It appears you have the original metric TRX tires and rims on your car. TRX tires were developed by Michelin and I believe they actually do a run of this size tires about once a year. However, the TRX technology is over 20 years old and not considered very good by today's standard.
What you need to do is THROW THOSE WHEELS AWAY and buy some new ones that will fit normal tires. The advantage of getting new wheels and tires are you can get the latest technology in tires using normal size tires in 17, 18, 19 or even 20", depending on how big you want to go. Many upgrade to 1988 BMW M5 wheels which are either 16x8 or 16x7.5.
The disadvantage are you'll have to come up with money to pay for these new wheels and tires. However, at least for the wheels, that is a one time expense and you can just get new tires thereafter.
As bfd says, you need to get new rims/tires. Best place is tirerack.com - I believe it recommends 225/60R16.
And as I was typing before a power outage so rudely interrupted me (no UPS on this computer), you should have gotten new tires 10 years ago, since tires get brittle and lose grip as they age.
Those tires are a dismal experiment gone bad. You are gonna have to buy new rims and tires. Sorry for the bad news.
Frankly, you should look at this as good news. I drive a '94 3 Series that came witht eh Sports Package that included 225/55x15 tires. Over time, this tire size became obsolete for lack of a better term. In any case, to continue with that tire size, I would be spending $250 per tire, mounted and balanced and out the door. This seemed like too much money for tires, so I shopped eBay for 17" rims. My car takes a full-size spare, so I needed 5 rims. I found them and got them to my house for about $600 including shipping. This put the unit price at $120 per rim. I bought a 225/45x17 tire to mount on the rims, and they ran me about $100 out the door. My initial cost to shoe my car with 17s was equal to putting a set of 15s, but subsequent sets of 17s are considerably cheaper than continuing with the obsolete 15" size that came on the car.
Since the overall diameter is the same, and the width is also the same, then my steering geometry hasn't changed appreciably, so the suspension still works the same. Yes, I suppose the ride could be a bit stiffer due to lesser sidewall height, but as a practical matter I can't tell any difference -- at least a difference that makes me complain.
I was hopinig to find tires, as the car is perfect condition...and with would eventually be worth more as an "all original equipment" car for concoursing...(I know, I know...the resale value on 1988 M6's is like nothing compared to other marques - Ferrari, Porsche, etc. etc....but one can only hope).
Still looking for a solution (maybe I have to place an order with Michelin for their once-a-year run)...
I see your point, and yes... if you are attempting to maintain the car as 100% stock you can get the metric TRX tires. Michelin still made them as recently as the past year, but they were the only ones. You should be able to get some at a premium price.
So keep the TRXs you have for concourse shows and run 16" on the road. They handle a LOT better, especially in the wet. You'll also be able to keep your TRX cross spokes much cleaner. You could fit E38 7 series 16" cross spokes which suit the car well and don't look too modern.
Well, they still make the TRX tires, but they are very costly. You could retain the set you have for nostalgia purposes, and get a new set for driving around on.
You could get BMW rims that fit the car and take the inch-size tires that are more common, and less costly.
Personally, I think you probably have a nice car, and the original equipment is worth having. But the reality is that current tire design surpasses the performance tires you have, and are cheaper. If you can find some 5 Series rims from the same era as your car, then you may be able to retain the original look and fitment at a fraction of the cost of installing new TRX tires.
If you're going to *drive* the car, I'd strongly recommend that.
OTOH, if you simply want it to look original, there are very similar BMW wheels in inch sizes. If you have the 'bottlecaps', there was a
14" and a 15" version of these. I have a set of the 14"s that I can use to make my originally-TRX-shod 535is look 'stock'. But I drive on either 15" E36-style or 16" TSW Hockenheims.
I don't recall whether your M6 might have had the BBS cross-spoke wheels but, if it does, a set of the 16" BBS cross spokes from an E28 M5 would be perfect.
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