Solution Method and Application Verification of the K-curve as a Highway Transition Curve

Because of the singular form and low flexibility of the clothoid as a highway transition curve in highway horizontal alignment, the K-curve, whose ratio of the chord-tangent angle to the tangential angle at any point is fixed, was proposed in a previous work, including the corresponding parametric equations and basic characteristics, and its high flexibility and various shapes were proved. Here, the application and verification of the K-curve in highway alignment is further studied. The solution methods of the K-curve for different connections are given. Through theoretical calculations and specific real-world examples, the geometric positions and lateral forces of the K-curve and the clothoid under different connection conditions are compared. The results show that the difference between the K-curve and clothoid in the above two aspects under a straight line-to-circle connection is greater than that under a circle-to-circle connection as an egg curve, and although the lateral force coefficient of the K-curve is smaller than that of the clothoid, the K-curve suffers from rapid change in the lateral force coefficient and a higher lateral acceleration change rate. Finally, the application conditions of the K-curve for highway alignment design are given with consideration of the centrifugal acceleration change rate.