10.7 CUBIC SPIRAL AND CUBIC PARABOLA

Approximation of the clothoid formula produces the cubic spiral and cubic parabola, the latter being used on railway and tunnelling work because of the ease in setting out by offsets. The cubic spiral can be used for minor roads, as guide for excavation prior to the clothoid being set out, or as check on clothoid computation.

(10.25)

Approximating equation (10.23) gives

(10.26)

In both cases:

(10.27)

(10.28)

(10.29)

(10.30)

The deflection angles for these curves may be obtained as follows (the value of N being ignored):

(10.31)

When the value of ? ? 24 , the radius of these curves starts to increase again, which makes them useless as transitions.

Refer to worked examples for application of the above equations, and note 'back-angle to origin' would be ( ? - ?) or .