Length of transition required for super-elevation development: a 7 m wide road requires a maximum super-elevation of 1 in 15, and the rate of change of super-elevation is 1 in 150. What is the maximum transition length to be provided at either end?

Introduction / Context:
Transition length is needed to rotate the roadway from normal camber to full super-elevation smoothly, ensuring comfort and safety. The “rate of change of super-elevation” specifies how quickly crossfall may be introduced.

Given Data / Assumptions:

• Roadway width b = 7 m.
• Maximum super-elevation e = 1/15.
• Rate of change (run-out) N = 150 → length per unit crossfall change.

Concept / Approach:
Length L to develop full super-elevation is calculated as L = N * b * e. This formula represents the distance required so that the edge level difference b * e is achieved at the permitted rate N (i.e., 1 vertical in N horizontal).

Step-by-Step Solution:

Verification / Alternative check:
A quick proportional check: if N = 150 per unit rise and required rise is 7/15 ≈ 0.467 m, then 150 * 0.467 ≈ 70 m, confirming the arithmetic.

Why Other Options Are Wrong:
65 m and 75–90 m do not match the product N * b * e and would either over- or under-provide the transition.

Common Pitfalls:
Using the carriageway half-width instead of full width; mixing up e as a percentage versus a ratio.

Final Answer:
70 m