Minimizing Errors in Levelling: Techniques and Calculations for Reducing Levelling Errors, Summaries of Cost Accounting

Download Minimizing Errors in Levelling: Techniques and Calculations for Reducing Levelling Errors and more Summaries Cost Accounting in PDF only on Docsity! i] NOTTINGHAM School of Architecture, Design & the Built Environment TRENT UNIVERSITY Civil Engineering Module Notes 3. Minimising Errors in Levelling Some of the main errors associated with levelling are listed below. The list is not exhaustive. 1) Stability of the instrument/tripod: if they move, the results are corrupted. 2) Levelling up of instrument: incorrect instrument setting results in a non-horizontal line of sight. 3) Focusing: incorrect focusing results in blurred vision and parallax effects. 4) Verticality of the staff: non-vertical staff leads to incorrect height reading. 5) Collimation error: see later, potentially incorrect results unless IS and FS distances = BS distance. 6) Observing: reading the wrong cross-hair, or simply mis-reading the value. 7) Booking: untidy, illegible or simply incorrect. 8) Change point: unstable, causing errors between readings. 9) Weather conditions: poor visibility; atmospheric refraction causes shimmer; high winds make holding of the staff vertical very difficult. 10) Lack of checking: not taking time or care in the work. Full consideration of the above whilst carrying out field observations should lead to good accurate results. Levelling Misclosure In the notes ‘Levelling — the basics’, it was stated that levelling must always start and close on points of known height value, since otherwise there is no check on the correctness of the observations. The difference in value between the known height difference and the observed height difference between starting and closing points, is termed the levelling misclosure. Initially you must determine if the misclosure is within the acceptable tolerance. For the levelling you carry out during practical work within this module, the acceptable tolerance is 3Vn (where n is the number of instrument set-ups). In practice, you must check the tolerance requirements of the survey specification as it could be greater than or less than 3\\n. In the example on the next page there is a misclosure of +5 mm which is deemed to be within the acceptable tolerance of 3Vn; this misclosure is then distributed through the results in proportion to the number of instrument set-ups used. 3. Minimising Errors in Levelling Page 1 of 13 i] NOTTINGHAM School of Architecture, Design & the Built Environment TRENT UNIVERSITY Civil Engineering BS IS FS Rise Fall Reduced Adj. Adjusted RL | Remarks Level 1.245 15.000 - 15.000 A(TBM) 0.650 0.595 15.595 -0.001 15.594, B 1.010 0.360 15.235 -0.001 15.234 Cc 1.655 0.890 0.120 15.355 -0.001 15.354 change point 2.125 1.210 0.445 15.800 -0.002 15.798 change point 1.950 1.465 0.660 16.460 -0.003 16.457 change point 0.875 1.075 17.535 -0.004 17.531 D 0.310 0.565 18.100 -0.004 18.096 E 1.170 2.730 2.420 15.680 -0.004 15.676 change point 1.845 0.675 15.005 -0.005 15.000 A(TBM) 8.145 8.140 3.460 3.455 15.005 -8.140 -3.455, -15.000 Checks 0.005 0.005 0.005 All the checks have been carried out and this survey is showing a +5mm misclosure. The acceptable misclosure = 3\n=3x2=6 mum, therefore the survey is within tolerance, so the 5mm misclosure can be distributed to determine Adjusted Reduced Levels. From the number of backsights taken it can be seen that 5 instrument set-ups have been used, therefore the +5 mm misclosure is distributed through the reduced levels by: (-5/5) =- 1 mm per instrument set-up The actual changes in reduced level values are built up cumulatively through the circuit such that the final result for TBM A comes back to the known value of 15.000 m. ¢ Fill in the adjustments, followed by the adjusted RL’s as shown during the lecture. Note that the original survey data is not altered -- only the final quoted reduced levels. 