Vehicle flat ride dynamics

By modelling a four-wheel vehicle as a bicycle, it has been suggested (Olley 1934) that if the radius of gyration, r, in pitch is equal to the multiplication of the distance from the center of gravity of the front, a, and rear, b, wheels of the car (r2 ¼ a _ b), the bounce center of the vehicle will be located at one spring and the pitch center on the other spring of a bicycle car model. Employing the flat ride condition, r2 ¼ a _ b, the system of the sprung masses of a vehicle can be considered as two separate mass-spring systems. Therefore, front and rear suspensions may be modelled as two separate one degree of freedom spring-mass system. This paper mathematically derives the flat ride condition and clarifies analytically how exact is the suggested condition.