The Magic Formula Tyre Model

An account is given of the latest version 3 of the Magic Formula tyre model. The model provides a set of mathematical formulae from which the forces and moment acting from road to tyre can be calculated at longitudinal, lateral and camber slip conditions, which may occur simultaneously. The model aims at an accurate description of measured steady-state tyre behaviour. The coefficients of the basic formula represent typifying quantities of the tyre characteristic. By selecting proper values, the characteristics for either side force, aligning torque or fore and aft force can be obtained. The new version of the model contains physically based formulations to avoid the introduction of correction factors. Double-sided, possibly non-symmetric pure slip curves are employed as the basis for combined slip calculations. Suggestions are given to estimate the driving part of the longitudinal slip curve and to represent the characteristic at rolling backwards.

The magic formula tyre model

The accomplishments to date on the development of automatic vehicle control technology in the Program on Advanced Technology for the Highway (PATH) at the University of California, Berkeley, are summarized. The basic principles and assumptions underlying the PATH work are identified, and the work on automating vehicle lateral (steering) and longitudinal (spacing and speed) control is explained. For both lateral and longitudinal control, the modeling of plant dynamics is described, and the development of the additional subsystems needed (communications, reference/sensor systems) and the derivation of the control laws are presented. Plans for testing on vehicles in both near and long term are discussed. >

Automated vehicle control developments in the PATH program

ADVISOR 2.1 is the latest version of the National Renewable Energy Laboratory's advanced vehicle simulator. It was first developed in 1994 to support the US Department of Energy hybrid propulsion system program and is designed to be accurate, fast, flexible, easily sharable, and easy to use. This paper presents the model, focusing on its combination of forward- and backward-facing simulation approaches, and evaluates the model in terms of its design goals. ADVISOR predicts acceleration time to within 0.7% and energy use on the demanding US06 to within 0.6% for an underpowered series hybrid vehicle (0-100 km/h in 20 s). ADVISOR simulates vehicle performance on standard driving cycles between 2.6 and 8.0 times faster than a representative forward-facing vehicle model. Due in large part to ADVISOR's powerful graphical user interface and Web presence, over 800 users have downloaded ADVISOR from 45 different countries. Many of these users have contributed their own component data to the ADVISOR library.

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ADVISOR 2.1: a user-friendly advanced powertrain simulation using a combined backward/forward approach

SUMMARY Modelling of the generation of shear forces by pneumatic tyres under steady state conditions is reviewed. The review is placed in a practical context, through reference to the uses to which models may be put by the vehicle dynamicist and the tyre designer. It will be of interest also to the student of rolling contact problems. The subject is divided into sections, covering physically founded models which require computation for their solution, physically based models which are sufficiently simplified to allow analytical solutions and formula based, empirical models. The classes are more nearly continuous than this strict division would imply, since approximations in obtaining analytical solutions may be made, empirical correction factors may be applied to analytical results and formula based methods may take into account tyre mechanical principles. Such matters are discussed in the relevant sections. Attention is given to the important matter of choosing model parameters to best represent the beha...

Lars Lidner

Papers

A New Tire Model with an Application in Vehicle Dynamics Studies