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MR3 same range as P3D+? Possibly more?
- Thread starter Nate977p
- Start date
From my experience as a P3D+ owner, I am also getting about 302 wh/mi over 1000 miles driven. So I think likely MR M3 will be very similar in range capability as is configured in real life with a single motor. when I am driving, P3D+ is a range hog as it is configured with 20-inch summer tires although blast to drive every day.
Holy Smokes! If I stay in the truck lane at 55 MPH I can go 413 miles in my RWD LR!?!? Wow!
This is a great chart, but it's worth noting that the source for the numbers (the EPA dyno tests) may introduce inaccuracies.
To explain what I mean I need to go into a little detail on how the EPA test works. This is going to get fairly technical, so apologies in advance.
Basically, rather than testing a real car on the road (which introduces a lot of environmental variables, making it hard to get consistent results), the way the EPA has car manufacturers do the test is to run the car on a dynamometer - a set of rollers that the car is strapped to that can provide artificial resistance that's designed to simulate real-world resistance. This way, each test car can be run through exactly the same "cycle", giving something close to an "apples to apples" comparison of different vehicles.
From a perspective of physics, a car's drag (expressed as force) from all sources can be expressed as a quadratic polynomial:i.e., drag = a + b * speed + c * speed squared (d = a + bx + cx^2, where x is speed)
Basically in (mostly) plain English, the drag can be split into three components:
- a - The constant drag - these are things like friction in the drivetrain
- b - The drag that varies linearly with speed - Primarily rolling resistance
- c - The drag that varies with the square of speed - Primarily aerodynamic drag
The conundrum here is that you can't directly measure the drag at a given speed, so you need to figure out some way to derive what the drag is.
The EPA has car manufacturers determine this by using coast-down tests of a real car under known atmospheric conditions and on a level surface. Basically, by measuring the distance it takes for the car to coast down from several known speeds, it is possible to calculate the three coefficients. (There's an SAE process that describes exactly how to do this).
If you want to read up on the details of how this is supposed to be done, the regulations are available here: Vehicle Testing Regulations | US EPA
Here's where the issues come up. While this process is theoretically sound, in practice it's somewhat difficult to very accurately measure results.
This is particularly evident in the coefficients that were calculated by Tesla for the LR M3 (note that the same test data was used for both the 2017 and 2018 model year certification).
Here are the coefficients computed for three Tesla cars (from: https://www.epa.gov/sites/productio...vehicle-test-results-report-2014-present.xlsx):
Model S 75 RWD: a: 40.35, b: 0.1324, c: 0.01557
Model 3 LR RWD: a: 38.51, b: -0.0811, c: 0.0161
Model 3 LR AWD: a: 41.72, b: 0.0515, c: 0.01498
So what's weird about this set of numbers?
Here are a few things the numbers imply:
- The model 3 LR RWD has a *negative* rolling resistance (this is impossible from a perspective of physics)
- The model 3 LR RWD has the *highest* aerodynamic drag coefficient - significantly higher than the identically shaped Model 3 LR AWD (not likely in real life)
- The model 3 LR AWD has the lowest aerodynamic drag coefficient (with the significantly larger Model S 75D somewhat implausibly in the middle)
Basically, this simply points to the fact that there are likely significant inaccuracies introduced through the coast-down protocol, which are then multiplied by using the EPA dyno process.
Because of the way the coefficients came out, the Model 3 LR AWD is being modeled as having significantly higher drag at lower speeds (which even the EPA freeway cycle includes quite a bit of). I believe this is exaggerating the real-world efficiency differences of the cars when reflected in the numbers.
TL;DR: The EPA numbers are derived from a procedure that may introduce significant inaccuracies (which is supported by weirdnesses in the numbers reported by Tesla). Because of that, any calculations that use these numbers as a source may also be inaccurate.
