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Extrapolation of Range and Battery Size(s)

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viperboy

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Dec 18, 2012
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#1
  • Here's what we know:
  • EM states base Model 3 gets 215 miles of range
  • Model s Range is already published
    • EPA Range for 70 is 230
    • EPA Range for 70D is 240
    • 90D is 288
    • P90D is 270
  • From one of the "first ride" videos, the driver states there will be single and dual motor options. Therefore we have to assume that the base model is a single motor unit.

Extrapolation:

I took some liberties here but I think my assumptions come out to a reasonable conclusion. The main assumption I came up with is that the Model 3 will be 20% more efficient than the Model S (due to a lower weight and lower drag coefficient).

Model S 70 (non-D) gets 3.285 miles per kw (230 / 70). If the model 3 is 20% more efficient, that comes to 3.94 miles per kw. Given the 215 base range you can back into a 55kw base pack.
  • efficiencies of dual motor give you 4.11 mpkw, resulting in 226 mile range

The largest model S pack is 30% larger than the small pack. Applying this to the model 3, you get a large pack of 71.5kw. (This fits in quite nicely with a 70 kw pack they already designed, manufacture and sell). I applied the same math of efficiency to the 70kw pack and come up with 274.6 mile range for the M3 70D and a 257 mile range for the top of the line PM3 70DL.



Second exercise: Assume the model 3 is 30% more efficient:
  • Base 50kw gets a range of 213.5
  • 50D gets a range of 222.9
  • 70D gets a range of 297.44 (Matching the specs leaked on electric.co)
  • P70D gets 278.9
 
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#2
20% reduction in drag area times reduction in Cd, plus other efficiency improvements. I assume 3rd gen inverter for more drive and regen efficiency.
I would guess 45-50kWh base with rated 210Wh/mi

I counted 8 bricks, with what looks like room for 2 more bricks under the rear seats. If there was 70% fill in the regular bricks, going to full bricks brings it to about 80kWh, or about 360 miles for the top model.
 
#3
The main assumption I came up with is that the Model 3 will be 20% more efficient than the Model S (due to a lower weight and lower drag coefficient).
Click to expand...

Fairytale. That is higher efficiency than i3.

210Wh/mi
Click to expand...
Motorcycle territory.
This is a car. Base is 55 - 60kWh. S60 had 208 EPA range.
Don't expect magical efficiency.
 
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#5
WarpedOne said:
Fairytale. That is higher efficiency than i3.


Motorcycle territory.
This is a car. Base is 55 - 60kWh. S60 had 208 EPA range.
Don't expect magical efficiency.
Click to expand...

Motorcycles actually suck at highway efficiency because their aerodynamics suck. A 450-pound Zero S consumes 15kW at 75 mph, not that substantially much less than a MS. The BMW i3 also has reasonably bad aerodynamics. It's tall so it's A is high even though it's narrow, and it's CD isn't anything special. It's CdA is about 0.7 meters-squared, 20 percent worse than a model S which is about 0.58 meters-squared. BMW designed it to be a city car, where its light weight really helps on an urban cycle. I've been assuming, based on the published rumors that Tesla was trying to reach a 0.20 or better Cd on the M3, that its CdA will come in about 0.45 meters-squared, so almost 20 percent better than a MS. We'll see, as no data to verify that was given yesterday, but it's at least conceivable that the M3 will consume substantially less power than a MS.
 
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#6
WAGs:

Cd: 5% improvement
Frontal area: 20% less
Tyres: 5% less RR
Weight: 20% less

Weight is not a clear variable to me when it comes to highway driving,
but overall a weighted 20 - 25% reduction in energy/mile seems reasonable.

4 miles/kWh strikes me as conservative,
4.5 miles/kWh would be a home-run

A a comparison marker, both the new Prius plug-in and BMW i3 are around 180 Wh/mile at 60 mph.
 
#7
Rashomon said:
I've been assuming, based on the published rumors that Tesla was trying to reach a 0.20 or better Cd on the M3, that its CdA will come in about 0.45 meters-squared, so almost 20 percent better than a MS. We'll see, as no data to verify that was given yesterday, but it's at least conceivable that the M3 will consume substantially less power than a MS.
Click to expand...
I find this photo a nice place to start guessing games:

ev-CdAs.jpg
 
#10
Cd of 0.21 is a bit better than fantastic.
And all the more surprising given the air dam in front.

We can guess about 24 ft*ft frontal area, for a CdA of 5.04
Once we know car weight and tyre RR, we can get a good estimate of energy economy.

By the way, google says that a kWh of Li-x battery weighs about 6.7 Kg, so about 335 Kg for 50 kWh before packaging.

If my arithmetic is right, starting from

CdA - 5.04 ft*ft
Air density - 1.225 kg/meter_cubed

I get a power requirement of 7.3 kW to oppose the air at 65 mph.
If that is about half of total power, then ~ 15 kW to for flat road, steady state 65 mph travel, or 224 Wh/mile
 
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#11
SageBrush said:
Cd of 0.21 is a bit better than fantastic.
And all the more surprising given the air dam in front.

