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Why do the largest tires have a harsh ride?

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True, but it indicates that low profile isn't the end-all-be-all of performance. The main thing that low profile tires do is stabilize the tread at very high speeds (over 200 km/h). For those of you who recall 70% aspect ratio V rated tires, they got around this by having a floating bias ply layer in the sidewall to stiffen them up (ride wasn't great). A short sidewall reduces the amount of flexing making the tires safer at those very high speeds.

Short/stiff sidewall transmitte steering force faster thus giving a sharper steering response and better road feel at any speed. It's not just for high speed stablilization.

I would add that it is not an apples to apples comparison linking side wall to performance. There is a lot of difference in compound between the 19s and 21s. I'm running Pilot Super Sports on 20" rims which have more side wall than Tesla 21" PS2 yet my 20s have better grip. Part of that is better compound in the PSS' and part of it is 10 lbs per wheel less in unsprung weight (my 20" rims are 10 lbs each lighter than the Tesla 21s). The CR generalization works if you are only talking about Tesla's offerings but it falls apart when you consider other/better tire options irrespective of rim diameter.

That's definitely another factor that accounts for grip and tire wear differences between the two Tesla options. Tire companyies usually will use more gripy compounds only for lower profile tires on the (mostly correct) assumption that those who buy softer tires are usually not willing to compromise tire life for performance gain. Sometimes it could be hard to find a higher profile tire using real soft compound. Your setup of 20" gripy tire with coil, I believe that's what you have, seems to be a great combination.
 
I should point out ride "harshness" is relative. The 19" feel like I'm floating along on a barcalounger with wheels. I would never recommend them to anyone. The 21" aren't tight enough for me, although I suppose it will have to do. It just depends what your previous cars were I guess.

And me, just from what you wrote, I'd have to special order 17" (or 16") so that I could feel even less bumps (as well as do all the artsci sound deadening modifications to the car). If I could afford a new luxury vehicle, I've already said I want Mercedes Magic Body Control, and the air-suspension Tesla Model S with 19" I test-drove felt very harsh to me, so I'm in an entirely different world than you. If I was super rich I'd probably end up buying a few Teslas and keep them in the garage because no MBC.

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This is also somewhat known as D Plus fitment. On the Tesla S the normal D is 19" and the 21" is D + 2"

D + 1 would be a 20" wheel and tire combo on the Model S and would be a compromise between the two other fitments.

Aha! I'd like a D Minus fitment, like a D - 2" or D - 3" :) That's a very good nomenclature. I love it. Perfect.
 
If I recall, some of the early SIG Model X screen shots did show that the Model X will have a 20" Tesla Wheel and a 22" wheel as an option. I suspect that a lot of the 20" wheels may find their way onto Model S. And who knows, possibly be offered as an option for the S?
 
And me, just from what you wrote, I'd have to special order 17" (or 16") so that I could feel even less bumps (as well as do all the artsci sound deadening modifications to the car). If I could afford a new luxury vehicle, I've already said I want Mercedes Magic Body Control, and the air-suspension Tesla Model S with 19" I test-drove felt very harsh to me, so I'm in an entirely different world than you. If I was super rich I'd probably end up buying a few Teslas and keep them in the garage because no MBC.

Aha! I'd like a D Minus fitment, like a D - 2" or D - 3" :) That's a very good nomenclature. I love it. Perfect.
You MIGHT be able to go -1 or -2 but you wouldn't be able to go very much smaller without having to change the brakes too. The rotors and calipers on the S and X are pretty large and for good reason. These are really heavy vehicles that need big brakes to get them stopped in a timely manner.

Even more so if you plan on towing (yes, referencing your other post in the towing thread).
 
Model X will most likely have larger tire circumference than the S. Many SUVs come with much bigger tires than sedans. So perhaps both 20" and 22" rims may have plenty of tire sidewall. We won't know until the tire size is revealed.

We know the mules with 20" were on 265/45R20 and it looks like the closest match for 22" tires would be 265/35R22 or the 295/30R22. The 20"s are Continentals and the 22"s are Pirellis.
 
One thing that you will get with shorter sidewalls is increased stiffness - both ride (vertical) and steering (lateral) transients will propagate through the tyre faster. This has a number of (mostly bad) implications, but some people prefer the feel.

Higher cornering stiffness is not at all the same thing as higher grip. As others have pointed out, the limit of adhesion is largely determined by the rubber compound (for given conditions.)

The same is true of the transmission of axle torque to longditudinal force, i.e. braking and acceleration. I doubt this makes any practical difference in the Model S (with its driver aids and near-perfect traction control,) but drag racers prefer larger sidewalls to make managing wheelspin easier.

Anyone who thinks larger rims are in themselves a performance upgrade should take a look at F1 Grand Prix cars and note how their 13" rims don't seem to handicap them much. (They're actually thinking of changing this next year. It's expected to have a number of effects, including making the cars harder to drive.)

Also note that Model S OEM tyres are different in some territories - e.g. in the UK new deliveries come with summer tyres on all rim sizes.