**How to Calculate Superelevation in Road | Purpose | Superelevation Formula | Purpose of Providing Superelevation | Methods of Superelevation**

In this Article today we will talk about the **What is Superelevation | Superelevation of Road Formula ****| Maximum Superelevation | Methods of Superelevation | How to Calculate Superelevation in Road | Superelevation Calculation**** | Advantages of Superelevation | Superelevation in Highways**

**What is SuperElevation | How to Calculate Superelevation in Road**

**Superelevation** on the horizontal curve is one of the most important features in the **construction** of the **roads**. It is very essential to provide **superelevation in roads** for the safe movement of vehicles on the curved portion of the **roads**.

It helps the fast-moving vehicles to safely **pass through the curved portion of the roads with stability**. **Superelevation Calculation**

**Superelevation Definition**

The inward transverse inclination which is provided to the cross-section of the **pavement** of road at the horizontally curved portion of the roads is known as **superelevation**.

**Superelevation** is also known as **Cant** or **Banking**. **Superelevation Calculation**

Superelevation in roads isbasically provided on the horizontally curved portion of the roads in which the outer edge of the roadpavement is raised with respect to the inner edge, thus providing a transverse slope throughout the length of the horizontal curve of the road.

This transverse inclination to the surface of the road pavement is known as **Superelevation**. **Superelevation Calculation**

**Purpose of Providing Superelevation in Roads**

- The main aim of providing
**superelevation**is to**counteract**the effect of**centrifugal force**acting on the moving vehicle. - To prevent the
**damaging effect**on the surface of the roads due to improper distribution of load on the roads. - To help the fast-moving vehicles to pass through a curved path without
**overturning**or**skidding**. - To
**reduce**the**maintenance cost of the road**on the curved portion. - To ensure the
**smooth**and**safe movement**of vehicles and passengers on the curved portion of the roads.**Superelevation Calculation**

**Superelevation** is expressed as the height of the outer edge of the pavement with respect to the width of the pavement. **Superelevation of Road Formula**

**Derivation of Super Elevation:**

As per the figure, the below forces are acting on a car

In order to find out the angle of elevation (Super Elevation) the “tan” formula is used

From above fig, tanθ = ^{Opposite Side}⁄_{Adjacent Side}

therefore, tanθ = ^{E}⁄_{B}

The below forces are acting on the vehicle as mentioned in figure:

Weight of the vehicle = **W kg (**↓**) ; **

Centripetal force =** P (→);**

Frictional forces = **F _{1} & F_{2} (← ); Superelevation of Road Formula**

You can check out the below figure more idea. Hence, P.Cosθ = W.Sinθ+F_{1}+F_{2}

where, F = fR

P.Cosθ = WSinθ + fR_{1} + fR_{2}

= W.Sinθ + f(R_{1} + R_{2})

= W.Sinθ + f(PSinθ+WCosθ)

P.Cosθ-f.PSinθ = W.Sinθ+f.WCosθ

Divide with “W.Cosθ”; **Maximum Superelevation**

^{(P.Cosθ-f.PSinθ)}⁄_{W.Cosθ} = ^{(W.Sinθ+f.WCosθ)}⁄_{W.Cosθ}

^{P}⁄_{W} -(^{f.P}⁄_{W})tanθ = tanθ + f

^{P}⁄_{W} (1-f.tanθ) = tanθ+f

^{P}⁄_{W} = ^{(tanθ+f)}⁄_{1-f.tanθ}

^{P}⁄_{W} = e + f But,

^{P}⁄_{W }= V^{2}/ gR

Therefore, e + f = V^{2}/ gR

Where, **Maximum Superelevation**

e = rate of Super elevation in %

V = velocity of vehicle in m/s

f = lateral friction factor = 0.15

g = acceleration due to gravity = 9.81 m/s^{2}

R = radius of circular curve in meters.

If velocity is in KMPH then ** e + f = V ^{2}/ 127R Maximum Superelevation**

**Super Elevation Formula | How to Calculate Superelevation in Road**

The above formula is used only to calculate one of the missing value either **e** or **f** or **V** or **R** for design purpose consider the below procedure. **Maximum Superelevation**

**How to Calculate Superelevation in Road:**

**Design procedure of Superelevation / Banking of road**

Design procedure includes following steps **Methods of Superelevation**

**Step – 1: How to Calculate Superelevation in Road**

Calculate the Super elevation (e) necessary for 75% design speed[0.75V] and assume no lateral friction is developed

