Question

a meter gauge railway track is to be banked at a circular curve of radius 450m. what should be the elevation of the outer rail above the inner rail for an optimum speed of 54km/hr so that there is no side thrust on the outer rail.

Answer 1

Okay so, meter gauge railway track is something like that in the attachment. Now acc. to ques. we need to find the distance/height between outer rail above the inner rail.

So, from question, we have;

• Velocity of train = 54 km/h = 15 m/s
• Radius = 450 m
• length = 1m

Now, we know that, in the case of a banked railway track;

• Tanθ = v²/rg ( where g is the acceleration due to gravity. )

= Tanθ = v²/rg

= Tanθ = 15²/450 × 9.8

= Tanθ = 225 / 4410

= Tanθ = 0.0510204

= θ = tan⁻¹( 0.0510204 )

= θ = 2.9°

Now, finally the elevation of outer rail above inner rail;

• h = l × sinθ
• h = 1 × sin(2.9°)
• h = 0.05059 m

Thus, the height of outer rail from inner will be 0.0506 m.

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Thank youu! :)) $\:$