Chapter: Civil : Highway Engineering : Geometric Design Of Highways
Highways Design: Horizontal curve
Horizontal
curve
The presence of horizontal curve imparts
centrifugal force which is reactive force acting outward on a vehicle
negotiating it. Centrifugal force depends on speed and radius of the horizontal
curve and is counteracted to a certain extent by transverse friction between
the tyre and pavement surface. On a curved road, this force tends to cause the
vehicle to overrun or to slide outward from the centre of road curvature. For
proper design of the curve, an understanding of the forces acting on a vehicle
taking a horizontal curve is necessary. Various forces acting on the vehicle
are illustrated in the figure.
They are the centrifugal force (P) acting outward,
weight of the vehicle (W) acting downward, and the reaction of the ground on
the wheels (RA and RB ). The centrifugal force and the weight is assumed to be
from the centre of gravity which is at h units above the ground. Let the wheel
base be
assumed
as b units. The centrifugal force P in kg=m2 is given by
where W is the weight of the vehicle in kg, v is the speed of
the vehicle in m=sec, g is the acceleration due to gravity in m=sec2
and R is the radius of the curve in m.
The centrifugal force has two effects: A tendency to overturn
the vehicle about the outer wheels and a tendency for transverse skidding.
Taking moments of the forces with respect to the outer wheel
when the
vehicle is just
The second tendency of the vehicle is for
transverse skidding. i.e. When the centrifugal force P is greater than the
maximum possible transverse skid resistance due to friction between the
pavement surface and tyre. The transverse skid resistance (F) is given by:
where FA
and FB is the fractional force at tyre A and B, RA and RB is the reaction at
tyre A and B, f is the lateral coefficient of friction and W is the weight of
the vehicle. This is counteracted by the centrifugal force (P), and equating:
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