Levelling in surveying is the process of determining the height of one level relative to another. It is used to establish the elevation of a point relative to a datum, or to establish a point at a given elevation relative to a datum

1. Topic 2 : Levelling

2. How levelling is conducted
In the figure below the height (or reduced level) of A is known and the heights of B
and C need to be estimated.
To determine the height of point B a level is set up at position I1 is between A and
B. staff readings R1 and R2 are taken. Since the reduced level of A is known (RLA)
the height of the line of sight or height of the plane collimation (HPC) at I1 is:
1 1
HPC at I RL R
A
= +

3. To obtain the reduced level at B (or RLB):
The direction of the levelling is from A to B. Reading R1 is taken with the level
facing in the opposite direction, for this reason it is called a back sight (BS).
Reading R2 is taken with the level facing in the direction from A to B, for this reason
it is called a fore sight (FS).
The change in height from A to B, in magnitude and sign, is given by the difference
of the two staff readings. Because R1 is bigger than R2, (R1 – R2) is positive and is
know as a rise.
To obtain the height of C the level is moved to a new position I2. A back sight is
taken at B (R3) and a foresight at C (R4) the reduced level of C is:
2 1 2 1 2
RL HPC - R (RL R ) - R RL + (R R )
B A A
= = + = −
3 4
RL RL (R R )
c B
= + −

4. In this case R4 is bigger than R3 , (R3 - R4) is negative and is known as a fall.
At point B, both a FS (R2) and a BS (R3) have been taken from different instrument
positions this is called a change point.
When calculating a rise or fall this is always given by (back sight – foresight). If
this is positive a rise is obtained and if negative a fall is obtained.
A back sight is the first reading taken after the level has been set up, a foresight is
the last reading taken at an instrument position.
Any readings taken between a back sight and a foresight are known as
intermediate sights.

5. Example

6. 1. The level is set up at some convenient position I1 and BS of 2.191m is taken to
TBM 1.
2. The staff is then moved to points A and B in turn and intermediate sights of
2.505m and 2.325m are taken
3. A change point must be used in order to reach point D.
4. The position of the change point is at C, the staff is moved to this and a FS of
1.496m is taken
5. While the staff remains at C, the instrument is moved to another position, I2
6. A BS of 3.019m is taken from the new level position to the staff at change point
C
7. The staff is moved to D and E in turn and readings of 2.513m (IS) and 2.811m
(FS) are taken where E is another change point (CP)
8. The last step is to move the level to I3 , a BS of 1.752m taken to E and a FS of
3.824m is taken to TBM 2.

7. The final staff position is at a TBM, this is most important as all levelling field work
must start at and end at a bench mark – otherwise it would be difficult to detect
errors when levelling.
When levelling, all readings must be identified as back sight, fore sight or
intermediate sight.
Calculating reduced levels
Two methods of calculating reduced levels:
1. Rise and fall method
2. The height of collimation method

8. Rise and fall method
Example: calculate the reduced level of points A to E in the previous example
using the rise and fall method.
Solution: all the readings for the survey from A to E are shown in the table below.
These measurements would be taken from the field book used on site. Each row of
the field book corresponds to a staff position and which is shown in the remarks
column.
The calculations for this method follow a point by point basis starting at TBM1.

9. From TBM1 to A there is a small fall. A BS of 2.191m was recorded at TBM1 and
an IS of 2.505. The fall from TBM1 to A is given by (2.191-2.505) = -0.314m. The
negative sign indicates that there is a fall and this is entered in the fall column.
This fall values is subtracted from the RL of TBM1 as (49.873-0.314) = 49.559m
The procedure is repeated for point B with the height difference given by
2.505-2.325 = +0.180m. This positive sign demonstrates a rise from point A and
the RL at B is given by (RLA + 0.180m) = 49.739m
The rise from B to C up to the first change point is (2.325 – 1.496) = +0.829m. To
continue the level table height change from C to D is (3.019 – 2.513) = +0.506m
This step by step procedure is repeated until the reduced level of TMB2 is
calculated.
When the initial RL column is completed a check on the arithmetic is applied:
ΣBS – ΣFS = ΣRises – ΣFalls = Last initial RL and First RL
The difference between the calculated and the known values of TBM2 is -0.006m.
This is known as the misclosure. If the misclosure is greater than an allowable
limit the survey needs to be repeated.
The usual method of correction is to apply an equal but cumulative adjustment
opposite to the misclosure. In this case a correction of +0.006m/3 instrument
positions = +0.002m is applied

10. Height of collimation method
Example: calculate the reduced levels of the previous examples using the height of
collimation method.
This method is based on the calculation of height of plane collimation (HPC) for
each instrument position.

