1. What is the Radius of Curve Exact for Chord Formula?

The Radius of Curve Exact for Chord formula calculates the radius of a circular curve based on the degree of curve. This is particularly useful in civil engineering and road design for determining the curvature of roads and railways.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( R_c \) — Radius of Circular Curve (meters)
• \( D \) — Degree of Curve (radians)
• \( \sin \) — Sine trigonometric function

Explanation: The formula calculates the exact radius of a circular curve using the sine of half the angle and the degree of curve.

3. Importance of Radius Calculation

Details: Accurate radius calculation is crucial for designing safe and efficient transportation infrastructure, ensuring proper curvature for vehicle dynamics and comfort.

4. Using the Calculator

Tips: Enter the degree of curve in radians. The value must be valid (degree > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the Degree of Curve?
A: Degree of Curve is the angle subtended at the center of the curve by a chord of standard length (usually 100 feet or 30 meters).

Q2: Why use this specific formula?
A: This formula provides an exact calculation of the radius for a given degree of curve, accounting for the trigonometric relationship.

Q3: What are typical values for radius in road design?
A: Typical values range from 50 meters for sharp curves to over 1000 meters for gentle curves, depending on design speed and road type.

Q4: Are there limitations to this formula?
A: The formula assumes perfect circular curves and may need adjustments for spiral transitions or compound curves in complex designs.

Q5: How does radius affect vehicle operation?
A: Smaller radii require lower speeds and affect vehicle stability, while larger radii allow higher speeds and smoother transitions.