This document discusses transition curves, which are curves used to gradually change a roadway from a straight alignment to a circular curve. This allows vehicles to smoothly negotiate the curve without sudden shifts in centrifugal force. Transition curves decrease the radius gradually from infinity to the curve radius. They also provide a gradual increase in superelevation or banking from 0 to the level needed for the circular curve. Common transition curve types include spiral curves and parabolic curves. The length of a transition curve depends on factors like design speed, curve radius, and the rate of superelevation introduction. Formulas are provided to calculate superelevation and transition curve length for road design. Examples are included to demonstrate using the formulas.

1. Transition Curve & Superelevation
Batch 2019 QUEST Larkana
2019 Batch

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.

5. 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.

11. Ideal Curve

12. Lemniscate Curve

13. All in One

14. Length Of Transition Curve
For mountainous and steep terrain
Ls = V²/R

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.

17. Shift and Length

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

19. Superelevation

20. Superelevation

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.

23. Superelevation Formula

24. Superelevation Formula

25. Superelevation Formula

26. Superelevation Formula

27. From width and superelevation rate or
rising slope
• e, or h = 1/n x width of road

28. Rate Of Superelevation

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]