Continuous Welded Rail (CWR) Movement Calculator

This tool calculates the total thermal movement in a section of CWR and helps determine the correct physical gap for an adjustment switch (breather) based on the current rail temperature.

Total Thermal Movement

Calculates the total expected expansion or contraction over a given temperature range.

(e.g., for a rail installed at 20°C that drops to -10°C, the $\Delta T$ is 30)

Breather Setting Calculation

Determines the required physical overlap for a breather at the current rail temperature.

Reference Mathematical Formulæ

Thermal Expansion Formula

The change in length ($\Delta L$) of a rail due to temperature change is given by:

$$\Delta L = \alpha \times L \times \Delta T$$

Where:

  • $\Delta L$ is the change in length (in metres)
  • $\alpha$ is the coefficient of thermal expansion for steel (approx. $11.5 \times 10^{-6} \text{ mm/mm/}^{\circ}\text{C}$)
  • $L$ is the original length of the rail section (in metres)
  • $\Delta T$ is the change in temperature (in °C)

Breather Overlap Formula

The required physical overlap ($O_{current}$) of the breather at the current rail temperature is a function of its nominal overlap at the stress-free temperature ($O_{sf}$) and the thermal movement ($\Delta L$) of the rail section.

$$O_{current} = O_{sf} + \Delta L$$

Where:

  • $O_{current}$ is the required breather overlap (in mm)
  • $O_{sf}$ is the nominal breather overlap at the stress-free temperature (in mm)
  • $\Delta L$ is the thermal movement of the rail section relative to $T_{sf}$ (in mm)
  • $\Delta L = \alpha \times L \times (T_{current} - T_{sf})$