Tyre modelling

Tyre performance has a huge effect on the dynamic behaviour of a Formula One car, or any race vehicle for that matter. In order to fully understand tyre behaviour, all the teams use virtual tyre models to assess the impact of changes to the chassis and aerodynamics on the way a tyre performs. Predicting tyre behaviour is complex though, and teams are constantly looking for the best balance between maximising grip and extending tyre life. 

In addition, the 2014 Formula One rubber is notoriously fickle, with many teams saying it is hard to get it into the correct operating temperature widow without unduly impacting its durability. At the 2014 British GP for example, Andy Green, technical director at Force India, explained that while it was possible to get the tyre to the correct temperature through aggressive warming, this led to very rapid degradation, and finding a chassis set-up that could get the tyre up to temperature reasonably quickly without this being an issue was challenging.  

One widely used tyre model in motorsport is Pacejka’s ‘Magic Formula’, which uses data on slip angle, slip ratio, camber and tyre load to calculate tyre force. However, it misses out on one key variable, which in the closely fought world of Formula One has a huge bearing on performance – tyre temperature. Only when the tyre compound is at the correct temperature will it perform optimally. As a result, if the car does not work the tyre hard enough to get it to this temperature, performance will be compromised. Also, changes in tyre temperature due to slow laps behind safety cars need to be accounted for in race strategies, as does the variation in tyre behaviour from one heat cycle to the next. 

Although the spec tyre supplier, Pirelli, provides teams with a tyre model, most chose to develop their own, which allows for far greater flexibility of development. A few years ago, Honda, which withdrew from Formula One in 2009, developed just such an in-house model, by identifying the elements with the greatest effect on the accuracy of calculations for tyre forces. 

Tyre forces are determined chiefly by the structural deformation of the tyre and the friction characteristics between it and the road surface. The friction coefficient of a tyre changes significantly according to environmental conditions and driving conditions, including road surface roughness, dust on the road surface, tyre surface temperature, tyre slip speed, rubber wear and thermal degradation. 

When devising the model, Honda separated characteristics such as structural deformation and heat transfer – which could be modelled on the basis of theoretical concepts and the results of bench tests – from elements such as the friction coefficient, which depend on track conditions, the parameters for which were established using data gathered on track. By accounting for these variables, Honda was thus able to develop a model that gave a far more accurate picture of tyre performance than would be possible with more readily available models. A brief look at some of the aspects of the model gives a good insight into just how complex a task this was. 

For example, the model treated deformation of the tyre contact patch by dividing it into a belt section and a tread rubber section. Belt deformation was approximated by expressing it as a quadratic function in relation to the position of the tyre contact patch in the longitudinal direction. The deformation obtained in this manner was corrected using the tyre side force, self-aligning torque, internal pressure and longitudinal force, all of which needed to be calculated theoretically or derived from on-track data from sensors recording tyre temperate, wheel loads and so on. 

The complete details of such a model are far too complex to go into fully in a single article, but suffice to say, such models are essential in Formula One these days. However, it also has to be remembered that a model is only as accurate as the data fed into it, so for it to be effective a team must also be on top of all the other aspects of vehicle simulation and data recording. 

The benefits of getting it right are considerable, and not only in terms of performance and development efficiency. Simply through observing tyre behaviour phenomena and analysing the mechanisms by which they take place, previously unforeseen avenues of development and performance enhancement can be discovered.

Written by Lawrence Butcher