The super elevation is

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The correct answer is Option A: directly proportion to the speed of the vehicle. Super elevation (e) is defined as the transverse inclination provided to the road surface to counteract the centrifugal force acting on a vehicle moving along a curved path. Since the centrifugal force is proportional to the square of the velocity ($V^2$), the super elevation required for a given radius is directly proportional to the square of the design speed.

Step-by-Step Solution & Concepts:
Super elevation (e) is defined as the transverse inclination provided to the road surface to counteract the centrifugal force acting on a vehicle moving along a curved path. Since the centrifugal force is proportional to the square of the velocity ($V^2$), the super elevation required for a given radius is directly proportional to the square of the design speed.

Working Principle: When a vehicle negotiates a curve, it experiences a centrifugal force $P = \frac{WV^2}{gR}$. To balance this, the weight component of the vehicle $W \cdot e$ acts in the opposite direction. Equating these gives $e + f = \frac{V^2}{gR}$, showing that for a constant radius and coefficient of friction, $e$ must increase as $V$ increases.

Key Formulas: $e + f = \frac{V^2}{gR}$ — Fundamental relation between super elevation ($e$), lateral friction ($f$), velocity ($V$), and radius ($R$); $e = \frac{V^2}{127R}$ — Design formula for super elevation when friction is neglected (equivalent to $75\%$ of design speed)

Key Points: Super elevation is inward tilting of the road cross-section.; It helps maintain stability against overturning and skidding.; Maximum value of super elevation is generally limited to 0.07 for plain and rolling terrain.; It is independent of pavement width in the basic design equation.

Advantages: Reduces the tendency of vehicles to skid outwards.; Ensures uniform distribution of wheel pressure on pavement.; Increases comfort for passengers during curve negotiation.

Disadvantages: Difficult to provide at intersections.; Excessive super elevation can cause slow-moving vehicles to slide inward.; Complexity in drainage design at the inner edge.

Applications: Horizontal curves on Highways.; Railway tracks to prevent derailment.; Velodromes (racing tracks) where high speeds require significant banking.

Additional Info: Standard IRC:73 guidelines recommend $e_{max} = 0.07$ for plain terrain.. Option B is incorrect because super elevation increases, not decreases, with speed.. Options C and D are incorrect because $e$ is independent of pavement width $W$ in the standard mechanics of point-mass vehicle dynamics.

Answer: A is correct — Super elevation is directly proportional to the square of the speed of the vehicle to counteract the centrifugal force.

Exam Tip: Always remember the $V^2$ relationship; in design problems, if speed doubles, required super elevation theoretically quadruples.

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Option B: Inversely proportional to the speed of the vehicle

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Option C: directly proportion to the speed of the width of the pavement

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Option D: Inversely proportional to the width of the pavement

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