CIVIL ENGINEERING FORMULAS

SURVEYING FORMULAS 179

whereE 1 ,E 2 , E 3... are probable errors of the separate measurements.
Error of the mean is

(7.4)

whereEsspecified error of a single measurement.
Probable error of the mean is

(7.5)

MEASUREMENT OF DISTANCE WITH TAPES

Reasonable precisions for different methods of measuring distances are

Pacing (ordinary terrain): to

Taping (ordinary steel tape): to (Results can be improved by use of

tension apparatus, transit alignment, leveling.)

Baseline (invar tape): to

Stadia: to (with special procedures)

Subtense bar: to (for short distances, with a 1-stheodolite, 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.

(^1) 
7000
(^1) 
1000
(^1) 
500
(^1) 
300
(^1) 
1,000,000
(^1) 
50,000
(^1) 
10,000
(^1) 
1000
(^1)  50 1  100
PEm
PEs
n

0.6745

B

d^2

n(n1)

Em

Esum

n



Esn

n



Es

n

TABLE 7.1 Probability of Error in a Single Measurement

Probability

Confidence of larger

Error level, % error

Probable (0.6745s) 50 1 in 2

Standard deviation (s) 68.3 1 in 3

90% (1.6449s) 90 1 in 10

2 sor 95.5% 95.5 1 in 20

3 sor 97.7% 99.7 1 in 370

Maximum (3.29s) 99.9 1 in 1000