Levelling continued

1
Levelling (continued)
This presentation covers booking, reduction,
calculation checks, actual and allowable
misclosure and how we deal with an allowable
misclosure.
The booking example that is used here is covered
in the presentation called Levelling example
in the Surveying Index. The presentation
Levelling Example should be followed before
this presentation.
2
The RL value of 9.083m is our measured and
calculated value.
It should be 9.09m.
This gives an actual misclosure of 9.083 - 9.09
-0.007m
This actual misclosure may be because of
calculation errors or field errors
3
If it is due to calculation errors we MUST NOT
continue.
Therefore the first thing we always do after
reducing our field booking is
Carry out Calculation Checks
4
3.975
4.892
? FS - ? BS 1st RL - Last RL
LHS 4.892 - 3.975 0.917
RHS 10.000 - 9.083 0.917
Therefore LHS RHS Therefore
Calculations are OK
5
NOT CHECKED
NOT CHECKED
NOT CHECKED
3.975
4.892
? FS - ? BS 1st RL - Last RL
This Simple Check does not check the calculations
for RL values calculated from IS
6
Full Calculation Check
? IS ? FS ? (RLs except first)
? (each HPC x number of applications)
7
LHS ? IS ? FS ? (RLs except first)
0.251 4.892 63.103 68.246
RHS ? (each HPC x number of applications)
(11.546x1
11.402x4
(11.546 45.608 11.092)
68.246
11.092x1)
Therefore LHS RHS
Therefore the calculations for all the RL values
are correct.
8
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 lt Allowable
Therefore our Fieldwork is OK
9
We have carried out the calculation checks and
have an acceptable misclosure.
The final stage is to apply a correction
procedure to distribute the actual misclosure.
The actual misclosure was -7mm, so we need to add
7mm in order to correct it.
We can add these 7mm to our Reduced Levels in any
way, but it is best to assumethat the 7mm error
occurred gradually as a set of small
errors,rather than all in one go.
We assume that we made a similar error every time
we set up the instrument.
There are 3 backsights, so we set up the
instrument 3 times.
We cannot divide our 7mm misclosure evenly
between 3 positions, but we can do our best (we
do not use fractions of a millimetre).
We could divide 7 between 3 like this 3 2 2

Or like this 2 3 2
Or like this 2 2 3
Let use choose the middle method. We will give
2mm to the 1st instrument position,an extra 3mm
to the 2nd position, and an extra 2mm to the 3rd
position.
We must not correct the initial Reduced Level.
We apply the same correction to all readings up
to and including each foresight.
10
We cannot correct the given TBM value
x
10.000
2
9.986
5
10.017
5
10.126
5
13.827
5
10.086
7
9.090
We MUST end up with the correct final reduced
level.
Corrections are applied with a ve or -ve sign
depending on the sign of the misclosure
11
Calculation checks
Simple check
? FS - ? BS 1st RL - Last RL
Full check
? IS ? FS ? (RLs except first)
? (each HPC x number of applications)
Check Misclosure
Allowable Misclosure 5 ?N mm. ("Rule of Thumb")
When calculations are checked and if the
misclosure is allowable
Distribute the misclosure.