Question

A train rounds a curve of radius 150m at a speed of 20 m/s . Calculate the angle of banking so that there is no side thrust on the rails . Also find the elevation of the outer rail over the inner rail, if the distance between the rails is 1m

Answer 1

banking angle = 15⁰, elevation = 0.28 m

explanation

radius (r) = 150 m

velocity (v) = 20 m/s

gravitational constant (g) = 9.8 m²/s

Banking angle = tan θ = v²/ rg

tan θ  = (20)² / (150) (9.8)

tan θ  = 400/ 1470

tan θ  = 40/147

θ = (tan)⁻¹ (40/147)

θ  = 15⁰

distance between rails (adjacent)  = 1 m

tan 15⁰ = opposite / adjacent

tan 15⁰ = $\sqrt{3}$ / 6 = opposite/ 1

opposite (elevation) = 0.28 m