When a vehicle passes from a straight to a curved path or in other words when a vehicle negotiates horizontal curve following two forces act on vehicle:
- Centrifugal Force
- Weight of the Vehicle
The centrifugal force is a function of the speed of the moving vehicle. It always acts at the centre of gravity of the vehicle. It’s direction always tends to outside, i.e., it always tends to push the vehicle out of the track. to counteract this tendency, the outer edge of the road is raised above the inner edge. This rise of the outer edge is called superelevation or cant or banking.
Thus superelevation e is the ratio of the height of the outer edge with respect to the horizontal width.
e = tan θ
In practice, the value of θ is kept as 4° or a slope of 1 in 15 with horizontal.
The total height of the outer edge with respect to the inner edge
E = e × width of road
= e B
The centrifugal force P = Wv2/gR
W = weight of the vehicle
v = velocity of the vehicle
R = radius of circular curve
P = centrifugal force
g = acceleration due to gravity
Effect of Centrifugal Force
- The tendency to overturn the vehicle.
- The tendency to skid the vehicle laterally.
Stability Condition Against Overturning
The figure shows a vehicle moving on horizontal a curve. Forces acting on the vehicle are
- Centrifugal force P acting outward at C.G.
- Weight W acting downward at C.G.
Let h be the height of C.G. of the vehicle above the road level. The overturning moment due to centrifugal force.
= P × h
The restoring moment = W × b/2
where b is the centre to centre distance of wheels of the vehicle.
In limiting equilibrium
Ph = Wb/2
P/W = b/2h
When the centrifugal ratio, P/W is equal to B/2h there is a danger of overturning.
Thus to avoid overturning, the centrifugal ratio should always be less than b/2h. Also
P/W = v2/gR
Stability Condition Against Skidding
The lateral thrust P = Wv2/gR is resisted by the frictional force between the tyre and pavement surface. If the lateral resisting friction is less than the centrifugal force P, then skid will occur. Thus in limiting equilibrium, P = Maximum lateral friction developed as shown in the figure.
P = Fa + Fb
or P = f (RA + RB)
P = fW
Or P/W = f
Thus when the centrifugal ratio attains the value equal to the lateral coefficient of friction, there is a danger of lateral skidding.
If f < b/2h skidding would occur.
If f > B/2h overturning at the outer edge would occur.
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