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This paper presents theoretical consideration of a travel route and speed profile while turning at an intersection. These two are important for vehicle movement and ride comfort. The curvature distribution of a travel route is an important physical quantity that generates a traveling track. The formulation and characteristics of a transition curve at connection points for a noninterpolation curve, a single clothoid curve, and a multiple clothoid curve are investigated. The physical variable derived from a curvature distribution function is demonstrated, and the features of the three types of transition curves are explained. The integration value of a curvature distribution function represents an azimuthal angle. Therefore, the curvature distribution curve is the velocity of the azimuthal angle. Then, the first-order differential value of the curvature distribution curve is the acceleration of the azimuthal angle, and the second-order differential value of the curvature distribution curve is the jerk of the azimuthal angle. The theoretical equation of a traveling path is derived from the curvature distribution curve of the three types of transition curves, and their characteristics are formulated. Theoretical expressions of a speed profile of a real running vehicle at a traffic intersection are also proposed. Theoretical values agreed well with the measurement results. The validity of the multiple clothoid curve is discussed analytically as compared with the other two cases where it is interpolated by the noninterpolation curve or the single clothoid curve. It was also found that the influence of the multiple clothoid curve on vehicle movement and ride comfort was superior to those of the non-interpolation and single clothoid curve. Some results are presented in the form of parametric plots.

Theoretical studies of a travel route and velocity profile while turning at an intersection