Page 249 - 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:

2
H Ki(cos a) ( f c) cos a (7.25)
1
V Ki(sin 2a) ( f c) sin a (7.26)
2
where H horizontal distance between center of transit and rod, ft (m)
V vertical distance between center of transit and point on rod inter-
sected by middle horizontal crosshair, ft (m)
K stadia factor (usually 100)
i rod intercept, ft (m)
a vertical inclination of line of sight, measured from the horizontal,
degree
f c instrument 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
f
D R i C (7.27)

f 1 f 2
C
c f d
B
a´
a m
i R
b
b´ F
D A

FIGURE 7.1 Distance D is measured with an external-focusing telescope by determining
interval R intercepted on a rod AB by two horizontal sighting wires a and b.