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?
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A65 m
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B70 m
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C75 m
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D80 m
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E90 m
Answer
Correct Answer: 70 m
Explanation
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:
Compute edge level difference: b * e = 7 * (1/15) = 7/15 m.Compute L: L = N * b * e = 150 * 7/15 = 10 * 7 = 70 m.Select 70 m as the required transition length at either end.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