If the sight distance length SD lies outside the curve length R, the following
formula can be derived for estimating the minimum offset clearance:
Ms =L(2 ¥ SD -L)/8R (6.23)
For a derivation of this equation, see O’Flaherty (1986).
6.5.4 Transitions
These curve types are used to connect curved and straight sections of highway.
(They can also be used to ease the change between two circular curves where
the difference in radius is large.) The purpose of transition curves is to permit
the gradual introduction of centrifugal forces. Such forces are required in order
to cause a vehicle to move round a circular arc rather than continue in a straight
line. A finite quantity of time, long enough for the purposes of ease and safety,
will be required by the driver to turn the steering wheel. The vehicle will follow
its own transition curve as the driver turns the steering wheel. The radial accel-
eration experienced by the vehicle travelling at a given velocity vchanges from
zero on the tangent to v^2 /Rwhen on the circular arc. The form of the transition
curve should be such that the radial acceleration is constant.
The radius of curvature of a transition curve gradually decreases from
infinity at the intersection of the tangent and the transition curve to the
designated radius Rat the intersection of the transition curve with the circular
curve.
Tr ansition curves are normally of spiral or clothoid form:
RL=A^2
where
A^2 is a constant that controls the scale of the clothoid
Ris the radius of the horizontal curve
Lis the length of the clothoid
Geometric Alignment and Design 173
Example 6.4
Using the same data as in Example 6.3, calculate the value of Ms using the
approximate method.
Solution
Applying Equation 6.22:
Ms = 1602 /(8 ¥600)
=25600/4800
=5.33 m
