The Science of …Tires (Part I)

Let’s start by pointing out that tire performance is a really, really complicated issue. There are a lot of variables involved. This post ended up getting way too long, so I’m going to address the issue in two (or three, depending on how part two goes) parts. The first part (today) is going to focus on the overall idea of what determines grip and those factors that Goodyear has control over. The second part will address the things that Goodyear has little or no influence over. The third part (if it doesn’t get absorbed by the second part) will be an analysis of the comments from drivers and others along the lines of the political sites that post statements from the candidates and analyze whether the statements are, in fact, accurate and/or fair.

So let’s start off with what gives a car grip.

Grip depends on two things: The force pushing the tires into the track, and how well the tires stick to the track. I’ve illustrated this schematically in the figure below, which includes the equation for the relationship between the frictional force F_friction and the force pushing downward F_down, where the Greek letter μ (pronounced mew, like a kitten vocalization) is the coefficient of friction between the tire and the track. This nice linear relationship doesn’t hold in all cases: At some point, you get a less-than-linear improvement in friction when you increase the downforce. (For more information on the details, I highly recommend Paul Haney’s book The Racing & High-Performance Tire: Using the Tires to Tune for Grip and Balance.

The force pushing the tires into the track (F_down) is a combination of mechanical downforce (the weight of the car pushing on the tires) and aerodynamic downforce (how hard air pushes down on the car). The second factor, how hard the tires grab the track is determined by the nature of the track surface and the nature of the tires – that’s what the coefficient μ measures.

A large value of μ means you’ve got a lot of stickiness between the tires and the track. Importantly, the value of μ depends on the tires AND the track, which introduces even more variability. Just within one race weekend, the track changes temperature and the amount of rubber on the track increases as cars practice or decreases if it rains. There are also year-to-year variations: Track surfaces age and wear, which changes their characteristics, not to mention the potentially large changes when a track is totally repaved and/or reconfigured, as happened last year with Bristol and Las Vegas. I’ve seen figures for μ quoted from 0.9-1.3. These aren’t numbers that Goodyear or the teams tend to publicize, so these should be taken as educated guesses rather than gospel.

Goodyear controls two primary tire features: The tire compound and the tire construction. The tire compound is the particular recipe for the rubber on the tread (the part that rubs against the road). There are many different types of rubber formulations, ranging erasers to bump stops. Rubber compound recipes are a lot like chocolate chip cookie recipes. The ratio of flour to fat affects whether you get dense, chewy cookies or soft, airy cookies. The same ingredients are used, but in different proportions and the different proportions produce very different results.

Tires are the same way. By varying the materials used (e.g. ratio of natural to synthetic rubber, how much sulfur relative to the amount of polymers in the rubber) and the processing conditions (how long and the temperature and pressure at which the tire is vulcanized), the tire manufacturer controls whether the tire is hard or soft.

Tire grip is due to friction, so you want as much friction as possible; however, there is no free lunch in physics. Rub your hands together for thirty seconds and then put them to your cheeks. Feel the heat? Friction creates heat and heat creates issues for tires.
When tires get hot, thin layers of the tire surface (and we’re talking about a few thousands of an inch each lap) melt. Some of the melted rubber deposits on the track and some comes off the tire, mixes with track dirt and gravel, and forms ‘marbles’, those irregular chunks that build up on the outside of the track.

A second issue is heat cycling. A heat cycle is heating and cooling the tire. A brand new sticker tire will outgas–small amounts of chemicals in the tire turn to vapor when heated and exit the tire as it heats. Also, some of the melted rubber doesn’t come off the tire, but cools back down again, and that rubber can have very different characteristics. The tire softens as it warms up. The rate at which it softens can change after it has been through a heat cycle. A single set of tires can behave very differently if run for 50 green flap laps than if they were run for a few laps of green, run under caution for a few laps (allowing them to cool down) and then run under green-flag conditions again. Sometimes a crew chief will have a driver ‘scuff’ the tires during practice–run them for just a few laps to roughen up the surface and put the tires through a heat cycle.

The other primary variable Goodyear can change is the tire construction, which includes the shape of the mold used to form the ‘green’ (prior to vulcanization) tire, the sidewall stiffness, and the cording. (Cording is steel and/or Kevlar that reinforces the body of the tire.) Each of these things impact the mechanical behavior of the tire – how much, for example, the sidewall gives when you go around a corner at high speed.

So that’s a run-through of some of the major things that impact the parameter μ. There are other variables that have less major, but still important impacts on μ, but those are small compared to the ones we’ve considered here. If you look at the diagram starting off this article, you’ll see that this is just one part of grip. Tomorrow, we’ll investigate the other part of grip: the force pushing down on the tire. And that’s something that Goodyear has minimal control over.