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Drag Equation for Dummies: The Model ☰

Discussion in 'Model 3' started by SageBrush, May 4, 2016.

  1. SageBrush

    SageBrush Active Member

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    I stuffed the equation into a spreadsheet to play around with the parameters. I would greatly appreciate any error corrections or comments.

    Feel free to grab a copy if you find it useful.
     
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  2. physicsfita

    physicsfita Member

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    I'm assuming that you're just playing with this on level ground? If not, you need a cos(theta) in the rolling resistance portion.
     
  3. SageBrush

    SageBrush Active Member

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    Yes -- level ground
     
  4. zenmaster

    zenmaster Member

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    Only 12lbs difference for .21 vs .24 @ 80mph?
     
  5. SageBrush

    SageBrush Active Member

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    #5 SageBrush, May 4, 2016
    Last edited: May 4, 2016
    Sorry, I am not following. Except for the last column of Wh/mile all units are SI. What cell are you referencing ?

    After much fumbling about, here is a graph grouped by Cd:

    Screenshot 2016-05-04 at 11.13.31 PM.png

    116 kph (72 mph) shows ~ 200 Wh/mile friction forces for my presumed Model ☰. EM has said before (I think related to the Model 'S') that battery to wheels has a 20% loss. I prefer 15% for the Model 3 (it is my graph, after all,) so the on road energy consumption works out 200/0.85 = 235 Wh/mile. I came up with the same number by comparing cars so I have some additional confidence it is close.

    In case anybody is curious, that works out to 50 kWh usable pack for a 215 mile range.
     
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  6. SageBrush

    SageBrush Active Member

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    #6 SageBrush, May 5, 2016
    Last edited: May 5, 2016
    Another day, another graph ...
    I presumed that the Bolt and Model ☰ would have the same weight, and compared them to the new Prius PHEV that has an intermediate Cd and lower weight. Keep in mind that only aero and road forces are included. I doubt the battery to wheels consumption is much different between the cars so the relative differences seem qualitatively correct.

    Screenshot 2016-05-05 at 9.02.52 AM.png

    Game on, Toyota
     
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  7. omgwtfbyobbq

    omgwtfbyobbq Member

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    Nice post. I think the 3 will test a smidge lower than 215 miles on the 5-cycle test with a 50kWh pack and .24CdA, but Tesla might be able to tweak the baseline/HVAC power consumption to push it a little higher.
     
  8. zenmaster

    zenmaster Member

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    How do you figure same frontal area?
     
  9. SageBrush

    SageBrush Active Member

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    Fair question.

    It seemed a fair number for the 'Prius' and the 'M3.' As for the 'Bolt,' I had no idea so I left it alone. Grab a copy and change things to your satisfaction :)
     
  10. Rashomon

    Rashomon Member

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    #10 Rashomon, May 5, 2016
    Last edited: May 5, 2016
    Some relevant CdA numbers, in meters squared:

    Tesla Model S 0.58 m2 (Car and Driver number, I'm pretty sure done at GM's tunnel though not claimed in the story)
    Tesla model 3 0.47 m2 (estimate based on Cd of 0.21 and some A reduction)
    BMW i3 about .7 m2 from BMW
    Nissan Leaf .73 m2 (car and driver again)
    Toyota Prius about 0.58 m2 (car and driver again)

    I like working with CdA because that gives you the important numbers directly, and is useful for vehicle to vehicle comparisons. Cd by itself is useful when you're refining a given package that can't have an A reduction -- but usually you really could have an A reduction with different packaging.
     
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  11. Zoomit

    Zoomit Part 3 Awaiter

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    The Bolt EV frontal area is 25.8 sq ft, per Car&Driver. More data is in the spreadsheet in my signature.
     
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  12. Rashomon

    Rashomon Member

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    From C&D: "The Bolt’s claimed 0.312 aerodynamic-drag coefficient and modest 25.8-square-foot frontal area help this electric cut through the air with minimal ruffle."

    GM plays aero numbers very square: these are likely real, and almost certainly comparable to the C&D test numbers on the Tesla MS and Toyota Prius. That gives the Bolt a CdA of 0.75 m2, just awful, worse than the i3, which is not good. (This is embarrassing for the company that did the EV1, which is still a record holder at 0.37 m2) If a Bolt can get over 200 mile range on 60 kWh, the M3 will not require more than 55 kWh. If they don't round it to the nearest 5, I would bet on something like 52 kWh.
     