As per practical conditions, it is suggested that superelevation should be provided to fully counteract the centrifugal force due to 75% of the Design Speed(V) by neglecting lateral friction (f=0) developed. **Methods of Superelevation**

Super Elevation formula = e + f = [V^{2}]/127R

Consider lateral friction f = 0;

75% of design speed which means V= 0.75V

As per formula,

e + f = [V^{2}]/127R

e + 0 = [0.75V]^{2}/127R **Methods of Superelevation**

e = V^{2}/ 225R

**Note: e value should not be more than 0.07 **

If the calculated value (e_{cal}) is less than (e_{max}) then consider the value of (e_{cal}) if not proceed to next step, **Advantages of Superelevation**

if (e_{cal}<e_{max}) thene = e_{cal }

If the calculated value (e_{cal}) is greater than (e_{max}) then consider the value of (e_{max})

if (e_{cal}<e_{max}) thene = e_{max }

**Step – 2: How to Calculate Superelevation in Road**

Lets assume **e = e _{max }** = 0.07 and proceed to next step.

Step-3: Calculate the value of friction for ‘e’ Value

Super Elevation formula = e + f = [V^{2}]/127R

= 0.07 +f = [V^{2}]/127R **Advantages of Superelevation**

f = [V^{2}]/127R – 0.07

**Step – 3:**

From the above step we found the value of e. Now lets find the value of the lateral friction (f) for the known value of e_{max} Value

Super Elevation = e_{max} + f = [V^{2}]/127R

= 0.07 + f = [V^{2}]/127R

f_{cal }= [V^{2}/127R] – 0.07 **Advantages of Superelevation**

If f_{cal }< f_{max}(0.15)

Then f_{cal}= f ;

If f_{cal }> f_{max}(0.15)

Then e = 0.07 is safe.

But if f_{cal }> 0.15

Then f_{cal}=f_{max}(0.15)

**Step – 4: How to Calculate Superelevation in Road**

Lets calculate the value of Restricted Speed (V_{a})

**V = V**

_{a}^{2}]/127R

_{a})

^{2}/127R

**Advantages of Superelevation**

V = [127R(0.22)]^{1/2}

If V

_{a}> V then e = 0.07, f = 0.15

_{a}< V still e = 0.07 and f = 0.15 but the speed restriction board is provided along with consists the value of V

_{a }

**Method of Providing Superelevation to the Roads**

**Superelevation**plays an important role to counteract the centrifugal force which is acting on the vehicle moving from the horizontal curve of the road. The attainment of superelevation in roads is done into two parts

**Elimination of the Crown and the cambered section****Rotation of the pavement by attaining full superelevation**

**Elimination of the Crown and the Cambered Section**

**Method – 1:**

In the first method, the outer half of the cross slope is rotated about the crown at the rate such that the surface of road falls on the same plane and the elevation of the centre line is not varied.**Superelevation in Highways**

**Method – 2:**

In the second method, the crown is gradually shifted by increasing the width of the inner half of the cross-section.**negative superelevation**on to a portion of the outer half.

**Superelevation in Highways**

**Rotation of the pavement by attaining full Superelevation**

In this method, the inner edge of the road is made the pivot point. The Crown, as well as the outer edge, are **raised in such a way that the full amount of superelevation is achieved**.

**Superelevation in Highways**The disadvantage of this method is that the centre of the pavement is raised and the entire pavement width and the outer shoulder are to be

**raised with respect to the inner edge by additional filling of the earth**.

**Superelevation in Highways**

**NOTES for How to Calculate Superelevation in Road**

**Superelevation:**

**Superelevation**is the transverse

**slope provided to counteract**the effect of centrifugal force and reduce the tendency of the vehicle to overturn and to skid laterally outwards by

**raising the pavement outer edge with respect to the inner edge**.

**Superelevation**is represented by “

**e**”.

**Superelevation**

**in Highway Engineering**.

**Super Elevations:**

**Super elevation**is tilting the roadway to help offset centripetal forces developed as the vehicle goes around a curve. Along with friction they are what keeps a vehicle from going off the road. A

**super**elevated section is proceeded by a transition section.

**Superelevation Formula:**

The rate of change in **superelevation**is found by dividing the difference between normal crown and full super by the transition length. 11000 – 10971.61 = 28.39. The rate of change is the same as for the transition at the beginning end of the curve.

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**Conclusion:**

Full article on **What is Superelevation | Superelevation of Road Formula**

**| Maximum Superelevation | Methods of Superelevation | How to Calculate Superelevation in Road | Superelevation Calculation**

**| Advantages of Superelevation | Superelevation in Highways**

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