Page 344 - Civil Engineering Formulas

CHAPTER 11
HIGHWAY AND ROAD

FORMULAS

CIRCULAR CURVES

Circular curves are the most common type of horizontal curve used to con-
nect intersecting tangent (or straight) sections of highways or railroads. In
most countries, two methods of defining circular curves are in use: the first,
in general use in railroad work, defines the degree of curve as the central
angle subtended by a chord of 100 ft (30.48 m) in length; the second, used
in highway work, defines the degree of curve as the central angle subtended
by an arc of 100 ft (30.48 m) in length.
The terms and symbols generally used in reference to circular curves are
listed next and shown in Figs. 11.1 and 11.2.

PC point of curvature, beginning of curve
PI point of intersection of tangents
PT point of tangency, end of curve
R radius of curve, ft (m)
D degree of curve
I deflection angle between tangents at PI, also central angle of curve
T tangent distance, distance from PI to PC or PT, ft (m)
L length of curve from PC to PT measured on 100-ft (30.48-m) chord for
chord definition, on arc for arc definition, ft (m)
C length of long chord from PC to PT, ft (m)
E external distance, distance from PI to midpoint of curve, ft (m)
M midordinate, distance from midpoint of curve to midpoint of long
chord, ft (m)
d central angle for portion of curve (d D)
l length of curve (arc) determined by central angle d, ft (m)
c length of curve (chord) determined by central angle d, ft (m)
a tangent offset for chord of length c, ft (m)
b chord offset for chord of length c, ft (m)

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