Hi, @ulrichw. If you look at the range numbers under the 65 mph column here, 3 of them have little black triangles at the corner. These 3 numbers are range test scores by Consumer Reports at 65 mph. The table matches Consumer Reports scores. In fact, I don't use the dyno scores to find range numbers. Instead, I use them to calculate what the Consumer Reports test would be if they had tested that other trim level or that other wheel option. I explained all that in the opening message here (same link).
You might say, yes but you used the coefficients to calculate how the range changes at different speeds. Nope. I didn't. Instead, I used research-based data like the graph Tesla published here and the test scores on page 3 here.
As for the negative number in coefficients, I'm sure there is an explanation for it. If you look at the tab, "Test Car List Data" column G here, 8 different cars from BMW, Tesla, Volvo, and Hyundai have negative numbers. One possible explanation is that the coast down test doesn't involve the following drivetrain losses that should be considered during the dyno test:
The important thing here is whether or not the dyno scores are comparable to other dyno scores. For example, if the Model 3 LRD's dyno score is lower than LR, that should mean the LRD has less range than LR. As long as that's proportionally correct, that's all I need. I already know that Consumer Reports tested the LR and scored 350 miles at 65 mph with regen set to standard (source). All I need is to figure out how much lower LRD is than LR in percentage. That's where the dyno scores come in.
You might say, yes but you used the coefficients to calculate how the range changes at different speeds. Nope. I didn't. Instead, I used research-based data like the graph Tesla published here and the test scores on page 3 here.
As for the negative number in coefficients, I'm sure there is an explanation for it. If you look at the tab, "Test Car List Data" column G here, 8 different cars from BMW, Tesla, Volvo, and Hyundai have negative numbers. One possible explanation is that the coast down test doesn't involve the following drivetrain losses that should be considered during the dyno test:
- Inverter
- Motor
- Motor controller and wires
- Gearbox
The important thing here is whether or not the dyno scores are comparable to other dyno scores. For example, if the Model 3 LRD's dyno score is lower than LR, that should mean the LRD has less range than LR. As long as that's proportionally correct, that's all I need. I already know that Consumer Reports tested the LR and scored 350 miles at 65 mph with regen set to standard (source). All I need is to figure out how much lower LRD is than LR in percentage. That's where the dyno scores come in.
Tjhappel
Member
5500 miles on my p3+ and averaging 278 wh/mi. I am driving basically like a grandma and my buddies who have the 19’s lr 2wd and driving like A holes are getting like 225 wh/mile....
Seems the new motor is extremely efficient... I’m curios to see what people get on a p3+ with 18’s...
Seems the new motor is extremely efficient... I’m curios to see what people get on a p3+ with 18’s...
SageBrush
REJECT Fascism
Strictly by the numbers, no.
Compared to you -- sure
Numbers (highway):
P3D+ MPGe: 112
LR MPGe: 123
We don't have confirmation of MR usable battery yet but presuming 260 miles at 250 Wh/mile,
P3D+ : 78 kWh
MR: 65 kWh
Presuming the MR has the same efficiency as the LR,
The MR will have (123/112)*(65/78) = 91.5% the P3D+ range
Troy - thanks for the detailed response, and I stand by my previous statement: Great chart! I wasn't trying to impugn the overall methodology you used - I just wanted to note one aspect which I thought might have skewed the results as far as the 3LR vs. 3AWD/3P were concerned.
I'm unable to come up with any reasonable explanation for the negative coefficients other than measurement error.
The way I understand it, the model with the coefficients is needed to properly program the resistance of the dyno to simulate forces not present in the lab environment. Things like the inverter, motor, gearbox are all present in the lab test and operating at the proper simulated speeds, so there shouldn't be any need for the model to take these into account.
A negative coefficient means there's an effective propulsive force that increases with speed, or a resistive force that decreases with speed. Neither of these seems plausible to me.
Far more plausible is a discrepancy between a high speed and low speed coast-down test which skewed the curve so that it appeared that linear drag was lower but quadratic drag was higher (this could happen with an abnormally short coast-down from higher speed or an abnormally long coast-down from lower speed).