11. If the BS taken on TBM1 is added to the RL for TBM1 then the HPC for the
instrument position I1 is obtained. i.e. 49.873 + 2.191 = 52.064m. This is then
entered into the HPC column.
To obtain the initial RLs of A, B and C the staff readings at those points are
subtracted from the HPC:
RLA= 52.064 – 2.505 = 49.559m
RLB = 52.064 – 2.325 = 49.739m
RLC = 52.064 – 1.496 = 50.568m
At point C (a change point) the instrument is moved to position I2 and a new HPC
is established by taking a BS onto a point C. This BS staff reading added to RLc
yields the new HPC for position I2 , i.e. 50.568 + 3.019 = 53.587m
This procedure is continued until the initial RL of TBM2 is obtained. The arithmetic
check applied in this case is:
BS + FS = Last initial RL - First RL
∑ ∑

12. This test only checks the FS and BS calculations and another check must be
applied to account for the IS readings:
Any acceptable misclosure in the survey is redistributed as for the rise and fall
method.
The arithmetic checks must be done for all levelling calculations
When establishing the heights of new TBMs and other important points, only BS
and FS should be taken and the rise and fall method should be used.
The HPC method of calculation can be much quicker when a lot of intermediate
sights have been taken and it is a good method to use when mapping or setting
out where many readings are often taken from a single instrument position.
A disadvantage of the HPC method is that the check on reduced levels calculated
from IS can be lengthy and there is a tendency for it to be omitted.
IS + FS + RLs (except the first) = (each HPC * number of applications)
∑ ∑ ∑ ∑

13. Precision of levelling
As with all techniques used in engineering surveying it is important to estimate how
accuracy of the measurements taken.
An assessment of the quality of levelling can be made by calculating the
misclosure for a line of levels. This is determined by comparing the reduced level
of the closing bench mark with the level obtained for it by calculation from the staff
readings.
On construction sites and other engineering projects, levelling is usually carried out
over short distances and it can involve a lot of instrument positions. The allowable
misclosure for a line of levels is given by:
Allowable misclosure =
Where, m is a constant and n is the number of instrument positions used.
The value most often used for m is 5mm
m n
±

14. When the misclosure obtained from staff readings is compared to the allowable
misclosure, if miscloure is greater than the allowable value the levelling is rejected
and must be repeated.
If the misclosure is less than the allowable value the levelling is accepted and the
levelling is adjusted.
The value of m depends on the site conditions. For example if the levels found are
to be used for earth work excavations m might be 30mm. For setting out steel and
concrete structures excavations m might be 3mm. In some cases m is specified in
the contract documents.
Specifications for levelling are also given in:
BS5964: building setting out and measurement
ICE Design and Practice Guide: The management of setting out in construction
BS5606: Guide to accuracy in building

15. Sources of error in levelling
There are three main groups of errors that can occur when levelling. The most
common errors fall into one of the following groups:
1. Errors in the equipment
2. Field or on-site errors
3. The effects of curvature and refraction on levelling
Errors in the equipment
Collimation error
This can be a serious error in levelling if the sight lengths from one instrument
position are not equal, since the collimation error is proportional to the
difference in these. So, in all types of levelling all types of levelling, sight
lengths should be kept equal, particularly back sights and fore sights and
before using any level it is advisable to carry out a two-peg test to ensure the
collimation error is within acceptable limits.

16. Compensator not working
For an automatic or digital level, the compensator is checked by moving a foot
screw slightly off level, by tapping the telescope gently or by pushing the
compensator check lever to ensure that a reading remains constant. If any of the
checks fail then the compensator is not working properly and needs to be repaired.
Parallax
This effect must be eliminated before staff readings are taken.
Defects of the staff
The base of the staff should be checked to see if it has become worn – if this is the
case then the staff has a zero error. This does not affect height differences if the
same staff is used for all the levelling, but introduces errors if two staffs are being
used for the same series of levels.
When using multi-section staff, it is important to ensure that it is properly extended
by examining the graduations on the other side of each section as it is extended. If
any of the sections become loose the staff should be returned for repair.