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  13. Zoomit

    Zoomit Part 3 Awaiter

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    Not at all! GM and BMW just made different design decisions when balancing the size, shape, utility, range, and cost of the vehicle than Tesla did for the Model 3. A low CdA is important for long range cruising, but plays a much lower roll in urban, slower driving where vehicle size and utility tend to have a priority and results in boxy hatchbacks.
     
  14. SageBrush

    SageBrush Active Member

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    #14 SageBrush, May 6, 2016
    Last edited: May 6, 2016
    Exactly so for all the people who understand the EPA numbers and utility. The other 99% look at the poor(er) range despite the bigger battery and conclude that the Tesla is better.

    Or they buy the boxy EV, enjoy the utility around town, and then complain bitterly when the car does not meet "EPA'" range on the highway. The box manufacturers face a catch 22 they cannot avoid due to consumer ignorance. Tesla avoids this by using a shape that no one views as an appropriate car for a run to the home improvement store for lumber and drywall.

    The other piece of the story though is that the GMs of the world reuse prior car shape designs so they start out with limited choices and trade-offs.
     
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  15. Topher

    Topher Energy Curmudgeon

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    I'll take the utility and shape of a Prius then. More cargo space and better aerodynamics.

    Thank you kindly.
     
  16. SageBrush

    SageBrush Active Member

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    Yup. I expect the G2 plug-in Prius and Model ☰ to have similar Wh/mile ratings in both the city and highway.
     
  17. Rashomon

    Rashomon Member

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    #17 Rashomon, May 6, 2016
    Last edited: May 6, 2016
    We're still at the point in battery capabilities that engineering for low drag and lower power usage is going to yield better results for most consumers. The i3 is an awesome city car for European conditions, and the new 33 kWh battery will make it better. But it's more than $45K in the US. The Bolt is better yet from a utility point of view, but it's $37,500, more expensive than the base M3 that is going to out-range it in most real-world US driving conditions, and a big chunk of that cost difference is the pack size. A M3 with the optional pack and access to the Supercharger network is going to be a far better vehicle for most US drivers, and won't be that much more expensive than the base Bolt. Perhaps some statistic out there might give a hint of consumer preference . . . can anyone think of anything that might indicate that customers prefer Tesla's trade-offs?

    I get the point on utility, it's just that until batteries get really, really cheap and higher-energy density, high-drag utility vehicles like pick-ups and vans and SUVs will do better with hybrid powertrains. The Germans face this issue for a different reason because of the high speeds and high-energy use of Autobahn driving in the home market, and it's why they're mostly working on hybrids of one form or another. It's why the MX is a sleek CUV and not a Chevy Suburban equivalent. Musk and company have been excellent at understanding the advantages and disadvantages of electric powertrains, and have done vehicles that have maximized the former and minimized the latter.
     
  18. Rashomon

    Rashomon Member

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    I think having Musk overseeing Tesla engineering and insisting on creative low-drag solutions is the key for Tesla. The utility of the Bolt dictated the frontal area, but not necessarily the Cd. If Tesla could achieve 0.24 Cd on a Mx, you have to think GM could have done better than 0.31 on the Bolt -- they just didn't have leadership willing to demand that and make the necessary styling and other trade-offs that would have been required.
     
  19. Jeff N

    Jeff N Active Member

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    I am really not an aero expert, but I have the vague impression that taller cars can get better Cd numbers when they are longer -- shorter makes it harder to obtain a smaller Cd. That helps a big car like the X vs. a smaller car like the Bolt.

    Anyone with a better clue care to comment?
     
  20. Rashomon

    Rashomon Member

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    #20 Rashomon, May 6, 2016
    Last edited: May 6, 2016
    Audi_A2_L_Silber.jpg Audi_A2_prototype.jpg
    You are absolutely right in that a longer vehicle is generally easier to make aerodynamic than a shorter one. It's one of the impressive things about the M3 in that Musk is indicating its Cd may be 15 percent better than the MS. The point I was making that a 0.31 Cd is about 30 percent worse than what Tesla achieved with the MX, and isn't totally explained by the differing slenderness ratios.
    As a counterpoint, Audi's Bolt-sized A2 from the mid-2000s was 61 inches tall, and achieved a CdA of .54 m2, almost a third better than the Bolt -- and that's with the added cooling drag of an internal combustion power train. Claimed Cd for the lowest drag version was 0.25. It was the most economic car of its day, and in diesel form achieved "3 liter" status, or three liters of fuel for 100 kilometers of travel, or over 80 mpg, though that is on the very optimistic EU drive cycle. Here are some pictures of it. The rear fastback or drop away are certainly part of what gave it its reduced drag. The question is whether the decreased interior volume and rear seat headroom that entails is worth a 20-plus percent increase in highway range at speeds around 70.
     

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