Equilibrium superelevation (cant) for railway curves: for gauge G (m), train speed V (km/h), and curve radius R (m), the equilibrium cant is given by

Introduction / Context:
Superelevation (cant) balances the centrifugal effect on curves so that wheel loads are more evenly distributed and lateral forces are reduced. The equilibrium value depends on gauge, speed, and curvature, and is essential for safe, comfortable high-speed operation.

Given Data / Assumptions:

• G = track gauge in metres (distance between gauge faces).
• V = train speed in km/h.
• R = curve radius in metres.
• e is required in millimetres (mm).

Concept / Approach:

Equating centrifugal acceleration V^2/(R g) to the component of gravitational acceleration along the plane of the superelevated track leads to the familiar relationship e/G = V^2/(127 R) when V is in km/h and e in mm. The constant 127 incorporates unit conversions and g.

Step-by-Step Solution:

Verification / Alternative check:

For G = 1.676 m, V = 80 km/h, R = 600 m: e ≈ 1.676 × 6400 / (127 × 600) ≈ 0.141 m ≈ 141 mm, consistent with practice.

Why Other Options Are Wrong:

Options (b)–(d) are incorrect rearrangements; (e) ignores gauge and uses a different empirical constant unrelated to the standard derivation.

Common Pitfalls:

Using R in degrees of curve instead of metres; forgetting that sanctioned cant may be less than equilibrium to accommodate mixed traffic; exceeding maximum cant or cant deficiency limits.

Final Answer:

e (mm) = (G × V^2) / (127 R)