CURVES Flashcards
These curves are on a horizontal plane viewed from the top. The types of horizontal curve are simple circular curves, compound curves, reverse curves, and spiral curves.
Horizontal Curves
These curves are used to provide smooth transition or gradual change in direction which takes place in a vertical plane die to grade changes.
Vertical Curves
PC
Point of curvature
PT
Point of tangency
PI
Point of intersection
T
Length of tangent fromPCtoPIand fromPItoPT
R
Radius of simple curve, or simply radius
L
Length of chord fromPCtoPT
Lc
Length of curve fromPCtoPT
E
External distance
m
Middle ordinate
I
Deflection angle/Angle of intersection/Central angle
x
offset distance from tangent to the curve
theta
offset angle subtended at PC between PI and any point in the curve
Formula for Length of Tangent, T
R tan(I/2)
Formula for External Distance, E
R sec(I/2) - R or R [sec(I/2) - 1]
Formula for Middle Ordinate, m
R - R cos(I/2) or R [1 - cos(I/2)]
Formula for Long Chord, L
2R sin(I/2)
Formula for Length of Curve, Lc
(Pi R I)/180 degrees
_________ is the central angle subtended by an arc (arc basis) or chord (chord basis) of one station. It will define the sharpness of the curve.
In English system, 1 station is equal to _____ ft.
In SI, 1 station is equal to ___ m.
Degree of Curve, D
100, 20
The degree of curve is the central angle subtended by one station of circular arc. This definition is used in highways.
Arc Basis
Formula for Degree of curve, D (Arc Basis)
1 station/D = (2 Pi R)/360 degrees
D = 1145.916/R
Chord definition is used in railway design. The degree of curve is the central angle subtended by one station length of chord.
Chord Basis
Formula for Degree of curve, D (Chord Basis)
sin(D/2) = half station/R
D= 2 arcsine(half station/R)
