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LabEx 05 Computations x RD

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  COMPUTATIONS The figure below shows the level net connecting the four benchmarks. The arrows indicate the directions of higher elevations. Figure X. Level network and their differences in elevation. Condition Equations: −   −   −    +    = 0   −   −   +    = 0   −   −    +    = 0   −(   +  )−(   +  )−(   +  )+(   +  ) = 0   −(   +  )−(   +  )+(   +  ) = 0   −(   +  )−(   +  )+(   +  ) = 0   So that,    = −   −   +   −1.367−0.785−11.923+12.295      = −   +   −1.367− 12.187+12.295      = −   +   −0.785− 11.923+12.187   Function to minimize: ∅ =   +  +  +  +   ∅ = (−   −   +   −1.78)  +(−   +    −0.521)  +  +  +   To minimize, the partial derivatives with respect to   ,  ,  ,    were equated to 0: ∅  = 2(−   −   +   −1.78)(−1) = 0   ∅  = 2(−   −   +   −1.78)(−1)+2(−   +   −0.521)(−1)+2   = 0   ∅  = 2(−   −   +   − 1.78)+2   = 0   ∅  = 2(−   +   −0.521)+2   = 0   Solving simultaneously,    = 0      = −1.259      = −0.521      = −0      = −0.521   Finally, the adjusted differences in elevation are:    = 1.367       = −0.474       = 11.402       = 12.295       = 11.666     RESULTS AND DISCUSSION The accuracy of each loop were checked by connecting the observations of each leveling line that are within the respective loops. The allowable errors were computed and the difference between the set and the observed elevation was determined for both the forward and backward runs. Loop Allowable Error (cm) Difference in Elevation (cm) Forward Run Backward Run Kam-Vinz-Oble-Kam 1.28093 5.99 5.73 Vinz-Oble-SC-Vinz 1.43657 7.96 7.75 Kam-Oble-SC-Vinz-Kam 1.49972 1.97 2.02 The table above shows the allowable error and the difference in elevation of the BMs for each of the loop. The difference in elevation of the three loops were not able to meet the allowable error of the 2 nd  order accuracy. The loop with the smallest difference in elevation was the outside loop (KAMIA-OBLE-SC-VINZONS-KAMIA) with an average difference in elevation (at BM KAMIA) of 1.995cm. The other 2 loops had elevation differences of about 6cm and 8cm. it may  be observed that line VINZ-OBLE is common to both loops with the larger elevation difference, whereas the one with the smallest did not contain this line. It may be concluded that this line (VINZ-OBLE) may have contributed the largest source of error among all the leveling lines. A possible source of error could have resulted from the placing of some of the benchmarks such as the one near Quezon Hall which was located on the base of a lamppost and not on the actual ground. The higher elevation of BM OBLE due to its location made taking measurements more difficult and made the group resort to taking measurements on the ground right beside the  benchmark and then applying adjustments to the backsight and foresight readings. This could have added to the error in elevation difference between the two points. ***NOTE: Keith, pabasa kung tama and kung oks lang na isama sa report.  After each leveling lines were adjusted and the c-factor was applied, the difference in elevations  between the benchmarks in each line was determined. The table below summarizes all the elevation differences between the benchmarks. BM1 BM2 Elevation Difference (m) KAMIA VINZONS -0.785 VINZONS OBLE 12.187 OBLE SC -12.295 KAMIA OBLE 11.923 VINZONS SC -1.367 The observations in the table above were used to formulate the condition equations that was used in the least squares adjustment. The final level network diagram after least squares adjustment is shown below. Figure X. Final level network loop. BM1 BM2 Elevation Difference (m) KAMIA VINZONS -0.474 VINZONS OBLE 11.666 OBLE SC -12.295 KAMIA OBLE 11.402 VINZONS SC -1.367 Apparently, the benchmark near Kamia Residence Hall turns out to be of lower elevation than that of the benchmark located near Vinzons Hall. The benchmark near the oblation also seems to have the lowest elevation amongst all the benchmarks used. The stations with the greatest elevation difference were BM SC and BM OBLE, while the stations with the least were between BM VINZONS and BM KAMIA.

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Sep 10, 2019
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