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
