2. Transition Curve
• A curve of Variable Radius is known as
Transition curve.
• Transition curve is a curve in plan which is
provided to change the horizontal alignment
from straight to circular curve gradually means
the radius of transition curve varies between
infinity to R or R to infinity.
3. • As soon as a vehicle commences motion on a
circular curve from a straight line track, it is
subjected to a sudden centrifugal force, which
not only causes discomfort to the passengers
but also distorts the track alignment and
affects the stability of the rolling stock.
• In order to smoothen the shift from the
straight line to the curve, transition curves are
provided on either side of the circular curve so
that the centrifugal force is built up gradually.
4. Transition Curve
• A transition curve is, therefore, the cure for an
uncomfortable ride, in which the degree of
the curvature and the gain of superelevation
are uniform throughout its length, starting
from zero at the tangent point to the specified
value at the circular curve. The following are
the objectives of a transition curve.
6. Objectives of Transition Curve
• To decrease the radius of the curvature
gradually in a planned way from infinity at the
straight line to the specified value of the
radius of a circular curve in order to help the
vehicle negotiate the curve smoothly.
• To provide a gradual increase of the
superelevation starting from zero at the
straight line to the desired superelevation at
the circular curve.
7. • To ensure a gradual increase or decrease of
centrifugal forces so as to enable the vehicles
to negotiate a curve smoothly.
• To introduce extra widening gradually
• To provide comfort for the driver that is to
enable smooth vehicle operation on road.
• To prevent the possibility of overturning of
vehicles on horizontal curve.
• To improve in design speed on horizontal
curves.
• Reduce wear and tear of rail section .
8. Properties Of Transition Curve
• 1)Rate of change of Super elevation must
equal to that curve.
• 2) Radius of Transition curve at junction
should equal to radius of circular curve.
• 3) Must meet the circular curve tangentially.
• 4) Length of Transition Curve is inversely
proportional to Radius.
9. Types Of Transition Curve
• a) Spiral or clothoid
• b) Cubic parabola
• c) Lemniscates
10. Spiral or clothoid Ideal Transition
Curve Why?
• Rate of change or centrifugal acceleration is
consistent (smooth)and
• Radius of the transition curve is Infinity at the
straight edge and changes to R (Ls ∝ 1/R) at
the curve point and calculation and field
implementation is very easy.
• It satisfies that rate of change of centrifugal
acceleration is constant.
15. Length Of Transition Curve
• b) By definite Rate of Superelevation
• Ls = nh/100
• Wher n = rate of Superelevation 1 in n and h =
superelevation
• C) By Arbitrary Gradient Ls = hv/x
• Where x = time rate in cm/sec which can varey
from 2.5 cm/sec to 5 cm/sec.
16. Length Of Transition Curve
• D) Based on rate of change of superelevation
and extra widening:
• Ls =( W+We)nh
• The maximum of above conditions will be
considered as the length of transition curve.
18. Superelevation
• The inward transverse inclination provided to
the cross-section of the carriage way at
horizontal curved portion of a road is called
superelevation, cant or banking .
• In other words superelevation is raising of
outer edge (of curved portion of road of
railway) with respect to its inner edge is called
superelevation. It is generally denoted by the
‘e
21. Objective of providing superelevation
• 1.To counteract the effect of centrifugal force
acting on the moving vehicle to pull the same
outward on a horizontal curve.
• 2. To help a fast moving vehicle to negotiate a
curved path without overturning and skidding.
• 3. To ensure safety of the fast moving vehicle.
• 4. To prevent damaging effect on the road
surface due to improper distribution of load.
22. Advantages of providing superelevation
• It permits running of vehicle at high speed on a
curved path or a straight path without any danger
of overturning and thus results into increased
volume of traffic.
• It also helps to keep the vehicle to their proper
side on the pavement and thus prevents collision
of vehicles moving in opposite direction on a
curved portion of the road.
• It provides drainage of the whole width of the
road towards the inner side. Thus, there is no
necessity of providing side drain on the outerside
of the road.
31. Ex:1
• Calculate the length of transition curve for
V=65kmph, R=220m, rate of introduction of
super elevation is 1 in 150, W+We= 7.5 m.
(Hint: c=0.57)
• [Answer: Ls1=47.1m, Ls2=39m (e=0.07,
pavement rotated with reference to
centerline), Ls3=51.9m, Ls =52m]
32. Ex:2
• NH passing through rolling terrain of heavy
rainfall area, R=500m. Design length of
Transition curve. (Hint: Heavy rainfall.
Pavement surface rotated with respect to
inner edge. V=80kmph, W=7.0m, N=1 in 150)
[Answer: c = 0.52, Ls1 = 42.3, Ls2 = 63.7m(e =
0.057, W+We = 7.45), Ls3 = 34.6m, Ls = 64m]
