Mechanics
Banking
of a Road Surface
Moving
in a Straight line on a Horizontal Surface
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The
normal reaction, R, has no
component acting towards the centre of the circular
path.
Therefore
the required centripetal acceleration is provided by
the force of friction, Ff, between the
wheel and the road.
If the
force of friction is not strong enough, the vehicle
will skid.
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The
normal reaction, R, now
has a component acting towards the centre of the
circular path.
If
the angle,
 ,
is just right, the correct centripetal acceleration
can be provided by the horizontal component of the
normal reaction.
This
means that, even if there is very little force of
friction the vehicle can still go round the curve with
no tendency to skid.
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Angle
of Banking
The magnitude
of the horizontal component of the normal reaction is
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This force
causes the centripetal acceleration,
so, the magnitude of RH is also given by
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equation
1
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So,
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equation
2
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The vertical
forces acting on the vehicle are in
equilibrium.
Therefore,
considering magnitudes only
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Dividing
equation 1 by equation 2 gives:
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This
equation allows us to calculate the angle
needed for a vehicle to go round the curve at a given
speed, v, without any tendency to skid.
needed for a vehicle to go round the curve at a given
speed, v, without any tendency to skid.
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