Question

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 formula/formulae:

• A. \(C = \dfrac{GV^2}{127R}\)
• B. \(C = \dfrac{13.76\,V^2}{R}\)
• C. \(C = \dfrac{13.20\,V^2}{R}\)
• D. \(C = \dfrac{8.33\,V^2}{R}\)

Hint:

Start from \(C=GV^2/127R\) and substitute the Broad Gauge dynamic gauge \(G \approx 1750\) mm; check which options this matches.

Answer 1

The Correct Option is A, B

Step 1: Understanding the Question.
We need to identify which formula (or formulae) correctly gives the cant (superelevation) \(C\) required on a Broad Gauge (BG) curved railway track for an equilibrium speed \(V\), in terms of the dynamic gauge \(G\) and the radius of curvature \(R\).

Step 2: Key Formula or Approach.
Cant is provided so that the resultant of the weight of the vehicle and the centrifugal force at the equilibrium (design) speed acts perpendicular to the plane of the rails. Equating the centrifugal effect to the cant gives the general (theoretical) relation:
\[ C = \frac{GV^2}{127R} \]
Here \(C\) and \(G\) are in mm, \(V\) is in km/h, and \(R\) is in m; the constant \(127\) comes from converting \(V\) from km/h to m/s and using \(g = 9.81\,\text{m/s}^2\) in the force balance. This is a general formula that works for any gauge, once the correct dynamic gauge \(G\) is substituted; so option (A) is always correct.

Step 3: Detailed Explanation.
For a Broad Gauge track, the standard dynamic gauge (distance between the centres of the rail heads, i.e., the actual gauge plus roughly half the rail head width) is taken as \(G \approx 1750\) mm. Substituting this value into the general formula:
\[ C = \frac{1750 \times V^2}{127R} \approx \frac{13.78\,V^2}{R} \]
which, using the constant adopted in Indian Railways design practice, is quoted as:
\[ C = \frac{13.76\,V^2}{R} \]
So option (B) is simply option (A) evaluated at the BG dynamic gauge; it is also correct for BG track. Option (C), \(C = 13.20V^2/R\), and option (D), \(C = 8.33V^2/R\), correspond to smaller dynamic-gauge values (used for Metre Gauge and Narrow Gauge tracks respectively, where \(G\) is smaller than the BG dynamic gauge), and so are not valid for a Broad Gauge track. For instance, taking \(G \approx 1058\) mm (as used for a Metre Gauge track) gives \(1058/127 \approx 8.33\), which is option (D); this constant belongs to a different gauge, not BG.

Step 4: Final Answer.
Both the general theoretical formula \(C = GV^2/127R\) and its Broad-Gauge-specific numerical form \(C = 13.76V^2/R\) correctly give the cant on a BG track.
\[ \boxed{\text{Options (A) and (B)}} \]