Rim Width vs Tire Width
 

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Interesting figures, IMHO. If folks are following that table, it makes more sense why I see more and more tires with sidewalls that stretch out from the tread to the rim (i.e.- 215 on an 8" rim).

I think tire to rim width is more predicated on tire sidewall design and aspect ratio. I have now run (2) different tires on my 17x8" rims (Mustang, not Mini) and both have been 245/45's and the sidewalls are perfectly square to the edges of the rim, which is what I prefer from a look as well as how I was always guided on how to size a tire to a rim. It puts the sidewalls in the same angular orientation to the tread face as when the tire is not mounted. Running anything narrower will simply start to pitch the bead out from its 'relaxed' state and start to stress the shoulder of the tire, since it will now be at a greater than 90 deg angle. Same is true to running a wider tire on a narrow rim, just the sidewall is reverse. Back in the day, it was common to run a much wider tire on a narrow rim, mainly due to tire/rim selections, but those could handle the offset 'better' due to the much taller aspect ratio (sidewall height).

My suggestion is to try and follow the tire manufacturer's specific rim width recommendation, as they know best as to what rim width works 'best' with the specific tire. An example brings me back to the Bridgestone RE-71R's I run on my Mustang. The 245/45R17 tire size specs are given when mounted to an 8" rim width and they recommend a rim width ranging from 7.5 - 9", which does conflict with the chart above on the narrow end of the scale. I happen to run my RE-71R's on an 8" rim, so I can have some confidence that I will get expected performance from the tire. YMMV.

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