# Extra widening in Highway | Extra widening formula of Road

## What is extra widening of highway?

Extra widening on the curves of the road refers to the additional width of the carriageway that is required on a curved section of the road over and above the width required on the straight section.

## Why extra widening in highway required?

Additional width at the horizontal curve is required due to the following reasons.

1) Rigidity of wheelbase:- Due to the rigidity of wheelbase, the rear wheel of the vehicle moving along the curve does not follow the same track/path taken by front steering curves. i.e Off-tracking.

2) Preferential use of outer lanes:- A driver prefers the outer lane for greater visibility and easy gradient.

3) More clearance between opposite vehicles:- Where the road visibility is inadequate, drivers, to be on the safer side, have a tendency to keep greater clearance between opposite vehicles on curves of the road.

4) Difference in slip angle:- It has been observed that when the vehicle is understeering, the slip angle of the front tires is more than of the rear tyre/wheels and the front tyre may tend to go out of pavement. In oversteering vehicles vice versa.

## Types of Extra Widening

A) Mechanical extra widening (Wm)

B) Psychological extra widening (Ws)

## A) Mechanical extra widening

It is the amount of extra width required due to the rigidity of the wheelbase. If the vehicle with its base L is traversing a curved path of radius R.

In triangle ABC and BCD

AC/BC = BC/CD

(BC)2= AC * CD

L2= Wm(2 R – Wm )

L2= Wm(2 R – Wm ) Tends to Zero

Wm = L2/2R

Wm = n (L2/2R) extra widening

## B) Psychological extra widening is given by empirical relation.

The widening required due to the psychosocial tendency to maintain greater clearance between vehicles is called psychological widening.

Where, v = Design speed in kmph

Hence, total extra widening = Mechanical widening + Psychological widening

W = Wm + WPsy

#### Widening Pocess

As per IRC recommendation, extra widening should be provided in all curves of radius less than 900 m.

Extra widening or additional width is provided gradually from zero at the beginning of the transition curve and its maximum value at the circular curve. The introduction of extra widening may be studied under two heading.

1. introduction of widening on curve without spiral
2. Introduction of widening on curve with spiral. i.e Transition Curve.

#### 1) Introduction of widening on curve without spiral

In this case, the total extra width should be provided to the inside of the carriageway, while the outside edge and centerline are both kept as a circular arc. the result is much the same as providing a transition curve on the centerline.

The main drawback is that the full width of the carriageway may not always be in use. since a fast-moving vehicle will tend to curve in from the outer edge at the beginning and end of the curved section as it makes its own transition.

#### 2) Introduction of widening on curve with spiral. i.e Transition Curve

The widening is introduced gradually, starting from the beginning of the transition and progressively increasing at a uniform rate, till the full value of deigned additional width is reached at the beginning of the circular curve.

The rate of introducing extra width will be the same as the rate of introducing superelevation or radial acceleration. here again, three cases may arise.

a) For a reasonably large radius (900>R>60 m), extra width is introduced equally to the outer and inner lane at the expanse of the inner and outer shoulder, keeping the width of roadways changed. So, far as the remaining width of the shoulder is as wide as 1 m. In cases, the shoulder width may be obtained less than 1 meter as a result of increased carriageway width.

b) At curves with a radius in the range of 30 m to 60 m and for single-lane roads radius less than 150 m, the pavement is widened only on the inside of the curve. However, the centerline marking shall be placed halfway between the edges of the widened carriageway.

c) On mountainous roads where the curve radius is sometimes 20 m to 30 m. vehicles with long wheelbase can not keep within the inner half of the carriageway. In this case, extra width should preferably be applied fully on the outer side.

## Numerical Example

Q) Find the total pavement width required for a four-lane highway on a horizontal radius of 250 m. The design speed is 60 kmph. The length of the longest wheelbase is 61 m.

Solution:-

Total extra widening = Mechanical widening + Psychological widening

Wt = Wm + WPsy

Total pavement width = w + wt

= 3.5 *4 + 0.7 (Assume lane width 3.5 m)

= 14.7 meter

## Design of Transition Curve

A transition curve has a radius that decreases from infinity at the tangent point to a designed radius of the circular curve. It is provided on either side of the circular curve.

Read full details of transition curve:- How to calculate the length of transition curve

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