We refer to the methods for clothoid designing and, particularly to the observance of the minimum development of the residual arc that could be brought from a formal point of view to unjustified designing solutions incompatible with territorial pre-existences and costs.
Particularly, relations between the value of circumference arc R and deflection angle [alpha] between two straights have been analyzed when the parameter A of the clothoid varies.
Obviously, in case of small angles of deflection, it is necessary to use very large radius R, otherwise, the development of too long clothoid branches would not guarantee the other verifications of parameter A.
In the numerical application, for the sake of simplicity, the maximum speed on the clothoid will be posed equal to [V.
Condition A = R is purely theoretic, because there is no possibility of using the excessive lengths of the clothoid that would be incompatible with the maintenance of an arc with circumference long enough to assure a run of 2.
Clothoid is often prefered for highways and railway route design (Meek, Walton 2004a; 2004b).
It is also recorded that, these clothoid curves provides a coherent course of curvature.
This parabola provides a smaller shift-P with a longer transition and a larger spiral extension (K), besides having the advantage of vis-a-vis the clothoid.
Comparison of transition curves 1 and 2 with clothoid, sinusoidal and bloss curves
The clothoid and bloss curves have almost the same deviation angle.