A general theory of Pirelli's 2012 F1 tyres

The volatility of this season's Formula 1 season has been attributed to the temperature sensitivity of Pirelli's 2012 Formula 1 tyres. All of the teams are finding it difficult to keep the tyres in their optimum temperature band between 85 and 100 degrees C.

I'd like to propose a theory which explains what is happening. As I see it, there are two key facts, outlined by Mark Hughes in this week's Autosport, which need to be explained:

(1) Ferrari, Williams and Sauber tend to run their tyres hotter than Lotus, McLaren and Red Bull.

(2) In the past, when a tyre overheated, it would lose grip, and the temperature would then fall back into the operating band. This year, when a tyre overheats, it never recovers. Hence, a negative thermal feedback process has been replaced with a positive feedback process.

My theory depends upon the following facts about the physics of tyres:

(i) Tyre grip is generated by two mechanisms, sometimes referred to as physical grip and chemical grip. The first process involves the shear deformation of the contact patch, whilst the second involves the coefficient of friction of the tyre. The internal stress response to shear deformation depends upon the shear modulus of the tyre, which is temperature dependent, and the friction coefficient is dependent on both tyre temperature and slip velocity, (as depicted in the image below from Michelin's tyre modelling efforts). So both mechanisms by which grip is generated, are temperature dependent.

(ii) Tyre temperature is generated in a tyre by the deformation it undergoes, and by the friction associated with tyre slip.

The key difference between this year's Pirellis and last year's, is that the 2012 tyre has a flatter contact patch. I hypothesise that what this has done is to change the balance between the heat generated by deformation and the heat generated by friction, in favour of the latter. This can explain our two key facts:

Firstly, if we accept that Red Bull, Lotus and McLaren have more downforce than Ferrari, Williams and Sauber, then the former teams will tend to suffer from less tyre slip than the latter teams. This explains why the former teams now run their tyres cooler than the latter trio.

Secondly, we can now explain why thermal degradation is a positive feedback process. When a tyre overheats and loses grip, it slides more. When the balance between slip-generated heat and deformation-generated heat has been tipped in favour of the former, a car which slides more will generate ever hotter tyres, leading to runaway thermal degradation. In contrast, in 2011, when a tyre lost grip, the deformation reduced, hence the temperature returned to the optimum operating band.

It's just a theory...