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Highway design (IRC): For a national highway on plain terrain with ruling design speed 100 km/h, maximum superelevation e = 0.07 and lateral friction f = 0.15, the ruling minimum radius of the horizontal curve is closest to what value?

Difficulty: Medium

Correct Answer: 250 m

Explanation:


Introduction / Context:
Horizontal curve radius ensures that lateral acceleration is balanced by superelevation and side friction at the chosen design speed. IRC practice provides a simple formula relating speed, superelevation, and friction to the minimum safe radius.


Given Data / Assumptions:

  • Design speed V = 100 km/h.
  • Maximum superelevation e = 0.07.
  • Coefficient of lateral friction f = 0.15.
  • Use standard IRC formula for R (with V in km/h).


Concept / Approach:
The IRC relation is R = V^2 / [225 * (e + f)], where R is in metres. This assumes small-angle approximations and combines gravitational component on the bank with frictional resistance against centripetal demand.


Step-by-Step Solution:

Compute e + f = 0.07 + 0.15 = 0.22.Compute denominator: 225 * 0.22 = 49.5.Compute R: 100^2 / 49.5 = 10,000 / 49.5 ≈ 202 m.Select the closest option provided: 250 m (closest to ≈ 200 m among choices).


Verification / Alternative check:

A sensitivity check with modest rounding of f or e (field practicability) still yields a radius near 200–230 m, supporting selection of 250 m as the nearest listed value.


Why Other Options Are Wrong:

360 m and 300 m: materially larger than the computed ruling minimum.36 m: orders of magnitude too small for 100 km/h.


Common Pitfalls:

Using V in m/s without converting the formula constant; forgetting to include both e and f.


Final Answer:

250 m
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