GATE 2024 CE (CE2) – Question 62
A horizontal curve of radius 1080 m (with transition curves on either side) in a Broad Gauge railway track is designed and constructed for an equilibrium speed of 70 kmph. However, a few years after construction, the Railway Authorities decided to run express trains on this track. The maximum allowable cant deficiency is 10 cm.
The maximum restricted speed (in kmph) of the express trains running on this track is _______________ (rounded off to the nearest integer).
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Correct answer: 113
Explanation
The cant provided is the equilibrium cant for 70 km/h: $e = \frac{GV^2}{127R} = \frac{1750 \times 70^2}{127 \times 1080} = 62.5$ mm (taking $G = 1750$ mm, the centre-to-centre distance of the rails used for a broad gauge). A train can run faster if its equilibrium cant exceeds the cant provided by at most the permitted deficiency: $62.5 + 100 = 162.5$ mm. So $\frac{1750V^2}{127 \times 1080} = 162.5$, giving $V^2 = 12736$ and $V = 112.9 \approx 113$ km/h.