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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.
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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.
Burnaby Building L 52 Site: …………………………………. Instrument: …………………………………. 07/10/98 M.A.R. Date: …………………………………. Observer: …………………………………. M.A.R. Good Weather: …………………………………. Booker: …………………………………. TBM 10.00m AAD 1.546 11.546 10.000 11.402 9.984 C.P. 1.562 1.418 Point 1 1.390 10.012 10.121 GL Struct. Lab Door 1.281 -2.420 Top Struct. Lab Door 13.822 1.011 11.092 1.321 CP 10.081 2.009 TBM 9.09m AAD 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
Simple Calculation Check: FS - BS = 1st RL - Last RL 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
Burnaby Building L 52 Site: …………………………………. Instrument: …………………………………. 07/10/98 M.A.R. Date: …………………………………. Observer: …………………………………. M.A.R. Good Weather: …………………………………. Booker: …………………………………. TBM 10.00m AAD 1.546 11.546 10.000 11.402 9.984 C.P. 1.562 1.418 Point 1 1.390 10.012 10.121 GL Struct. Lab Door 1.281 -2.420 Top Struct. Lab Door 13.822 1.011 11.092 1.321 CP 10.081 2.009 TBM 9.09m AAD 9.083 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
Burnaby Building L 52 Site: …………………………………. Instrument: …………………………………. 07/10/98 M.A.R. Date: …………………………………. Observer: …………………………………. M.A.R. Good Weather: …………………………………. Booker: …………………………………. TBM 10.00m AAD 1.546 11.546 10.000 11.402 9.984 C.P. 1.562 1.418 Point 1 1.390 10.012 10.121 GL Struct. Lab Door 1.281 -2.420 Top Struct. Lab Door 13.822 1.011 11.092 1.321 CP 10.081 2.009 TBM 9.09m AAD 9.083 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
Full Calculation Check: IS + FS + (RLs except first) = (each HPC x number of applications)
TBM 10.00m AAD 1.546 11.546 10.000 11.402 9.984 C.P. 1.562 1.418 Point 1 1.390 10.012 10.121 GL Struct. Lab Door 1.281 -2.420 Top Struct. Lab Door 13.822 1.011 11.092 1.321 CP 10.081 2.009 TBM 9.09m AAD 9.083 63.103 0.251 4.892 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.
TBM 10.00m AAD 1.546 11.546 10.000 11.402 9.984 C.P. 1.562 1.418 Point 1 1.390 10.012 10.121 GL Struct. Lab Door 1.281 -2.420 Top Struct. Lab Door 13.822 1.011 11.092 1.321 CP 10.081 2.009 TBM 9.09m AAD 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 < 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 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.
Burnaby Building L 52 Site: …………………………………. Instrument: …………………………………. 07/10/98 M.A.R. Date: …………………………………. Observer: …………………………………. M.A.R. Good Weather: …………………………………. Booker: …………………………………. TBM 10.00m AAD 1.546 11.546 10.000 11.402 9.984 C.P. 1.562 1.418 Point 1 1.390 10.012 10.121 GL Struct. Lab Door 1.281 -2.420 Top Struct. Lab Door 13.822 1.011 11.092 1.321 CP 10.081 2.009 TBM 9.09m AAD 9.083 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
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.
