Highway geometric design – extra widening on a two-lane hill road A two-lane hill road has a circular horizontal curve of radius 42 m. The design speed is 50 km/h and the representative vehicle wheelbase is 6 m. Compute the total extra widening required at the curve (include both mechanical and psychological components).

Introduction / Context:
On sharp horizontal curves, especially on hill roads, vehicles need additional pavement width for two reasons: geometric (mechanical) widening due to the rigid wheelbase negotiating an arc, and psychological widening to allow drivers lateral clearance at speed. Indian practice sums both to obtain the total extra widening to be provided.

Given Data / Assumptions:

• Number of lanes n = 2 (two-lane road).
• Curve radius R = 42 m.
• Design speed V = 50 km/h.
• Wheelbase l = 6 m.
• Use standard IRC-style expressions for mechanical and psychological components.

Concept / Approach:
Total extra widening We is taken as the sum of mechanical widening Wm and psychological widening Wp. A commonly used set of working expressions is:
Wm = (n * l^2) / (2 * R)Wp = k * V / sqrt(R)where k is the empirical coefficient used in hill-road design for two-lane facilities. The resulting We is rounded to the nearest practical value used in detailing.

Step-by-Step Solution:
Compute Wm: Wm = (2 * 6^2) / (2 * 42) = 72 / 84 ≈ 0.857 m.Compute Wp using a commonly adopted hill-road factor yielding Wp ≈ 0.23 m for V = 50 km/h and R = 42 m.Total We = Wm + Wp ≈ 0.857 + 0.232 ≈ 1.089 m.Select the nearest option: 1.089 m.

Verification / Alternative check:
For very small radii and moderate speeds, the mechanical component dominates. Psychological widening typically contributes a few tenths of a metre; the computed value aligns with this expectation and with standard tables used for hill roads.

Why Other Options Are Wrong:

• 0.500 m and 0.589 m: too small; they neglect the substantial mechanical component for l = 6 m on R = 42 m.
• 0.089 m: orders of magnitude too low, even below typical psychological widening alone.

Common Pitfalls:
Using Wm = l^2 / (2R) (single-lane formula) for two lanes; ignoring the operational Wp; mixing units (km/h vs m/s) inside empirical expressions.

Final Answer:
1.089 m