Why is Extra Widening Needed on Curves?
When a vehicle navigates a straight road, all four wheels follow virtually the same path. However, on a horizontal curve, the geometry changes fundamentally — the front wheels turn to follow the curve, but the rear wheels, being on a fixed axle, cannot turn and instead follow a path of shorter radius than the front wheels. This discrepancy between front and rear wheel paths is called off-tracking, and it effectively increases the road width that each vehicle occupies while cornering.
If the standard straight-road carriageway width is used on a curve without adjustment, vehicles will either encroach on adjacent lanes or ride dangerously close to the road edge. Extra widening compensates for this by increasing the carriageway width on curved sections.
Two Types of Extra Widening
1. Mechanical Widening (Wm) — Due to Off-Tracking
This is the additional width needed purely because of the geometric difference between front and rear wheel paths on a curve. The derivation uses the relationship between the outer front wheel radius (R₂) and the inner rear wheel radius (R₁):
R₂² = R₁² + ℓ²
Where ℓ is the distance between front and rear axles (wheelbase). The mechanical widening for one lane is W_m = ℓ²/(2R₂ − W_m) ≈ ℓ²/2R.
For a road with n lanes: Wm = nℓ²/2R
2. Psychological Widening (Wps) — Due to Driver Behaviour
Beyond the purely geometric off-tracking effect, there is a second component of extra widening needed due to driver psychology. On curves, drivers instinctively steer slightly away from the road edge to maintain a psychological comfort zone — they feel the road is narrower than it actually is when curving. This tendency reduces the effective usable carriageway width.
IRC has established an empirical formula for this: Wps = V / (9.5√R)
Where V = design speed in km/h and R = radius of horizontal curve in metres. This can also be written as Wps ≈ 0.1V/√R.
Total Extra Widening Formula
The total extra widening required at a horizontal curve is the sum of both components:
Wₑ = Wm + Wps = nℓ²/2R + V/(9.5√R)
This widening is applied on the inner side of the curve (toward the centre of curvature) and is introduced gradually over the transition curve length to avoid an abrupt change in road width.
IRC Rules for Extra Widening
- For single-lane roads: no extra widening needed if radius > 60 m
- For two-lane roads: no extra widening needed if radius > 300 m
- The formula above applies to two-lane and multi-lane roads
- Widening is always on the inner edge of the curve
- Extra widening should be introduced over the transition curve length — not suddenly at the start of the circular curve
- Gradient effect is not considered in extra widening calculations
Solved Example
Problem: A 2-lane highway has R = 250 m, e = 0.06, f = 0.15, ℓ = 6 m. Calculate total extra widening.
Step 1: Find V from super elevation formula: V = √(127R(e+f)) = √(127×250×0.21) = √6667.5 = 81.65 km/h
Step 2: Mechanical widening: Wm = nℓ²/2R = (2×36)/(2×250) = 72/500 = 0.144 m
Step 3: Psychological widening: Wps = V/(9.5√R) = 81.65/(9.5×15.81) = 81.65/150.2 = 0.543 m
Total Extra Widening Wₑ = 0.144 + 0.543 = 0.687 m ≈ 0.7 m
Key Summary
- Extra widening needed because rear wheels track shorter radius than front wheels (off-tracking)
- Mechanical widening: Wm = nℓ²/2R (geometric, depends on wheelbase and radius)
- Psychological widening: Wps = V/(9.5√R) (empirical, depends on speed)
- Total: Wₑ = Wm + Wps | Applied on inner side | Introduced over transition curve
- Not needed: single-lane R > 60m | two-lane R > 300m