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first thing to do after tire swap?

any recommendation above that is purely for efficiency.
Or ride comfort or wear characteristics. The tire forms part of the suspension and the pressure in it is part of the suspension tuning. The manufacturer may have many reasons to choose higher than the designed load pressure.

It's still true that there is not just one pressure printed on all the Model 3 door stickers, and manufacturers do change pressure recommendations based on many things.
 
Or ride comfort or wear characteristics. The tire forms part of the suspension and the pressure in it is part of the suspension tuning. The manufacturer may have many reasons to choose higher than the designed load pressure.
May have? Sure.
Do they actually have anything other than efficiency? I strongly doubt it. Jacking up pressures will wear out the center rib on most tires (may be not on some tires specifically made as Tesla OEM, and making tire producers make tires specifically for Teslas definitely increases production costs). Increasing tire pressures will make preserving the same level of comfort more expensive, which makes zero sense from a business standpoint.
 
(may be not on some tires specifically made as Tesla OEM, and making tire producers make tires specifically for Teslas definitely increases production costs)
A lot of tires on Teslas are Tesla specific already, so Tesla is already going through this effort and thinks it is worth it. I know the Model X and M3P have T0/T1 tires. It doesn't necessarily mean higher costs to Tesla though- their volume is high enough that a Michelin or Continental will do custom work to get the volume, and the tire manufacturer likes it because it tends to lock a lot of people into those OEM tires, which are priced higher as replacements (for instance a T0 Michelin for a M3P is $401 vs $364 for the same size without the T0 designator).

None of this is uncommon- look at the MPS4S at tire rack. There are *7* versions of the 235/45/20 tires, all with the same load rating, and almost always more than one of any given size for other sizes. Why? Because the tire was tuned for a specific car. You really think they did all of that just for efficiency and all tell you to set the tire pressure high for the same reason? And they all paid a lot more for their tires?

 
A lot of tires on Teslas are Tesla specific already, so Tesla is already going through this effort and thinks it is worth it. I know the Model X and M3P have T0/T1 tires. It doesn't necessarily mean higher costs to Tesla though- their volume is high enough that a Michelin or Continental will do custom work to get the volume, and the tire manufacturer likes it because it tends to lock a lot of people into those OEM tires, which are priced higher as replacements (for instance a T0 Michelin for a M3P is $401 vs $364 for the same size without the T0 designator).

None of this is uncommon- look at the MPS4S at tire rack. There are *7* versions of the 235/45/20 tires, all with the same load rating, and almost always more than one of any given size for other sizes. Why? Because the tire was tuned for a specific car. You really think they did all of that just for efficiency and all tell you to set the tire pressure high for the same reason? And they all paid a lot more for their tires?

Doing custom work definitely involves some additional development costs that would be passed onto the buyer. Tesla would've gotten the same-sized tire cheaper at the same volume w/o going for custom specs. The 'lock people into OEM tires' is the demand side argument that doesn't have anything to do with production costs. Ok, maybe it costs 2c to slap 'tesla spec' onto the sidewall to make people want to buy those at a premium. Tesla could/would've done it regardless of asking for custom spec'd tires.

The bulk of those custom specs are for performance applications (Porsches/Ferrari) and don't have much in common with Tesla specifics. The load rating being the same is not an artefact, it is literally a fixed formula based on tire dimensions. Actual sidewall stiffness is likely very different for low-3000lbs performance car and 4100+ lbs Tesla.

The simple truth of that matter is that the range matters for EVs, and pumping tires to 45psi allows Tesla to advertise somewhat higher numbers. Doing so requires some compromises on comfort and necessitates custom-spec tires that won't wear excessively in the middle due to high pressures.

When going for non-OEM aftermarket tires, going for pressures above 41psi (maximum XL-rated tires are rated at) is pretty pointless, except for maximizing range. One can safely go for lower pressures, if one can do some simple math. Even the lowest rated OEM tire, at 92Y XL (at ~1400lbs per tire), is more than necessary to carry a car+driver. You only need ~1100lbs for that. A non-XL tire of the same size is rated at ~1200lbs @35psi, and should be plenty to drive with a few people on board. Going for 35psi will do wonders for comfort.
Now, going for 35psi on an XL rated tire may actually lead to more edge wear, so I wouldn't do that. But 38ish should be fine to run long term, IMO.

I can find no evidence of this in the Model 3 manual. It makes no mention that a TPMS reset "learns" the current tire pressure as normal.
Try hitting the 'Reset TPMS sensors' button. The car tells you specifically that it will learn new pressures as the new target.
 
Try hitting the 'Reset TPMS sensors' button. The car tells you specifically that it will learn new pressures as the new target.
Good old Tesla, where the user manual doesn't match the software at all.
For anybody looking for this later- you hit Reset TPMS, and then you get a "Learn Pressures" button.
You also get an undocumented "factory reset" option.

The 'lock people into OEM tires' is the demand side argument that doesn't have anything to do with production costs.
And production costs don't have anything to do with the price a product is sold at. Michelin might sell tires to Tesla directly at the same price as a non-custom tire even if it costs Michelin more in NRE or per unit costs, in order to maximize future revenue from lock in. Tesla specifically helps with this lock in right in their manual:
When a tire set becomes worn, replace all four tires at the same time. Choose a Tesla-approved tire which is designed specifically for your vehicle. Most Tesla-approved tires can be identified with a Tx specification (for example, T0, T1, T2). Tesla-approved tires are designed to reduce road noise and optimize handling, ride, and range. Contact Tesla Service for information.
Both Tesla and the tire manufacturer benefit from having brand specific tires, at what is likely a very minimal cost given the huge number of SKU's that already exist.
 

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