all measurements have error in the case of levelling these errors will be instrumental observational and natural
instrumental errors
the main source of instrumental error is residual collimation error . As already indicated , keeping the horizontal lengths of the backsights and foresights at each instrument position equal will cancel this error ,
where the observational distance are unequal , the error will be proporational to the difference in distance .
the easiest approach to equalizing the sight distance is to pace backsight to instrument and then set up the foresight change point the same number of pace away from the instrument .
2- parallax error has already been described .
3- staff graduation errors may result from wear and tear or repairs and the staffs should be checked against a steel tape , zero error of the staff , caused by excessive wear of the base , weill cancel out on backsight and foresight difference however , if two staffs are , errors will result unless calibration corrections are applied .
4- in the case of the tripod , loose fixing will cause twisting and movement of the tripod . ovvertight fixing makes it difficult to open out the tripod correctly . loose tripod shoes will result in unstable calibration corrections are applied .
4- in the case of the tripod will cause twisting and movement of the tripod . overtight fixing make it difficult to open the tripod correctly , losse tripod shoes will also result in unstable set-up .
observational errors
levelling involves vertical measurements relative to a horizontal plane so it is important to ensure that the staff is held strictly vertical ,
it is often suggested that one should rock the staff and forth in the direction of the line of sight and accept the minimum reading as the truly vertical one . however , this concept is incorrect when using a flat-bottomed staff on flat ground , due to the fact that staff is not being tilting about its face , thus it is perferable to use a staff bubble , which should be checked frequently with the aid of a plumb - bob .
(2) there may be errors in reading the staff , particularly when using a tilting level which gives an inverted image , these errore may result from inexperience ., poor observation conditions or overlong sights limit the lengh of sight to about 25-30 m .
to ensure the graduations are clearly defined .
(3) ensure that the staff is correctly extended or assembled in the case of extending staffs listen for the applies to jointed staffs.
(4) Do not move the staff off the CP position , particularly when turning it to face the new instrument position , Always use a well defined and stable position for CPs . levelling plates , should be used on soft ground
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| the effect of rocking the staff on readings |
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| levelling plate |
5- Avoid sttlement of the tripod , which may alter the height of collimation between sights or tilt the line of sight , set up on firm ground , with the tripod feet firmly thrust well into the ground , on pavements . locate the tripod shoes in existing cracks joins , in precise levelling , the use of two staffs helps to reduce this effect
observers should also refrain from touching or leaning on the tripod durring observation.
6 - booking errors can of course ruin good field work .Neat , clear , correct booking of field data is essential in any surveying operation. typical booking errors in levelling are entering the values in the wrong columns or on the worng line . and making airthmetical errors in the reducation process . very often the use of pocket calculators simply enables to avoid this error source , use neat , legible figures : read the booked value back to the observer and have them check the staff reading again ; reduce the data as it recorded .
(7) when using a tilting level remember to level the tubular bubble with the tilting screw prior to each new staff reading . with the automatic level carefully centre the circular bubble and make sure the compensator is not sticking .
residual compensator errors are counteracted by centring the circular bubble with the instrument throughout the levelling .
natural errors
(1) Curvature and refraction have already been dealt with . their effects are minimized by observation distances to backsight and foresight at each set-up and readings more than 0.5 m above the ground .
(2) wind can cause instrument vibration and make the staff difficult to hold in a steady position. precise levelling is impossible in strong winds . in tertiary levelling keep the staff to its shortest length and use a wind break to shelter the instrument.
(3) heat shimmer can make the staff reading difficult if not impossible and may make it necessary to delay the work to an overcast day . in hot sunny climes , carry out the work early in the morning or in the evening ,
careful consideration of the above error source , combined with regularly calibrated equipment , will ensure the best possible results but will never precude random errors of observation.
closure tolerances
it is important to realize that the amount of misclosure in levelling can only be assessed by ;
(1) connecting the levelling back to the BM from which it started , or
(2) connecting into another BM of known and proved value .
whwn the misclosure is assessed one must then decide if it is acceptable or not . in many case the engineer may make the decision based on his/her knowledge of the project and the tolerance required .
Alternatively the permissible cirteria may be based on the distance levelled or the number of set-ups involved.
A common criterion used to assess the misclosure (E) is :
E = m(k) 2
where k = distance levelled in kilometers , m = a constant with units of millimeters , and E = the allowable misclosure in millimetres .
the value of m may vary from 2 mm for precise levelling to 12 mm or more for engineering levelling , in many case in engineering , the distance involved is quite short but the number of set- ups quite high.
in which case the following criterion may used ;
E = m (n) 2
error distribution
in previous levelling examples in this chapter misclosures have been shown , the misclosure cannot be ignored and the error must be distrbuted among the point concerned , in the case of a levelling circuit , a simple method of distribution is to allocate the error in proportion to the distance levelled for instance , consider a levelling circuit commenncing from a BM at A , to establish other BMs at B, C ,D and E - for which the heights have computed without taking the misclosure into account ,
on completing the circuit the observed value for the BM at A is 20.018 m compared , with its known and hence starting value of 20,000 m , so the levelling 0.018m . the distance levelled is 5,7 km considering the purpose of the work , the terrain and observational conditions , it is decided to adopt a value for m of 12 mm , hence the acceptable mislosure is 12 (5,7)2 = 29mm , so the levelling is acceptable .
the difference in heights is corrected by (0.018/5.7) × distance in kilometres travelled , therefore correction to AB = - 0.005 m , to BC = - 0.002m , to DE = - 0.006 m and to EA = - 0.002 m . the value of the BMs will then be B = 28.561 m , C = 35.003 m , D = 30.640 m .
E = 22.829 m and A = 20.000 m .
in many instance ,a closing loop with known distance is not the method used and each reduced level is adjusted in proporation to the cumulative number of set-ups to that point from the start . consider the table
vertical control
below which shows the observations for a fhort section of levelling between two bench marks of known height:
(1) there are four set- ups , and therefore E = 5(4)2 = 0.010 m , As the misclosure is only 0.008 m . the levelling is acceptable .
(2) the correction per set - up is (0.008/4) = - 0.002 m and is cumulative as shown in the table .
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