Radius Given Apex Distance Calculator

Formula Used:

\[ \text{Curve Radius} = \frac{\text{Apex Distance}}{\sec(\frac{\text{Deflection Angle}}{2}) - 1} \]

Curve Radius:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Radius Given Apex Distance Formula?

The formula calculates the curve radius based on the apex distance and deflection angle. It is commonly used in surveying and civil engineering to determine the radius of a circular curve.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Curve Radius} = \frac{\text{Apex Distance}}{\sec(\frac{\text{Deflection Angle}}{2}) - 1} \]

Where:

\( \text{Apex Distance} \) — Distance from the point of intersection to the apex of the curve (meters)
\( \text{Deflection Angle} \) — Angle between the first sub chord of curve and the deflected line (radians)
\( \sec \) — Secant trigonometric function

Explanation: The formula calculates the radius of a circular curve using the apex distance and half of the deflection angle through trigonometric relationships.

3. Importance of Curve Radius Calculation

Details: Accurate curve radius calculation is essential in road design, railway engineering, and other infrastructure projects to ensure proper alignment, safety, and smooth transitions between straight and curved sections.

4. Using the Calculator

Tips: Enter apex distance in meters and deflection angle in radians. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is apex distance in curve geometry?
A: Apex distance is the distance from the point of intersection (PI) to the apex of the curve, which is the highest point on a vertical curve or the furthest point on a horizontal curve.

Q2: Why is the deflection angle divided by 2 in the formula?
A: The deflection angle is divided by 2 because the formula uses half of the total deflection angle to calculate the secant value, which corresponds to the geometry of circular curves.

Q3: What units should be used for input values?
A: Apex distance should be in meters and deflection angle should be in radians. Make sure to convert degrees to radians if necessary (1 degree = π/180 radians).

Q4: Are there any limitations to this formula?
A: This formula is specifically designed for circular curves. It may not be accurate for spiral curves or other complex curve types commonly used in modern transportation design.

Q5: How is this calculation used in practical applications?
A: This calculation is fundamental in road design, railway engineering, and surveying for determining curve parameters, setting out curves in the field, and ensuring proper geometric design of transportation infrastructure.