During straight-ahead running, the longitudinal axis of road vehicles, notably cars, is not parallel to road axis. This occurrence is general and is due both to road cross slope (road banking) and to tyre characteristics, particularly ply-steer and conicity. In order to describe such a phenomenon, the paper develops a new and relatively simple analytical model. Despite the model is linear, the solution which is provided is exact, since straight-ahead motion occurs with small angles and both the elastokinematics of suspension system and tyre characteristics can be modelled by linearised equations.The Handling Diagram theory is updated and completed by introducing the actual shifts of tyre characteristics influencing running at vanishing lateral acceleration.The validation of the analytical expressions is performed by using a MSC Adams TM full model of a car. The lateral drift coming from the null steering manoeuvre is simulated by both the simple model and the full MSC Adams TM model, with satisfactory results. The same two models are used to simulate successfully the weave test.A subjective-objective experimental test campaign provides preliminary substantiation of the ability of the derived formulae to describe tyre performance.By means of the unreferenced analytical formulae developed in the paper, we allow, given the vehicle, the proper tyre design specification, and vice-versa. In particular, a formula is given to make null the steering torque during straight-ahead driving. The derived analytical formulae may provide a sound understanding of the straight-ahead running of road vehicles.

A rigid ring model of the tire for the study of in-plane dynamics and a new technique for determining the parameters of the model are presented in this paper. This model can be used for studying the comfort of vehicles, problems of driving, and braking problems in the longitudinal direction. Comparison with finite element models shows that the rigid ring model of the tire is capable of describing the in-plane eigenmode shapes in the frequency range of 0–130 Hz. The well-known “brush model,” integrated into the tire model, is introduced to take into account the slide phenomena in the contact patch. The parameters of the model can be correlated with the physical properties of the tire so that designers can take advantage of such a correlation in the development of new tires in terms of time, cost, and performance. The technique used to determine the parameters of the model for some automobile tires include the direct measurements of some physical properties (mass, moment of inertia, stiffness) and a method of identification applied on the results from a dynamic test. The model is able to predict experimental data in terms of natural frequencies and relative dampings. Results from the application of this technique on two tires are reported.

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<div class="section abstract"><div class="htmlview paragraph">The aim of the paper is to provide simple and accurate analytical formulae describing the <i>straight motion</i> of a road vehicle. Such formulae can be used to compute either the steering torque or the additional rolling resistance induced by vehicle side-slip angle.</div><div class="htmlview paragraph">The paper introduces a revised formulation of the Handling Diagram Theory to take into account tire ply-steer, conicity and road banking. Pacejka’s Handling Diagram Theory is based on a relatively simple fully non-linear single track model. We will refer to the linear part of the Handling Diagram, since straight motion will be considered only. Both the elastokinematics of suspension system and tire characteristics are taken into account.</div><div class="htmlview paragraph">The validation of the analytical expressions has been performed both theoretically and after a subjective-objective test campaign.</div><div class="htmlview paragraph">By means of the new and unreferenced analytical formulae, practical hints are given to set to zero the steering torque during straight running. Additionally, the vehicle rolling resistance during straight motion is studied. It is found that front toe seems primarily set for reasons that are related to the steering system, other than tires. Reducing front toe could reduce energy consumption up to 1% on a WLTP mission.</div></div>

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