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So why does increasing the size of the rims force a decrease in the width of the wheels/tires?

Because side profiles have now a minimum limit, that varies with the year. When you increase the rim diameter, while keeping the same wheel diameter, the side profile will decrease. The game, thus, decreases the wheel width.

Since the side profile, the number after the slash in the tyres spec i.e. the 50 in 205/50 R16, is calculated in relation to the width, in that case the side profile is 50% of the width, the game will decrease the width, therefore increasing the percentage between them to the minimum ratio compatible with the available tech.

Sorry about the repetition of the word width.

I think you mean the aspect ratio of the tire decreases with increased wheel sizes. The overall height of the tire is fixed and selectable (600mm is starting point I believe), and can only go as high as the body chosen will allow. The width is also fixed and selectable (175mm is starting point I believe) and is also limited by the body chosen. The aspect ratio indicates sidewall height.

For example 215/35R18 is what size tires are on my car, but my factory tires were 195/60R15. The two sets of tires are within .5" of each other overall, but the sidewall is drastically reduced on the 18" wheels. 215 is the width of the tire measured in mm. 35 is the ratio of the sidewall to the width, written as a percentage. Obviously, the R18 is an 18" wheel opening (R used to be used to indicate Radial Tire, but not so much anymore). So the height of the sidewall is 215*.35mm or 75.25mm. The wheel is 457.2mm so the overall height of the tire is 607.7mm. The factory tires are 195mm wide, so the sidewall is 195*.60 or 117mm tall. The wheel is 381mm, so the overall height of the tire is 615mm.

These are not exact measurements, but are close enough for comparison purposes. There are exact formulas, which I am too lazy to bother with at this moment, to calculate such matters. The point is, the tire width does not decrease with increasing wheel size, the aspect ratio decreases with increased wheel size. The other point is, the height of the tire determines this aspect ratio, and is adjustable within limits of the body.

With that being the case, are we going to have different wheel sizes for either end of the car?

are there any production cars with different sized wheels front and rear?

Plenty. I am sure there are a lot, but one that immediately comes to mind is the Alfa 4C.

Most musclecars do, but that is in width, which is allotted for.

Why would you need such a thing? Just curious. I don't know if there is any advantage to using 15" wheels on the front and 16" wheels on the back, other than space/weight reasons or aesthetics. The large majority of cars (but not all) have the same wheel diameter for front/rear, but quite a few cars have different tire sizes for front/rear. We need to distinguish between tire size and wheel size. The terms are not interchangeable.

This.

Mod edit (Der Bayer): Was this post really neccessary? You quoted the very last sentences of the previous post and added exactly no information to it...