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SUPERELEVATION AND ITS DESIGN FOR HIGHWAYS

What is Superelevation in Highway Engineering?

To counter-act the effect of centrifugal force and reduce the tendency of vehicle to overturn and to skid laterally outwards, pavement outer edge is raised with respect to inner edge. Thus, providing a transverse slope is known as Super elevation. It is represented by “ e ”.

Superelevation in Highway Engineering

Analysis of superelevation

Let us say Design speed = V m/s

Radius = R m

Various forces acting on the vehicle:

Where e = rate of super elevation in %

f = lateral friction factor = 0.15

V = velocity of vehicle in m/s

g = acceleration due to gravity = 9.81 m/s2

R = radius of circular curve in meters.

Limits for maximum super elevation:

According to IRC the Maximum Super elevation in Areas

Which Are Bound by Snow fall – 7%

Which are not bounded by Snow fall – 10%

Limits for minimum super elevation:

Minimum super elevation = camber or cross slope

Camber: Slope provide in the transverse direction to drain off rain water quickly is known as Camber or Cross slope. This will also prevents slipping and skidding of vehicles.

IRC Recommendations for Camber:

Type of pavement	Light rainfall intensity	Heavy rainfall intensity
C.C pavements & thick bituminous pavements	1 in 60	1 in 50
Thin Bituminous Pavements	1 in 50	1 in 40
W.B.M & Gravel Pavements	1 in 40	1 in 33
Earthen Pavements	1 in 33	1 in25

Design of super elevation:

There are four steps involved in the design of super elevation. And they are,

Step 1:

Calculate the super elevation necessary for 75% design speed and assume No lateral friction is developed

If e value is less than emax = 0.07, provide calculated e value. Otherwise proceed to next step

Step 2:

When ecal > emax

Provide e = emax = 0.07 in this step and go to next step.

Step 3:

From the above step we have the value of e. so, check for lateral friction factor is applied in this step for the known value of e.

If fcal < fmax (0.15)

Then e = 0.07 is safe.

But if fcal > 0.15

Then restrict the values to f = 0.15, e = 0.07

And go to last step.

Step 4:

In this step we will find out the value of restricted speed.

Let V = Va

If Va > V, then e = 0.07, f= 0.15

If Va < V , then also e = 0.07, f = 0.15 but, speed restriction board is provided which consists the value of Va As shown in figure below.

  

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Horizontal Transition Curves for Highways and Its Calculation

What is transition curve and when it is needed?

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.

Objectives for providing transition curves

1. For the gradual introduction Centrifugal force
2. To introduce super elevation gradually
3. To introduce extra widening gradually
4. To provide comfort for the driver that is to enable smooth vehicle operation on road.
5. To enhance aesthetics of highways.

Types of transition curves

• Spiral or clothoid
• Cubic parabola
• Lemniscate

IRC recommends Spiral or clothoid as the ideal transition curve due to following reasons:

1. It satisfies that rate of change of centrifugal acceleration is constant i.e., Ls.R = constant. Where Ls = length of transition curve R = radius of curve.
2. The calculation and field implementation of spiral curve is simple and easy.
3. It enhances aesthetics also.

Determining length of transition curve

The length of transition curve can be calculated by 3 conditions.

• Based on rate of change of acceleration
• Based on rate of change of super elevation and extra widening
• Based in IRC empirical formula

Based on rate of change of acceleration

Radius of curve is infinity at the tangent point and hence centrifugal acceleration is zero. Similarly at the straight end radius of curve has minimum value means centrifugal acceleration is maximum. So, the rate of change of centrifugal acceleration should be adopted such that the design should not cause any discomfort to the drivers.

Let Ls be the length of transition curve and a vehicle is moving with a speed of V m/s.

Force P = (mV2/R)

Since it is similar to F= ma

P = m (V2/R)

Therefore, centrifugal acceleration = V2/R

Let “C” be the coefficient of rate of change of centrifugal acceleration.

C = (V2/R). (1/t)

Where t= time taken to travel the transition curve of length Ls, with a speed of V

t = Ls/V

C = (V2/R). (V/Ls)

Ls = (V3/CR)

According to IRC, C = 80/(75+V) and C should be (0.5<C<0.8).

Based on rate of change of superelevation and extra widening

Let 1 in N is the allowable rate of introduction of super elevation and E is the raise of the outer edge with respect to inner edge. W is the normal width of pavement in meters. We is the extra width of pavement in meters. And e is the rate of superelevation.

E = (W+We).e

Therefore length of transition curve, Ls = (W+We).e.N

If the pavement outer edge is raised and inner edge is depressed with respect to center of pavement then,

Ls = [(W+We).e.N]/2

Typical range of introduction of super elevation is as follows according to IRC

Type of terrain	Rate of super elevation 1 in N
For plain and rolling terrains	1 in 150
For built up areas	1 in 100
For hilly and steep terrains	1 in 60

Based on IRC empirical formula

IRC given some direct formulae for finding the length of transition curve.

• For plain and ruling terrain:

Ls = 2.7 (V2/R)

• For mountainous and steep terrains

Ls = V2/R

Hence these are the three criteria to determine the length of transition curve. The maximum of above three conditions will be considered as the length of transition curve.