Track speed on curves — determine the safe speed on a Broad Gauge curve of radius 970 m with two transition curves provided.

Introduction / Context:
Safe speed on railway curves depends on cant (super-elevation), permissible cant deficiency, curve radius, and provision of transition curves. With transition curves on Broad Gauge (BG), standard design relationships allow quick estimation of the safe speed for passenger comfort and track forces.

Given Data / Assumptions:

• Gauge: Broad Gauge (BG).
• Curve radius R = 970 m; two transition curves are provided.
• Use typical Indian practice values: design cant (Ea) ≈ 165 mm and permissible cant deficiency (Eu) ≈ 75 mm for passenger routes (representative values used in many exam problems).
• Speed formula (km/h): V ≈ 0.27 * sqrt( (Ea + Eu) * R ), with Ea and Eu in mm and R in m.

Concept / Approach:

Cant (Ea) balances centrifugal force, and cant deficiency (Eu) allows slightly higher speed than perfect equilibrium. With transitions, comfort and safety are improved, making the combined limit (Ea + Eu) applicable in the standard speed formula. Substituting typical values yields the best matching choice among the options.

Step-by-Step Solution:

Verification / Alternative check (if short method exists):

Sensitivity check: modest changes in Ea or Eu shift V slightly; among the discrete options, 132 km/h is the nearest realistic speed for R ≈ 1 km with transitions on BG.

Why Other Options Are Wrong:

112 and 122 km/h undervalue the allowable deficiency; 142 km/h is optimistic for R = 970 m under typical Ea/Eu limits; 102 km/h is too conservative given transitions and BG practice.

Common Pitfalls (misconceptions, mistakes):

Forgetting to include cant deficiency; mixing units (mm vs m); using the equilibrium-speed-only formula without Eu; not recognizing that transitions permit higher comfort speeds.

Final Answer:

132 km/h