Super-elevation computation from crossfall: a 12.5 m wide carriageway has its outer edge 50 cm higher than the inner edge. What is the required super-elevation expressed as a slope ratio?
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A50 cm
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B1 in 25
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C1 in 400
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D1 in 40
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E1 in 24
Answer
Correct Answer: 1 in 25
Explanation
Introduction / Context:Super-elevation is the upward transverse inclination provided to counteract centrifugal effects on curves. It is commonly specified as a slope ratio (1 vertical in N horizontal) or as a percentage.
Given Data / Assumptions:
- Carriageway width (run) = 12.5 m.
- Height difference (rise) between outer and inner edges = 50 cm = 0.50 m.
- Uniform crossfall assumed across the width.
Concept / Approach:Super-elevation e (as a ratio) equals rise divided by run. Converting the numeric result into the common “1 in N” form helps compare with standards and check reasonableness.
Step-by-Step Solution:
Compute e = rise / run = 0.50 / 12.5 = 0.04.Express as a ratio: 0.04 = 1 / 25 → “1 in 25”.Check plausibility: 4% is a typical, moderate super-elevation value.Verification / Alternative check:Convert to percent: 0.04 * 100 = 4%. Compare to usual caps (e.g., 7–10% depending on context) to verify the value is realistic.
Why Other Options Are Wrong:(a) “50 cm” is not a slope; (c) 1 in 400 equals 0.25%, far too small; (d) 1 in 40 equals 2.5%; (e) 1 in 24 ≈ 4.17% and does not match the computed value exactly.
Common Pitfalls:Mistaking carriageway width with lane width; mixing units (centimetres and metres) without conversion.
Final Answer:1 in 25