Chosing A Tire
Here are some concepts to keep in mind while selecting a tire. These are guidelines, not rules- just things consider.
1) Load rating is important.
While a tire's load rating is more a safety guideline for DOT regulations, it does give a user a vague guess of how much load that tire is meant to handle. A tire with a low load rating will tend to saturate earlier because it isn't designed to bear lots of weight. Low profile and/or reduced diameter tires can be a problem here. Larger diameter, wider tires generally have much higher load ratings.
Be careful though, changing the width and especially diameter have many other effects on the suspension, some good and others not. Going to a larger diameter tire may increase the tire's load rating substantially but also raise the car, causing increased overall weight transfer. Also keep in mind that the load rating of a tire changes with its inflation pressure, which I'll mention shortly.
2) Aggressive Tires Handle Aggressive Loads:
Not all load ratings are equal: a racing compound tire tends to have a much higher saturation point than a street tire. Racing tires work best at much lower slip angles than street tires. This means less heat generation and less propensity to overwhelm the tread.
Notice how aggressive tires have a much narrower "ideal" range of grip, whereas street tires allow a nice progressive slip. This makes aggressive tires a bit harder to control at the limit (but with higher peak potential):
I believe the ability of R-compounds to handle heavy loads without their coefficient of friction substantially dropping off is one reason autocrossers can get away with running huge front bars without understeer.
3) Shorter contact patches are better. (Get a wide tire.)"
If a skinny tire and a wide tire are at the same exact tire pressure, they should have the exact same contact patch area. Think about it. If you inflate your tires to 32psi, than no matter what tire you run, there should only be 32 inches of pressure per square inch of tread. That's what psi means!
So, what's with the trend for wider tires? They change the shape of the contact patch. Tire Rack has these two images showing the difference between wide and skinny tires and their respective contact patches:
A wider tire will have a shorter contact patch, and this is important for a variety of reasons. A shorter contact patch means less lateral tread deformation, the latter of which leads to a lower slip angle as shown here:
The lower the slip angle, the longer the tread will be able to deform along that angle. This improves grip but also, in my experience, gives the tire a greater ability to handle huge loads without its coefficient of friction dropping rapidly. It's harder to saturate a wider tire.
Just remember that wider tires often necessitate a wider wheel, too. (More on that later.)
4) Higher tire pressures can help.
Higher tire pressures give you a smaller contact patch. This is both bad and good for grip at the same time. Say, for example, that you are having mid-corner understeer and decide to raise the tire pressure in your front tires beyond their factory pressures. Doing so may decrease mid-corner understeer but increase corner exit understeer. Why this trade?
You want as much rubber on the ground as possible, right? This is true up until the tire reaches its saturation point. When a tire becomes saturated, it is no longer making the most of its contact patch. Thus, you want to run tire pressures just high enough to prevent the tire from reaching its saturation point.
When you put more air in your tires, their saturation point and the tires were able to grip more mid-corner when they were overloaded. However, on corner exit (when the front tires have little weight on them), saturation was not a problem so they lost grip from having a smaller contact patch.
Thus, there is no one "ideal" tire pressure. It depends on what you're doing. Drag racers run at very low pressures because they need not worry about lateral tread deformation. Higher tire pressures can fix one problem but cause another, and if you find yourself stuck with a problem perhaps you simply need wider or different tires. Your goal should be a tire that works well even at lower tire pressures.
5) Stiff sidewalls aren't always best.
This is complex. You want as large of a contact patch as possible, right? A narrow tire with stiff sidewalls will work against this goal as it reaches its saturation point and doubly so if the tire is off camber. Think about it: a stiff sidewall will prevent the contact patch from growing uniformly by resisting the necessary bend in the carcass that allow the contact patch to balloon. When this happens, the center and edges of the contact patch get a disproportionate amount of load on them, overwhelming the rubber in those areas. This causes the tire's coefficient of friction to drop.
Since we want a short contact patch, this isn't always a huge problem, however we also want weight on the contact patch to be uniformly distributed. Thus, control over the size of the contact patch is best regulated with tire pressures since air pressure is uniformly distributed. For this to happen, some sidewall flex must be allowed, and the narrower the narrower the tire, the more flex it'll need.
I made this ugly, not-to-scale graphic to illustrate why stiff sidewalls can be bad. In the wide tire, the sidewall need not deflect much so no problem exists, but in the narrow tire, it leads to an uneven distribution of load in the contact patch (illustrated by darker shades of gray):
The most recent trend in high and max performance street tires has been towards slightly softer sidewalls, and perhaps this is the reason? Stiff sidewalls make great sense when the tires are extremely wide and camber is well controlled, but with new cars being heavier and softer than their predecessors, stiff sidewalls might hurt more than they help. I believe the stiff sidewalls in the stock tires are one reason they are so tire pressure sensitive.
I don't mean to imply stiff sidewalls are bad; on a properly set up car they are very desirable. They provide immediacy and lateral stability. I don't think they are automatically better for every car, though.
If running one of the more modern tires with a softer sidewall, be warned: you [i]will[/i] want to mount them on the widest wheels possible to prevent the sidewall from rolling over in turns. This happens when the sidewall cannot support the lateral force the tread is generating, and it flexes so much that the side of the tire touches the asphalt. If this happens, your are losing a lot of grip. You have no choice but to raise your tire pressure, change tires, or change wheels. Wider wheels act as a natural brace for tires (since lateral forces can be more easily pushed onto the outside lip of the wheel), and this adds greatly to lateral stability.
Other Considerations:
Remember that the above outlines assume the tire is able to operate at its peak grip. A tire that is not perfectly perpendicular to the ground (not off camber) will not be at its peak level of grip. Here is a graph illustrating this:
Likewise, tires must be in their ideal operating temperature. Street tires can overheat, whereas racing tires might not heat up enough. Furthermore, tires might heat up at different rates, giving much more grip to one end of the car compared with the other. Here is a graph illustrating this:
Finally, remember that tires differ greatly from one another! Remember that your other suspension modifications play a large roll in what is ideal for your car, especially things like overall vehicle weight, wheel size, suspension geometry modifications, and suspension travel. Driving style is another huge variable. Unless you have advanced data acquisition available (with the know-how to understand and adjust to it), then it may be best to optimize to the driver's wishes rather than for a theoretically faster setup.