Spiral Length Design

In the literature, the length of a clothoid spiral usually is determined by three equations. These equations do not lead to the same length. As a result, all equations are applied and the maximum length is chosen. Of these three equations, two are based on actual and unbalanced superelevation with speed. These two equations are theoretically inaccurate. Thus, after selecting a spiral length, designers need to check the length against comfort criteria, even though these two equations are based on the same comfort criteria. Then, the length is adjusted. In fact, all parameters, such as jerk ($\mathrm{g}/\mathrm{s}$), actual superelevation runoff ($\mathrm{mm}/\mathrm{s}$), unbalanced superelevation runoff ($\mathrm{mm}/\mathrm{s}$), rotational runoff ($\mathrm{deg}/\mathrm{s}$), cant gradient, and twist ($\mathrm{mm}/\min$), are interrelated. Jerk criteria can fix the spiral length. In this paper, the writer presents spiral length equations that lead to equal spiral length by exploiting the interrelation between actual and unbalanced superelevation runoffs. With this process, the roll, superelevation gradient, and twist are internalized and designers need not recheck the comfort criteria. A single equation would replace the need for many, saving design time. This paper is a revised, improved version of an earlier, peer-reviewed conference paper by the writer.