dE = sine 161 12' 30" x 548.74 meters
= +0.322128 x 548.74 meters = +176.76 meters
Example 3: Given an azimuth from Station C to Station A of 294, 40' 45" and a distance of 783.74
meters (this falls in the fourth [northwest] quadrant), compute the dN and the dE.
dN = cosine 294 40' 45" x 783.74 meters
= 0.417537 x 783.74 = +327.24 meters
dE = sine 294 40 '45" x 783.74 meters
= -0.908660 x 783.74 meters = -712.15 meters
t. Accuracy and Specifications. The overall accuracy of a traverse depends on the equipment, the
methods used in the measurements, the accuracy achieved, and the accuracy of the starting and closing
data. An accuracy ratio of 1:5,000 is the minimum accuracy sought in topographic surveying. In
obtaining horizontal distances, an accuracy of at least 2 millimeters per 100 meters must be obtained.
When using a 1-second theodolite, surveyors turn the horizontal angles twice in each position (two
direct and two reverse observations) with an angular closure of 10 seconds per station.
u. Linear Error. To determine the acceptability of a traverse, surveyors must compute the linear
error of closure (LEC) (using the Pythagorean theorem), the AE, and the accuracy ratio. The first step in
either case is to determine the linear error in dN and dE. In the case of a loop traverse, the algebraic sum
of the dNs should equal zero. Any discrepancy is the linear error in dN. The same is true for dEs.
Surveyors then compute the AE using the appropriate accuracy ratio (1:5,000 or better) and the total
length of the traverse. Compare this to the LEC. If the AE is greater than the LEC, the traverse is good
and can be adjusted. If it is not good, it must be redone.
v. Accuracy Ratio. The accuracy ratio provides a method of determining the traverse accuracy and
comparing it to established standards. The accuracy ratio is the ratio of the LEC (after it is reduced to a
common ratio and rounded down) to the total length of the traverse. If the accuracy ratio does not fall
within allowable limits, the traverse must be redone. It is very possible that the measured distances are
correct and that the error can be attributed to large, compensating angular errors.
w. Coordinate Adjustment. Surveyors make adjustments to the traverse using the compass rule.
The compass rule states that on any leg of the traverse, corrections to the dN or the dE are also
corrections to the total correction for the dN or the dE, as the length of the leg is to the total length of the
traverse. The total correction for the dN or the dE is numerically equal to the error in northing (En) or
the error in easting (Ee) but with the opposite sign.
3-33
EN0593
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