Model 3 aerodynamics should make a BIG difference

[insaneoctane]

I've been wondering just how much the extremely low goal of Cd=0.21 (drag coefficient) for M3 was going to make, especially when compared to, say, the Chevy Bolt. I found a great start on figuring it out here:
Chevrolet Bolt EV Range at Constant Speeds
I used this to calculate ranges at different Cd to see how much difference would it make since the Bolt has a terrible Cd of 0.31, particularly at speed. The result from my calculation is quite intriguing! The article mentioned above is geared mostly towards higher speed results, so the formula results are not that accurate at low speeds, but I was interested to know the effects of Cd, which really only come into play above say 35 mph. The formulas result in the Bolt getting 238mi at constant 65mph. If I ONLY change the Cd and put the M3 value of .21 the range at constant 65 mph goes to 306mi. So, while the Bolt may have lower resistance tires and a more efficient motor, the M3 should be able to cruise on the freeway with significantly reduced aerodrag. This is just to show the impact, not to say the same numbers will apply to the M3.

 

[WarpedOne]

Reading comprehension not?
The results are not that acurate at low speed.

 

[WarpedOne]

The post I responded to is gone ... bad manners ...

@insaneoctane:

Grate work!

Can you just remove every second line to better represent the difference?

Another very interesting chart would be percentage of increased range due to lower Cd:
- range @50 with 0.31 is ~330 miles, with 0.21 it goes to 400 miles, a 20% increase
- range @60 with 0.31 is ~260 miles, with 0.21 it goes to 340 miles, a 30% increase
- range @70 with 0.31 is ~210 miles, with 0.21 it goes to 280 miles, a 33% increase
- range @80 with 0.31 is ~170 miles, with 0.21 it goes to 240 miles, a 40% increase
...

 

[22522]

So, while the Bolt may have lower resistance tires and a more efficient motor, the M3 should be able to cruise on the freeway with significantly reduced aerodrag. This is just to show the impact, not to say the same numbers will apply to the M3.
View attachment 231717

Thank you. I think this is important, as it explains a lot of design decisions, especially if you include frontal area.

The Bolt may have raised the bar on motor efficiency. The Model 3 aero shell is Tesla's motor mule. I would think they want to crush the Bolt on every parameter, so that says a dual motor base three has the same list price as the Bolt? That makes it a $2500 option? I don't know.

The reference shows: Force goes as 1/2 (air density) (velocity X velocity) (Cd) (Frontal Area)
Did you include frontal area - look at Cd X Frontal Area?

I think sagebrush said the CdA was 5?

Real SUVs are bad at that. Others have slated Honda Crosstour like electric SUVs to keep that number low. It gets you into the SUV category, but what is the biggest seller in the small frontal area SUV catagory? Volvo XC90? X4? Subaru?

Tesla needs to displace the CRV, RAV4 and Rogue. A Honda Crosstour like SUV has not done that in Iceland.

The SUV will build off the efficient motor learned from the 3, and Battery Pack/automation cost reductions. These are prerequisites because of the frontal area x Cd requirements of a legitimate SUV.

Could you add frontal area effects to the graph and draw lines for specific vehicle shells, maybe use a CRV shell for the Y to see how battery size/range works out?

 

[22522]

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

 

[SageBrush]

I've been wondering just how much the extremely low goal of Cd=0.21 (drag coefficient) for M3 was going to make, especially when compared to, say, the Chevy Bolt.

You are making this more difficult than required.
A Cd of 0.21 is about 2/3rds that of 0.31; the air resistance values between the two cars will maintain the same ratio if they travel at the same speed and have similar frontal areas.

An interesting way to look at this drag difference is to ask how much faster can the Model 3 go compared to the Bolt and end up with the same air resistance. It works out to 22.5% faster*
So e.g. if the two cars only differ by the Cd as stated above, a Bolt at 60 mph has the same fuel consumption as a Model 3 at 60*1.225 = 73 mph.

*the square root of 1.5

 

[insaneoctane]

@insaneoctane:

Grate work!

Can you just remove every second line to better represent the difference?

Another very interesting chart would be percentage of increased range due to lower Cd:
- range @50 with 0.31 is ~330 miles, with 0.21 it goes to 400 miles, a 20% increase
- range @60 with 0.31 is ~260 miles, with 0.21 it goes to 340 miles, a 30% increase
- range @70 with 0.31 is ~210 miles, with 0.21 it goes to 280 miles, a 33% increase
- range @80 with 0.31 is ~170 miles, with 0.21 it goes to 240 miles, a 40% increase
...

Yeah, I thought about removing half the lines right after I created it, but I had company downstairs and needed to hit submit and exit the office quickly! I will repost with fewer lines... I will also look into posting one specific to % gain at speed...

...
Could you add frontal area effects to the graph and draw lines for specific vehicle shells, maybe use a CRV shell for the Y to see how battery size/range works out?

Yes, but the frontal area actual or goal has not been announced like the Cd, so it is speculation. But, as a graph parameter, a great idea...

