Quantcast Calculating the Allowable Error - 14070_126

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136.442 ft. The elevation found through differential leveling was 136.457 ft. The error of closure of the level circuit is 136.457 – 136.442 = 0.015 ft. therefore, is the actual distance leveled. For third-order leveling, the allowable error is Assume that errors have occurred progressively along  the  line  over  which  the  leveling  was accomplished. You make adjustments for these errors by distributing them proportionally along the line as shown by the following example. If you refer to figure 7-4, you will notice that the total distance between BM 35 and BM 19, over which the line of levels was run, is 2,140 ft. The elevation on the closing BM 19 is found to be 0.015 ft greater than its known elevation. You must therefore  adjust  the  elevations  found  for  the intermediate BMs 16, 17, and 18. The amount of correction is calculated as follows: BM 16 is 440 ft from the starting BM. The total length distance between the starting and closing BMs is 2,140 ft. The error of closure is 0.015 ft. By substituting these values  into  the  above  formula,  the  correction  is  as follows: Since  the  observed  elevation  of  the  closing  BM is greater than its known elevation, the adjustments are  subtracted  from  the  intermediate  BMs. Therefore,   for   BM   16,   the   adjusted   elevation   is 134.851 – 0.003 = 134.848. The adjustments for inter- mediate BMs 17 and 18 are made in a similar manner. Calculating the Allowable Error The error of closure that can be allowed depends on the precision required (first, second, or third order). The allowable error of closure in leveling is expressed in terms  of  a  coefficient  times  the  square  root  of  the horizontal length of the actual route over which the leveling was accomplished Most  differential  leveling  (plane  surveying)  is third-order work. In third-order leveling, the closure is usually made on surveys of higher accuracy without doubling back to the benchmark at the original starting point of the level circuit. The length of the level circuit, Refer again to figure 7-4. By adding the sight distances in the sixth and seventh columns of the figure, you will find that the length of the level circuit is 2,140 ft (or 0.405 miles). The allowable error of closure, then, is Since the actual error is only 0.015 ft, the results are sufficiently accurate for third-order precision. First-  and  second-order  levels  usually  close  on themselves; that is, the leveling party runs a line of levels from an old BM or station to the new BM or station, and then doubles back to the old BM for closure. The actual distance leveled is twice the length of the level circuit. For second-order leveling, the allowable error is First-order  leveling  is  even  more  precise.  The allowable error cannot be greater than Adjusting  Level  Nets When a level survey system covers a large area, you, in turn, adjust the interconnecting network in the whole system.  Adjustment  of  an  interconnecting  network  of level circuits consists of adjusting, in turn, each separate figure in the net, with the adjusted values for each circuit used in the adjustment of adjacent circuits. This process is repeated for as many cycles as necessary to balance the values for the whole net. Within each circuit the error of closure is normally distributed to the various sides in proportion to their lengths. Figure 7-5 represents a level net made up of circuits BCDEB, AEDA, and EABE. Along each side of the circuit is shown the length of  the  side  in  miles  and  the  observed  difference  in elevation  in  feet  between  terminal  BMs.  The  difference in elevation (plus or minus) is in the direction indicated by the arrows. Within each circuit is shown its total length (L) and the error of closure (Ec) that is determined by  summing  up  the  differences  in  elevation  in  a clockwise  direction.  Figure  7-6  shows  the  computations required to balance the net. The circuits, sides, distances (expressed in miles and in percentages of the total), and differences in elevation (DE) are listed. 7-6

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