CIVIL ENGINEERING FORMULAS

SURVEYING FORMULAS 183

STADIA SURVEYING

In stadia surveying, a transit having horizontal stadia crosshairs above and
below the central horizontal crosshair is used. The difference in the rod read-
ings at the stadia crosshairs is termed the rod intercept. The intercept may
be converted to the horizontal and vertical distances between the instrument
and the rod by the following formulas:

(7.25)

(7.26)

where Hhorizontal distance between center of transit and rod, ft (m)
Vvertical distance between center of transit and point on rod inter-
sected by middle horizontal crosshair, ft (m)
Kstadia factor (usually 100)
irod intercept, ft (m)
avertical inclination of line of sight, measured from the horizontal,
degree
fcinstrument constant, ft (m) (usually taken as 1 ft) (0.3048 m)

In the use of these formulas, distances are usually calculated to the foot (meter)
and differences in elevation to tenths of a foot (meter).
Figure 7.1 shows stadia relationships for a horizontal sight with the
older type of external-focusing telescope. Relationships are comparable for
the internal-focusing type.
For horizontal sights, the stadia distance, ft, (m) (from instrument spindle to
rod), is

DR (7.27)

f

i

C

V

1

2

Ki(sin 2a)(fc) sin a

HKi(cosa)^2 (fc) cos a

f 1 f 2

c

C

a ́

b ́

m

i

a

b

F

D

fd

B

A

R

FIGURE 7.1 DistanceDis measured with an external-focusing telescope by determining

intervalRintercepted on a rod ABby two horizontal sighting wires aandb.