Featured Tesla has been cheating EPA on mpge and range numbers

Wrong again—at two fronts.

First, the plots have more than the rolling resistance and aerodynamic drag. It is everything as Bob said, including the internal drag forces. In the the Prius Prime, you also get significant lubricant (automatic-transmission fluid) drag in the transmission.

Yes, it is all fluid dynamics, but there are different kinds of flow. The flow within a lubricant is called laminar flow because it is low-speed, and the drag force is proportional to the viscosity and speed to the first power (at least approximately). The aerodynamic drag is caused by high-speed turbulent flow, and it doesn't depend on the viscosity but it's proportional to the square of the speed. From Wikipedia:

"Drag force is proportional to the velocity for low-speed flow and the squared velocity for high speed flow, where the distinction between low and high speed is measured by the Reynolds number. Even though the ultimate cause of drag is viscous friction, turbulent drag is independent of viscosity."

 

This great. So, what is your current tire model and size? Any wheel covers? What wheels did you get?

 

What are you talking about? I never said that. What I said was

F = R + bv + cv^2,

with R being the rolling resistance, b being a coefficient for laminar-flow hydrodynamic (ATF) drag, and c being a coefficient for turbulent-flow aerodynamic drag.

 

LOL Couldn't you choose different colors for the curves in your plot, as it's impossible to tell which is which? Great work though!

So, my conclusion was correct! Prius Prime has a lower aerodynamic-drag (turbulent-flow) coefficient c (quadratic in v) than Model 3, but it has a higher hydrodynamic-drag (laminar-flow) coefficient b (linear in v) than Model 3 if you model the total drag force as in my formula below. This linear-in-v laminar-flow hydrodynamic drag is probably being caused by the ATF in the Prius Prime transmission.

F = R + bv + cv^2

Note that in my formula the rolling resistance is a constant I called R.

Nevertheless, as I said before, CdA (drag coefficient times the area) of Prius Prime and Model 3 are extremely similar, Prius Prime being slightly lower or higher depending on the particular Model 3 year and trim.

I wouldn't call b the rolling-resistance coefficient. It's a hydrodynamic-drag coefficient. SAE should have definitely included a constant term in their fit. You're right that the rolling resistance is fairly constant at low to moderate speeds, only depending on the tire model and size and vehicle weight. It only stars to vary when the tire approaches its speed limit.

Calculating rolling resistance with a parametrical equation

 

One interesting thing I noticed is when you compare Prius Prime to vanilla Prius.

Prius Prime has a smaller aerodynamic-drag coefficient c than Prius, but it has a larger hydrodynamic-drag coefficient b.

Looking at the new-car features manuals, they both use the P610 transaxle. However, Prius Prime has different number of teeth on the final drive and driven gears, with the total speed-reduction ratio for Prius Prime and Prius being 3.218 and 2.834, respectively. Could subtle differences explain the different hydrodynamic-drag coefficients b for Prius Prime and Prius or there is some other factor? I don't know. Of course, Prius Prime is a heavier car than Prius, and perhaps the coefficient is larger for Prius Prime because SAE omits the constant term that would normally represent the rolling resistance, which is absorbed into this linear b term. So, the b term could simply differ because of the rolling resistance.

Nevertheless, I also seem to be right in that Prius Prime has a lower aerodynamic drag than Prius. I also showed the EPA highway mpg numbers as evidence for that, but the EPA numbers can somewhat vary according to the tester even for ICE cars, which was the topic of the original post. If the EPA numbers are accurate, Prius Prime has certainly less aerodynamic drag than Prius.

 

When you turn on the defogger, Prius Prime tends to turn on the ICE even in the EV mode. Perhaps Bob is talking about that.

 

Good question. The answer is nontrivial. Obviously, the car needs to be actually driven as opposed to putting it on a dynamometer and some actual driving data needs to be collected to actually measure the aerodynamic drag force. This is explained in detail here:

https://ww2.arb.ca.gov/sites/default/files/2020-04/13_313_ac.pdf

 

Note that what is relevant is the "target coefficients," not the set coefficients.

Target coefficients are actually measured on a test track, not on a dynamometer. They represent the actual total drag force F on the car, and the equation is

F = A + Bv + Cv²,

which is a simple quadratic equation.

Set coefficients are irrelevant for our purpose. They are used to set the dynamometer so that the tire rolling resistance and internal drag forces are not double-counted. If you simply used the target coefficients to set the dynamometer, these forces would have been included twice. What they do is to set the target coefficients first and then let the vehicle coast down in neutral. Then the tire and internal drag subtracts from the target drag and can be measured from the acceleration of the dynamometer. Once it is known, the set coefficients to subtract it are calculated, and the dynamometer is reset using these set coefficients so that they don't double-count the tire and internal drag.

These are the target coefficient A, B, and C values, which model the actual tire rolling resistance, internal drag, and aerodynamic drag in the quadratic model, the lower the better, from best to worst:

	Year	Make	Model	A (tire-rolling-resistance coefficient)	B (internal-drag coefficient)	C (aerodynamic-drag coefficient)
1	2022	Toyota	Prius Prime	18.816	0.38689	0.012501
2	2022	Toyota	Prius	18.272	0.29545	0.013793
3	2022	Toyota	Prius Eco	17.130	0.28731	0.013857
4	2022	Tesla	Model 3 RWD	37.170	0.04700	0.014400
5	2022	Tesla	Model 3 LR AWD	34.980	0.08650	0.014800
6	2022	Toyota	Prius AWD	25.590	15.868	0.015074
7	2022	Tesla	Model 3 Performance AWD	49.010	−0.20010	0.020000

So, Prius Prime is the absolute winner in aerodynamic drag here, readily beating Prius and any Tesla Model 3.

Source: Data on cars used for testing fuel economy | US EPA

This is the resulting actual total drag force F for 2022 Toyota Prius Prime (133 mpge) vs. 2022 Tesla Model 3 RWD (132 mpge).



To clarify the confusion by some earlier on why the two curves come very close around 90 mph and then start to slowly separate again: Prius Prime has a very large internal-drag force—the Bv term—in the quadratic model, which becomes more pronounced when the vehicle speed increases. However, eventually the aerodynamic-drag force—the Cv² term—wins and the two curves start to separate again.

Note that later the vehicle weight additionally factors in fuel economy after the dynamometer tests with the EPA drive cycles are done, along with this total drag force that was measured coasting down on field track.

This addresses the point in the original post that the EPA EV fuel efficiency of Model 3 is greatly exaggerated over that of Prius Prime—by 27% according to my previous rough calculations.