Shear Force and Moment Descriptions by Normalisation of Parameters and the “Magic Formula”

Summary Previous work by Radt on the use of normalised parameters to bring economy to the task of measuring, describing and computing tyre shear forces and parallel works of Pacejka on the ‘similarity method’ are reviewed, extended and applied. Similarity ideas are used in association with the ‘Magic Formula’. Some published tyre force and moment results are divided into basic and nonbasic sets. The basic set contains a notional minimum amount of information from which the full spectrum of results can be obtained by applying similarity ideas. Calculations are carried out to show how the nonbasic results can be reconstructed from the basic set. Advantages are obtained by using a novel nonlinear transformation of the longitudinal and sideslip variables. The results are shown to be qualitatively excellent and quantitatively quite good. Of course, the accuracy is not as high as with a full Magic Formula treatment but the economy is remarkable. The process is captured in a MATLAB algorithm, included as an appendix. It is thought that this provides a useful facility for enabling vehicle dynamics studies of a more generic flavour, in which circumstances conspire to make high precision of tyre force descriptions inappropriate or impossible.