For some reason, just about all the car companies have been going with big rim, low sidewall tires, and the aftermarket is going even kookier.
To be perfectly clear, any performance advantages of these is only marginally discernible and couldn't possibly make any difference to you unless you're in a racing situation. Otherwise, unless you count appearance, it's all bad.
The good:
Low sidewalls provide a somewhat stiffer ride and are less compliant. This affects lateral stability slightly at the extremes and might give you slightly better cornering on a smooth road. So slightly that if you can actually feel it, you can probably make a pretty good living driving race cars.
Large rims allow larger diameter brake rotors. This doesn't improve braking at all. It does allow better brake cooling, which could only possibly be meaningfully relevant if you're decelerating at more than about half a G several times a minute. Basically, fairly serious racing. It would also help you if you do the stupid thing and forget to downshift for a long downhill and ride the brakes instead.
The metal rim can be slightly lighter than the rubber tire, reducing unsprung weight. Again, if this actually makes a difference for you, you're probably making a living driving race cars.
The bad:
Low sidewalls provide a somewhat stiffer ride and are less compliant. This gives you a bumpier ride, resulting in a loss of traction unless it's compensated for in the suspension.
Low sidewalls require the surface of the tire to be stiffer, which in addition to reducing compliance, results in poorer traction on slippery surfaces like leaves and ice. So much that people who use them and live in snowy areas need to replace them with higher sidewall tires for winter.
Low sidewalls have limited deflection. If you hit a rock or some other hard thing, the sidewall may completely depress, translating the impact to the rim and damaging it. At the extreme, the thinnest sidewalls cannot tolerate the one inch curb in front of a driveway.
Sidewalls thinner than standard curbs do not protect the rim from lateral impacts when you take a turn a little too close. This is such a problem that there's a business selling aftermarket rim protectors.
The are stiffer and less compliant, which results in reduced fuel economy. For example, Tesla measures slightly over 2% range reduction when switching from 19" to 21" rims.
Formula 1, IndyCar, NASCAR, and many other high end motor racing series do not use these things and manage to get pretty good performance nevertheless. Some sports car racing does, but most of the top cars do not, and have sidewall/rim ratios comparable to ordinary road cars. They have much wider tread, but that's not the same thing at all.
The silly standard way the measurements of tires are specified is part of the problem. My Tesla Model S takes 245/45R19 tires. This is 245mm wide, on a 19 inch rim. The sidewalls of the tire are 45% of 245, which is 110 mm, which is 4.33 inches. So the total tire diameter is 19+2*4.33 = 27.66. Aftermarket 21 inch wheels use 245/35R21, which gives a 3.38" sidewall or 27.76 total tire diameter--basically the same. In addition to using two separate measuring systems (mm and inches), emphasizing sidewall/width ratios has confused people so that they think that's important. In addition, you have to do some calculation to figure out whether your wheelwell can accommodate any particular tire (I'm good at math, but I had to use a calculator to figure out what 45% of 245 was and convert it to inches)
I think they look stupid and I know the are almost entirely a negative for ordinary driving.
Way back in the olden days of tires with tubes, they had to be pretty close to 100% aspect ratio to accommodate the round tube. Tubeless tires and radial cords allowed wider tires and significantly better traction, but for a road car, less than about 60% is just silly.
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