Superelevation formula on horizontal curves For a vehicle of speed V (km/h) negotiating a horizontal curve of radius r (m) on a level road without relying on side friction, the required superelevation e (as a ratio) is best given by:

Introduction / Context:
Superelevation tilts the pavement to counteract the lateral acceleration on curves. A common design expression (with V in km/h and r in metres) relates e to speed and radius when friction is not mobilized.

Given Data / Assumptions:

• Level road, no grade effects.
• Superelevation alone balances the centrifugal force (no side friction component).
• V in km/h; r in m; e is dimensionless (e.g., 0.07 = 7%).

Concept / Approach:
From lateral equilibrium, v^2/(g r) = e when friction is neglected. Converting V from km/h to m/s brings in the constant 225 so that e = V^2 / (225 * r).

Step-by-Step Solution:

Verification / Alternative check:
The more general relation is e + f = V^2/(225 r). Setting f = 0 recovers e = V^2/(225 r).

Why Other Options Are Wrong:
Options B and D introduce the carriageway width W erroneously; C is the reciprocal of the correct form.

Common Pitfalls:
Mixing units for V and r; forgetting that practical designs cap e (e.g., 7% in plains).

Final Answer:
e = V^2 / (225 * r)