Buffelspoort TIME2008 Peer-reviewed Conference Proceedings, 22 – 26 September 2008 - 1 - Data acquisition and mathematical modelling: a case study ACM Bekker , SV Joubert and TH Fay Department of Mathematics and Statistics Tshwane University of Technology Pretoria, South Africa Abstract This article derives a mathematical model of a motor-vehicle tyre tread surface striking a speed bump on a stretch of otherwise smooth horizontal road. A mathematical concept is outlined to derive the model and a simple experiment, involving a typical vinyl record player stylus, is described to measure the coefficient of damping of the tangential vibration of the rubber tyre. 1 Introduction An elementary and simple definition of mathematical modelling is the use of Mathematics to describe and predict real world phenomena. Although mathematical modelling is an accepted procedure in (especially) engineering design, it usually requires experimental validation of the ability of the model to predict the behaviour of the system under investigation. This involves data acquisition, which is the setting up of the experimental apparatus and the measurement of the functioning of the system under a set of predefined conditions. Proper assessment of the results obtained by recording primary experimental information provides the foundation information on which subsequent data analysis and conclusions can be made. 2 Mathematical model Many useful and interesting phenomena in engineering and life sciences that continuously evolve over time can be modelled by ordinary differential equations or a variety of different mathematical procedures [1]. The following describes at length, the method employed in studying the behaviour of an inflatable car tyre when stimulated externally in a particular way. While considering a strategy to design tyres to minimize the formation of dirt road corrugations, the following model can be considered. abekker@hermanus.co.za Permanent address: University of Southern Mississippi, Hattiesburg, USA