This is borne out when you look at the difference in the quadratic coefficients Tesla measured for the 3 LRD and 3 LR- the quadratic coefficient (which should be proportional to CdA) of the LRD is around 7% lower than the coefficient for the LR - these two numbers should be identical given the identical shape of the cars - instead it seems the LR's model has the negative linear coefficient to offset this discrepancy.
I think the fact that all these negative coefficients exist is simply a sign that the EPA is tolerant of significant error margins. As long as the coast down tests were properly executed the model should be representative , if not completely accurate (i.e., the broad brush stroke results are ok).
This is the part I'm not comfortable with. I don't believe that the results are proportionally correct. I think the error margin is significant due to the difference in models.
In the case of the coefficients for the LR and LRD, the coefficients yield a model that disproportionately favors the LR at low speeds and the LRD at high speeds. The mix of speeds in the test will determine which way the bias pulls the range determination. The highway drive cycle has an average speed of (only?) 48.3 mph (Dynamometer Drive Schedules | US EPA), and spends a significant amount of time between 40 and 50 mph - speeds when aerodynamic drag is just starting to become the predominant drag factor.
Given that the modeled efficiency difference is less than 10%, the error margin introduced by the weird coefficients could be quite significant.
Again - thanks for your detailed response, and thanks also for the detailed references.
@ulrichw, there is a spreadsheet on the EPA website that has the coefficients of thousands of cars. You can download it here. Click on the link next to 2018. I have looked at the file and 1232 entries out of 4664 have negative values. That's 26%. Then I looked at who the manufacturer is for these 1232 lines where the B-Coefficient is negative. Here is a list:
There are two possibilities:
There are two possibilities:
- The B coefficient is negative because there is a reason behind it that makes sense like a road that isn't flat or back wind or some other reason that we don't know because we haven't looked into it in detail.
- 26% of entries are incorrect and BMW blundered 343 times in 2018, Toyota blundered 121 times etc.
Thanks, I have that file: You'll note that I referenced this site in my original post.
This paper's actually making my point: Here's how the "negative" force is defined: "the driving force at the wheel Fw that propel the vehicle."
And where it shows up in the context of the word "negative": "Because the engine is out of gear, at coasting vehicle the force Fw become negative due to the friction in axle mechanisms, drive line (if any) and transmission: -Fw = Rf = Mf/rd (8) where Mf represents an equivalent friction moment applied to the driving wheels." (apologies for the loss of formatting)
This paper is defining Fw in the reverse direction as the EPA test. The EPA's test procedure expresses all forces as drag forces. The paper defines Fw as a *propulsive* force.
So basically what the paper's saying is consistent with my point: While the car's coasting, friction should create a negative propulsive force, which translates to a positive drag force - therefore the contribution of this force to the coefficients should never be negative.
First of all, coming up with an entry is not a "blunder" - it is simply measurement inaccuracies or tolerances. Because the linear component and the quadratic components are being derived indirectly, and because a potentially small range of speeds is used for the measurements, the split between the linear and quadratic components may be quite sensitive to small variances in raw measurements.
Second of all, it's not just the negative numbers that are inaccurate: All of the numbers are likely inaccurate. The negative numbers are just the thing that calls attention to the inaccuracy, because as far as I can determine, they're physically impossible (or at the very least implausible).
The overall impact of this when comparing cars with differing efficiencies is probably significant but not huge. The reason I point it out in the context of your chart is that when comparing two very similar cars (the Model 3 LR and LRD, for example), the error may render the comparison significantly less reliable.
In trying to come up with any reasonable explanation for the negative coefficients, I found this interesting paper:
http://www.mdpi.com/1996-1073/9/8/575/pdf
The main point of the paper is not directly relevant to this discussion, but the introduction is quite interesting.
