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Does tire size affect the displayed range?

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It doesn't change the range, but it changes the calculation used for range estimation. It even says it right in the wheel change window. I can't watch right now, but in this video I tested it and the different calculation meant arriving with ~3% less battery with 20" wheels on the TM3 vs 18" wheels if I remember correctly.

The calculation difference with different wheels has always been a thing, but with this update Tesla allowed us to change the wheels ourselves. Previously, only Tesla could change the wheels in the software.

Hi. I was watching your video and noticed when you go on your tesla screen another screen popped up with floating icons. What are those?
 
Since I believe all the stock Tesla Model 3 wheel and tire packages have the same tire O.D., I don't believe there is any speed adjustment to be made. The tire O.D. is the only factor that will affect mph.
Yep, 18, 19 and 20 have about the same circumference so there is no significant change in speedometer accuracy or range calculation...
 
I know this thread is older, but I did run into this issue myself after just changing to aftermarket 18" wheels and tires for winter. I thought I would share my findings and hopefully clear some things up. My Model 3 came with OEM 19" wheels and tires, which appear to be a different outside diameter from the new ones. My spedo measures ~2-3mph too fast on the highway now.

This website...
Tesla OEM wheel/tire configurations
...seems to confirm the different OEM wheel and tire configurations are not exactly the same, which would account for all the differences reported by many people in this thread. I'm going to try setting the car to the 20" wheel configuration to get my range and speed numbers correct again. I measure speed using an iPhone speedometer app that uses GPS with cruise control on open road over several miles to make sure it's a fair test.
 
I know this thread is older, but I did run into this issue myself after just changing to aftermarket 18" wheels and tires for winter. I thought I would share my findings and hopefully clear some things up. My Model 3 came with OEM 19" wheels and tires, which appear to be a different outside diameter from the new ones. My spedo measures ~2-3mph too fast on the highway now.

I think the previous posters were talking about miles of range, not mph. If you are referring to mph (how did you determine the mph difference?), continue reading.

As mentioned previously in this thread, if you are running the Model 3 stock 18 and 19 inch tires sizes, the difference in mph between the two would be minimal (0.2 to 0.3 mph), unless you have a pretty large difference in tire diameters. That's pretty insignificant!

Changing the wheel diameters in the Tesla software will give you results based on the Tesla recommended tire sizes, which only results in the 0.2 to 0.3 mph mentioned previously, not close to the 2 to 3 mph change you stated.


 
I measure speed using an iPhone speedometer app that uses GPS with cruise control on open road over several miles to make sure it's a fair test.

It could indeed be that the iPhone is measuring slow and the car is closer to correct, but since I had no reason to question it before changing wheels I didn't measure it. I'll have to wait until summer for it to be worth changing back to stock wheels and measure with the phone again. I have always noticed though that the "side of the road, you're going this fast" signs do always measure lower than my spedo says by 1-2mph, but I've always chalked that up to crude measurement and delays in changing speeds vs measuring speeds.

It's true that people in the thread mostly were talking about computer estimated ranges, but the way the car measures wh/mi (a key variable in that calculation) almost certainly is based on distance traveled as measured by revolutions of the wheels and not by GPS. So, it follows that a wrong spedometer would generate a wrong estimated range.

I realize that I'm splitting hairs by caring about 2 mph, but I wanted to try to calculate efficiency different after changing wheels and tires, and now my confidence in the onboard computer's readings is suspect. Since even Teslafi's output is based on the onboard computer's data download via API, I really have no way to check other than having another car or a radar measure and compare with both sets of wheels. I'm sure I'll quickly forget that I cared and just keep being a happy M3 owner soon.
 
Weight and inertia of the wheels is the range changer. Look at the wheels specs pages on Tsportline.com. Weight can change by several pounds between the wheel versions. Also tire weight can vary. The 18's are the lightest of the Tesla wheels.

Wheel weight is a contributing factor, but the biggest difference in the range between the 18" wheels and the 20" wheels is the tire construction and rubber compound. Tesla assumes that you're using their factory-installed tires on any wheel set that you've selected. The 18" wheels come with the highly efficient grand touring tires, (Michelin Primacy MXM4) which have a harder rubber compound and are tuned for low rolling resistance. The 20" wheels come with the Michelin Pilot Sport 4S, which is a summer performance tire, has sticky rubber, larger contact patch, and more flexibility. This increases the rolling resistance a lot, making the car use more energy (up to 15% more than the Primacy's).

Wheel and tire weight contribute to energy usage differences during acceleration, as the moment of inertia is higher with the 20" tires (i.e. there is more mass to spin up with higher weight wheels). But steady-state, constant-speed energy usage is not really affected by wheel and tire weight.