The Equilibrium super elevation is given by

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Option C:

\frac{V^{2}}{127 R}

Explanation & Concepts: Equilibrium superelevation is the rate of superelevation that exactly neutralizes the centrifugal force acting on a vehicle by utilizing the component of gravity. When the vehicle weight and centrifugal force are balanced by the banking of the road, the pressure on the inner and outer wheels remains equal. Working Principle: The principle relies on the lateral force balance on a curved path. The centrifugal force is given by $P = \frac{WV^2}{gR}$. To counteract this, the component of gravity $W \sin heta$ acts to pull the vehicle inward. Equilibrium is achieved when the centrifugal force component $P \cos heta$ equals the gravitational component $W \sin heta$. Since $ heta$ is small, $ an heta \approx \sin heta \approx e$. Substituting $V$ in km/hr leads to the conversion factor of $127$. Key Formulas: $e = \frac{v^2}{gR}$ — Equilibrium superelevation (v in m/s); $e = \frac{V^2}{127R}$ — Equilibrium superelevation (V in km/hr) Key Points: Equilibrium superelevation eliminates lateral friction demand.; It is calculated specifically for the design speed.; IRC specifies limits for $e$ to ensure safety for slow and fast-moving vehicles.; The constant 127 is derived from $g imes 3.6^2 \approx 9.81 imes 12.96 \approx 127$. Advantages: Uniform distribution of pressure on wheels; Enhanced comfort for passengers on curves Disadvantages: Can be problematic for slow-moving vehicles on steep slopes; Requires significant construction precision Applications: Design of horizontal curves on highways; Railway track banking to maintain stability Additional Info: Option B is mathematically incomplete as it lacks the numerical conversion constant when using km/hr.. Option A represents the radial acceleration formula $\frac{V^2}{R}$ without gravitational or unit constants. Answer: C is correct — The equilibrium superelevation formula for velocity in km/hr is given by $e = \frac{V^2}{127R}$. Exam Tip: Always verify units when dealing with Highway Engineering formulas; $V$ in km/hr always results in a conversion constant like 127, whereas $v$ in m/s uses $g$ (9.81).

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Option A: V2R

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Option B: V2gR V in Km/hr
 
V2gR V in Km/hr

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Option D: None of the above

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