Radius for given Degree of Curve in Railways Calculator

Radius of Curve Formula:

\[ R = \frac{1720}{D_c} \times \frac{\pi}{180} \]

Radius of Curve (m):

Minimum Radius (5% tolerance):

Maximum Radius (5% tolerance):

1. What is Radius for given Degree of Curve in Railways?

Definition: This calculator determines the radius of a railway curve based on the degree of curvature, with optional tolerance percentage.

Purpose: It helps railway engineers and designers calculate appropriate curve radii for track design and safety assessments.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ R = \frac{1720}{D_c} \times \frac{\pi}{180} \]

Where:

\( R \) — Radius of curve (meters)
\( D_c \) — Degree of curve for railways (degrees)
\( \pi \) — Mathematical constant pi (≈3.14159)

Explanation: The formula converts the degree of curve (which is based on a 100-foot chord) to the actual radius in meters.

3. Importance of Railway Curve Radius Calculation

Details: Proper curve radius calculation ensures safe train operation, prevents derailments, and maintains passenger comfort.

4. Using the Calculator

Tips: Enter the degree of curve (must be >0) and tolerance percentage (default 5%). The calculator provides the exact radius plus minimum and maximum values within the tolerance range.

5. Frequently Asked Questions (FAQ)

Q1: What is degree of curve in railways?
A: It's the central angle that subtends a 100-foot chord on the curve, used to describe curve sharpness.

Q2: Why 1720 in the formula?
A: This constant comes from the relationship between the 100-foot chord definition and the circle geometry (100ft ≈ 30.48m).

Q3: What's a typical tolerance percentage?
A: ±5% is common, but this may vary based on specific railway standards and safety requirements.

Q4: How does curve radius affect train speed?
A: Sharper curves (smaller radii) require lower speeds to maintain safety and comfort.

Q5: What's the minimum radius for mainline railways?
A: This varies by country and train type, but typically ranges from 200m to 600m for mainlines.