Question

Derrive an expression for maximum permissible speed

Answer 1

The proper velocity or optimum v on a road banked by an angle θ with the horizontal is given by  

v = [rg(µs + tan θ)/(1−µs tanθ)]½

 where r = radius of curvature of road,  g = acceleration due to gravity ,  µs = coefficient of friction between road and tyres.  

Substituting  

r = 1000 m, µs = 0.5, tan θ = 1, g = 9.8 m/s2,  

we get

v = 171.46 m/s