Every tyre -- each brand, size, and for that matter at each location on the car -- has a theoretical best pressure for a given car's weight, including weight distribution, and for its suspension settings and layout. The manufacturer's pressures are generally given, not surprisingly, for the tyres -- including brand, construction, and size -- included on the car by the factory. If you change tyres, you may need to change the recommended pressures as well. There's a cheap and simple way to get pretty close to these theoretical best pressures for your tyres on your car.
Here’s the theory. Changing tyre pressures changes two primary variables, which are related in how they affect a car's handling/grip. Variable 1 is the tyre's stiffness, including not only resistance to vertical loads (such as bumps) but also its resistance to rollover under hard cornering. Most modern high-performance tyres are designed to give best performance when the contact patch of the tyre is flat, especially from side to side. If the tyre rolls too much from side to side when the car leans in a corner, the contact patch can lift up and you lose grip, alternatively, if the tyre rolls off the contact patch and onto the sidewall, the tyre loses grip. Both of these happen at lower speeds if they tyre's pressure is below this theoretical best. So in general, adding air pressure raises the point at which these two bad things happen, though at a cost in comfort over bumps and surface roughness.
However, this doesn't mean you should immediately rush out and put in 100 psi in all four tyres. Variable 2 is the tyre's contact patch itself -- the roughly circular area at the bottom of the tyre where the car's weight at that corner presses the rubber into the pavement. If you increase tire
pressure beyond the theoretical best pressure, the center of the tread will expand circumferentially more than the sidewalls. This causes the edges of the tyres to make less contact with the road, which a) wears the center of the tyre more than the edges and b) reduces the amount of rubber that's actually on the ground, reducing grip. You want a tyre to deform a certain amount, to deflect as the car rolls in a corner -- you just want it to deflect the right amount, and too little deflection is as dangerous as too much.
So in general, if the tyre has too little air in it the contact patch lifts or rolls and you lose grip; if the tyre has too much air in it the contact patch shrinks and you lose grip. Therefore, the trick is to find out how much is, "just right." This is pretty easy to determine experimentally. You'll need a big piece of chalk, a tyre pressure gauge, and a source of compressed air, plus a big car park or empty dual carriageway.
Place a little white chalk at the "shoulder" of your tyre right where the tread and the sidewall come together. You don't need much, just a section an inch or two long and which
wraps an inch or two up into the sidewall and down onto the tread. Do this on all four tyres -- just one or sometimes two marks on each tyre will do the trick. Again, if you use chalk it'll wash off easily when you're done. The easiest way to proceed is to overinflate the tyres slightly because it's quicker and easier to let air out than to add it. Also, in general an overinflated tyre is safer than an underinflated one -- if you're 5 psi too high, the tyre's grip will still be less than at the optimum level, but it'll be higher than if the tyre is 5 psi too low. Read the sidewall for the
maximum recommended pressure and fill the tyres up to that level; you'll adjust the pressures down from that value as you proceed with the tests.
So, with (say) 40 psi in your tyres and a few chalk squares on each tyre's shoulder, go out and take a high speed run, but do it safely. At the end of the run you put the car back in line and hop out, inspecting each tyre in turn: If the chalk is rubbed off all the way up the sidewall, that tells you the tyre is rolling over too far and needs more air. Since you're already at the maximum, this is unlikely, but if it happens it tells you you're overstressing the tyres and you need to drive slower or buy better tyres.
If the chalk isn't rubbed off anywhere except the tread surface, you aren't rolling enough for the tyre to work properly. Let out 2 PSI or so and repeat the test.
When you get to the point at which the chalk is rubbed off the entire tread surface (including the shoulder blocks) but NOT rubbed off from the smoother rubber of the sidewall, that's the correct pressure for that tyre, on your car, with you driving. You may find that the numbers are unique to each corner of the car -- that is, you may find that your car works best with 38 PSI in the right front, 36 PSI in the left front, 32 PSI in the right rear and 28 PSI in the left rear. Why would they be different? Mainly because of weight distribution, a nose-heavy car with a driver on the right, will have more load on the right front tyre, meaning it takes more air than the left rear tyre to balance between stiffness and contact patch size.
Once you've done this a few times, you'll begin to get a sense of what a change of a few PSI will do to your car's handling. That can sometimes be of more value than just getting the pressures right, because you can start sensing when a tyre is running low before it becomes dangerous.
As an alternative, you can chalk the tyres and then go take a spin through some long sweeping bends, working up to your accustomed speeds, then quickly (but safely) stop and check the pressures in each tyre. Now you see why I suggested overinflating the tyres, because it's easy to keep a pressure gauge in a shirtpocket, and you can use the gauge to drop the pressures 1 or 2 PSI in a few seconds at the side of the road. If you're doing this on public roads, proceed with caution as the tyre's grip will probably be very different at the maximum pressure than you're used to and the handling may change, it's likely to be better, but it will almost certainly NOT be what you're used to. This is why it's best to perform these tests somewhere like a racetrack where the worst that will happen if you spin is that you'll knock down a cone or two and maybe get laughed at. The only down side is you’ll waste valuable track time doing this, in fact you’d be better off having this all sorted before you got to the track !!