3. Minimising Errors in Levelling Page 2 of 13 i] NOTTINGHAM School of Architecture, Design & the Built Environment TRENT UNIVERSITY Civil Engineering Instrumental errors Automatic level When setting-up an automatic level, the circular bubble is first centred using the footscrews. The circular bubble is not sensitive or accurate enough to ensure that the line of collimation of the instrument will be perfectly horizontal, so the “automatic” prism mechanism inside the instrument ensures the line of sight is horizontal, making sure that the instrument will define a horizontal plane. However, if the lenses within the instrument are slightly out of alignment, then the horizontal line of sight may not be truly horizontal and the line of collimation will not be horizontal but inclined either up or down. In that case, all staff readings will be in error, with the size of the error being directly proportional to the distance between instrument and staff. The reading to staff R in the figure below will contain twice as much error as the reading to staff Q. Line of collimation It should be apparent that the readings to any two staffs which are the same distance away from the instrument will be in error by the same amount. Therefore, provided that the backsight and foresight distances are the same, the difference in the readings (BS — FS) will give the correct height difference even though the instrument has a collimation error. This is the basis for the first part of the Two-peg test (which is the test which determines the sign and size of error in the level instrument prior to the instrument being adjusted), and is shown diagrammatically in figure (a) of the Two-peg test section following. It is also the reason that, during all observations and regardless of the fact that a Two-peg test might have shown the instrument to have an acceptably small collimation error, backsight and foresight distances are always kept as close to being equal as possible. 3. Minimising Errors in Levelling Page 5 of 13 i] NOTTINGHAM School of Architecture, Design & the Built Environment TRENT UNIVERSITY Civil Engineering It should be noted that equalising backsight and foresight distances does not remove collimation error from the instrument, it merely minimises (if the distances are approximately equal) or eliminates (if the distances are exactly equal) the effect of collimation error. The instrument will still contain collimation error. For a levelling instrument to give accurate results it should be tested frequently and adjusted if necessary. Testing is carried out by means of the Two-peg test; the procedure is described below, first graphically, then in words, and then by means of a worked example. 3. Minimising Errors in Levelling Page 6 of 13 i] NOTTINGHAM School of Architecture, Design & the Built Environment TRENT UNIVERSITY Civil Engineering Two peg test S1, S2, 83, Sa = observed staff readings S1', S2', $3', Sa) =‘ true readings if instrument is in adjustment a) True difference in height A-B = s;'—s)' Observed difference in height = s;—s2 = (si' +x) —(s2' +x) = si +x—9'-x = sj'—s)' = true height difference S Line of collimation Si a) ) Sz DA 1/10) L kK l b) Apparent height difference = s3 - s4 If instrument is adjusted correctly, (s;—s4) = (s3'— sa’) (si'—s2') = true height difference Otherwise, (si — s2) — (s3— $4) = error ‘e’ in instrument over the length of the baseline. To adjust the instrument, it is necessary to calculate what the correct reading at B should be when the instrument is at D, e.g. if L= 50m, L/10 = 5m so distance BD = 55m .°. required reading sy’ = s4—e.55/50 If AD <<L/10, e.g. = 1m, then error at A = 0 and required reading at B = sy—e 3. Minimising Errors in Levelling Page 7 of 13 i] NOTTINGHAM School of Architecture, Design & the Built Environment TRENT UNIVERSITY Civil Engineering Note that alternative methods of booking the observations for a Two-peg test can be used: 4 8 * Rise Fall Reduced Remarks 0.826 1.328 0.502 0.804 1.307 0.503 0.785 1.286 0.501 Mean| TnueAH | AB =-0.502 1.265 1.792 0.527, 1.248 1.775 0.527, 1.235 1.764 0.529 Mean| Apparent | AHAB | =-0.528 Colimation error = TRUE — APPARENT = - 0.502 — (- 0.528) = + 0.026 m over 50m Correction to 54 is — 0.026 x55/50 = - 0.029m o. tequired reading at B = 1.764 — 0.029 = 1.735 Recheck afer