Page 248 - Civil Engineering Formulas

182 CHAPTER SEVEN

where M, F, and K are distances in miles, thousands of feet, and kilometers,
respectively, from the point of tangency to the earth.
Refraction causes light rays that pass through the earth’s atmosphere to
bend toward the earth’s surface. For horizontal sights, the average angular dis-
placement (like the sun’s diameter) is about 32 min. The displacement R , ft, or
f
R , m, is given approximately by
m
2
R f 0.093M 0.0033F 2 (7.19)
R m 0.011K 2 (7.20)

To obtain the combined effect of refraction and curvature of the earth, subtract
R from C or R from C .
f
m
m
f
Borrow-pit or cross-section leveling produces elevations at the corners of
squares or rectangles with sides that are dependent on the area to be covered,
type of terrain, and accuracy desired. For example, sides may be 10, 20, 40,
50, or 100 ft (3.048, 6.09, 12.19, 15.24, or 30.48 m). Contours can be located
readily, but topographic features, not so well. Quantities of material to be
3
3
excavated or filled are computed, in yd (m ), by selecting a grade elevation or
final ground elevation, computing elevation differences for the corners, and
substituting in
nxA
Q (7.21)
108
where n number of times a particular corner enters as part of a division block
x difference in ground and grade elevation for each corner, ft (m)
2
2
A area of each block, ft (m )

VERTICAL CONTROL

The NGS provides vertical control for all types of surveys. NGS furnishes
descriptions and elevations of bench marks on request. As given in “Standards
and Specifications for Geodetic Control Networks,” Federal Geodetic Control
Committee, the relative accuracy C, mm, required between directly connected
bench marks for the three orders of leveling is

First order: C 0.5 2 K for Class I and 0.7 2 K for Class II (7.22)
Second order: C 1.0 2 K for Class I and 1.3 2 K for Class II (7.23)

Third order: C 2.0 2 K (7.24)

where K is the distance between bench marks, km.