You are making this more difficult than required.
...

I will disagree a bit on this point. Yes, we can ratio the Bolt's Cd to the M3s and while empirically the Cd is inversely proportional to the range *for the aerodynamic drag component*, you have account for the fact that there are other components. Now as speed increases, the aero drag component becomes the driver, but I wanted to simply see the approximated real world range effects with as many other factors considered as possible (ie rolling resistance, accessories, etc)

 

[SageBrush]

Now as speed increases, the aero drag component becomes the driver, but I wanted to simply see the approximated real world range effects with as many other factors considered as possible (ie rolling resistance, accessories, etc)

Errr.... what ?

Let me refresh your memory of your title:
"Model 3 aerodynamics should make a BIG difference."

"Big" is useless term; at similar speeds the Model 3 has 2/3rds the Aero friction as the Bolt, presuming all else* equal

For range questions I suggest using speed*newtons = watts where speed is meters/second
So e.g.,
If aero friction of a Bolt at 62 mph (27.8 meters/second) is 9675 watts, the Model 3 will be 2*9675/3 = 6450 watts. Then you know that after an hour of driving the Model 3 has conserved ~ 3.2 kWh or about 12 miles of extra range.


*all else: rho, mass, frontal area, tyres

 

[dhanson865]

The post I responded to is gone

Use the quote function and that isn't a problem.

Quoting also makes it easier for us to know who you were replying to. What the heck you are talking about. Context is everything.

 

[EdFerg]

My state requires a front license plate. How will that affect the equation?

 

[WarpedOne]

Use the quote function and that isn't a problem.

Quoting also makes it easier for us to know who you were replying to. What the heck you are talking about. Context is everything.

Yes, of course... see the problem?

 

[WarpedOne]

My state requires a front license plate. How will that affect the equation?

Non-measurably.

 

[22522]

Non-measurably.

The appearance equation is what it hurts the most.

 

[insaneoctane]

Errr.... what ?

Let me refresh your memory of your title:
"Model 3 aerodynamics should make a BIG difference."

"Big" is useless term; at similar speeds the Model 3 has 2/3rds the Aero friction as the Bolt, presuming all else* equal

For range questions I suggest using speed*newtons = watts where speed is meters/second
So e.g.,
If aero friction of a Bolt at 62 mph (27.8 meters/second) is 9675 watts, the Model 3 will be 2*9675/3 = 6450 watts. Then you know that after an hour of driving the Model 3 has conserved ~ 3.2 kWh or about 12 miles of extra range.


*all else: rho, mass, frontal area, tyres

I really don't want to get into a pissing war over what I meant with my title. Your simple ratio of 2/3 to conclude that at 62mph the M3 would have 12 miles of extra range exactly proves my point! That "extra" 3.2 kWh does NOT take into consideration all the other accessory and rolling resistance loads on the car. So while, yes, the M3 is only 2/3 the Cd of the Bolt and, yes, that is 3.2 kWh that is not used to fight aero drag (at 62mph), those savings must be appropriately consumed by the correct percent of accessory usage, rolling resistance, and aero drag to get what I was after, which is the best approximated real-world range.

Also, your calc of just aero shows the Bolt could drive for 5.9 hours at 9.675 kW/hr before exhausting all 57 kWh of available battery; that's 365 miles. You can see the other loads are significantly real. According to your math, the 0.21 Cd Bolt could drive for 8.8 hours at 6.45 kW/hr before exhausting all 57 kWh of battery; that's 547 miles. This is "big" to me.

I think my results are still quite relevant to relate the 1/3 improvement in Cd to approximate real world results. If you think the results, or math that I've shown are wrong, let's have that discussion.

 

[insaneoctane]

Here's some of the requested data....

 

[SSonnentag]

Bolt has less rolling resistance due to smaller tires.
Bolt has more efficient permanent magnet motor.
M3 has better coefficient of drag.
M3 has smaller cross sectional area.

As far as I know, all other efficiency variables are unknown at this point. I'd guess that the known efficiencies in favor of each over the other pretty much negate each other though.

 

[SageBrush]

I'd guess that the known efficiencies in favor of each over the other pretty much negate each other though.

Not even close if you are talking about long distance driving at 75+ mph. Tyre related road friction is about 160 Newtons, +/- 10% for different tyres. At 75 mph aero friction is 75% of the total (road + aero) in the Bolt

Look at this table
It is the drag formula in spreadsheet form
You can make a copy and change kph

 

[insaneoctane]

Is anyone familiar with the EPA test cycle? How much high speed driving is found in the cycle?

 

[Saghost]

Is anyone familiar with the EPA test cycle? How much high speed driving is found in the cycle?

Well, it does hit 80, momentarily - the average speed on the "highway" test is 48 mph, though:

EPA US06 or Supplemental Federal Test Procedures (SFTP) | US EPA

 

[ItsNotAboutTheMoney]

Is anyone familiar with the EPA test cycle? How much high speed driving is found in the cycle?

Not much. There's one high-speed highway test and that's not going fast much of the time. Better than the old one though.