Measuring friction

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Friction is commonly misunderstood and is deceptively challenging to get to grips with. Firstly, friction is an interaction between two surfaces, not just one. So it’s incorrect to say, “This tire is grippier than that one,” as grip is dependent on both the tire and the road.

So while on dry asphalt this particular trackday tire may well be grippier than that all-season tire, if you change the asphalt to ice then this may no longer be the case. Furthermore, the actual level of grip is sensitive to just about everything. Vertical load, size of contact area, roughness of each surface, road materials, tire compound, sliding velocity and temperature of each surface, among many other factors, all influence the level of grip between a tire and the road.

So what’s going on? Well, the truth is, the real physics of friction occurs at a molecular level and is almost impossible to calculate. Let’s look at contact area for instance, one of the variables that affects friction. Determining the actual contact area between the tire and the road is almost impossible. Even if we assume that all the tire and road properties are known (which is not a trivial assumption), then when you consider the road surface contains peaks and troughs, the tire rubber will partly, but not completely, fill those troughs.

The amount the tire sinks into the troughs will affect the true contact area over that square centimeter of surface. With enough computer power, this could be physically modeled using finite element analysis of the deformable rubber.

However, the exact same phenomenon occurs when we zoom in to look at square millimeters, or zoom in further and look at a microscopic level where again there are peaks and troughs and the rubber will partly fill some, but not all, of the microscopic troughs. Finite element modeling at this level would require the mesh size to be almost atomically small, which is far beyond what is practical. Add to this the effort required to map a sensibly sized section of road surface along with handling contaminates such as movable stones, dust, leaves, etc, and you are heading for a dead end.

Unfortunately, what’s happening at this level cannot be written off as chasing the last word in accuracy, as the effect at this atomic level is multiplied billions of times to cover the whole contact patch, creating a significant net effect on the tire. The more you zoom in, the smaller the microscopic effect but the larger the multiplier gets to determine the total effect at a tire level. The result of this is surprising, and according to acclaimed physicist and friction expert Dr Bo Persson, “The true contact area covers only a fraction of the geometrical surface visible to the naked eye – typically just a few percent.” (Tire Technology International, October 2013, p34). This means that you may think of a tire’s contact patch as being about the size of your hand, whereas in fact it’s about the size of a fingernail.

With a true physical calculation of friction from first principles requiring data and analysis at an atomic level, it can be ruled out as a viable commercial option. Instead, a far more practical approach to determining the net effect of all the complex friction phenomena is to simply do an experiment and measure it. An empirical model can then be built to reproduce the measured results.

Unfortunately, measuring friction explicitly is also difficult. Tire tread can be cut up and mounted to various types of friction testers; however, most of these cannot match the vertical load the tire would be subjected to when mounted to a vehicle and even less can apply and maintain the required sliding velocity. Therefore, tire friction testing is usually carried out implicitly at a full-scale tire level, using Flat-Trac rigs or similar.

The downside of this is that a physical tire is required. However, while being less elegant, it is this empirical build, test, model, approach that is the principle behind most of the tire models commonly used for handling simulations.

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