Page 2 of 4
2. Level Circuit LS Adjustment
For the leveling circuit in Figure B-1
Figure B-1 Level Circuit |
and these observed elevation differences
Obs | Line | dElev | Obs | Line | dElev | |
1 | BMA-Q | +8.91 | 5 | BMA-R | -3.56 | |
2 | BMB-Q | -2.92 | -- | -- | ||
3 | BMC-Q | -4.67 | 6 | BMC-R | -17.12 | |
4 | BMD-Q | -8.66 | 7 | BMD-R | -21.10 |
what are the elevations of points Q and R?
A traditional simple adjustment is difficult to apply in this situation. Because point Q is connected to four benchmarks and point R to three, any simple adjustment attempted will result in multiple elevations for each point.
With a small network like this, a Brute Force approach might be feasible. Using the observed elevation differences, compute all possible elevations for points Q and R, then simply average them.
Point Q elevations and their average are:
Similarly, for point R:
Compute S_{o}
Compute residuals using the adjusted elevations and the individually computed elevations used for the averages.
v = MPV_{Q}-Elev_{Q} | v^{2} | sums |
-0.015 | 0.000225 | |
+0.015 | 0.000225 | |
-0.035 | 0.001225 | |
+0.035 | 0.001225 | 0.002900 |
v = MPV_{R}-Elev_{R} | v^{2} | |
+0.007 | 0.000049 | |
-0.033 | 0.001089 | |
+0.027 | 0.000729 | 0.001867 |
0.004767 |
There are seven observations (m) and two unknown elevations (n).