Banking of Road Formula: Angle of Banking, Solved Questions

Definition

Banking Of Road Formula: Road banking, also known as superelevation, refers to the tilting or inclination of a road's surface on curved sections. It is a deliberate design technique applied to ensure safety and stability for vehicles navigating curves. The key principle is to provide a centripetal force that assists vehicles in remaining on the road during turns.

Relevance: Understanding the relevance of road banking is paramount. It is employed to counteract the lateral forces that occur when a vehicle traverses a curved path. By creating a banking angle, engineers reduce the reliance on friction for vehicle stability, thus making driving on curves safer and more efficient. Road banking is particularly crucial on high-speed roads with numerous curves, where ensuring the safety of motorists is paramount.

Books for Banking Exam Preparation

Angle of Banking

The formula to calculate the angle of banking (θ) for a road is derived from the equilibrium between gravitational force and centripetal force acting on a vehicle:

Angle of Banking (θ) = tan -1 (v² / (g * r))

Here's a step-by-step breakdown of the formula:

-Angle of Banking (θ): This is the inclination or tilt of the road surface, which we are trying to calculate.

v: Represents the speed of the vehicle traveling along the curved road.

g: Denotes the acceleration due to gravity.

r: Stands for the radius of the curve.

The formula's core purpose is to determine the necessary angle of banking required for a specific curve, taking into account the speed of vehicles and the curve's radius.

Solved Questions of Banking of Road Formula

Let's explore a series of practical questions to demonstrate how the road banking formula is applied in real scenarios:

Solved Question 1: Calculate the angle of banking for a curved road with a radius of 100 meters and a vehicle speed of 30 meters per second.

Step 1 - Gather the given values:

- Radius of the curve (r) = 100 meters

- Vehicle speed (v) = 30 meters per second

- Acceleration due to gravity (g) is a constant, approximately 9.81 m/s².

Step 2 - Apply the banking formula:

Angle of Banking (θ) = atan(v² / (g * r))

Step 3 - Plug in the values:

θ = atan((30 m/s)² / (9.81 m/s² * 100 m))

Step 4 - Calculate the angle of banking:

θ ≈ atan(900 / 981) ≈ atan(0.918) ≈ 44.16 degrees

Also Check – Electric Field Formula

Solved Question 2: A highway curve has a radius of 200 meters, and a car is traveling at 25 meters per second. What is the required angle of banking?

Step 1 - Gather the given values:

- Radius of the curve (r) = 200 meters

- Vehicle speed (v) = 25 meters per second

Step 2 - Apply the banking formula:

Angle of Banking (θ) = atan(v² / (g * r))

Step 3 - Plug in the values:

θ = atan((25 m/s)² / (9.81 m/s² * 200 m))

Step 4 - Calculate the angle of banking:

θ ≈ atan(625 / 1962) ≈ atan(0.319) ≈ 17.77 degrees

Also Check – Horsepower Formula

Solved Question 3: If a motorcycle is moving at 20 meters per second on a bend with a 50-meter radius, what should be the angle of banking to ensure safety?

Step 1 - Gather the given values:

- Radius of the curve (r) = 50 meters

- Vehicle speed (v) = 20 meters per second

Step 2 - Apply the banking formula:

Angle of Banking (θ) = atan(v² / (g * r))

Step 3 - Plug in the values:

θ = atan((20 m/s)² / (9.81 m/s² * 50 m))

Step 4 - Calculate the angle of banking:

θ ≈ atan(400 / 490.5) ≈ atan(0.815) ≈ 39.67 degrees

Solved Question 4: What happens if a road is improperly banked, and how can it lead to accidents?

Step 1 - Understanding improper banking:

Improper banking can result in insufficient or excessive banking angles. When the banking is too little for a given speed and curve radius, vehicles might slide outwards in a curve, potentially leading to accidents. On the other hand, excessive banking can cause vehicles to tip over.

Solved Question 5: How does weather, such as rain or snow, impact road banking, and what adjustments may be necessary?

Step 1 - Weather impact on road banking:

Weather conditions affect the friction between tires and the road surface. In wet or icy conditions, the coefficient of friction decreases, making it easier for vehicles to skid. To address this, road authorities may adjust the banking angle or apply road treatments such as de-icing chemicals to maintain safety.

Also Check – Strain Formula

Solved Question 6: Can road banking be customized for different vehicle types, including trucks and motorcycles?

Step 1 - Customized banking for different vehicles:

Yes, road banking can be customized to accommodate various vehicle types. Heavier vehicles, like trucks, may require slightly different banking angles compared to lighter vehicles like motorcycles. Engineers consider factors such as vehicle weight and size when designing road banking for specific road sections.

Solved Question 7: What common materials are used for road surfaces in road banking projects?

Step 1 - Common road surface materials:

The materials used for road surfaces in banking projects often include asphalt and concrete. These materials provide a smooth and durable surface that can withstand the forces exerted by vehicles as they navigate curves.

Solved Question 8: Are there innovative approaches to sustainable road banking that minimize environmental impact?

Step 1 - Sustainable road banking:

Innovative approaches to sustainable road banking focus on using eco-friendly materials and designs to reduce the environmental impact. This may include materials with lower carbon footprints and road designs that enhance water drainage and reduce pollution.

These are the stepwise solutions for all the solved questions. If you have any more questions or need further explanations, please feel free to ask, and I'll be happy to assist you.