Model 3 Battery size

[JeffK]

Hi, everybody. Recently, I've calculated the drag area of the Model 3 and Model S using the method described here. To do that, first I created silhouette versions of the front photos that you see below. I assumed that the height is 1435 mm for both models. At least that's what wikipedia shows here and here. The difference is only 2.9%:

Model S drag area: 2.43 m^2
Model 3 drag area: 2.36 m^2

We also know the drag coefficient numbers:
Model S drag coefficient = 0.24 (source)
Model 3 drag coefficient = 0.21 (source)

Using these numbers, here is how I would calculate the estimated EPA range numbers for the Model 3 for different battery sizes:

Model 3 trim levels likely to be released in 2017:
Model 3 55 = (210/60)* 55 * 0.24 * 2.43 / (0.21 * 2.36) = 226 mi EPA
Model 3 55D = (218/60)* 55 * 0.24 * 2.43 / (0.21 * 2.36) = 235 mi EPA

Model 3 75 = 249 * 0.24 * 2.43 / (0.21 * 2.36) = 293 mi EPA
Model 3 75D = 259 * 0.24 * 2.43 / (0.21 * 2.36) = 304 mi EPA
Model 3 P75D = 294/315*304= 284 mi EPA

I included the Model 3 75 kWh rear-wheel-drive because of this tweet.

The next upgrade in 2018 or 2019 might include these versions:
Model 3 60 = 210 * 0.24 * 2.43 / (0.21 * 2.36) = 247 mi EPA
Model 3 60D = 218 * 0.24 * 2.43 / (0.21 * 2.36) = 257 mi EPA

Model 3 80 = (249/75)* 80 * 0.24 * 2.43 / (0.21 * 2.36) = 312 mi EPA
Model 3 80D = (259/75)* 80 * 0.24 * 2.43 / (0.21 * 2.36) = 325 mi EPA
Model 3 P80D = 294/315*325= 303 mi EPA

Are you accounting for weight differences as well?

 

[Troy]

@JeffK, no I haven't included that. The calculations only show range gains because of reduced air drag. There should be additional range gains because of reduced weight. The Model 3 75D will be lighter than the current Model S 75D because the car is smaller and the battery pack will use 2170 cells which weigh about 20% less.

 

[Brando]

I suspect the Model 3 has about 20% less space for the battery pack, right? So it would seem reasonable that comparing the max battery pack of Model 3 to Model S/X would be 20% less. Why would you expect it to be equal?

Seems that the 200-300 mile range works well for most. Offering battery options above that seems a fine solution. Enough said?

 

[JoseBQ]

The 0,21 drag coefficient is a goal but I'm not really sure they will succeed.

Real number I think will be closer to the 0,24 of the MS.

 

[Brando]

Weight for cruising has a very small effect on mileage. Consider Trains.

 

[Booga]

The other variable we don't necessarily know is the impact of whether the battery pack sizes will be the usable amount of power or the entire capacity of the battery pack. Recent changes with the P100D seem to indicate even greater range, because the stated amount is now likely the usable capacity, which is a departure from the past.

 

[dsvick]

@JeffK, no I haven't included that. The calculations only show range gains because of reduced air drag. There should be additional range gains because of reduced weight. The Model 3 75D will be lighter than the current Model S 75D because the car is smaller and the battery pack will use 2170 cells which weigh about 20% less.

Weight might not be that different, don't forget that the M3 will be made with at least some, if not a majority of, steel. So, while it will be smaller it might not be that much less weight.

 

[JeffK]

Weight might not be that different, don't forget that the M3 will be made with at least some, if not a majority of, steel. So, while it will be smaller it might not be that much less weight.

engineers during launch said 20% weight reduction if I remember correctly.

I can't find the exact video, but at the end of this one he does mention about the Model 3 weighing less than Model S.

 

[JeffK]

I suspect the Model 3 has about 20% less space for the battery pack, right?

No, the area of the vehicle is only 10% smaller than the Model S given current Model 3 dimension estimates.

 

[Brando]

It is the battery area that counts (i.e. not the wheel/suspension and overhang) So are you sure about only 10% smaller? I really don't know as of course % don't tell you anything unless you're sure % of what is being measured. AND the 2170 battery may well give higher power density which would require less space, so your only 10% loss of battery pack space might well be correct.

So does this also suggest that the Model 3 would only weigh 500 lbs less than Model S?

 

[JeffK]

It is the battery area that counts (i.e. not the wheel/suspension and overhang) So are you sure about only 10% smaller? I really don't know as of course % don't tell you anything unless you're sure % of what is being measured. AND the 2170 battery may well give higher power density which would require less space, so your only 10% loss of battery pack space might well be correct.

So does this also suggest that the Model 3 would only weigh 500 lbs less than Model S?

We don't know anything for sure until the final version is shown to the public but:
from wikipedia:

Model S:
Length 4,976 mm (195.9 in)
Width 1,964 mm (77.3 in)

Model 3 (estimated)
Length 4,676 mm (184.1 in) est
Width 1,885 mm (74.2 in) est

( 1- (4676*1885)/(4976*1964) ) * 100 = 9.808% about 10%.

No idea on the final battery compartment dimensions.

We also don't know how these cells will be arranged. For example: if arranged vertically like the Model S then each cell takes up 36% more area than before. ((21*21) / (18*18)) = 1.36...

 

[dhanson865]

Weight for cruising has a very small effect on mileage. Consider Trains.

which is true for steady speed but EPA tests vary speed drastically (so vehicle weight will matter). Also trains tend to accelerate slowly. I guarantee the tests below don't have train like acceleration.

graphs from Detailed Test Information , all 5 will be used for cars made after 2008.

