When a vehicle travells aloung a circular curve,a centrifugal force will be develop which will try to pull away the vehicle in the direction perpendicular to the tangent of the curve at that point.In order to prevent the vehicle from this centrifugal force,little height will provide at the outer part of the curve.The raised height is called the cant.Superelevation prevents the lateral skidding of vehicle outwards.
Super elevation can be provided in two methods
1.Rotation about the centre line.
2 Rotation about the outer line.
The centrifugal force
P= mv² / R
m = Mass of the body
v=Velocity of the vehicle
Consider the equlibrium of the vehicle
= f *w/2 +f *w/2
=f * w
where f is the coefficient of lateral friction
w is the weight of the vehicle
p /w =f
P/W = f = v²/gR
Cases of superelevation
No skidding friction
f > P/W or V² / gR
Consider the equillbrium correspoding to the overturning.At the verge of overturning,the contact between the inner wheel and the ground will be lost
Taking moment about the outer wheel
P*h = W * B/2
P/W = B/2h = v² /gR
B/2h > P/W implies No overturning
From the two above cases
- P/W < f ,P/W < B/ 2h Safe against both skidding and overturning
- P/W > f ,P/W < B/ 2h Skidding but no overturning
- P/W ≤ f ,P/W ≥B/ 2h No skidding ,but overturning
- P/W > f ,P/W > B/ 2h
F> B/2H Overturning occures.
F< B/2H Skidding occures then overturning.
F=B/2H Always overturning happens first, after overturning there is no value for skidding.