Ferrari and thermal tyre modelling

Flavio Farroni, currently Research Fellow at the University of Naples Federico II, has been developing a suite of tyre-performance models for several years in collaboration with both Ferrari GT and the Ferrari Formula 1 team. Flavio has now published some of his work, and it may be of more than a little interest to those outside Maranello.

The snappily-titled Development of a grip and thermodynamics sensitive procedure for the determination of tyre/road interaction curves based on outdoor test sessions, provides an overview of all three of Farroni's models.

TRICK appears to be a tool for inferring tyre performance characteristics from empirical telemetry data; TRT is a thermal tyre model, specifically designed to calculate bulk tyre-temperature in real-time; GrETA is a grip model which takes the output from TRT and incorporates the influence of tyre compound and road-surface roughness on tyre performance.

Farroni reports that "TRICK and TRT have been successfully employed together, constituting an instrument able to provide tyre thermal analysis, useful to identify the range of temperature in which grip performances are maximized, allowing to define optimal tyres and vehicle setup."

Recent work on the thermal tyre model, published as An Evolved version of Thermo Racing Tyre for Real Time Applications, is worth considering in some detail.

Here, Farroni's model calculates bulk and sidewall tyre temperatures by representing: (i) the heat generated by the rolling deformation of the tyre and the tangential stresses at the contact patch between the tread and road surface; (ii) the heat flux between the sidewalls, carcass, bulk and surface layers; (iii) the heat transfer due to conduction between the tyre and the road; (iv) the convective heat transfer from the gas inside the tyre to the inner surface of the sidewall and the 'inner liner' (aka the 'carcass'); and (v) the convective heat transfer from the surface of the tread and the outer surface of the sidewall to the external atmosphere. Farroni neglects radiation as a heat transfer mechanism.

This particular paper reports that the measured surface and carcass temperatures can be reproduced despite resort to a simple model in which the bulk, carcass and sidewalls are replaced by single nodes rather than a full-blown mesh. This simplification enables the model to run in real-time, and Farroni reproduces some interesting graphs (below).

There are four graphs here, one for each corner of the car. The horizontal axes represent time, and the vertical axes represent temperatures, which "are dimensionless because of confidentiality agreements."

Those sufficiently cursed to spend their working lives staring at telemetry in ATLAS will recognise the fluctuating signature of the surface tyre-temperatures, which suffer transient peaks under cornering. The peak surface temps are greater than the bulk and carcass temps, but are on average lower that the latter. One can see that the outer sidewall temps are lower than the inner sidewall temps. Also possibly of interest is the fact that the bulk temps are lower than the inner liner temps, which implies there is a net heat flux from the inner liner into the bulk of the tyre.

Now, it's something of a pity that the vertical axes on those diagrams are "dimensionless because of confidentiality agreements." Happily, however, Farroni's PhD thesis is somewhat more forthcoming, printing a pair of fully-dimensionalised temperature plots on p98-99, (below).

 

The first diagram here plots the measured carcass ('inner liner') temps, the simulated carcass temps, and the calculated bulk temps. Once again, the calculated bulk temps are lower than the carcass temps throughout. The delta seems to be about 10 degrees at the outset, and increases over the course of what appears to be a stint. Being 850 seconds long, the segment of data reproduced covers about 10 laps of data. 

Farroni points out that "Proper time ranges have been selected to highlight thermal dynamics characteristic of each layer; in particular, as concerns bulk and inner liner, temperature decreasing trend is due to a vehicle slowdown before a pit stop." 

This is the drop in carcass and bulk temperatures which occur as a tyre loses its ability to generate and/or retain heat over the course of a stint, due to physical wear and/or irreversible thermal degradation. All four corners suffer this temperature reduction, but the effect appears most marked on the left-front and left-rear. The left-rear drops from ~130 degrees to ~110 degrees, while the left-front drops from ~120 degrees to ~100.

All four corners begin in the range 115-130 degrees, so perhaps this was a set of Softs?

The second diagram (above) is "with reference to a different circuit," and once more displays simulated bulk temperatures lower than the carcass temps. In each case, the bulk temp seems to match the carcass temp at the outset, and then swiftly decline. Both front tyre carcass temps start at 100 degrees, whilst the rear carcass temps start at only 80 degrees.

The left-front carcass temp increases to about 110 degrees, the right-front remains fairly constant, the left-rear increases by almost 20 degrees, whilst the right-rear increases by about 10 degrees. All of which might suggest a set of Mediums?

As a final flourish, Farroni also studies the rather alarming effect that exhaust blown diffusers had on tyre temps (below), suggesting that rear bulk temps could have reached ~200 degrees in some regions.

Farroni suggests that this would "bring the tyre to a too fast degradation and to average temperatures not able to maximize the grip." Quite.