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The aim of the paper is to provide simple and accurate analytical formulae describing the straight motion 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. 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. The validation of the analytical expressions has been performed both theoretically and after a subjective-objective test campaign. By means of the new and unreferenced analytical formulae, practical hints are given to set to zero the steering torque during straight running.