What do Formula One racing tires have in common with fly's feet? This apparently bizarre question can be answered with the aid of physics: They are both soft and supple and exude a more or less sticky liquid. In this way, irregularities on the asphalt or - in the case of the fly - on the window pane are filled in. The area of contact becomes greater and the adhesion is thus increased.
Dr. Bo Persson of the Institute of Solid State Research at Research Centre Jülich in Germany is on the track of these and other adhesion phenomena. His newly developed theory now makes it possible for the first time to calculate and predict how well a tire made of a certain rubber mixture will grip the asphalt - without having to manufacture a whole tire.
Car tires have very different compositions. The different rubber mixtures are optimized with respect to the season and its average temperatures. That is why winter tires should not be used in summer.
The industry is continually on the lookout for even better materials. Every year, the tire companies test thousands of mixtures of the most varied types of rubber in order to develop new car tires. Test tires are then manufactured from these rubber mixtures in order to test their properties on asphalt. With his new theory of static friction, Bo Persson can make an enormous reduction in the long test series.
"All the information I need for my calculations is how elastic a small rectangular sample of rubber is and how well it cushions jolts," says Persson. "It is no longer necessary to produce a whole tire in order to judge the later grip on the asphalt. In 2001, we first calculated ten new test components and then sent them off to be tested in practice. The results of theory and practice are in very good agreement."
The decisive aspect for the success of the new theory is that Persson can calculate the area of contact between the rubber and the asphalt more precisely than has previously been the case. Earlier models only made use of an averaged surface roughness.
"I include all length scales - from one centimeter down to the atomic level," Persson remarks. The theory's contribution is to predict what the elasticity and damping of the rubber mixture should be to achieve optimum grip on a rough surface.
One of the major effects to be calculated is the ability of the rubber to cushion jolts. In physical terms, this ability is based on the fact that the material is capable of storing energy.
If a soft material is pressed onto a hard uneven surface it is not uniformly loaded. Stones and elevations in the asphalt dent the tires, while the rubber clings to "valleys" and gaps. This clinging effect is not perfect, since the tire is not liquid.
In contrast to dry-weather tires in Formula One racing, which exude resins and actually even out irregularities in the asphalt, thus considerably improving the area of contact, normal tires do not secrete any fluid since the disadvantage of "Schumi" & Co's good road holding properties is the considerable tire wear. Racing tires are literally sucked dry.
Wherever normal tire material is dented, energy is accumulated and at a different location the material relaxes. Persson has found a mathematical description for the irregularities of the asphalt which calculates them down to the atomic level.
It is important to know how big the actual surface of contact between the rubber and asphalt is and what forces act on the material. A tire that moves over the asphalt under the weight of the car when the brakes are slammed on is subjected to quite different forces from a tire standing still on the road.
In addition to the irregularities of the road, the internal frictional forces of the material must also be taken into consideration. Dr. Persson puts it like this: "The rigidity of the rough ground exerts oscillating forces on the surface of the rubber, which lead to cyclical deformations inside the material. This results in a large production of heat in the rubber and to a large friction force. At a certain frequency of these deformations the elastic modulus of the tire may increase one thousand fold. This naturally also changes the road holding properties."
Persson also includes these physical properties of the elastic material in his calculations.
A middle course is being sought between optimal adaptation to the road - a soft, clinging material - and the most durable possible tire that doesn't go to pieces when the brakes are slammed on. The new theory will help to discover this material more rapidly than has previously been possible.
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Dr. Persson with his formula and some Formula One tires
12-Jun-2002
