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Extrapolation of Range and Battery Size(s)

Discussion in 'Model 3' started by viperboy, Apr 1, 2016.

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  1. WarpedOne

    WarpedOne Supreme Premier

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    Test your method against two known wehicles: Model S and Model X. Their dimensions, weight and efficiency are well known and published.

    You ignored one *very* important factor: rim/wheels size. Change 19" with 21" rims on the same car and you just lost 10% efficiency.
     
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  2. Rashomon

    Rashomon Member

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    I
    \

    That's less change on the frontal area on the M3 than I've been assuming; I thought the width difference was enough to drop it lower. That implies the effective frontal area of the M3 will be about 0.49 m^2, and I've been assuming about 0.46-0.47 m^2. Not a big difference, but my range calculations are slightly optimistic if true. Then again, the M3 and MS/MX will probably all lose their sideview mirrors before long; can you do an area calculation with the mirrors deleted?
     
  3. Troy

    Troy Active Member

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    @Rashomon, the two mirrors together are 0.0456 m^2 = 456 cm^2 which is 1.9% of the frontal area.
     
  4. Rashomon

    Rashomon Member

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    So delete the mirrors and you might get just under 0.48 m^2 on a M3. Such a deletion would make the targeted 0.21 overall Cd easier to achieve, as the truncated flat rear of a sideview mirror inherently limits the drag coefficient achievable on the mirror itself.
     
  5. Zoomit

    Zoomit Active Member

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    #105 Zoomit, Nov 18, 2016
    Last edited: Nov 18, 2016
    That method is heavily dependent on pictures without parallax. The MotorTrend front picture does have parallax so it will add error to the calculation. I got excited when I first saw that picture for this very purpose but I couldn't figure out a realistic way to calibrate out the effects of the parallax. The best place to see that parallax is the tire positions. In the Model S picture, the rear tires are almost completely hidden behind the fronts. In the Model 3 picture, the camera focal length is shorter and so the rear tires are visible inside of the front tires. The parallax will result in an overly large frontal area calculation for the Model 3.

    However, it appears your results are pretty close to what I estimate. The Model 3 and S look to have the same ground clearance, height, and overall frontal view shape. So I estimated the frontal area by reducing down the Model S frontal area by the difference in width of the cars, as Rashomon implies here:
    The Model S frontal area that I've seen comes from C&D's Drag Queens article: 25.2 ft^2 or 2.34 m^2. Since the Model S is 77.3" wide and the Model 3 is expected to be 74.2", that's a 4% decrease. That yields a 24.2 ft^2 (2.25 m^2) [25.2*0.96] frontal area. Multiplying these numbers by Cd results in these drag areas:

    Model S: 25.2 x 0.24 = 6.05 ft^2 (2.34 x 0.24 = 0.56 m^2)
    Model 3: 24.2 x 0.22 = 5.32 ft^2 (2.25 x 0.22 = 0.49 m^2)

    (Note I've hedged a little and used 0.22 for the 3 because Musk only said 0.21 was the goal not it's final number.)

    That results in a 12% reduction in aerodynamic drag area for the Model 3, with a similar reduction in drag force. If I also assume a Cd of 0.21, the difference is a 16% reduction between the S and 3.
     
  6. Zoomit

    Zoomit Active Member

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    Here's my current guess. I'm frequently refining my assumptions though.
     
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  7. Swampgator

    Swampgator Member

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    Zoomit,

    I like this. This also reinforces my belief that there will only be a 50 and 70 kwh Option.
    70 kwh will get over 300 miles EPA and that is enough. Elon has already stated no need to go much higher than 300, and I suspect the 350+ ranges will be left for the 100D Model S going forward.
    70 kwH battery at 40% greater energy density will shave 400+ pounds from the battery weight alone. This means lighter components like suspension, motors, etc are need to move the car a given range. I'm also sticking to Randy Carlson's estimate of a loaded P M3 coming in at 3600 pounds or so.
    If that turns out to be true, we will have a 300+ mile range car capable of accelerating to 60 in under 3 seconds and costing around 70K loaded.

    Not too shabby.
     

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