We can guess about 24 ft*ft frontal area, for a CdA of 5.04
Once we know car weight and tyre RR, we can get a good estimate of energy economy.

By the way, google says that a kWh of Li-x battery weighs about 6.7 Kg, so about 335 Kg for 50 kWh before packaging.
Click to expand...

20% smaller means 20% smaller. You're taking too little off the frontal area.

Pack should be lighter than Model S since we know Tesla is likely optimizing cell size (and therefore pack mass).
 
#12
SageBrush said:
Cd of 0.21 is a bit better than fantastic.
And all the more surprising given the air dam in front.

We can guess about 24 ft*ft frontal area, for a CdA of 5.04
Once we know car weight and tyre RR, we can get a good estimate of energy economy.

By the way, google says that a kWh of Li-x battery weighs about 6.7 Kg, so about 335 Kg for 50 kWh before packaging.
Click to expand...

That Cd of 0.21 produces a CdA of about .47 meters-squared (maybe a little high depending on the A estimate), but that compares to about 0.58 meters-squared on the MS. I'm assuming new-generation tires will have a very exceptional rolling resistance coefficient of about 0.007, so the M3 will require about 15 kW delivered (after powertrain losses) at 75 mph, or roughly the same as a Zero motorcycle at that speed. That's assuming the base model weighs about 1750 kg (3850 pounds). It might be a little lighter than that. I think this all argues for a pack size under 55 kWh for the base model, maybe as low as 50 kWh depending on motor and inverter efficiency. I think the published rumor of a 65 kWh pack just might be referring to the big pack!

The Panasonic cells that Tesla are currently using weigh a little more than 4kg/kWh, and every indication is that the M3 will get new, larger, and more energy dense cells. That might bring the cell weight down to 3.5kg/kWh or less, so a 55 kWh pack would have 193 kg of cells -- or less. Tesla's current packs are fairly heavy relative to cell weight, and I'm sure they're looking at some improvement there. Perhaps the small pack will come in at 280 kg or better, maybe 60 percent of the weight of a MS large pack.

Again, we're not seeing a vehicle as efficient as an EV1, which was a moonshot effort in an attempt to make bad batteries work in an EV by improving efficiency everywhere -- but it's not that far off, and in an immensely more practical and visually acceptable (even beautiful) vehicle. It also tells everyone else that they have to go back to first principals. The Bolt and i3 are nowhere close to this level of efficiency on the highway. There's a reason Mercedes' last show car was one that achieved a sub 0.20 Cd! The Germans (at least at Mercedes and Porsche) certainly get it.
 
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#13
SageBrush said:
Cd of 0.21 is a bit better than fantastic.
And all the more surprising given the air dam in front.

We can guess about 24 ft*ft frontal area, for a CdA of 5.04
Once we know car weight and tyre RR, we can get a good estimate of energy economy.

By the way, google says that a kWh of Li-x battery weighs about 6.7 Kg, so about 335 Kg for 50 kWh before packaging.
Click to expand...

That splitter on the nose has to be a big part of the reason for the low drag numbers, even if I don't understand it fully - there's no reason they picked it for appearances.

I think the 24 square feet is high - that's barely 5% less than a Model S, while the car is visibly lower and I believe is also narrower?
 
#14
Saghost said:
That splitter on the nose has to be a big part of the reason for the low drag numbers, even if I don't understand it fully - there's no reason they picked it for appearances.

I think the 24 square feet is high - that's barely 5% less than a Model S, while the car is visibly lower and I believe is also narrower?
Click to expand...

I'd love to have a width measurement . . . The A is almost certain to be within 10 percent of that of the MS, but we're just guessing right now how much less. 5 percent is reasonably conservative. As for where the low drag coefficient comes from, it comes from everywhere! You're looking at Tesla's aerodynamicists running CFD models on a supercomputer or near-supercomputer for 1000s of hours, and iterating with the structural engineers and the ID department to get the result Musk just tweeted. There's not a surface on the car that didn't change because of that analysis and those iterations. I've chased drag reductions on products before, and it's hard, tedious, iterative, and -- often -- non-intuitive work. And keep it in mind when all the aspiring car designers on the internet post sketches of how the M3 can be improved visually -- they're not having to work with the aerodynamacists!
 
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#15
Rashomon said:
As for where the low drag coefficient comes from, it comes from everywhere! You're looking at Tesla's aerodynamicists running CFD models on a supercomputer or near-supercomputer for 1000s of hours, and iterating with the structural engineers and the ID department to get the result Musk just tweeted. There's not a surface on the car that didn't change because of that analysis and those iterations. I've chased drag reductions on products before, and it's hard, tedious, iterative, and -- often -- non-intutive work.
Click to expand...

Agreed. The point I was trying to make, however poorly, was that Tesla would never have adopted that nose if they didn't think it gave them an advantage in drag - written in response to a prior comment which seemed to suggest the nose was causing more drag that they had to make up elsewhere.
 
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