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. Site:………………………………….Instrument:…………………………………. Date:………………………………….Observer:…………………………………. Weather:………………………………….Booker:…………………………………. Burnaby BuildingL 52 07/10/98M.A.R. Good M.A.R. Top Struct. Lab Door-2.420 13.822 TBM 10.00m AAD 1.546 10.00011.546 C.P. 1.562 9.984 1.418 11.402 Point 1 1.390 10.012 GL Struct. Lab Door 1.281 10.121 CP1.321 10.081 1.011 11.092 TBM 9.09m AAD2.009 9.083 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  FS -  BS = 1st RL - Last RL Simple Calculation Check:

4. Site:………………………………….Instrument:…………………………………. Date:………………………………….Observer:…………………………………. Weather:………………………………….Booker:…………………………………. Burnaby BuildingL 52 07/10/98M.A.R. Good M.A.R. Top Struct. Lab Door-2.420 13.822 TBM 10.00m AAD 1.546 10.00011.546 C.P. 1.562 9.984 1.418 11.402 Point 1 1.390 10.012 GL Struct. Lab Door 1.281 10.121 CP1.321 10.081 1.011 11.092 TBM 9.09m AAD2.009 9.083  FS -  BS = 1st RL - Last RL  3.9754.892 LHS = 4.892 - 3.975 = 0.917RHS = 10.000 - 9.083 = 0.917 Therefore LHS = RHS Therefore Calculations are OK

5. Site:………………………………….Instrument:…………………………………. Date:………………………………….Observer:…………………………………. Weather:………………………………….Booker:…………………………………. Burnaby BuildingL 52 07/10/98M.A.R. Good M.A.R. Top Struct. Lab Door-2.420 13.822 TBM 10.00m AAD 1.546 10.00011.546 C.P. 1.562 9.984 1.418 11.402 Point 1 1.390 10.012 GL Struct. Lab Door 1.281 10.121 CP1.321 10.081 1.011 11.092 TBM 9.09m AAD2.009 9.083 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  3.9754.892

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

7. 1.418 1.546 Top Struct. Lab Door-2.420 13.822 TBM 10.00m AAD 10.00011.546 C.P. 1.562 9.984 11.402 Point 1 1.390 10.012 GL Struct. Lab Door 1.281 10.121 CP1.321 10.081 1.011 11.092 TBM 9.09m AAD2.009 9.083 LHS =  IS +  FS +  (RLs except first)  0.251  4.892  63.103 = 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 = RHSTherefore the calculations for all the RL values are correct.

8. Top Struct. Lab Door-2.420 13.822 TBM 10.00m AAD 1.546 10.00011.546 C.P. 1.562 9.984 1.418 11.402 Point 1 1.390 10.012 GL Struct. Lab Door 1.281 10.121 CP1.321 10.081 1.011 11.092 TBM 9.09m AAD2.009 9.083 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 < AllowableTherefore 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. 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: 3 2 2 Or like this: 2 3 2 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: 2 2 3 We must not correct the initial Reduced Level. We apply the same correction to all readings up to and including each foresight.

10. Site:………………………………….Instrument:…………………………………. Date:………………………………….Observer:…………………………………. Weather:………………………………….Booker:…………………………………. Burnaby BuildingL 52 07/10/98M.A.R. Good M.A.R. Top Struct. Lab Door-2.420 13.822 TBM 10.00m AAD 1.546 10.00011.546 C.P. 1.562 9.984 1.418 11.402 Point 1 1.390 10.012 GL Struct. Lab Door 1.281 10.121 CP1.321 10.081 1.011 11.092 TBM 9.09m AAD2.009 9.083 x We cannot correct the given TBM value 10.000 2 5 5 5 5 7 Corrections are applied with a +ve or -ve sign depending on the sign of the misclosure 9.986 10.017 10.126 13.827 10.086 9.090 We MUST end up with the correct final reduced level.

11. 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