Page 245 - Civil Engineering Formulas

SURVEYING FORMULAS 179

TABLE 7.1 Probability of Error in a Single Measurement
Probability
Confidence of larger
Error level, % error
Probable (0.6745 ) s 50 1 in 2
Standard deviation ( ) 68.3 1 in 3
s
90% (1.6449 ) 90 1 in 10
s
2 or 95.5% 95.5 1 in 20
s
3 or 97.7% 99.7 1 in 370
s
Maximum (3.29 s ) 99.9 1 in 1000
where E , E , E . . . are probable errors of the separate measurements.
1 2 3
Error of the mean is
E s n E s
E sum
E m (7.4)
n n n
where E specified error of a single measurement.
s
Probable error of the mean is

d 2
PE s
PE m 0.6745 (7.5)
n Bn(n 1)

MEASUREMENT OF DISTANCE WITH TAPES

Reasonable precisions for different methods of measuring distances are
1 1
Pacing (ordinary terrain): 50 to 100
1 1
Taping (ordinary steel tape): 1000 to 10,000 (Results can be improved by use of
tension apparatus, transit alignment, leveling.)
1 1
Baseline (invar tape): 50,000 to 1,000,000
1 1
Stadia: 300 to 500 (with special procedures)
1 1
Subtense bar: 1000 to 7000 (for short distances, with a 1-s theodolite, averag-
ing angles taken at both ends)
Electronic distance measurement (EDM) devices have been in use since the
middle of the twentieth century and have now largely replaced steel tape mea-
surements on large projects. The continued development, and the resulting drop
in prices, are making their use widespread. A knowledge of steel-taping errors
and corrections remains important, however, because use of earlier survey data
requires a knowledge of how the measurements were made, common sources for
errors, and corrections that were typically required.