# Reversible clothoid

Representation of the turning clothoid
Curvature band of the turning clothoid

The spiral clothoid (also turning line ) is a design element sequence in the line routing of roads and railway lines . In this case two clothoids with different curvatures meet at their zero point. This will connect two arcs of different curvatures. Similar ( asymmetrical turning clothoids ) or the same ( symmetrical turning clothoids ) clothoid parameters should be used for both clothoids in order to achieve good driving dynamics. The use of the reversible clothoid is the rule in relation to routing and has proven to be a satisfactory solution in the past, as it creates a good transition between two circular arcs that are curved in opposite directions.

A common clothoid parameter results from the radii and the adjacent circular arcs as well as the total clothoid length to be measured from the formula ${\ displaystyle A}$${\ displaystyle R_ {1}}$${\ displaystyle R_ {2}}$${\ displaystyle L_ {ges}}$

${\ displaystyle A = {\ sqrt {\ frac {L _ {\ mathrm {ges}} \ cdot R_ {1} \ cdot R_ {2}} {R_ {1} + R_ {2}}}}}$

The lengths of the clothoids can be calculated using the general clothoid formula. ${\ displaystyle A ^ {2} = R \ cdot L}$

Alternatively, there is the possibility of inserting a so-called intermediate straight line between the circular arc radii if, for example, local constraint points require this. However, this measure is a very imperfect substitute for the transition curve and should only be used on roads and paths with low demands on driving dynamics . In addition, the length of the intermediate straight should not exceed a certain amount in order to get the impression of a turning clothoid.

## Individual evidence

1. ^ Günter Wolf: Street planning . Werner Verlag, Munich 2005, ISBN 3-8041-5003-9 , pp. 124 .