Chemical adhesion and Formula One tyres

In the early 1980s, John Watson enjoyed what can only be described as a 'spree' of remarkable Grand Prix victories, achieved by overtaking numerous cars from mediocre or lowly grid positions.

Watson's success at Zolder and Detroit in '82, and Long Beach in '83, is commonly ascribed to using a harder compound of tyre, but John himself has commented that "it wasn't so straightforward [as a harder compound] because in those days there were extremely subtle differences between grades, compounds and construction of tyres and Michelin operated with great secrecy anyway," (1982, Christopher Hilton, p126). In particular, John mentions that the tyre he took on the left-hand side at Zolder in '82 was recommended by Michelin's Pierre Dupasquier on the basis of its performance on Bruno Giacomelli's Alfa Romeo at Las Vegas in 1981.

One can hypothesize that John achieved those stunning victories using a Michelin compound which was not only harder, but which generated an unusually high proportion of its grip from chemical adhesion.

In this context, recall that there are two distinct but related mechanisms by which a rubber tyre generates grip: (i) the viscoelastic deformation of the tyre by the 'asperities' in the road surface, ultimately leading to the viscous dissipation of kinetic energy into heat energy; and (ii) chemical adhesion at the interface between the tyre and the road surface.

The viscoelastic mechanism is often dubbed the 'hysteretic friction'. This is not our main concern here, but the interested reader is referred to Tyre friction and self-affine surfaces for an introduction to the representation and role of asperities.

Chemical adhesion is maximised by higher temperatures and higher contact areas. When a tyre gets hotter, it gets softer, and this allows it to deform further into the crenellations in the road surface, increasing the contact area. Hence, adhesion is maximised on smooth, hot surfaces.

Now, let's hypothesise that Las Vegas, Zolder, Detroit and Long Beach shared the following combination of characteristics: the asphalt was very smooth, and, (with the exception of Detroit), somewhere between fairly warm and very hot.

Certainly, Dupasquier has attested to the fact that Long Beach was a low 'severity' surface, (Alpine and Renault, Roy Smith, p148), and it seems likely that Detroit, as another street circuit, would have possessed similar characteristics. Las Vegas was basically just the car-park to a casino, so the same presumably applied there.

Whilst Detroit in '82 was slightly overcast, it was warmer than anticipated at Zolder, and the races at Las Vegas in '81 and Long Beach in '83 were run in high temperatures. On balance, then, Watson's amazing victories were mostly achieved on hot, smooth circuits, and the best tyre on a hot, smooth surface is one which generates a larger proportion of its grip from adhesive friction than hysteretic friction. 

A useful graph in this respect can be found in the latest paper co-authored by rubber-friction expert, B.N.J. Persson, concerning the dependency of rubber friction on normal load, (hereafter referred to as Fortunato et al). The graph, reproduced above, plots viscoelastic friction and adhesive friction as a function of the sliding velocity of a tyre.

The latter concept requires a brief digression: When a tyre is turned at an angle to the direction in which the car is moving, (the so-called slip-angle θ), the contact patch is deformed at a velocity which has a component parallel to the direction in which the tyre is rolling, and a transverse component, perpendicular to the rolling direction. The latter component is the sliding velocity which generates a cornering force. In the figure above, this sliding velocity is plotted in logarithmic form on the horizontal scale. In other words, it expresses the sliding velocity as a power of 10.

If the car-velocity is v_c, and the slip-angle is θ, then the transverse slip-velocity is v_y = v_c Sin θ. Hence, approximately the same slip velocity can be generated by a large slip-angle in a slow-speed corner, and a smaller slip-angle in a high-speed corner. The actual slip velocities seen by an F1 contact patch, of the order ~1 m/s, correspond to a value of 0 on the log scale in the figure above.

Now, the friction coefficient generated by a tyre is actually a function of at least two principal variables: (i) the 'bulk' temperature of the tyre tread, and (ii) the sliding velocity. Hence, the coefficient of friction (mu) should always be imagined as a 2-dimensional surface.

If one represents bulk temperature along the x-axis, sliding velocity along the y-axis, and the friction coefficient as a vertical function mu = f(x,y), then peak adhesive and hysteretic friction can each be pictured as diagonal escarpments running from the bottom-left to the top-right of the horizontal plane. At a fixed sliding velocity, one can plot the mu as a function of bulk temperature; and at a fixed bulk temperature, one can plot the mu as a function of the sliding velocity. The figure above from Fortunato et al represents only a slice of the latter type.
 
As a tyre ages and wears, it loses the ability to generate and retain heat, and its temperature begins to fall. If a driver continued inducing the same slip-velocities as the tyre temperature dropped, then the mu would follow a track parallel with the x-axis, and the drop in grip would be quite precipitous. It's more likely that as a tyre ages, either the cornering speed will reduce, or the driver will fractionally reduce the slip-angles, thereby reducing the slip velocities, and the grip will follow more of a diagonal path, down the ridge of the escarpment towards the bottom left of the mu surface.

Fortunato et al make the crucial point that "at room temperature the maximum in the adhesive contribution is located below the typical slip velocities in tire [sic] applications (1 - 10 m/s), while the maximum in the viscoelastic contribution may be located above typical sliding speeds...Increasing the temperature shifts both [the adhesive and hysteretic mu] towards higher sliding speeds, and also increases the area of real contact A, making the adhesive contribution more important. Depending on the relative importance of the adhesive and viscoelastic contribution to the friction, the friction coefficient may increase or decrease with increasing temperatures."

John Watson's victories in the early 80s were achieved on tyres which took some laps to 'come in', hence this all adds up to a tyre which generated a higher proportion of its grip from adhesion, and only generated peak mu when it had been strained sufficiently to reach a higher temperature. In this case, the greater adhesion at high temperatures more than offset the loss of hysteretic friction.

During the Michelin and Bridgestone tyre war of the early 2000s, Formula One tyres continued to generate a significant proportion of their grip from chemical adhesion, hence a driver was able to 'push' on consecutive laps, without losing grip. The gain in chemical adhesion would offset the loss of hysteretic friction.

In contrast, if we consider the hypothetical case of a tyre which generated only a small proportion of its grip from chemical adhesion, then even before the effects of wear kick-in, a racing driver would find such tyres to be constantly balanced on a knife-edge of hysteretic grip. Push too hard for several laps, and as the tyre gets hotter, it would lose hysteretic grip without a compensating gain in adhesion...