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The paper presents some new and unreferenced analytical formulae describing the dynamic behaviour of the suspension system of road or off-road vehicles. The quarter car model (2 degrees of freedom) is considered, the suspension can be either passive or active. Passive suspensions can be simplified as the spring-damper combination or the spring-damper combination with an additional in series spring (representing, e.g., the rubber bushing at the top of a McPherson strut or the rubber bushing at the end joints of the damper). The mathematical system is linear and the excitation is given by a random stationary and ergodic process. The standard deviations in analytical form are given referring to, respectively, the vehicle body acceleration, the relative displacement between sprung and unsprung mass, and the force at the ground. The so called invariant points of the frequency response functions are derived for both active and passive suspension.

The lightweight seat of a high performance car is designed taking into account a rear impact, i.e. the crash due to an impulse applied from the rear. The basic parameters of the seat structure are derived resorting to simulations of a crash with a test dummy positioned on the seat. The simulations provide the forces acting at the seat structure, in particular the forces applied at the joint between the seat cushion and the seat backrest are taken into account. Such a joint is simulated as a plastic hinge and dissipates some of the crash energy. The simulations are validated by means of indoor tests with satisfactory results. A tool has been developed for the preliminary design of lightweight seats for high performance cars.

The friction estimation at the tire-ground contact is crucial for the active safety of vehicles. Friction estimation is a key problem of vehicle dynamics and the ultimate solution is still unknown. However the proposed approach, based on a simple idea and on a simple hardware, provides an actual solution. The idea is to compare the tire characteristic at a given friction (nominal characteristic) with the actual characteristic that the tire has while running. The comparison among these two characteristics (the nominal one and the actual one) gives the desired friction coefficient. The friction coefficient is expressed in vector form and a number of running parameters are identified. The mentioned comparison is an efficient but complex algorithm based on a mathematical formulation of the tire characteristic. The actual tire characteristic is somehow measured in real time by a relatively simple smart wheel which is able to detect the three forces and the three moments acting at the hub.