Superelevation or Banking of Road|Derivation of Super Elevation|How to Calculate Super Elevation
Superelevation formula | banking of road banking of road derivation |How to Calculate Super Elevation
INTRODUCTION :
When a vehicle travels in a circular path or curved path, it is subjected to an outward force which makes a car overturn and skid due to Centrifugal force. To overcome this force and for the safe travel of a car, the outer edge of the road is raised above the inner edge. This is known as superelevation or banking of road.
SuperElevation / Banking of road reduces the effect of centrifugal force on the running wheels. If superelevation is not provided the entire centripetal force is produced by the friction between the vehicle’s tires and the roadway, thus resulting in reducing the speed of a vehicle.
- Superelevation is provided to achieve a higher speed for vehicles.
- It increases the stability of fast-moving vehicles when they pass through a horizontal curve, and it also decreases the stresses on the foundation.
- In the absence of superelevation on the road along curves, potholes are likely to occur at the outer edge of the road.
- The Indian road congress(IRC) has prescribed the max value of Super Elevation is 1 in 15.
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”;
(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,
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
How to Calculate Super Elevation Example:
Eg:
Calculate superelevation for a road having a radius of a curve as 150m. The design speed is 60km/hr. The coefficient of lateral friction is 0.15.
To find :
Superelevation=e =?
Calculation:
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The formula to calculate the superelevation of the road is
[e + f ] = [V² / 127R]
Where,
e = rate of superelevation =?
f = lateral friction factor = 0.15
V = Velocity of vehicle in km / hr. = 60km/hr
R = Radius of a circular curve in meters.= 150m.
[e + f ]= [V² / 127R]
[e + 0.15] = [60² ÷ 127 х 150 ]
[e + 0.15] = [3600 ÷ 19,050]
[e + 0.15] = 0.189
e = [0.189 - 0.15]
= 0.0389
Required slope = 1/0.0389
= 1 in 25.70
Superelevation in %
= [0.0389 х 100]
= 3.89%
According to IRC, the maximum allowable superelevations for mixed traffic over hills & terrains is 7%.
e = 3.89% < 7% hence safe.
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