CIVIL ENGINEERING FORMULAS

SURVEYING FORMULAS 181

hand calculator operation. For slopes of 10 percent or less, the correction to be
applied to Lfor a difference din elevation between tape ends, or for a horizon-
tal offset dbetween tape ends, may be computed from

(7.12)

For a slope greater than 10 percent, Csmay be determined from

(7.13)

Temperature Corrections

Forincorrect tape length:

(7.14)

Fornonstandard tension:

(7.15)

whereAcross-sectional area of tape, in^2 (mm^2 ); and Emodulus of elas-
ticity29,000,00 lb / in^2 for steel (199,955 MPa).

Forsag correctionbetween points of support, ft (m):

(7.16)

wherewweight of tape per foot, lb (N)
Lsunsupported length of tape, ft (m)
Ppull 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 earthcauses a horizontal line to depart from a level sur-
face. The departure Cf, ft; or Cm, (m), may be computed from

(7.17)

Cm0.0785K^2 (7.18)

Cf0.667M^2 0.0239F^2

C

w^2 L^3 s

24 P^2

Ct

(applied pullstandard tension)L

AE

Ct

(actual tape lengthnominal tape length)L

nominal tape length

Cs

d^2

2 L



d^4

8 L^3

Cs

d^2

2 L