 

[Yggdrasill]

@JeffK, no I haven't included that. The calculations only show range gains because of reduced air drag. There should be additional range gains because of reduced weight. The Model 3 75D will be lighter than the current Model S 75D because the car is smaller and the battery pack will use 2170 cells which weigh about 20% less.

Actually, you have accounted for it, to an extent. The way you've calculated, you've ascribed all the consumption to the aero-losses. You've basically calculated that as the Model 3 is ~15% more aerodynamic, therefore the range will be ~15% greater (per kWh). But if half the consumption is due to aero and the rest is due to weight and ancillary losses, a ~15% improvement in aero would only result in a ~7.5% improvement in range. (Figures are simplified, but are sufficiently accurate to make my point.)

For your calculations to be accurate, you're not only assuming a 15% improvement in aero, you're also assuming a 15% reduction in weight and a 15% reduction in ancillary losses. Now, the question is if the assumed 15% reduction is accurate. For weight, I think the reduction could be more, but probably not by a huge amount. Dropping the weight of an entry level Tesla from ~2000 kg to ~1700 kg isn't too shabby, given the greater use of steel. Most of the ancillary losses won't be affected meaningfully, like the power required by the Nvidia PX2, A/C, lights, etc, but they probably only make up something like 10% of the total consumption.

 

[Brando]

Exactly correct. It is the overall efficiency that really matters and in the real world (not some model).
So, driving at 55 should always be considered. The extra distance may well be worth the extra time.

 

[apacheguy]

I suspect the Model 3 has about 20% less space for the battery pack, right? So it would seem reasonable that comparing the max battery pack of Model 3 to Model S/X would be 20% less. Why would you expect it to be equal?

Seems that the 200-300 mile range works well for most. Offering battery options above that seems a fine solution. Enough said?

The cell chemistry could very well be different and more energy dense. Also, Tesla is moving away from 18650 format spec and this will enable them to cram more cells in the same space. A lot of variables to consider.

 

[ohmman]

Actually, you have accounted for it, to an extent. The way you've calculated, you've ascribed all the consumption to the aero-losses. You've basically calculated that as the Model 3 is ~15% more aerodynamic, therefore the range will be ~15% greater (per kWh). But if half the consumption is due to aero and the rest is due to weight and ancillary losses, a ~15% improvement in aero would only result in a ~7.5% improvement in range.

The math on range calculations nearly excuses weight as a factor, once you reach any reasonable speed. The aerodynamics eventually dwarf the weight effect, except on climbs and severe stop and go driving.

This is one reason that people are able to add aerodynamically shaped (and loaded) cargo trailers to existing boxy vehicles and improve their fuel economy. By organizing that turbulent flow at the back of a vehicle, the weight effect is more than offset by the aerodynamic benefit.

I know you said you simplified at 50/50, but I think it's more realistic to put the ratio at 90/10 (and I feel I'm being conservative).

 

[Yggdrasill]

The math on range calculations nearly excuses weight as a factor, once you reach any reasonable speed. The aerodynamics eventually dwarf the weight effect, except on climbs and severe stop and go driving.

This is one reason that people are able to add aerodynamically shaped (and loaded) cargo trailers to existing boxy vehicles and improve their fuel economy. By organizing that turbulent flow at the back of a vehicle, the weight effect is more than offset by the aerodynamic benefit.

I know you said you simplified at 50/50, but I think it's more realistic to put the ratio at 90/10 (and I feel I'm being conservative).

I'm thinking something like 50/40/10 for aero/weight/ancillary losses. An important factor here is that the more aerodynamic a car gets, the greater the impact of the weight.

Edit: At constant high speed, though, it may well be more like 75/20/5.

 

[Model 3]

We don't know anything for sure until the final version is shown to the public but:
from wikipedia:

Model S:
Length 4,976 mm (195.9 in)
Width 1,964 mm (77.3 in)

Model 3 (estimated)
Length 4,676 mm (184.1 in) est
Width 1,885 mm (74.2 in) est

You forgot one important thing here - it is not the length of the car that matter for the size of the battery pack, but the wheelbase, as more or less all of the pack is inbetween the wheels. Model 3 has a shorter overhang in the front and in the back vs. Model S.

Wiki Model 3:

Wheelbase 2,870 mm (113 in) est.[2]

Wiki Model S:

Wheelbase 2,960 mm (116.5 in)

 

[Troy]

Hi. I created a simple calculator you can find HERE. Some of the numbers like usable battery capacity and weight are estimates. At 62.75 mph, the range for the Model S 75 was 249 miles, same as the EPA rated range. At the same speed, Model 3 75 range would be 302 miles. A few messages ago, my estimate based on just air drag was 293 miles. In short, I would expect the Model 3 to achieve 17.7% to 21.1% more range than the Model S with the same battery capacity.

When you open the file feel free to duplicate the tab if you want to create your own tab and make changes. Alternatively, you can click "File > Make a copy" to copy the file.

 

[Zoomit]

I'm thinking something like 50/40/10 for aero/weight/ancillary losses. An important factor here is that the more aerodynamic a car gets, the greater the impact of the weight.

Edit: At constant high speed, though, it may well be more like 75/20/5.

I'll leave it to you to calculate all the ratios, but here's how consumption changes by steady-state speed for a theoretical Model 3. Both graphs have the same data, just plotted differently (stacked vs overlaid).

At highway speeds between 65 and 75mph, overcoming aero drag consumes between 44 and 50% of the power per mile. Even out to 100mph, which I didn't include on the graph, the aero losses are only 61% of the total.