Transition curve and Superelevation

Transition curve and Super-elevation
Transition Curve
Objectives of Transition Curve
Properties Of Transition Curve
Types Of Transition Curve
Length Of Transition Curve
Superelevation
Objective of providing superelevation
Advantages of providing superelevation
Superelevation Formula
Numerical

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 t o 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

29. 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]

30. 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]