# Levelling continued

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```					                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.
Site:
Burnaby Building
………………………………….               Instrument:
L 52
………………………………….

Date:         07/10/98
………………………………….               Observer:            M.A.R.
………………………………….

Weather:      Good
………………………………….               Booker:
M.A.R.
………………………………….

BS          IS        FS      HPC       RL        Cor r   Corr RL           Rem arks

1.546                         11.546   10.000                          TBM 10.00m AAD

1.418                 1.562 11.402     9.984                                C.P.
1.390                      10.012                             Point 1
1.281                      10.121                          GL Struct. Lab Door
-2.420                     13.822                           Top Struct. Lab Door
1.011                 1.321   11.092 10.081                                  CP

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
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

Simple Calculation Check:

 FS -  BS = 1st RL - Last RL
Site:
Burnaby Building
………………………………….               Instrument:
L 52
………………………………….

Date:         07/10/98
………………………………….               Observer:            M.A.R.
………………………………….

Weather:      Good
………………………………….               Booker:
M.A.R.
………………………………….

BS          IS        FS      HPC      RL         Cor r   Corr RL           Rem arks

1.546                          11.546   10.000                          TBM 10.00m AAD

1.418                  1.562 11.402     9.984                                C.P.
1.390                      10.012                             Point 1
1.281                      10.121                          GL Struct. Lab Door
-2.420                     13.822                           Top Struct. Lab Door
1.011                 1.321   11.092 10.081                                  CP

 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
Site:
Burnaby Building
………………………………….              Instrument:
L 52
………………………………….

Date:         07/10/98
………………………………….              Observer:            M.A.R.
………………………………….

Weather:      Good
………………………………….              Booker:
M.A.R.
………………………………….

BS          IS        FS      HPC      RL        Cor r   Corr RL          Rem arks

1.546                          11.546   10.000                         TBM 10.00m AAD

1.418                  1.562 11.402     9.984                              C.P.
1.390                      10.012                            Point 1
NOT
NOT
NOT
1.281                      10.121 CHECKED GL Struct. Lab Door
CHECKED
CHECKED
-2.420                     13.822          Top Struct. Lab Door
1.011                 1.321   11.092 10.081                                CP

 3.975     4.892
 FS -  BS = 1st RL - Last RL
This Simple Check does not check the calculations for RL values calculated from IS
Full Calculation Check:

 IS +  FS +  (RLs except first)
=  (each HPC x number of applications)
BS         IS      FS      HPC       RL    Cor r    Corr RL          Rem arks

1.546                      11.546   10.000                      TBM 10.00m AAD

1.418              1.562 11.402      9.984                           C.P.
1.390                     10.012                         Point 1
1.281                     10.121                      GL Struct. Lab Door
-2.420                    13.822                       Top Struct. Lab Door
1.011              1.321   11.092 10.081                              CP

0.251  4.892           63.103
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
+ 11.092x1)      = (11.546 + 45.608 + 11.092)              =     68.246

Therefore LHS = RHS         Therefore the calculations for all the RL values
are correct.
Now we can look at the magnitude of the misclosure

BS      IS       FS      HPC      RL      Cor r   Corr RL           Rem arks

1.546                    11.546   10.000                      TBM 10.00m AAD

1.418            1.562 11.402     9.984                            C.P.
1.390                     10.012                          Point 1
1.281                     10.121                      GL Struct. Lab Door
-2.420                    13.822                       Top Struct. Lab Door
1.011            1.321   11.092 10.081                               CP

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
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 assume
that 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.
Site:
Burnaby Building
………………………………….               Instrument:
L 52
………………………………….

Date:         07/10/98
………………………………….               Observer:            M.A.R.
………………………………….

Weather:      Good
………………………………….               Booker:
M.A.R.
………………………………….

BS          IS        FS      HPC      RL         Cor r   Corr RL          Rem arks
We cannot correct the given TBM value
1.546                         11.546   10.000         x 10.000 TBM 10.00m AAD
1.418                 1.562 11.402     9.984          2     9.986          C.P.
1.390                      10.012         5     10.017        Point 1
1.281                      10.121         5     10.126 GL Struct. Lab Door
-2.420                     13.822         5     13.827  Top Struct. Lab Door
1.011                 1.321   11.092 10.081           5     10.086          CP
2.009             9.083          7     9.090        TBM 9.09m AAD

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
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.

```
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