Super-elevation or cant or banking is the transverse slope provided at horizontal curve to counteract the centrifugal force, by raising the outer edge of the pavement with respect to the inner edge, throughout the length of the horizontal curve.
Analysis
of Super-elevation
Super-elevation or cant or banking is the
transverse slope provided at horizontal curve to counteract the centrifugal
force, by raising the outer edge of the pavement with respect to the inner
edge, throughout the length of the horizontal curve. When the outer edge is
raised, a component of the curve weight will be complimented in counteracting
the effect of centrifugal force. In order to find out how much this raising
should be, the following analysis may be done. The forces acting on a vehicle
while taking a horizontal curve with superelevation is shown in figure
Forces acting on a vehicle on horizontal curve of radius R m
at a speed of v m=sec^{2} are:
Analysis of super-elevation P the centrifugal force acting
horizontally out-wards through the center of gravity, W the weight of the
vehicle acting down-wards through the center of gravity, and F the friction
force between the wheels and the pavement, along the surface inward. At
equilibrium, by resolving the forces parallel to the surface of the pavement we
get,
P cos =
W sin?
+
FA+ FB
= W sin?
+
f (RA+ RB)
= W sin?
+
f (W cos?
+
P sin?)
where W is the weight of the vehicle, P is the centrifugal
force, f is the coefficient of friction, is the transverse slope due to super
elevation. Dividing by W cos?, we get:
By
substituting the value of P/W this in equation
Design of
super-elevation
While designing the various elements of the road
like superelevation, we design it for a particular vehicle called design vehicle
which has some standard weight and dimensions. But in the actual case, the road
has to cater for mixed traffic. Different vehicles with different dimensions
and varying speeds ply on the road. For example, in the case of a heavily
loaded truck with high centre of gravity and low speed, superelevation should
be less; otherwise chances of toppling are more. Taking into practical
considerations of all such situations, IRC has given some guidelines about the
maximum and minimum superelevation etc.
For fast moving vehicles, providing higher
superelevation without considering coefficient of friction is safe, i.e.
centrifugal force is fully counteracted by the weight of the vehicle or
superelevation. For slow moving vehicles, providing lower superelevation considering
coefficient of friction is safe, i.e. centrifugal force is counteracted by
superelevation and coefficient of friction. IRC suggests following.
.