Hairpin bends (mountain roads): While designing hairpin bends on highways in hilly terrain, which of the following minimum design provisions is commonly adopted?

Introduction / Context:
Hairpin bends are sharp reverse curves used to gain elevation on steep mountain roads. Their design must address low operating speeds, adequate turning radius for design vehicles, and safe superelevation within permissible limits considering ice, snow, and slow speeds.

Given Data / Assumptions:

• Mountain highway per IRC guidance.
• Sharp curves with very small radius.
• Conservative speeds are adopted due to visibility and traction limits.

Concept / Approach:
Because hairpins involve very small radii, the chosen design speed is low. A typical value used in many exam problems and practice is about 20 km/h, which influences minimum radius, transition length (often minimal or omitted), and superelevation (limited by comfort/skid and construction practicality). Gradient limitations vary by terrain class and are not universally fixed at the options stated.

Step-by-Step Solution:
Relate design speed to minimum radius using basic curve formula R = V^2 / (225 * (e + f)) for km/h.Use low V (≈ 20 km/h) to achieve feasible radius on steep terrain.Check superelevation e against practical limits (commonly ≤ about 7%–10% depending on conditions) and ensure adequate widening.

Verification / Alternative check:
Typical IRC tables for hill roads recommend very low design speeds for hairpins; 20 km/h is a commonly quoted figure for basic design vehicle considerations and stopping distances in tight bends.

Why Other Options Are Wrong:

• Fixed gradients 1 in 40 or 1 in 200 are not universal minima/maxima for all hairpins; allowable ruling/limiting gradients vary by terrain class.
• Superelevation fixed at 10% is not universally applicable; maximum e depends on climate, speed, and standards.
• All the above: incorrect because only the low design speed is a generally accepted common minimum for hairpins.

Common Pitfalls:

• Providing excessive superelevation on steep grades can cause drainage and low-speed instability issues.
• Neglecting extra widening on sharp curves for larger vehicles.

Final Answer:
design speed ≈ 20 km/h