Page 247 - Civil Engineering Formulas

SURVEYING FORMULAS 181

hand calculator operation. For slopes of 10 percent or less, the correction to be
applied to L for a difference d in elevation between tape ends, or for a horizon-
tal offset d between tape ends, may be computed from
d 2
C s (7.12)
2L
For a slope greater than 10 percent, C may be determined from
s
d 2 d 4
C s (7.13)
2L 8L 3

Temperature Corrections
For incorrect tape length:
(actual tape length nominal tape length)L
C t (7.14)
nominal tape length
For nonstandard tension:
(applied pull standard tension)L
C t (7.15)
AE

2
2
where A cross-sectional area of tape, in (mm ); and E modulus of elas-
2
ticity 29,000,00 lb/in for steel (199,955 MPa).
For sag correction between points of support, ft (m):
2 3
C w L s (7.16)
24P 2
where w weight of tape per foot, lb (N)
L unsupported length of tape, ft (m)
s
P pull on tape, lb (N)

Orthometric Correction
This is a correction applied to preliminary elevations due to flattening of the
earth in the polar direction. Its value is a function of the latitude and elevation
of the level circuit.
Curvature of the earth causes a horizontal line to depart from a level sur-
face. The departure C , ft; or C , (m), may be computed from
f m
2
C f 0.667M 0.0239F 2 (7.17)
C m 0.0785K 2 (7.18)