Figure  indicates a compound curve requiring transitions at T1, t and T2. To permit the entry of the transitions the circular arcs must be shifted forward as indicated in Figure where

Compound curve construction

 The lengths of transition at entry (L1) and exit (L2) are found in the normal way, whilst the transition connecting the compound arcs is:

The distance P1P2 = (S1 −S2) is bisected by the transition curve at P3. The curve itself is bisected and length bP3 = P3c. As the curves at entry and exit are set out in the normal way, only the fixing of their tangent points T
1 and T
2 will be considered. In triangle t1It2:

from which the triangle may be solved for t1I and t2I.

The curve bc is drawn enlarged in Figure 10.35 from which the method of setting out, using the osculating circle, may be seen.
Setting-out from b, the tangent is established from which the setting-out angles would be (δ1 − θ1), (δ2 − θ2), etc., as before, where δ1, the angle to the osculating circle, is calculated using R1. If setting out from C, the angles are obviously (δ1 θ1), etc., where δ1 is calculated using R2. Alternatively, the curve may be established by right-angled offsets from chords on the osculating circle, using the following equation:

Transition between arcs of different radii

Reverse compound curve

It should be noted that the osculating circle provides only an approximate solution, but as the transition is usually short, it may be satisfactory in practice. In the case of a reverse compound curve

otherwise it may be regarded as two separate curves.

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