The extra width of the carriageway required on a horizontal curved section of the road above the width required on a straight alignment is called the extra widening of the pavement. The extra widening consists of two components i.e., the psychological factor, and the mechanical factor, both of which are used to calculate the total extra width required at a curved section.
The Necessity of Extra Widening
Each vehicle occupies certain width while traveling in a straight path. But in a curved path, the width requirement for a vehicle increases. This is because of the fact that both the front and back wheels follow different paths while traversing a curved section. Because of this, the carrying capacity of the road would decrease. Therefore, extra widening becomes indispensable in curved sections to maintain the carrying capacity throughout the curved section.
Apart from this, the extra widening is also required to meet the following.
The first reason, as said, is due to the rigid wheelbase of the vehicle. This leads to from and back wheels following different paths at the curved section. This is called off-tracking.
Next, due to a speed higher than the design speed, the existing superelevation will not be sufficient to counteract the centrifugal force. This could lead to lateral skidding.
To have greater visibility on the cured sections, the driver could take the vehicle to the outer edge of the pavement.
To maintain a sufficient gap with vehicles in the opposite direction.
IRC Formula for Extra Widening
IRC Recommendations for Extra Widening
IRC recommends providing extra widening if the radius of the horizontal curve is less than or equal to 300m. IRC also recommends the minimum value of extra widening based on the radius of horizontal curves as follows.
The Radius of Horizontal Curve | Minimum Extra Width to be Provided |
up to 40m | 1.5m |
41 to 60m | 1.2m |
61-100m | 0.9m |
100-300m | 0.6m |
>300m | No extra widening required |
The width of the extra widening is the sum of two components i.e.,
Psychological Widening
Mechanical Widening
Psychological Widening Formula
As per IRC, psychological widening is totally dependent on the design speed and the radius of the horizontal curve. This is totally due to the psychological factor and doesn't depend on the wheelbase of the vehicle.
Wpsy = v / (9.5 * R^(1/2))
where
v - design speed in km/hr
R - radius of the horizontal curve in m
Note that, psychological widening need not be considered for single-lane roads.
Mechanical Widening Formula
This is dependent on the length of the wheelbase of the vehicle. This is given by the expression,
Wmech = (n * l^2) / (2*R)
where
n - is the number of lanes
l - length of the vehicle
R - radius of the horizontal curve
Total Widening
The total widening required is the sum of psychological widening and mechanical widening.
Wextra = Wpsy + Wmech
Wextra = {v / (9.5 * R^(1/2))} + {(n * l^2) / (2*R)}
For greater than two lanes, the extra width of widening is equal to the product of 1/2 of the total width of widening for two lanes and the number of lanes.
Practise Problem
This blog forms a small part of the topic of "Geometric Design of Highways". The geometric design of highways is an important topic from the GATE exam perspective and each year at least one question pops from the topic. Almost all topics within the geometric design of highways are already covered in our previous blogs. Links for the same are provided below.