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:………………………………….Instrument:…………………………………. Date:………………………………….Observer:…………………………………. Weather:………………………………….Booker:…………………………………. Burnaby BuildingL 52 07/10/98M.A.R. Good M.A.R. Top Struct. Lab Door TBM 10.00m AAD C.P Point GL Struct. Lab Door CP TBM 9.09m AAD The RL value of 9.083m is our measured and calculated value. It should be 9.09m.This gives an actual misclosure of = m 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  FS -  BS = 1st RL - Last RL Simple Calculation Check:

Site:………………………………….Instrument:…………………………………. Date:………………………………….Observer:…………………………………. Weather:………………………………….Booker:…………………………………. Burnaby BuildingL 52 07/10/98M.A.R. Good M.A.R. Top Struct. Lab Door TBM 10.00m AAD C.P Point GL Struct. Lab Door CP TBM 9.09m AAD  FS -  BS = 1st RL - Last RL  LHS = = 0.917RHS = = Therefore LHS = RHS Therefore Calculations are OK

Site:………………………………….Instrument:…………………………………. Date:………………………………….Observer:…………………………………. Weather:………………………………….Booker:…………………………………. Burnaby BuildingL 52 07/10/98M.A.R. Good M.A.R. Top Struct. Lab Door TBM 10.00m AAD C.P Point GL Struct. Lab Door CP TBM 9.09m AAD This Simple Check does not check the calculations for RL values calculated from IS NOT CHECKED NOT CHECKED NOT CHECKED  FS -  BS = 1st RL - Last RL 

 IS +  FS +  (RLs except first) =  (each HPC x number of applications) Full Calculation Check:

Top Struct. Lab Door TBM 10.00m AAD C.P Point GL Struct. Lab Door CP TBM 9.09m AAD LHS =  IS +  FS +  (RLs except first)    = = RHS =  (each HPC x number of applications) = (11.546x x x1) = ( )= Therefore LHS = RHSTherefore the calculations for all the RL values are correct.

Top Struct. Lab Door TBM 10.00m AAD C.P Point GL Struct. Lab Door CP TBM 9.09m AAD Now we can look at the magnitude of the misclosure We have already seen that the Actual misclosure = = m 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 < AllowableTherefore 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. 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 could divide 7 between 3 like this: Or like this: 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. 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 cannot divide our 7mm misclosure evenly between 3 positions, but we can do our best (we do not use fractions of a millimetre). Or like this: We must not correct the initial Reduced Level. We apply the same correction to all readings up to and including each foresight.

Site:………………………………….Instrument:…………………………………. Date:………………………………….Observer:…………………………………. Weather:………………………………….Booker:…………………………………. Burnaby BuildingL 52 07/10/98M.A.R. Good M.A.R. Top Struct. Lab Door TBM 10.00m AAD C.P Point GL Struct. Lab Door CP TBM 9.09m AAD x We cannot correct the given TBM value Corrections are applied with a +ve or -ve sign depending on the sign of the misclosure We MUST end up with the correct final reduced level.

Calculation checks  FS -  BS = 1st RL - Last RL  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. Simple check Full check