic level with a single
levelling staff set up alternately at 2 pegs A and
B placed 60m apart are as follows:
1. With the level midway between A and B
Staff reading at A = 1.283m
Staff reading at B = 0.860m
2. With the level positioned 5 m from peg B on
the line produced from AB
Staff reading at A = 1.612m
Staff reading at B = 1.219m
Find the collimation error (e) and corrected
staff reading (S4’)?
Elementary Land Surveying
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Errors in Levelling
Errors in Equipment
1. Collimation Error
ƒ
ƒ
Keep sight distance roughly equal
Check by two peg test regularly
2. Parallax Error
ƒ
Move eye with respect to eyepiece, see if any relative movement
between target & cross-hairs, if so adjust eyepiece
3. Defects of Staff
ƒ
ƒ
Zero error, check by tape, does not affect height difference if one
staff is used
3-section staff should be properly extended
4. Tripod
ƒ
ƒ
Robust, properly tightened
On soft ground, force it firmly into the ground
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14
Errors in Levelling (con’t)
Field Errors
1. Staff not vertical
ƒ
Staff is held vertical with aid of a bracket bubble
2. Unstable ground
ƒ
A change plate should be used
3. Instrument not level
ƒ
Ensure that the circular bubble is centered before and after a
reading is taken
4. Weather condition
ƒ
ƒ
Avoid windy condition
Avoid line of collimation close to the ground in hot weather
5. Checking
ƒ
ƒ
Start and finish at points of known height
Run a loop
Elementary Land Surveying
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Errors in Levelling (con’t)
Reading and Booking Errors
1. Misreading of the staff graduation
ƒ
Keep sight distance < 60 m, otherwise it becomes
impossible to take accurate readings
2. Erroneous Booking
ƒ
ƒ
Carefully entered the reading into the fieldbook
always read the staff, book the observation and then
check that the recorded entry agrees with a second
reading through the telescope.
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Error adjustments in levelling calculations
Elementary Land Surveying
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Error adjustments in levelling calculations
1. Rise and Fall Method
BS
IS
FS
Rise
Provisional
RL
Correction
Corrected
RL
Remarks
32.640
-
32.640
BM
32.893
0.003
32.896
CH0
0.318
32.575
0.003
32.578
CH20
Fall
1.944
1.691
0.253
2.009
0.367
2.114
4.425
0.833
31.742
0.003
31.745
CH40
1.223
2.842
0.856
30.886
0.005
30.891
CH60
1.347
0.124
30.762
0.005
30.767
CH80
0.775
0.572
31.334
0.005
31.339
CH100
0.816
1.298
32.632
0.008
32.640
BM
4.433
2.123
2.131
32.632
4.433
2.131
32.640
-0.008
-0.008
-0.008
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Error adjustments in levelling calculations
2. Height of Collimation Method
BS
Collimation
Provisional RL
Correction
Corrected
RL
Remarks
34.584
32.640
-
32.640
BM
32.893
0.003
32.896
CH0
32.575
0.003
32.578
CH20
31.742
0.003
31.745
CH40
1.223
30.886
0.005
30.891
CH60
1.347
30.762
0.005
30.767
CH80
31.334
0.005
31.339
CH100
0.816
32.632
0.008
32.640
BM
4.433
32.632
IS
FS
1.944
1.691
2.009
0.367
2.842
2.114
4.425
0.775
32.109
33.448
4.433
32.640
-0.008
-0.008
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Error adjustments in levelling calculations
Note:
¾ Misclosures = -0.008m
¾ No. of instrument station = 3
¾ Correction is +0.0027m and is added to the RL found
from each instrument station
¾ No adjustment is applied to the initial BM, since this
level cannot be altered.
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Additional Levelling Methods
1. Inverted Staff
¾ Used to determine the RL of
points, such as the soffit of a
bridge, underpass or canopy
¾ The inverted staff reading is
booked with a negative sign
BS
IS
FS
Rise
Fall
1.750
-3.100
4.850
1.490
4.590
-4.210
-2.560
1.640
8.900
Remarks
BM
77.150
A) Frame (lift-shaft)
72.560
B) Floor Level
76.610
C) Canopy
8.410
68.200
D) Kerb
13.000
68.200
4.050
4.200
-2.460
RL
72.300
1.640
13.000
72.300
-4.100
-4.100
-4.100
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Example
BS
IS
FS
1.432
-0.874
-1.235
Collimation
RL
31.432
30.000
TBM A
31.793
32.667
Top of wall
-1.107
0.558
32.900
Arch soffit
1.383
30.410
B
0.148
30.410
0.148
30.000
0.410
BS
Remarks
0.410
IS
FS
Rise
Fall
1.432
-0.874
-1.235
-1.107
2.667
0.233
1.383
0.558
0.148
2.900
RL
Remarks
30.000
TBM A
32.667
Top of wall
32.900
Arch soffit
2.490
30.410
B
2.490
30.410
0.148
2.490
30.000
0.410
0.410
0.410
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Additional Levelling Methods
2. Reciprocal Levelling
¾
¾
By means of reciprocal levelling, the need for applying
curvature and refraction corrections may be avoided
2 similar instruments in correct adjustment are required
H = ((a1 – b1) + (a2 – b2)) / 2
Elementary Land Surveying
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Example
In levelling across a river, reciprocal levelling
observations gave the following results for staffs
held vertically at X and Y from level stations A
and B on each bank respectively:
¾ Staff
¾ Staff
¾ Staff
¾ Staff
reading
reading
reading
reading
of
of
of
of
X
X
Y
Y
from
from
from
from
A
B
A
B
=
=
=
=
1.753m
2.080m
2.550m
2.895m
If the RL of X is 90.370m PD, calculate the RL of
station Y.
(note: Y is lower than X)
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19
Effects of Earth’s Curvature and Atmospheric Refraction
A. Earth’s Curvature
In Δ,
L2 + R2 = (R + c)2
L2 = (R + c)2 - R2
L2 = 2cR + c2
L2 ≅ 2cR
c ≅ L2 / 2R (km)
= 0.0785 L2 (m)
where
radius of the Earth,
R ≅ 6370 km
and L in km
Elementary Land Surveying
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Effects of Earth’s Curvature and Atmospheric Refraction
Refraction
¾ Line of sight is not really horizontal and bent
downwards towards the Earth
¾ Value not constant, affected by pressure, temperature,
latitude, humidity etc.
¾ Usually taken as 1/7 and opposite of the correction of
curvature
Combined correction
= 0.0785 L2 * (6/7) = 0.0673 L2 (m)
where L in km
If L = 120m, c = -0.00097m ≅ 0.001m ≅ 1mm
The effect is negligible for ordinary levelling
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Example
A staff is held at a distance of 200m from a level
and a reading of 2.758m obtained. Calculate the
reading corrected for curvature and refraction.
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