Radius of Curve using Midordinate Calculator

Formula Used:

\[ R_c = \frac{M}{1 - \cos\left(\frac{1}{2} \cdot I\right)} \]

Radius of Circular Curve (Rc):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Radius of Curve using Midordinate Formula?

The formula calculates the radius of a circular curve using the midordinate and central angle. This is particularly useful in civil engineering and surveying for designing curved paths and roads.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ R_c = \frac{M}{1 - \cos\left(\frac{1}{2} \cdot I\right)} \]

Where:

\( R_c \) — Radius of Circular Curve (m)
\( M \) — Midordinate (m)
\( I \) — Central Angle of Curve (rad)

Explanation: The formula derives the radius from the midordinate (the distance from the midpoint of the curve to the midpoint of the long chord) and the central angle of the curve.

3. Importance of Radius Calculation

Details: Accurate radius calculation is crucial for designing safe and efficient curved paths in roads, railways, and other infrastructure projects. It ensures proper alignment and helps determine banking angles and speed limits.

4. Using the Calculator

Tips: Enter the midordinate in meters and the central angle in radians. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is midordinate in curve geometry?
A: Midordinate is the perpendicular distance from the midpoint of a curve to the midpoint of the long chord connecting the endpoints of the curve.

Q2: Why is the central angle measured in radians?
A: Radians are the standard unit for angular measurements in mathematical calculations involving trigonometric functions like cosine.

Q3: Can this formula be used for any circular curve?
A: Yes, this formula applies to any circular curve where the midordinate and central angle are known.

Q4: What are typical values for road curve radii?
A: Road curve radii typically range from 15-300 meters for urban roads to 300-1000+ meters for highways, depending on design speed and terrain.

Q5: How does curve radius affect vehicle dynamics?
A: Smaller radii require lower speeds to maintain safety, while larger radii allow for higher speeds. Radius affects centrifugal force, which must be counteracted by road banking.