When a vehicle travels around a curve of constant radius at constant speed, it exerts radially an outward force known as “Centrifugal force”. This Centrifugal force (P) can be represented by, P = Wv2/gR. It acts horizontally at the centre of gravity of the vehicle and its load. The forces acting on the vehicle are
a. the centrifugal force acting radially outwards,
b. the weight of the vehicle acting vertically downwards,
c. the upward reaction of the road on the vehicle.
For equilibrium the centrifugal force must be counteracted either by lateral friction developed between the tyre and the road surface alone, by the inward tilt of the road surface known as “superelevation” alone or partially by friction and partially by superelevation while the weight of the vehicle is balanced by the reaction of the road on the vehicle. (IRC 38 – 1988)
P = ------------ = -------------
Centrifugal Ratio, -------- = -------- = e + f
Where, P = Centrifugal force
W = Weight of the vehicle
G = Acceleration due to gravity
v = Speed in m/sec
V = Speed in Kmph
e = Super elevation
f = friction
The value of co-efficient of lateral friction is a function of speed of the vehicle, the type and condition of the road surface, the condition of the tyres, the weather conditions at the time of contact between tyre and the road, the temperature of the road, etc. Tests indicate that the co-efficient of lateral friction is as low as 0.2 when the pavement is covered with mud. Allowing a factor of safety of 1 1/3, the safe value of friction for design of curves is taken as 0.15
The friction co-efficient has been called lateral ration, cornering ratio, unbalanced centrifugal ratio, friction factor, and side friction factor. (Source: AASHTO)
If the road is laterally level friction alone would have to counteract the centrifugal force and if friction developed is not sufficient, the vehicle will skid outwards. To prevent skidding, the surface of the road is given an inward tilt which is known as superelevation. When a road is superelevated, the component of the weight of the vehicle along the surface aids friction in counteracting the centrifugal force.
Maximum SE in Indian conditions (Source: IRC-38)
The maximum rates of superelevation used on highways are controlled by four factors: Climate conditions, terrain conditions, type of area and frequency of very slow-moving vehicles.
It has been observed that transverse slope of more than 70 percent is inconvenient to the slow-moving vehicle. So that maximum allowable superelevation on curves is taken as 7 percent. In hilly areas, since such carts are not prevalent and the number of curves is more, a higher superelevation is required. A value of 10 percent is recommended for design in hilly areas not affected by snow.
Providing superelevation to fully counteract the centrifugal force would necessitate giving a superelevation more than 7 percent for sharp curves causing inconvenience to slow moving vehicles. When a vehicle negotiates, a sharp curve friction would be developed to the maximum and none when traveling on flat curves. This is not a balanced design. It is desirable that the superelevation should be such that a moderate amount of friction is developed while rounding flat curves and friction not exceeding the maximum allowable be developed at sharp curves. Therefore, so designing superelevation to fully counteract the centrifugal force developed at a fraction of the design speed of the highway will provide the necessary balance.
It has also been observed that a majority of the vehicles using a highway travel at less than the design speed. Therefore, as a compromise, since we cannot provide the exact amount of superelevation required for varying speed of vehicles that will use the highway fully counteracting the centrifugal force developed at three-fourth of the design speed by superelevation is specified.
V2 (0.75V2) V2
Therefore, e = ------- = ---------- = -----------
127R 127R 225R
The superelevation given to the surface of the road should not be less than the camber required for the drainage of surface water on the road.
Method of building superelevation (Source: IRC 73)
There are three different methods for attaining the superelevation
A. Pavement revolved about centerline
B. Pavement revolved about outer edge
C. Pavement revolved about inner edge
The superelevation should be attained gradually over the full length of the transition curve so that the design superelevation is available at the starting point of the circular portion. In cases where transition curve can’t for some reason be provided, two-third superelevation may be attained on the straight section before start of the circular curve and the balance one-third on the curve.
In developing the required superelevation, it should be ensured that the longitudinal slope of the pavement edge compared to the centre-line (i.e., the rate of change of superelevation) is not steeper than 1 in 150 for roads in plain and rolling terrain, and 1 in 60 in mountainous and steep terrain.
Fig 2: Axis of Rotation for undivided highways
Fig 3: Axis of Rotation for multi lane highways (Source: Iowa Department of Transportation
(Source: Iowa Department of Transportation