Equilibrium Cant in Railways Calculator

Equilibrium Cant Formula:

\[ e_{eq} = \frac{G \times V^2}{127 \times R} \]

Gauge of Track:

Speed of Vehicle on Track:

km/h

Radius of Curve:

Tolerance:

Equilibrium Cant (m):

±5% Tolerance Range (m):

1. What is Equilibrium Cant in Railways?

Definition: Equilibrium cant is the difference between the height of the outer rail and the inner rail on a curve, designed to counteract the centrifugal force on trains.

Purpose: It ensures passenger comfort and safety by balancing the forces acting on a train when it negotiates a curve.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ e_{eq} = \frac{G \times V^2}{127 \times R} \]

Where:

\( e_{eq} \) — Equilibrium cant (meters)
\( G \) — Gauge of track (meters)
\( V \) — Speed of vehicle on track (km/h)
\( R \) — Radius of curve (meters)

Explanation: The formula balances the centrifugal force with the gravitational force component due to the cant.

3. Importance of Equilibrium Cant Calculation

Details: Proper cant calculation prevents excessive wear on rails and wheels, reduces lateral forces, and improves ride comfort.

4. Using the Calculator

Tips: Enter the gauge (default 1.6m for standard gauge), vehicle speed, curve radius, and tolerance percentage (default ±5%). All values must be > 0 except tolerance which can be 0.

5. Frequently Asked Questions (FAQ)

Q1: What's a typical gauge for railway tracks?
A: Standard gauge is 1.435m, but this varies by country (e.g., 1.6m in some cases).

Q2: Why include a tolerance percentage?
A: Tolerance accounts for variations in speed, load, and track conditions.

Q3: What happens if cant is too high or too low?
A: Excessive cant can cause discomfort, while insufficient cant increases wear and safety risks.

Q4: How does speed affect equilibrium cant?
A: Cant increases with the square of speed - double the speed requires quadruple the cant.

Q5: What's the practical range for cant values?
A: Typically 50-150mm, with maximum values set by railway authorities.