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Wheel sizes and its affect on range

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So we all know that 21" wheels on the Model S decreases range as compared to the 19" wheels. However, does anyone know the effects of 20" wheels? Would it have a similar, but less negative, effect on range? More specifically, I'm curious if anyone has first hand experience with these wheels: Tesla Model S 20

And lastly, would you get even better range (as compared to the stock 19" wheels) if you put 18" wheels on a Model S?
 
I don't think the calculations are as simple as "bigger wheel = worse range".

There are two major factors that influence efficiency...wheel weight and wheel diameter. Wheel weight determines the energy required to get the wheel spinning and wheel diameter determines rolling resistance.

Just pulling data off of the web for the Model S (Wheel and Tire Guide for Tesla Vehicles - Unplugged Performance)

  • 19" slipstream wheels with 245/45/19 tires have an overall diameter of 27.7" and a weight of 29 lbs.
  • 19" cyclone wheels with 245/45/19 tires have an overall diameter of 27.7" and a weight of 29.8 lbs
  • 21" x 8.5" turbine wheels with 245/35/21 tires tires have an overall diameter of 27.8" and a weight of 29.8 lbs.
  • 21" x 9" turbine wheels with 265/35/21 tires have an overall diameter of 28.3" and a weight of 38 lbs.
  • 21" Arachnid wheels actually weigh less (25.9 and 26.95lbs) than either the 19" slipstream or cyclone wheels with the same diameter as the turbine options.

So the calculations are not as simple as just wheel size because the weight and tire size also matters.

For example, you might actually see improved range running 21" x 8.5" square 245/35/21 Arachnid wheels on a Model S because the diameter is only 0.1" wider but the wheel weight is actually less and the tread width is the same between the 19" and 21" wheels.

If you do a lot of highway driving, the minimal diameter increases might actually be offset by fewer RPMs needed to get down the road. Especially with Arachnid wheels that actually weigh less than either 19" option.
 
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