17. Tripod defects
The stability of tripods should be checked before any fieldwork commences by
testing to see if the tripod head is secure and that the base of each leg are secure.
Field or on-site errors
Staff not vertical
As the staff is used to measure a vertical difference between the ground and the
plane of collimation, failure to hold the staff vertical will give an incorrect readings.
Since the staff is held vertical with the aid of a vertical bubble, this should be
checked at frequent intervals and adjusted if necessary.
Unstable ground
When the instrument is set up on soft ground and bituminous surfaces on hot
days, an effect that is often overlooked is that the tripod legs may sink into the
ground or rise slightly when the reading is being taken. This then will alter the
height of collimation and it is advisable to choose firm ground on which to set up
the level and the tripod, and to ensure that the tripod is pushed well into the
ground.

18. Handling the instrument and tripod
As well as the vertical displacement, the plane of collimation of a level may be
altered for any set-up if the tripod is held or leant against. When levelling, avoid
contact with the tripod and only use the level by light contact.
Instrument not level
For automatic and digital levels this source of error is unusual, but for a tilting level
in which the tilting screw has to be adjusted for each reading, this is a common
mistake. The best procedure here is to ensure that the main bubble is centralised
before and after the reading is taken.
Reading and booking errors
Many mistakes can be made during the booking of staff readings taken with an
automatic or tilting level, and the general rule is that staff readings must be
carefully entered into the levelling table or field book immediately after reading.
Weather conditions
In strong winds, a level can become unusable because the line of sight is always
moving and it is also difficult to hold the staff steady. For these reasons, it is not
possible to take reliable readings under these conditions which should be avoided
when levelling.

19. Errors at Change Points
Choose change points carefully, use manhole covers, kerbs and other hard
surfaces to ensure that the base of the staff remains at the same height in between
a back sight and fore sight.
When the tripod is set up in soft ground or on tarmac on hot days it may sink into
the ground or rise slightly when readings are taken. This alters the height of
collimation and causes errors. Try to set the level up on firm ground and always
push the tripod legs well into the ground.
The height of collimation may be altered if the tripod is held or pressed down
Do not lean on the level, If the tripod is knocked it is necessary to re-level the
instrument and repeat all the readings taken from that instrument position. Marking
or recording the position of each change point on a long line of levels is advisable.
If this is not done and the tripod is knocked all of the levelling will have to be
repeated.

20. Curvature and refraction
Over long distances level and horizontal lines through an instrument will diverge
because level lines follow the curvature of the Earth. This is a possible source of
error in levelling since all readings are taken along horizontal lines instead of level
lines. The difference between a horizontal and level line is know as curvature and
is given by
c = 0.0785 D2
Where, c = curvature in meters, D = sighting distance in km

21. The correction for length of sight of 100m is less than 1mm. This correction is
ignored for most levelling.
The effect of refraction of the line of sight is to bend it towards the Earth. This is
also ignored in most levelling. Whatever sight lengths are used, the effects of
curvature and refraction will cancel if the sight lengths are equal.
How to Reduce the Chance of Errors Occurring
Levelling should always start and finish at bench marks so that misclosures can be
detected. When only one bench mark is available, levelling lines must be run in
loops starting and finishing at the same bench mark
Where possible, all sights lengths should be below 50 m. The staff must be held
vertically by suitable use of a circular bubble or by rocking the staff and noting the
minimum reading. BS and FS lengths should be kept equal for each instrument
position.

22. For engineering applications, many intermediate sights may be taken from each
set-up – under these circumstances it is important that the level has no more than
a small collimation error.
For automatic and tilting levels, staff readings should be booked immediately after
they are observed.
Use a digital level where possible as it takes staff readings automatically
The rise and fall method of reduction should be used when heighting reference or
control points and the HPC method should be used when setting out.

23. Other levelling methods
Inverted levelling
This is a levelling technique that is used to obtain the heights of points above the
line of sight such as ceilings and undersides of bridges. To obtain these, the staff
is held upside down in an inverted position with its base on the elevated points. An
inverted staff reading is booked in a level table with a minus sign.
When calculating heights with these readings, the normal procedure is followed
taking into account the minus sign. Never use an inverted staff reading as a
change point because it is difficult to keep the staff in the same place for more than
one reading.

24. Exam Question: Supplement 2006 Q3
A client has asked for an as-constructed drawing of a recently built industrial
building. As part of the survey the following series of levels are taken. Prepare a
report for the client showing the reduced levels of the manhole inverts and the
calculated gradients on the sewer lines, and the soffit levels on the building
gutters.

25. Example 2
Lets repeat the reduced levels part of the previous exam question assuming we
were asked to use the rise and fall method instead