Figure indicates the usual situation of two straights projected forward to intersect at I with a clothoid transition curve commencing from tangent point T1 and joining the circular arc at t1. The second equal transition commences at t2 and joins at T2. Thus the composite curve from T1 to T2 consists of a circular arc with transitions at entry and exit.
(1) Fixing the tangent points T1 and T2:
In order to fix T1 and T2 the tangent lengths T1I and T2I are measured from I back down the straights, or they are set out direct by coordinates.
Transition and circular curves
The values of S and C are abstracted from the Highway Transition Curve Tables (Metric) .
(2) Setting out the transitions:
The theodolite is set at T1 and oriented to I with the horizontal circle reading zero. The transition is then pegged out using deflection angles (θ) and chords (Rankine’s method) in exactly the same way as for a simple curve.
The data are calculated as follows:
(a) The length of transition L is calculated (see design factors in Section 10.5.5 and 10.5.6), assume L = 100 m.
(b) It is then spliinto, say, 10 arcs, each 10 m in length (ignoring through chainage), the equivalent chord lengths being obtained from:
Setting out the transitions
(c) The setting-out angles θ1, θ2, . . . , θn are obtained as follows:
Basic formula for clothoid: l
(l is any distance along the transition other than total distance L)
(a) The values for l1, l2, etc., are accumulative.
(b) Thus the values obtained for θ1, θ2, etc., are the final setting-out angles and are obviously not to be summed.
(c) Although the chord length used is accumulative, the method of setting out is still the same as for the simple curve.