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
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 is basically provided on the horizontally curved portion of the roads in which the outer edge of the road pavement 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 = F1 & F2 (← );
You can check out the below figure more idea. Hence, P.Cosθ = W.Sinθ+F1+F2
where, F = fR
P.Cosθ = WSinθ + fR1 + fR2
= W.Sinθ + f(R1 + R2)
= 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 = V2/ gR
Therefore, e + f = V2/ 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/s2
R = radius of circular curve in meters.
If velocity is in KMPH then e + f = V2/ 127R Maximum Superelevation
Super Elevation Formula
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 = [V2]/127R
Consider lateral friction f = 0;
75% of design speed which means V= 0.75V
As per formula,
e + f = [V2]/127R
e + 0 = [0.75V]2/127R Methods of Superelevation
e = V2 / 225R
Note: e value should not be more than 0.07
If the calculated value (ecal) is less than (emax) then consider the value of (ecal) if not proceed to next step, Advantages of Superelevation
if (ecal<emax) then e = ecal
If the calculated value (ecal) is greater than (emax) then consider the value of (emax)
if (ecal<emax) then e = emax
Step – 2: How to Calculate Superelevation in Road
Lets assume e = emax = 0.07 and proceed to next step.
Step-3: Calculate the value of friction for ‘e’ Value
Super Elevation formula = e + f = [V2]/127R
= 0.07 +f = [V2]/127R Advantages of Superelevation
f = [V2]/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 emax Value
Super Elevation = emax + f = [V2]/127R
= 0.07 + f = [V2]/127R
fcal = [V2/127R] – 0.07 Advantages of Superelevation
If fcal < fmax (0.15)
Then fcal = f ;
If fcal > fmax (0.15)
Then e = 0.07 is safe.
But if fcal > 0.15
Then fcal =fmax (0.15)