adjustment: 1.259 1.760 0.501 Collimation error is now — 0.502 — (- 0.501) = - 0.001m over 50m =OK. Or: Bs is BS Rise | zat | Reduced | remarks Level A 0.826 0.804 0.785 B 1.328 1.307 1.286 at - 0.502 - 0.503 -0.501 | Mean Tus AH A-B =-0.502 After adjustment: A 1.265 1.248 1.235 1.259 B 1.792 1.775 1.764 1.760 dt - 0.527, - 0.527, - 0.529 - 0.501 Mean Apparent AH A-B =-0.528 Colimation error = TRUE — APPARENT = - 0.502 — (- 0.528) = + 0.026 m over 50m Correction to 54 is — 0.026 x55/50 = - 0.029m s. required reading at B = 1.764 — 0.029 = 1.735 After adjustment, collimation error is now — 0.502 — (- 0.501) = - 0.001m over 50m = OK. It does not matter which layout is used for the observations provided that each item is clearly and unambiguously identified and explained. 3. Minimising Errors in Levelling Page 10 of 13 i] NOTTINGHAM School of Architecture, Design & the Built Environment TRENT UNIVERSITY Civil Engineering Something For You To Do No. 2 From a two peg test the following results were obtained over a 40 m bay AB. With the instrument placed mid-way between points A and B the reading at A was 1.975 mand at B 1.700 m. When the level was moved to a point 5 m beyond A on the line AB produced, the reading to A was recorded as 2.014 m and to B was recorded as 1.719 m. Determine the collimation error per 40 m sight length for this instrument and also determine the readings that should be taken to the staffs at A and B if the instrument was correctly adjusted from the position 5 m from A. Other Checks on Instrumentation The preceding notes have focused on errors in the main level instrument; do not forget to check the ancillary equipment such as the staff and the tripod. The staff is often fitted with a circular pond bubble to assist in holding the staff vertical: check the accuracy of this bubble by aligning the edge and front face of the staff with the vertical crosshair of the level. Check that the staff is extended correctly and that the sections interlock correctly. Also check the baseplate of the staff for signs of irregularity: it should be a flat plane -- if not, work off the front edge of the baseplate to minimise the zero error. With the tripod, check for general wear and tear — are all the nuts and bolts present, do the legs slip on the catches? An unstable tripod will lead to poor results. Recommended Reading Surveying for Construction: 5" Edition, William Irvine, McGraw-Hill Elementary Surveying: 8" Edition, Elphick, Fryer, Brinker, Wolf, Harper Collins Surveying for Engineers: 4" Edition, J Uren and W F Price, Macmillan 3. Minimising Errors in Levelling Page 11 of 13 i] NOTTINGHAM School of Architecture, Design & the Built Environment TRENT UNIVERSITY Civil Engineering Further Examples ) Ans. 2) Ans. 3) Ans. A surveyor sets up an automatic level midway between two marks that are 60 m apart, and obtains staff readings of 1.816 m at A and 1.224 mat B. He then moves the level to a point 10 m beyond B hence 70 m from A. The staff readings become 2.440 m and 1.866 m. What should the surveyor do to make the line of sight truly horizontal? Set to read 2.461 m on A and adjust cross-hairs accordingly A surveyor sets up a level midway between two stations A and B 50 m apart and obtains staff readings of 1.334 m and 2.108 m respectively. He then moves the level to a point 10 m from A and 60 m from B and gets the readings 0.962 m and 1.790 m. What is the inclination of the line of sight of the telescope? +00° 03' 43" A, B, C and D are the vertices of a quadrilateral in which the sides have the following lengths in metres: AB = 33, BC= 85, CD = 24, DA = 90, A level was set up at ~A' and readings taken to “B' and ~D'; the level was then moved to *C' and the readings repeated: Instrument Station Staff Station Staff Reading (m) A B 1.467 A D 1.612 Cc B 0.797 Cc D 1.021 a) What is the inclination to the horizontal of the line of collimation b) If the height of the instrument at A was 1.494 m and at C was 1.627 m what are the R.L.'s of stations A, B and C? Given the R.L. of D is 107.520 m. -00° 02' 18" A=107.698 B=107.703 C=106.930 3. Minimising Errors in Levelling Page 12 of 13