Any motor vehicle follows a transition path as it enters or leaves a circular horizontal curve. The steering change and the consequent gain or loss of centrifugal force cannot be effected instantly. For most curves the average driver can effect a suitable transition path within the limits of normal lane width. However, with combinations of high speed and sharp curvature the resultant longer transition can result in crowding and sometimes actual occupation of adjoining lanes. In such instances transition curves would be appropriate because they make it easier for a driver to confine the vehicle to his or her own lane. The employment of transition curves between tangents and sharp circular curves and between circular curves of substantially different radii warrants consideration.

The principal advantages of transition curves in horizontal alignment are the following:

1. A properly designed transition curve provides a natural, easy-to-follow path for drivers, such that the centrifugal force increases or decreases gradually as a vehicle enters or leaves a circular curve. . . .
2. The transition curve length provides a convenient desirable arrangement for superelevation runoff. . . .
3. The spiral facilitates the transition in width where the traveled way section is to be widened around a circular curve. . . .
4. The appearance of the highway or street is enhanced by the application of spirals. . . .

Generally, the Euler spiral, which is also known as the clothoid, is used. The radius varies from infinity at the tangent end of the spiral to the radius of the circular arc at the circular curve end. . . .

Length of Spiral

The following equation, developed in 1909 by Shortt for gradual attainment of centripetal acceleration on railroad track curves, is the basic expression used by some for computing minimum length of a spiral:

L = (0.0702*V3)/(RC)

where:
L = minimum length of spiral, m;
V = speed, km/h;
R = curve radius, m; and
C = rate of increase of centripetal acceleration, m/s3.

The factor C is an empirical value indicating the comfort and safety involved. The value of C = 1 generally is accepted for railroad operation, but values ranging from 1 to 3 have been used for highways. . . . A more practical control for the length of spiral is that in which it equals the length required for superelevation runoff.