Railway/Highway superelevation formulation If G is the track gauge (distance between rail centrelines), v the vehicle speed, g gravitational acceleration, and r the curve radius, the equilibrium superelevation e (height by which outer rail is raised) is given by:

Introduction / Context:
Superelevation (cant) is provided on curved tracks and highways to balance the lateral acceleration and reduce reliance on side friction. The design relation links the required rail height difference to speed, radius, and gauge/width.

Given Data / Assumptions:

• Track gauge (or effective wheelbase width) G.
• Vehicle travels at speed v on a circular curve of radius r.
• Gravity g; steady-state condition (no transition dynamics).
• Equilibrium condition neglecting side friction (pure balancing of centripetal acceleration).

Concept / Approach:

At equilibrium, the resultant of weight and centrifugal inertia is perpendicular to the track plane. With track banked at angle θ, tan θ equals the required centripetal acceleration divided by g, i.e., tan θ = v^2/(g r). The rail height difference e relates to θ and gauge G by tan θ ≈ e/G for small angles, yielding the design formula.

Step-by-Step Solution:

Verification / Alternative check:

Dimensional check: G [L], v^2/(g r) dimensionless → e has length [L], consistent. For larger r or smaller v, e reduces as expected.

Why Other Options Are Wrong:

(b) omits G; (c)–(e) invert variables incorrectly and are dimensionally inconsistent for length.

Common Pitfalls:

Confusing gauge G with lane width; using degrees instead of radians for tan θ small-angle approximation.

Final Answer:

e = (G * v^2) / (g * r)