Superelevation with Friction – Compute e for Given Speed and Radius A vehicle travels at 60 km/h on a horizontal curve of radius R = 128 m. The pavement's side-friction factor is f = 0.15. What superelevation e should be provided (use e + f = v^2 / (127 R), with v in km/h and R in m)?
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Ae = 0.05
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Be = 0.07
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Ce = 0.09
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De = 0.11
Answer
Correct Answer: e = 0.07
Explanation
Introduction / Context:On horizontal curves, part of the lateral acceleration is balanced by roadway banking (superelevation e) and the remainder by side friction f between tires and pavement. Design aims to keep both within safe limits.
Given Data / Assumptions:
- Speed v = 60 km/h.
- Radius R = 128 m.
- Side-friction factor f = 0.15.
- Design relation: e + f = v^2 / (127 R).
Concept / Approach:
Compute the right-hand side from speed and radius, then subtract the allowable friction contribution to find the required superelevation e.
Step-by-Step Solution:
1) Evaluate v^2 / (127 R) = 60^2 / (127 * 128).2) 60^2 = 3600; denominator = 16256; ratio ≈ 0.22146.3) e = 0.22146 − f = 0.22146 − 0.15 ≈ 0.07146.4) Provide e ≈ 0.07 (7%).Verification / Alternative check:
Checking with design tables for v = 60 km/h and R = 125–130 m yields similar e values around 7%, confirming the calculation.
Why Other Options Are Wrong:
- 0.05: Too low, would overload friction.
- 0.09 or 0.11: Higher than required and may be uncomfortable or drain poorly.
Common Pitfalls:
Confusing the constants 127 vs 225; forgetting to subtract f from the total required e + f; rounding e to an impractically fine precision (use 7%).
Final Answer:
e = 0.07