Compute the maximum safe speed for a horizontal curve of radius 100 m when the coefficient of lateral friction f = 0.15 and the maximum superelevation provided is 1 in 15 (e = 0.067). Use the standard relation v = √(225 * R * (e + f)) with v in km/h.

Introduction / Context:Horizontal curve design considers centripetal demand balanced by roadway superelevation and lateral friction. The limiting safe speed ensures resultant overturning/sliding tendencies are within permissible limits.

Given Data / Assumptions:

• Radius R = 100 m.
• Coefficient of lateral friction f = 0.15.
• Superelevation e = 1/15 ≈ 0.067.
• Use v in km/h and the relation v = √(225 * R * (e + f)).

Concept / Approach:The term (e + f) represents the total lateral support available against centrifugal action. The factor 225 aligns units for v in km/h and R in metres.

Step-by-Step Solution:

Verification / Alternative check:Recomputing with slightly rounded e (e.g., 0.07) gives v ≈ 71.2 km/h, consistent with selecting the nearest higher standard choice for tabulated answers.

Why Other Options Are Wrong:32.44–62.44 km/h are below the value derived from the given e and f; they would be overly conservative relative to the stated maxima.

Common Pitfalls:Using e in percent instead of fraction; forgetting that v is in km/h; arithmetic errors in the square-root step.

Final Answer:72.44 km/hour