Radius Of Curve Given Cant For Road Calculator

Radius of Curve Formula:

\[ R = \frac{B \times V^2}{h \times g} \]

Pavement Width (B):

Vehicle Velocity (V):

km/h

Cant (h):

Acceleration due to Gravity (g):

m/s²

Radius of Curve (R):

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1. What is the Radius of Curve Formula?

The Radius of Curve formula calculates the appropriate radius for a curved road or railway track based on pavement width, vehicle velocity, cant (super elevation), and gravitational acceleration. This ensures safe and comfortable travel around curves.

2. How Does the Calculator Work?

The calculator uses the Radius of Curve formula:

\[ R = \frac{B \times V^2}{h \times g} \]

Where:

\( R \) — Radius of Curve (cm)
\( B \) — Pavement Width (cm)
\( V \) — Vehicle Velocity (km/h)
\( h \) — Cant/Super Elevation (cm)
\( g \) — Acceleration due to Gravity (m/s²)

Explanation: The formula balances centrifugal force with gravitational force to determine the optimal curve radius for vehicle stability.

3. Importance of Radius Calculation

Details: Proper curve radius calculation is essential for road safety, preventing vehicle rollover, ensuring passenger comfort, and maintaining optimal vehicle speed through curves.

4. Using the Calculator

Tips: Enter pavement width in cm, vehicle velocity in km/h, cant in cm, and gravitational acceleration in m/s². All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is cant/super elevation?
A: Cant refers to the transverse slope provided on curved roads or railway tracks to counteract centrifugal force and improve vehicle stability.

Q2: Why is gravitational acceleration important?
A: Gravitational acceleration (9.8 m/s²) provides the downward force that helps balance the outward centrifugal force on curved paths.

Q3: How does vehicle velocity affect curve radius?
A: Higher vehicle velocities require larger curve radii to maintain safety and comfort, as centrifugal force increases with the square of velocity.

Q4: What are typical values for road curve radii?
A: Curve radii vary widely based on road type and speed limits, ranging from 15-30 meters for low-speed urban roads to several hundred meters for highways.

Q5: Can this formula be used for railway tracks?
A: Yes, the same fundamental principles apply to railway track design, though specific parameters and safety factors may differ.