We mentioned earlier that 10 degrees F changes the tire pressure about 1 psig. If a tire starts with a certain cold pressure in the morning, the warming of the day is effectively adding pressure to the tire over the course of that day. The temperature the tire runs at will be affected by the combination of the ambient air temperature, the track surface temperature, and the amount of friction introduced (how hard you drive).
If for your first session of the day, it's overcast, the air temp is 65 and the track temp is 70, then in the afternoon the sky is clear, the air temp is 85, and the track temp is 105, there is considerably more heat to influence the temperature of the tire surface. If you drive just as hard, the tire will be hotter, and the pressure will be higher. This change from morning to afternoon is going to be much more pronounced in some climates than others. The southwestern U.S. can see days with a 45 degree morning and a 90 degree afternoon. This will increase the starting tire pressure by 4 psig by the end of the day. This will make a world of difference in the handling of the car during each session.
To maintain the same racing pressure settings in the afternoon as achieved in the morning, you'll have to compensate for the increased pressure due to ambient temperature. While there is probably a formula to understand the effect of the relationship of the ambient temperature and the track temperature, it will be complicated by the aerodynamics around the tires, and the heat generated by the brakes. You can generally use the ambient air temperature and the 10 degrees per 1 psig relationship as a guide for adjusting tire pressures throughout the day. Take ambient air temperature readings at the start of each session, and use this to determine how to adjust the tire pressures. As the day warms, you'll have to drop tire pressures accordingly before each session.
One more item related to ambient temperature--youll find that if the car is parked with one side of the car facing the sun, those two tires might be 10 to 20°F warmer than the shaded side (and therefore 1 to 2 psig higher in pressure). You should cover those tires up with some simple plywood panels, or at least know not to set them to the same pressure as the cooler side of the car.
The above sections provided some practical guidance to settings tire pressures. In these next sections, we'll take a little closer look at exactly what it is we're trying to do.
What exactly is the goal of tweaking tire pressure? The bottom line is that you're looking for the maximum traction possible over the largest portion of the track possible.
With a given set of tires (which have a determined rubber compound and size you can't change), the variables you can play with to achieve the maximum traction is finding the tire's best operating temperature, and optimizing the contact patch size. The discussion above in finding the best tire pressure settings is really just an indirect method of tuning the contact patch and having the tires operate at their peak temperature range.
The temperature of the tire is influenced by the ambient air temperature, the surface temperature of the track, and your driving (how hard you push the car). Because you won't have the luxury of choosing an optimum rubber compound for the conditions like the pros, your main tool for achieving the maximum grip temperature is driving the car at its maximum capacity without exceeding it (and overheating the tires). This assumes the ambient temperatures are warm enough to achieve the tire temperature needed. If it's 50 degrees outside, chances are, the tires will never get hot enough to produce their maximum grip potential.
The contact patch of a given tire size is affected by the suspension geometry, and by the tire pressure. In a stock street car, you don't have any adjustability at the track in the suspension, so tire pressure is your main tool.
While we start with setting tire pressures in their cold state, we're really interested in their pressures (and temperatures) when they're running hot.
Every tire will have a temperature range where the rubber reaches its most "sticky" point without becoming greasy, and without physically falling apart. Race tire manufacturers often have this temperature identified, but for a street tire, it's unlikely you'll find any spec sheet with this temperature data identified. Finding the best temperature range of the tire will come primarily from experience with driving on it, knowing how hard it can be pushed before overheating causes it to become slippery. When you get runs of 15 to 20 minutes or more that were fast (within a few tenths as fast as you've been able to achieve), and the tire grip stayed consistent, you've probably found the maximum grip operating temperature of the tire. Head back to the pits, and take pressure and temperature readings, and use that data as a target for that tire. For most street tires the temperature range can be expected to be about 180 to 200 degrees F before they get slippery. You may have sessions where faster laps are possible, but if, in attempting to keep that pace, the tire progressively gets slipperier, then you're driving the tires too hard and they're overheating.
We know the tires are going to heat up when they're driven on. The friction between the rubber and the road will generate heat. A lot of heat. This heat is going to transfer to the gaseous air in the tire, and cause it to expand which leads to an increase in the tire pressure. It happens to work out that an increase of about 10 degrees F causes about 1 psig increased tire pressure. During racing, a cold tire pressure setting will increase anywhere from 4 to 10 psig.
The increased pressure has an effect on changing the tire shape, and the resulting area in contact with the road. This "contact patch" is what we're trying to optimize. In fact, we're trying to maximize it.
To understand the effect of pressure on the contact patch, let's first look at a tire in a static load state (rolling straight or parked).
If the tire pressure starts out too high, the increased pressure from heat buildup will make the tire shape somewhat convex. The contact patch will be narrower with the outer edges of the tire not able to touch the road because the rounded middle has lifted the edges. This tire is said to be too "hard."
If the starting pressure is too low, even after heating up, the tire shape will tend towards being concave. The outer edges under the wheel rims will have firm contact with the road, but the middle will deflect inwards. This minimizes the contact patch in the middle. This tire is said to be too "soft."
The perfect tire will have a contact patch the full width of the tire with an even pressure across the width. This is the condition we're striving for.
We've just looked at the case of a static tire. However, when we're racing on a road course, the tires are not always in such a static state. The forces of cornering, braking, and accelerating will constantly be changing the shape of the contact patch as the rubber twists from these forces. Indeed, it is under cornering that we are typically looking for the highest levels of grip possible. All else being equal, a car that can get through corners the fastest, will be the quickest. Again, all else being equal, the car with the optimized contact patches will have the most grip and be the quickest through the corners.
While there are several suspension adjustments possible in race cars and modified street cars, we may also need to "tweak" the air pressure on an individual wheel basis to achieve the maximum contact patch under the dynamic conditions of the road course. In fact, these will be different for each track.
A harder tire may have a slight convex shape during a straight run, but may be necessary to help keep the sidewall stiff enough during cornering to prevent the tire from rolling under the wheel rim excessively. So, while in a static state, the contact patch is smaller than optimally possible, this actually increases the effective contact patch size during cornering.
These tire behaviors during cornering are what might lead us to having left side tires, right side tires, or even a single tire at a different pressure than the others. This would be done to fine tune the handling of the car through certain corners.
The final goal is actually a compromise in looking for the maximum contact patch during as much of the lap as possible. We may find that one settings is optimum for corners 3 & 7, but that another is optimum for corners 2 & 4. If corners 2 & 4 are faster than 3 & 7, then the emphasis must be placed on corners 2 & 4 as there is more to gain from them being optimized. In the end, the "correct" tire pressures are the ones that allow the fastest laps in long runs.