Central Angle of Curve for given Length of Long Chord Calculator

Formula Used:

\[ \text{Central Angle of Curve} = \frac{\text{Length of long Chord}}{2 \times \text{Radius of Circular Curve} \times \sin(1/2)} \]

Central Angle of Curve (I):

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1. What is the Central Angle of Curve?

The Central Angle of Curve is the deflection angle between tangents at the point of intersection of tangents in circular curve geometry. It represents the angle subtended at the center of the circular curve by the long chord.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ I = \frac{C}{2 \times R_c \times \sin(1/2)} \]

Where:

\( I \) — Central Angle of Curve (radians)
\( C \) — Length of Long Chord (meters)
\( R_c \) — Radius of Circular Curve (meters)
\( \sin \) — Sine trigonometric function

Explanation: The formula calculates the central angle based on the geometric relationship between the long chord length and the radius of the circular curve, using trigonometric principles.

3. Importance of Central Angle Calculation

Details: Accurate calculation of the central angle is crucial for road design, railway engineering, and other civil engineering applications where circular curves are used. It helps in determining the deflection angles for setting out curves and ensuring proper alignment.

4. Using the Calculator

Tips: Enter the length of the long chord in meters and the radius of the circular curve in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between central angle and deflection angle?
A: The central angle is the angle at the center of the circle subtended by the curve, while the deflection angle is the angle between the tangents at the point of intersection.

Q2: Can this formula be used for any circular curve?
A: Yes, this formula applies to all circular curves where the long chord length and radius are known.

Q3: What units should be used for input values?
A: The calculator uses meters for both length and radius inputs, and outputs the central angle in radians.

Q4: How accurate is this calculation?
A: The calculation is mathematically precise based on the input values, using trigonometric functions for accurate results.

Q5: Can I convert the result to degrees?
A: Yes, you can convert radians to degrees by multiplying by 180/π (approximately 57.2958).