Some key quotes:
"Previous studies, however, show that inconsistencies often exist between certification test results and actual test results and point to the use of the flexibility allowed in the manufacturer’s road load test procedures as being the cause of such inconsistencies"
"One of the reasons for a rapidly growing discrepancy between official and real-world fuel economy and emission values of new passenger cars is weaknesses in the certification testing schemes and in the compliance protocols. These weaknesses have allowed vehicle manufacturers to be increasingly able to misuse tolerances and flexibilities, leading to downward-trending type-approval emission levels that are not matched by a similar decrease in real-world emission levels—indeed, the real-world values contradict the type-approval results [19,20]. This discrepancy can occur from various factors, such as driving style and conditions [21–23]. However, about one-third of this gap is explained by vehicle manufacturers systematically exploiting technical tolerances and inaccurate definitions in the procedures specified for the coastdown tests that provide conclusive data used to set up the lab equipment for type-approval tests [24,25]."
Or there's this reference from Hyundai: BACKGROUNDER: U.S. EPA Fuel Economy Testing - Hyundai MPG Info
Here's a quote: "Current EPA requirements for fuel economy testing are inexact in that they provide vehicle manufacturers with wide latitude. As a result, vehicle manufacturer test results as a whole are imprecise, inconsistent and not repeatable"
Follow the link to see much more detailed arguments for why the test procedure is imprecise (Hyundai clearly has an axe to grind here, since this site was created as part of a settlement after they were accused of falsifying fuel economy data - their objections are worth considering, nonetheless)
In Tesla's situation I doubt there was any manipulation of numbers - they likely just did the minimum necessary work to get the numbers they were happy with.
In the case of BMW, I think a case could be made that there may be something more systematic going on, based on your findings. If my hypothesis is correct, and a smaller linear component (and therefore larger quadratic component) tend to skew reported efficiency higher, there may be some incentive to cherry-pick coast-down results to yield those coefficients.
Finally, here's a chart of the model 3 LR and LRD's coefficients converted into drag (lb force) at speed (mph):
The grey line is the percentage difference in modeled drag of the LR vs the LRD, the other two lines are the LR and LRD drags expressed in pounds force. The X axis is speed in mph
I charted the percentage difference between the two lines to illustrate the relationship of the efficiency and how it changes vs. speed. Based on a theoretical analysis of the two cars, you would expect this relationship to be smoothly decreasing as the aerodynamic drag takes over (Basically you'd expect the quadratic component for the two cars to be identical, and the linear and constant components to be larger for the LRD vs. the LR).
The other thing to take from this chart is that the quadratic component and the fixed component are by far the most important factors in determining the shape of the chart - the negative coefficient on the linear component affects things, too, but the impact is fairly subtle.
I've ratholed this thread on this discussion, so I'll make this my last detailed response. Again, I appreciate all the work you've put into your data, and on the whole your chart is very valuable.
Hopefully we'll get better empirical data on LR vs. LRD (vs P) efficiency. My feeling is that actual results will be significantly closer than the EPA numbers imply.
SageBrush
REJECT Fascism
I asked a favorite engineer/car enthusiast (Bob Wilson) this question a couple of years ago and was told to enjoy the graph but to not try to pigeon hole terms into forces. I know that it something of an unsatisfactory answer but the modeling software behind the expression is just fitting data. The negative term is probably just a nudge to make a better fit.
After digging a bit more into to this I have to correct myself probably because the M3 has very good aerodynamics even at low speed.
The negative coefficients are just a result of bad curve fitting.
Note the wheel friction is a function of speed squared also. Plotting the CdA, EPA, and CdA (constant Cf) drag's reveals this is important. The EPA estimate is probably much less accurate above 150MPH, not that it matters!
drag=(3800*Cf+0.5*0.002377*4.7*(MPH*1.47)^2)
3800 = weight with 1 human
Cf = Estimate of wheel friction drag coefficient (tweaked equation from Hoerner aerodynamic drag book).
Cf = 0.0075 + 0.15/psi + 0.000035*MPH^2/psi (note the constant portion of Cf = 0.0108, and 0.0075 is tweaked to match M3 tires)
psi = tire pressure = 45
4.7 = CdA
1.47 = ft/s divided by MPH
