1. What is External Distance?

External Distance (E) in circular curve geometry is the distance from the point of intersection (PI) of the tangents to the midpoint of the curve. It represents how far the curve "bulges out" from the straight tangent lines.

2. How Does the Calculator Work?

The calculator uses the External Distance formula:

Where:

• \( E \) — External Distance (m)
• \( R_c \) — Radius of Circular Curve (m)
• \( I \) — Central Angle of Curve (radians)
• \( \pi \) — Mathematical constant pi (approximately 3.14159)
• \( \sec \) — Secant trigonometric function

Explanation: The formula calculates how far the curve midpoint extends from the intersection point of the tangents, based on the curve radius and central angle.

3. Importance of External Distance Calculation

Details: External distance is crucial in road and railway design for determining clearance requirements, sight distances, and ensuring proper geometric alignment of curves.

4. Using the Calculator

Tips: Enter the radius of the circular curve in meters and the central angle in radians. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the inputs?
A: Radius should be in meters and central angle should be in radians for accurate results.

Q2: Can I use degrees instead of radians?
A: The formula requires radians. Convert degrees to radians by multiplying by π/180.

Q3: What is a typical range for external distance values?
A: External distance varies significantly based on curve radius and angle, ranging from centimeters for tight curves to meters for gentle curves.

Q4: How is external distance used in civil engineering?
A: It's used to determine clearance requirements, calculate curve offsets, and ensure proper geometric design of transportation infrastructure.

Q5: What if I get a negative external distance?
A: External distance should always be positive. A negative result indicates an error in input values or calculation.