spiral length design

on the circular curve, lateral acceleration affects comfort. on the spiral, both lateral acceleration and jerk affect comfort.  the determination of maximum curving speed on the basis of lateral acceleration only is not critical because the lateral acceleration is proportional to the square of speed whereas jerk is proportional to cubic power of speed. the maximum speed on a curve is thus significantly restricted by the spiral length. in this paper, spiral length is formulated on the basis of both lateral acceleration and jerk. the proposed formula is applied on curves of various curvature and validated against an earlier formula by the author.  on the basis of current choice of values of lateral acceleration and  jerk, a relation between jerk and lateral acceleration is given that can be used to determine the acceptable value of jerk for a given lateral acceleration. a single criterion is proposed to decide the requirement of a spiral curve.