Cant C on a Broad Gauge railway track is calculated for an equilibrium speed V (in km/h), dynamic gauge G (in mm) and radius of curve R (in m) using for mula/formulae:

The correct options are:
C = GV²/127R and C = 13.20V²/R

1. Understanding Cant (Superelevation):
Cant (or superelevation), represented by C, is the height by which the outer rail is raised above the inner rail on a curved track. This is done to counteract the centrifugal force experienced by a train navigating a curve at a speed V, ensuring lateral stability and passenger comfort.

2. General Formula Derivation:
The standard physical relation for superelevation under equilibrium conditions is given by the formula:

$$C=\frac{G·v^2}{g·R}$$

Where:
- C is the cant or superelevation (in mm or m)
- G is the dynamic gauge of the railway track (in mm or m)
- v is the equilibrium speed of the train (in m/s)
- g is the acceleration due to gravity (approximately 9.81 m/s²)
- R is the radius of the curve (in m)

To express the speed in kilometers per hour (km/h) represented by V, we substitute:
v = V / 3.6

Substituting this relationship into the equilibrium equation gives:

$$C=\frac{G·{\left(\frac{V}{3.6}\right)}^2}{9.81·R}=\frac{G·V^2}{{3.6}^2·9.81·R}$$

Calculating the constant in the denominator:

$${3.6}^2·9.81=12.96·9.81\approx 127.13$$

Rounding this standard engineering constant to 127, we obtain the general formula for cant:

$$C=\frac{G·V^2}{127R}$$

3. Application to a Broad Gauge Track:
For a standard Broad Gauge track, the dynamic gauge G (distance between center-to-center of rail heads) is taken as 1676 mm.
Substituting G = 1676 mm into the cant formula:

$$C=\frac{1676·V^2}{127·R}$$

Simplifying the coefficient numerical ratio:

$$\frac{1676}{127}\approx 13.197\approx 13.20$$

This gives the simplified formula for Broad Gauge track:

$$C=\frac{13.20·V^2}{R}$$