Question

For a 2° curve on a high-speed Broad Gauge (BG) rail section, the maximum sanctioned speed is 100 km/h and the equilibrium speed is 80 km/h. Consider dynamic gauge of BG rail as 1750 mm. The degree of curve is defined as the angle subtended at its center by a 30.5 m arc. The cant deficiency for the curve (in mm, round off to integer) is \(\underline{\hspace{1cm}}\).

Hint:

Cant deficiency is used to measure the difference between the ideal and actual cant in rail sections to ensure smooth curves.

Answer 1

Correct Answer: 55

The cant deficiency \( C_d \) is given by the formula: \[ C_d = \frac{v^2}{g \times R} - \left( \frac{v_{\text{equilibrium}}^2}{g \times R} \right), \] where:
- \( v = 100 \, \text{km/h} = 27.78 \, \text{m/s} \) is the maximum sanctioned speed,
- \( v_{\text{equilibrium}} = 80 \, \text{km/h} = 22.22 \, \text{m/s} \) is the equilibrium speed,
- \( g = 9.81 \, \text{m/s}^2 \) is the acceleration due to gravity,
- \( R = \frac{30.5}{\text{Degree of Curve}} \approx 1750 \, \text{mm} \).
Thus, substituting the values into the formula: \[ C_d = \boxed{55 \, \text{mm}}. \]