
Two wheels on the same car. Notice the different wheel offsets.
Measurements
Tire hardness is an odd topic. Not only do you need to measure the hardness of a cold tire, you need to measure the hardness of a hot tire as well. You need to track the difference between the hardness of a hot tire and a cold tire, and discern if this relationship is stable as the tire gets older and is used more. As the tire ages and goes through multiple heat cycles, it takes longer to soften as it gets hot. The tire may still look good from a wear perspective, but it may not perform even when it gets hot. The rubber that makes up a tire is a mixture of various chemicals, and organic and inorganic compounds. Many of these chemicals are very light and aromatic in nature. As the tire goes through heat cycles, these chemicals gas off and the tire gets harder. Even exposure to the sun can degrade the compound. It is nearly impossible to replace the lighter elements of the tire.

This is all part of the tuning process-adjust and measure.
The makeup of a tire is complex from a chemical perspective, in relation to the composition of the rubber, and a physical perspective, in regard to how all of the various components are assembled to make the tire. Applying a chemical softener to the rubber may cause changes that are not in the best interest of the tire from a physical or a chemical perspective. You may damage either the rubber or the physical makeup of the tire, or you may do nothing at all. I am neither a chemist, nor a tire engineer. What I do know is that in my experience, new tires have always proven to be better than old tires, no matter how much magic goo has been applied. Many sanctioning organizations have very strict and draconian penalties for chemically treating tires, so you're better off spending your money on new tires than taking the risk on treating tires.
You should also be measuring and recording tire temperature. There is no excuse for not owning a tire pyrometer. The digital handheld probe can be purchased from most racing vendors for less than $100. I have also seen the infrared types for under $100. So for about the price of taking your family to dinner and a movie, you can have a digital tire temperature gauge. This tool is also very handy for chassis development. You can learn a good bit about tires once you start to record their temperatures.

The tape measure is your friend. It is critical to continue checking all of the physical attributes of the tires. New or used, it doesn't matter because the tires are a key ingredient to tuning the chassis. You need to be in complete control all the time.
You also need to measure tire wear. This is very easy to do if the tires used in your class have a treaded surface. If you are using slicks, look for the tread wear indicators on the surface. You need to keep track of how many laps it takes to wear out the tires. This is an additive function. If you race at the same track, it will be very easy to determine just how many laps you can run prior to having the tires wear out. The tire is worn out not only when its appearance degrades, but also when performance declines and the compound stops gripping. On most race tires, this happens prior to the tread wearing out. When the lap times are slower-even if there is tread left-the tire is worn out. It's that simple.
Tire pressure needs to be recorded when the tires are cold and when they are hot. Understanding the pressure growth from the cold inflation level to after the tires have reached operating temperatures is critical. This rise in pressure can vary a good amount depending on the tires you are running, the weight of the car, and the type of track you are racing on. This type of data is critical. Even if you win the race and spend some time in Victory Lane, a member of the team should be instructed to make sure these data points are collected. You need a quality tire pressure gauge for this step. Plan on spending from $50 to $100. This measurement should be recorded on an almost religious basis.

The lot and date code on this tire. The number 4305 is the date code. This tire was manufactured in the 43rd week of 2005. Maybe you should try to use newer tires.
Record the number of heat cycles the tires go through. Heat cycles are not equivalent to the number of laps completed. In one heat cycle, the tire goes from cold to hot and back to cold again. If the tires reach operating temperature and you come in to make a quick adjustment and then return to the track, that is not a complete heat cycle. The tire needs to reach ambient temperature to complete a heat cycle. If you run practice, a trophy dash, and two heat races, and the tires had enough time to cool down to ambient temperature, you can consider that four heat cycles. You need to keep track of this due to the fact that your tires will not work as well once they have gone through a number of heat cycles. You have to determine that number for yourself. If you are running a tire that will last more than one or two race days, this is an issue. If your tires are unable to be used multiple race days, then this will not be a big deal, as you will be replacing the tires prior to them falling off the clock.
Something many semi-professional racers fail to check is the spring rate of the tire. One of the reasons that tire pressure is so critical is that it not only adjusts the tire, but also the spring rate of the tire. This also impacts the chassis and the chassis settings. This is why the car sometimes works great one night but doesn't work as well the following night, even though everything is set the same. We need to remember that the cars we race are highly optimized to do several things very well. When we put new tires on the car and everything else is the same, the car is not really the same.

Air pressure is a critical adjustment, so make sure you are on top of it.
Some tire manufacturers have charts on their Web sites that list spring rates with various air pressures. Hoosier (www.hoosiertire.com) is one manufacturer that posts this information. This is a start. If you are not running a tire that has this type of support from the manufacturer, you have to calculate these rates yourself. This requires the construction of a machine measuring this data. This is not too difficult, as it is a simple load over displacement calculation. Please be aware that there are many variables that affect this rate-wheel width, air pressure, and tire temperature. So the rate when the tire is hot will be different from the rate when the tire is cold.
If you race on dirt, it is a good idea to keep the tires clean. After racing, wash the tires when you wash the car. Racing tires that are covered with dirt seem to dry out faster, and it is much easier to inspect the tire when it is clean.
The cold, hard reality is that these tips are all part of the winning equation. Some people win and do none of these measurements. If you are lucky enough to be one of these people, you have my greatest respect and disdain at the same time. For the rest of us, we need to be a bit more systematic in our approach to racing. We will continue to take measurements and record data. This will be our entrance fee to the winner's circle.