Originally Posted by Jon Bogert
In the sterile world of theory, it is. In the real world, no one would ever keep all the other variables constant, so the old saw is wrong far more often than it's right.
So why not look at an actual case? Let's see what happens when you compare, say, a 205/55-16 RE92 on a stock wheel with a stiff sidewall, soft compound, max performance 245/40-17 on a 17x8.5 wheel--a typical WRX big meat upgrade. Then you optimize the tire pressure for maximum grip without peeling off the rim. Then measure the contact patch. Who knows--maybe it'll be bigger, maybe smaller, maybe exactly the same, but you won't find the answer from theory.
its not theory - it is physics and there are laws, not theories. The contact patch area
is the same, the shape changes. Its simple, your car weighs, for the sake of argument, 3000lbs and is perfectly balanced so that each wheel supports the same weight. Thus each tire is supporting 750 pounds. Say your running 30PSI in every tire, 750/30 = 25 square inches of contact patch for each tire. There is no magic here, if there is less weight on a tire the contact patch area shrinks, or if there is more weight it grows.
The contact patch area is based on the weight and tire pressure, period. It doesn't get bigger or smaller from the size of the tire but the shape of the contact patch will vary based on the tire's size and tread pattern. It will get bigger and smaller as the loads change, there is no way around it since its part of newton's laws
According to this, the sidewall can support some of the weight and not be reflected in the contact patch.
Edit: Added how stuff works link