1. What is the Radius of Curve given Tangent Formula?

The formula calculates the radius of a circular curve in surveying and civil engineering when the tangent length and deflection angle are known. It's derived from the geometric properties of circular curves.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( R_{Curve} \) — Curve Radius (m)
• \( T \) — Tangent Length (m)
• \( \Delta \) — Deflection Angle (radians)

Explanation: The formula relates the curve radius to the tangent length and deflection angle using trigonometric relationships in circular curve geometry.

3. Importance of Curve Radius Calculation

Details: Accurate curve radius calculation is essential in road design, railway engineering, and surveying for determining proper alignment, superelevation requirements, and safe vehicle operation.

4. Using the Calculator

Tips: Enter tangent length in meters and deflection angle in radians. Both values must be positive numbers greater than zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a deflection angle in curve geometry?
A: The deflection angle is the angle between the initial tangent and the tangent at any point on the curve, measured from the initial tangent.

Q2: Can this formula be used for both horizontal and vertical curves?
A: This specific formula is primarily used for horizontal circular curves in transportation engineering and surveying applications.

Q3: What are typical units for these measurements?
A: Tangent length is typically measured in meters or feet, while deflection angle is measured in radians or degrees (conversion may be needed).

Q4: Are there limitations to this formula?
A: This formula applies specifically to circular curves. For spiral curves or compound curves, different formulas and approaches are required.

Q5: How does curve radius affect vehicle operation?
A: Smaller curve radii require lower speeds and may necessitate superelevation (banking) to maintain vehicle stability and passenger comfort.