Compound Curve
A compound curve consists of two (or more)circular curvesbetween
two main tangents joined at point of compound curve (PCC). Curve at
PC is designated as 1 (R1, L1, T1, etc) and curve at higher station
is designated as 2 (R2, L2, T2, etc).
Elements of compound curve PC = point of curvature PT = point of
tangency PI = point of intersection PCC = point of compound curve
T1= length of tangent of the first curve T2= length of tangent of
the second curve V1= vertex of the first curve V2= vertex of the
second curve I1= central angle of the first curve I2= central angle
of the second curve I = angle of intersection = I1+ I2 Lc1= length
of first curve Lc2= length of second curve L1= length of first
chord L2= length of second chord L = length of long chord from PC
to PT T1+ T2= length of common tangent measured from V1to V2 = 180
I x and y can be found from triangle V1-V2-PI. L can be found from
triangle PC-PCC-PTFinding the stationing of PTGiven the stationing
of PC
Given the stationing of PI
Reversed Curve
Reversed curve, though pleasing to the eye, would bring
discomfort to motorist running at design speed. The instant change
in direction at the PRC brought some safety problems. Despite this
fact, reversed curves are being used with great success on park
roads, formal paths, waterway channels, and the like.
Elements of Reversed Curve PC = point of curvature PT = point of
tangency PRC = point of reversed curvature T1= length of tangent of
the first curve T2= length of tangent of the second curve V1=
vertex of the first curve V2= vertex of the second curve I1=
central angle of the first curve I2= central angle of the second
curve Lc1= length of first curve Lc2= length of second curve L1=
length of first chord L2= length of second chord T1+ T2= length of
common tangent measured from V1to V2Finding the stationing of
PTGiven the stationing of PC
Given the stationing of V1
Reversed Curve for Nonparallel Tangents
Reversed Curve for Parallel Tangents
Spiral Curve (Transition Curve)
Spirals are used to overcome the abrupt change in curvature and
superelevation that occurs between tangent and circular curve. The
spiral curve is used to gradually change the curvature and
superelevation of the road, thus called transition curve.
Elements of Spiral Curve TS = Tangent to spiral SC = Spiral to
curve CS = Curve to spiral ST = Spiral to tangent LT = Long tangent
ST = Short tangent R = Radius of simple curve Ts= Spiral tangent
distance Tc= Circular curve tangent L = Length of spiral from TS to
any point along the spiral Ls= Length of spiral PI = Point of
intersection I = Angle of intersection Ic= Angle of intersection of
the simple curve p = Length of throw or the distance from tangent
that the circular curve has been offset X = Offset distance (right
angle distance) from tangent to any point on the spiral Xc= Offset
distance (right angle distance) from tangent to SC Y = Distance
along tangent to any point on the spiral Yc= Distance along tangent
from TS to point at right angle to SC Es= External distance of the
simple curve = Spiral angle from tangent to any point on the spiral
s= Spiral angle from tangent to SC i = Deflection angle from TS to
any point on the spiral, it is proportional to the square of its
distance is= Deflection angle from TS to SC D = Degree of spiral
curve at any point Dc= Degree of simple curveFormulas for Spiral
CurveDistance along tangent to any point on the spiral:
At L = Ls, Y = Yc, thus,
Offset distance from tangent to any point on the spiral:
At L = Ls, X = Xc, thus,
Length of throw:
Spiral angle from tangent to any point on the spiral (in
radian):
At L = Ls,=s, thus,
Deflection angle from TS to any point on the spiral:
At L = Ls, i = is, thus,
This angle is proportional to the square of its distance
Tangent distance:
Angle of intersection of simple curve:
External distance:
Degree of spiral curve:
