## The Conclusion

If you are like me I like to the get to the good stuff right from the start, get confused (and motivated), and then learn the explanation. So right here is the big chart of numbers this post is all about for me and what I spent the last couple weeks learning about.

If this all makes sense to you then great, I hope you find it to be useful. If not, also great keep reading and learn along with me.

## Why Make This Chart

There are a few reports I have seen that indicate that the Tesla Model 3 Standard Range Plus does not live up to its reported range capability of 250 miles in the real world. Two of these are whatcar.com and youtuber Alex On Autos Model 3 Standard Range Plus in a two videos discussing their range test and viewer submitted efficiencies. In contrast, people seem to think that the Niro EV often matches or exceeds the EPA estimate in real world tests. How can I look at the real world test results of a video or forum post and understand if they match up with the published EPA efficiencies?

This sent me down the road of figuring out what the EPA estimates actually mean and how they were obtained. The first thing I noticed was that if you take the EPA combined city/Hwy eMPG and use that to calculated the estimated range you always came up short. You can do this calculation by using the EPA’s stat that a gallon of gas is the same as 33.7kWh. So if you do eMPG[mi/gal]/33.7 [kWh/gal]*battery[kWh], should give miles range where the brackets[] are units. Doing this, as I said, brings you up short of the EPA estimated range every time. Doing this for the Niro, range = 112/33.7*64=212 miles, well short of the 239 advertised. This lead me to my first bit of understanding.

## Wall kWh VS Battery kWh

The reason that the method above comes up short is that in the eMPG is designed to tell you about the cost to operate the vehicle not help you understand its range. It is trying to tell you how far you will get for each kWh you pay for coming out of your wall. Very useful from an economic perspective but not so useful if you are trying to understand the range of the car. In this case I really want to know the miles per kWh stored in the battery!

So what went wrong in the equation above? The reason that my range is not matching up is that I am inadvertently mixing units. While kWh appears twice in the equation and seem like they should cancel they are in fact not the same. One is wall kWh which I will denote as “kWh-wall” and the other is battery kWh, “kWh-batt”. These are linked by an efficiency that determined by the charger during the EPA testing. So that kWh-batt= eff_charging * kWh-wall where “eff_charging” is a car+charger dependent efficiency which tells you how much of the energy makes it to the battery. This is very useful number because it allows us to calculate the range based on the eMPG and what we should expect for miles per kWh-battery.

$$range = \frac{eMPG\left[\frac{mi}{gal}\right]}{33.7 \left[\frac{kWh-wall}{gal}\right]}\frac{battery\left[kWh-batt\right]}{eff_{charge} \left[\frac{kWh-wall}{kWh-batt}\right]}$$

and

$$\left[\frac{mi}{kWh-batt}\right]= \frac{eMPG\left[\frac{mi}{gal}\right]}{33.7 \left[\frac{kWh-wall}{gal}\right]}\frac{1}{eff_{charge} \left[\frac{kWh-wall}{kWh-batt}\right]}$$

The mi/kWh-batt is a very useful number because this, or its inverse kWh-batt/mi, is what the car will report for its efficiency. So when you are looking at videos or forums you can compare their results with the EPA and see if the car is living up to expectations. Just what I want!

Something to note here is that I haven’t said which eMPG is used here, City, Highway or combined. The nice thing is the equation can be used to find the expected range driving around the city or entirely on the highway for long road trips. Just plug in the appropriate eMPG. So if a youtuber goes for a long highway drive to demonstrate the car, like WeBackTesla does, plug in eMPG (HWY) found at https://www.fueleconomy.gov and you will get the expected range and mi/kWh of the car for comparison in the highway driving scenario.

## Getting the Efficiency

I have left out one key ingredient in the equation, the charging efficiency, “eff_charge”. This can be found directly by referencing the EPA filings by the companies published by the EPA here https://iaspub.epa.gov/otaqpub. In these documents they indicate they manufacture indicates battery size and how many wall kWh are used to charge the car back up after the test. I find it easier to just use the published range to estimate the efficiency. Using the range equation above we can plug in the expected range and the combined eMPG and solve for the charging efficiency. Once we have that we can plug in the City and Highway eMPG to get expected range in city only driving or highway only driving. Also the expected mi/kWh-batt you would hope to see the car report for the car to live up to expectations.

## Results

In the chart above I solved for the charging efficiencies for a number of cars on the market (yellow row). I then used this to calculate the efficiency I expect to see reported by the car both as mi/kWh(blue row) or as wH/mi (white rows below blue). The mi/kWh is seen in the Niro and Kona and the wH/mi is reported in the Tesla infotainment.

By referring to the chart you can tell if a car is doing better or worse than expected compared to EPA estimates. For example, in the video by WeBackTesla he goes on a 272 mile highway drive in his model 3 standard range and reports 237 wH/mi. In this case, we can see that he did a little worse than the EPA estimate of 230wH/mi using a little more energy per mile. He claims he was averaging speeds in the low 70s and going faster sometimes so this seems to match up.

Youtuber NiroEVJ did a highway test with his Kia Niro and got 3.4 mi/kWh driving in the low 70s which is better than the 3.35 mi/kWh calculated for the EPA numbers. He also took a slower route in this video averaging 50-60 miles on slower back roads and got about 3.7 kWh which better than the expected highway efficiency and matches well with the “combined” numbers. Note for mi/kWh bigger numbers a better, more efficient more range etc., and for wH/mi lower numbers are better.

## Tesla Mysteries

However, in the video by AlexOnAutos on his range test he concludes that he believes his Model 3 Standard Range Plus is getting 3.85 mi/kWh-batt. However, I think he is confusing battery kWh and he is actually using the wall kWh based on how he describes his math. He also complains that the range can possibly match the 240 miles advertised, only 192 miles, but he uses 50 kWh-batt for the size of the batter by I believe this incorrect with the actual size being closer to 54 kWh-batt (54.4 kWh seems to be the value in the EPA reports found at https://iaspub.epa.gov/otaqpub). More evidence from 54 kWh over the 50 kWh battery size possibility shown in the first column of the chart is that for the range to work out the charging efficiency needs to be 84%, which is much lower than the ~90% charging efficiency reported by Tesla in the EPA report. This also requires the Telsa to mi/kWh to achieve the range to be unreasonably high.

After receiving some comments on this he has another video going over viewer submitted values taken directly from their infotainment screen. From this he gets 4.2 mi/kWh-batt which is lower than the 4.63 mi/kWh-batt I am estimating for the combined driving efficiency but it is hard to say how the users submitting are driving. Some were doing much better than this though and met or exceed the necessary efficiency for the car to meet EPA expectations. In either case, we now have a concrete way to make that comparison. My conclusion is the battery must be closer to 54 kWh. An interesting note here in the documents submitted to the EPA the Standard Range (not plus) has the same size battery which probably means it is software limited.

The whatcar.com results indicating 3.1 mi/kWh I still cannot explain. They seem wildly off from what users are reporting on the internet, like the 4.2 mi/kWh in AlexOnAutos video. I recently learned that Tesla will lend you a car for a day so if I am able to arrange for that I will do my osn testing and post about it.

The numbers for the AWD long range is still a mystery to me though. The charging efficiency seems way too low which would seem to indicate that the battery size I am using is too small but 75 kWh is often stated. The EPA report for the car though seems to indicate that the battery weighs 480 kg and the specific energy is 150 kWh/kg. Multiplying this gives 72kWh which obviously much less than 75 kWh and will only make the charging efficiency worse. So I am not sure what is happening here.

## Wrapping Up

Hopefully this gives you the ability to take the eMPG values and convert them to numbers that can be easily compared to efficiency numbers reported by the car to determine if the car is living up to expectations. Also hopefully this has helped to illuminte the difference between wall kWh and battery kWh and gives you tools to spot when people online are accidentally mixing a matching to give odd numbers. In my next post, I am going to talk more about range in particular.

As a parting note some additional resources. I have already mentioned https://iaspub.epa.gov/otaqpub for official reports on efficiency and range. To understand the testing procedure this document is very useful. The 2 big take awaya from this are that they measure wall kWh and that while the procedure talks about 5 driving schedules (further description here) They actually only do 2 of them, UDDS and HWFET, but they aren’t very representative of real world driving so they multiply by .7 to correct for this. For example the highway test never goes above 60mph and averages 48 mph, not very realistic.

Happy comparing!