1. What is the Curve Radius Formula?

The curve radius formula calculates the radius of a circular curve given the length of the long chord and the deflection angle. This is essential in road design, railway engineering, and other construction projects involving curved paths.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( R_{Curve} \) — Curve Radius (m)
• \( C \) — Length of Long Chord (m)
• \( \Delta \) — Deflection Angle (radians)

Explanation: The formula derives from trigonometric relationships in a circle, where the long chord subtends the deflection angle at the center of the circle.

3. Importance of Curve Radius Calculation

Details: Accurate curve radius calculation is crucial for designing safe and efficient transportation routes, ensuring proper vehicle dynamics, and maintaining structural integrity in curved constructions.

4. Using the Calculator

Tips: Enter the length of long chord in meters and deflection angle in radians. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a long chord in curve geometry?
A: The long chord is the straight line connecting the two endpoints of a curve, representing the longest chord within that curve segment.

Q2: Why is the deflection angle divided by 2 in the formula?
A: The deflection angle is divided by 2 because the chord subtends an angle at the center that is twice the angle between the chord and the tangent.

Q3: Can I use degrees instead of radians?
A: The formula requires the angle in radians. Convert degrees to radians by multiplying by π/180 before calculation.

Q4: What are typical values for curve radius in road design?
A: Curve radii vary widely from 15-20m for sharp urban turns to several hundred meters for highway curves, depending on design speed and vehicle type.

Q5: How does curve radius affect vehicle dynamics?
A: Smaller radii require lower speeds to maintain safety and comfort, while larger radii allow higher speeds with less lateral acceleration.