When a vehicle transitions from a straight path to a curved path, it experiences the influence of two primary forces: the weight of the vehicle and the centrifugal force. Both of these forces act through the vehicle’s center of gravity. The centrifugal force, in particular, always acts in the horizontal direction. To counteract the centrifugal force and reduce the tendency of the vehicle to overturn, the outer edge of the pavement is raised with respect to the inner edge throughout the length of the curve. This technique is known as superelevation. Superelevation helps in balancing the lateral forces acting
The Role of Superelevation
Superelevation on curves is intended to counteract part of the centrifugal force, while the rest is resisted by lateral friction. In some cases, superelevation can be provided to fully counteract the centrifugal force, ensuring that vehicles maintain a safe and stable trajectory throughout the curve.
Calculating Superelevation
The superelevation “e” is expressed as the ratio of the height of the outer edge of the pavement with respect to the horizontal width. This can be understood more clearly with the help of a geometric representation.
From the figure, it can be seen that: e = PQ/QR = tanθ
E = tanθ = sinθ = E/B
It is measured as the ratio of the relative elevation of the outer edge, l.e E to width of pavement B
Here, 𝑃𝑄 represents the vertical rise of the outer edge of the pavement, 𝑄𝑅 represents the horizontal width of the pavement, and 𝜃 is the angle of superelevation.
Relationship Between Superelevation, Coefficient of Friction, and Centrifugal Force
To counteract the centrifugal force, the road surface is superelevated at an angle 𝜃 to the horizontal. Consider a vehicle moving perpendicular to the plane of the paper, as shown in the figure:
W = Weight of the vehicle
𝐹F = Frictional force between the wheels and the pavement
𝜃 = Transverse slope due to superelevation
For equilibrium, the sum of forces acting on the pavement surface must be zero. Therefore, we have:
Pcosθ=Wsinθ+FA+FB
Pcosθ=Wsinθ+F(RA+RB)
Pcosθ=Wsinθ+f(Wcosθ+Psinθ)
Dividing the entire equation by 𝑊 cos𝜃, we get:
P/W=tanθ+f+f P/W tanθ
P/W=tanθ+f/1-ftanθf
For small angles 𝜃, tan𝜃 ≈ 𝑒
𝑃/𝑊=𝑒+𝑓/1−ef
Given permissible values of 𝑒 and 𝑓, if 𝑓 is approximately 1-ef≈ 1,
The equation simplifies to: 𝑃/𝑊=𝑒+f
Centrifugal Ratio and Superelevation
We also know that the centrifugal ratio can be expressed as:
𝑃/𝑊=𝑣2/𝑔𝑅
if we Will Equating the two expressions, we get:
𝑒+𝑓=𝑣2/𝑔𝑅
Fundamental Equation for Superelevation
When the speed 𝑉 is expressed in kilometers per hour (KPH), the equation for superelevation is modified to:
e+f= 𝑣2/127R
This is the fundamental equation for horizontal curve design, where 𝑒e is the superelevation, 𝑓 is the coefficient of lateral friction, 𝑉 is the vehicle speed, and 𝑅 is the radius of the curve.
IRC Guidelines for Superelevation
The Indian Roads Congress (IRC) provides specific guidelines for superelevation:
- Vehicle Design: Superelevation is designed for standard vehicles with specified weight and dimensions.
- Bullock Cart Traffic: The maximum value of superelevation is governed by the needs of bullock carts, which are expected to use the roads for a considerable time.
- Maximum Superelevation: The recommended maximum superelevation for different types of terrain is as follows:
| Type of Road | Maximum Superelevation |
| Plain and Rolling Terrain | 7% (0.07) |
| Hill Regions | 10% (0.10) |
The minimum superelevation provided on a road should not be less than the camber required for adequate drainage.
The coefficient of lateral friction (𝑓) depends on several factors, including vehicle speed, road conditions, and also tyre conditions of vehicle.
The value of 𝑓 varies from 0.20 for muddy roads on rainy days to 0.15 for newly constructed asphalt roads. Due to the generally poor condition of Indian roads, the IRC recommends a value of 0.20. Taking a factor of safety of 4/3, the safe coefficient of friction is
0.20× 3/4=0.15
equilibrium Superelevation
Equilibrium superelevation (Eequilibrium) is the superelevation at which the pressure on the inner and outer tires is equal when the coefficient of friction is neglected (𝑓=0). The equation for equilibrium superelevation is:
tanθ=e=V^2/127R and θ=〖tan〗^(-1) (V^2/127R)
This means that if a road surface is superelevated by 〖tan−1(V2/127R) then, the Frictional force Will not be called upon to act and thus the pressure on both wheels will be equal. Then, the Frictional force Will not be called upon to act and thus the pressure on both wheels will be equal.
e_equilbrium V^2/gR=V^2/127R
If the provided superelevation is less than the Eequilibrium superelevation, lateral friction will come into play and will increase as the superelevation is reduced.
Practical Example of Equilibrium Superelevation
Scenario:
Imagine a car traveling on a curved section of a highway designed with a radius of curvature 𝑅R of 200 meters. The design speed for this section of the road is 80 km/h.
We have Given the value:
- Radius of curvature, R=200 meters
- Design speed,V=80 km/h
Calculations:
- Convert the speed into meters per second.
𝑉 = 80 km/h = 80 × 1000 m 3600 s = 22.22 m/s V=80 km/h=80× 3600 s 1000 m =22.22 m/s
2. Calculate the equilibrium superelevation angle,
tan(θ)= 127R V 2
tan(θ)= 127×200 (22.22) 2 = 25400 493.7284 ≈0.0194
θ=arctan(0.0194)≈1.11 ∘
This means that for the car to travel safely on this curved section of the highway without relying on friction, the road should be superelevated by an angle of approximately 1.11∘
What are the Practical Implementation:
- The road engineers design the curved section with a superelevation of 1.11∘. This ensures that at the design speed of 80 km/h, the pressure on the inner and outer tires of the vehicle will be equal, preventing the need for lateral friction to maintain the vehicle’s path.
- If the superelevation provided was less than 1.11∘, drivers would need to rely more on the friction between the tires and the road surface to avoid skidding. As a result, the tires would experience more wear and the risk of skidding would increase, especially in wet conditions.
Effect of Superelevation on Passengers
When designing roads with curves, it’s essential to consider not just the effect of superelevation on the vehicle, but also on the passengers. Superelevation helps to manage the lateral thrust that acts on both the vehicle and its passengers. This lateral thrust can push passengers sideways in their seats, which can be uncomfortable or even unsafe at higher speeds. Understanding the forces involved helps in designing safer and more comfortable roads.
Forces Acting on Passengers
When a vehicle navigates a curve, passengers experience a combination of forces due to the vehicle’s motion and the curvature of the road. These forces are depicted in Figure 3.23, which shows the forces acting on a passenger when the vehicle moves on a curve.
KW1 = Pcosθ - W1Sinθ = W1V^2/127RCosθ-W1sinθ
K=V^2/127RCosθ-sinθ
this if, e = tanθ =v^2/127R
K=tanθcosθ-sinθ=sinθ-sinθ=0
When e=V2/127R the passenger will not feel that the vehicle is taking a turn
Did you know that if superelevation is provided on curves using the formula V2/127R, the driver is not required to apply any force on the wheels? The speed at which this occurs is known as “Hands Off Speed.” As the value of 𝐾𝑤1 increases, the force required to be applied on the wheels also increases.
Hands Off Speed, V = √127RSinθ
