The Problem of EV Sizing: Weight, Battery Capacity, and Required Range

Weight is a problem for electric vehicles: almost invariably, EVs are heavier than their ICE counterparts of similar size. For example, the Chevrolet Blazer EV weighs 5163 lb in its lightest trim, 1245 lb more than the lightest ICE Blazer. Weight increases force and power required at speed, hinders maneuverability and negatively impacts driving dynamics, increases particulate matter pollution (from both tires and brake pads), and reduces efficiency—not to mention requiring greater energy inputs to construct commensurate with the greater mass of material needed to build the heavier car in the first place.

This Hyundai Ioniq 6 weighs 1000 lb more than the Sonata, despite the two having similar dimensions.

The reason EVs are heavy is because they require large batteries to have acceptable range; however, while total range increases with battery size, efficiency (range per unit of energy) goes down as more weight is added by the increased battery size, which requires more energy per unit distance traveled. So how does one find the right size battery for an EV—the correct balance between battery size, range and efficiency? Well, this is what we call a sizing problem and it has a straightforward (but not simple) answer.
 
Methodology
 
Basically, the issue here is that increasing battery size (for more range) also increases weight, which reduces efficiency and thus the added range, requiring more battery capacity for more range, which also increases weight, which reduces efficiency, etc. In mathematical expression:

In other words, weight is a function of itself, among other things such as vehicle dimensions. Put another way, weight and battery capacity are related (as battery capacity goes up, so does curb weight), and are determined in part by…weight and battery capacity. How do we solve a recursive problem like this?
 
We do it by using loops and iterating until our “guessed” weight and battery capacity agree with the calculated weight and battery capacity output by the equations in the model. For example, I might initially guess a curb weight of 3200 lb and battery capacity of 30 kWh for a required range of 150 miles; these values are input into the model and it returns, say, 3300 lb and 35 kWh. I then input those values as guesses, and the calculated values come back 3325 lb and 36 kWh. I put those values back in and get 3335 lb and 36.3 kWh, etc. Eventually, the guessed and calculated values will converge (i.e. land on the same value) or “blow up” (diverge). If the model diverges, no solution exists for that set of input parameters.
 
To build the model, I’ll use mathematical expressions relating various physical parameters and equations of motion describing an EV at constant cruise speed (in an Excel spreadsheet, which allows for easy visual programming to see what goes where). I’ll use a “seed”—an existing car of known dimensions, weight, drag, etc.—as an input and basis for calculating changes in weight and battery capacity when compared to new dimensions, drag coefficient, and battery size. Using this seed method introduces potential bias, but it is easier than building up the numbers from scratch—something I might try in the next iteration of this calculator.

To figure out how these dimensional changes affect structural weight, I collected data on several EVs available with different battery sizes and calculated an average weight change per kWh battery capacity (doing it this way rather than using a standard estimate for lb/kWh accounts for structural changes in the vehicle itself to support the additional battery weight—about 14 lb/kWh compared to the standard 11 lb/kWh); I used the same trim level if possible to try and account for different options between trims. I also calculated an average weight per unit volume of body, which will allow me to compute weight change from body size changes.
 
Then, I collected and averaged the length, width, and height of several vehicles (ICE and EV) in each of six classes: Small SUV, Small Sedan, Midsize SUV, Midsize Sedan, Large SUV, and Large Sedan. This gives me average dimensions for each vehicle class.
 
All this gets fed into the model. Once the model is working, we can run sweeps of the required range and drag coefficient for each vehicle class to see how calculated weight and battery capacity vary as functions of those, inputting guesses and checking them until convergence is achieved.
 
Model Limitations
 
“All models are wrong; some models are useful.”
 
Before delving into analysis of the results, it is important to recognize that this model, like all models, is flawed. I have made certain assumptions here—for example, 200 lb driver weight, cruise speed of 60 mph, 90% motor efficiency—that introduce bias in addition to bias from the seed car. Because of these assumptions, the model is not real and its predictions will differ from the performance of real EVs. But the model may still be useful….
 
I will “check” my results by inputting various EVs with known drag coefficient, weight, battery capacity, dimensions, and range into the calculator and checking how far off its predictions are (as percentage difference from real). Doing this for a vehicle in each size class I’m interested in simulating gives these results:
 

Size Class	Vehicle	Wprd (lb)	Wreal (lb)	% Diff	Cprd (kWh)	Creal (kWh)	% Diff
Small SUV	Hyundai Kona EV	3810	3759	1.4%	68.2	64.8	5.3%
Small Sedan	Tesla Model 3	3912	3891	0.5%	81.1	79.7	1.8%
Midsize SUV	Tesla Model Y	4337	4154	4.4%	90.5	78.1	15.8%
Midsize Sedan	Hyundai Ioniq 6	4293	4222	1.7%	82.2	77.4	6.2%
Large SUV	Kia EV9	5365	5313	1.0%	103.3	99.8	3.5%
Large Sedan	Lucid Air Pure	4715	4564	3.3%	98.2	88.0	11.6%

 
As you can see, the model hews fairly closely to reality for all the weights but strays a little in battery capacity, particularly in the Midsize SUV and Large Sedan classes. For some reason (perhaps because I have no accounting here for regenerative braking and have assumed a constant-speed cruise), the predicted battery capacities here are 10-15% off from the real cars. However, they are off in a conservative direction; that is, they predict a larger battery capacity than these cars actually have. In fact, in every case here the model’s predictions are conservative relative to the real cars. Keeping in mind the maxim “under-promise and over-deliver,” this is the direction I want it to be off in initial sizing because that means the real car is more likely to better its predicted performance—and if that happens, I can trade battery weight for, say, better (heavier) seats or a higher drag coefficient that requires less development time or a less efficient but cheaper motor or any number of other things. In that respect, this model seems useful enough for an initial, best-guess sizing estimate for starting an EV design.
 
Results
 
Running the simulation over a sweep of drag coefficients and driving ranges for each size class gives the following results for predicted weight and battery capacity as a function of C_D and range. Each chart is scaled to the same spread of values for easier comparison. Contour lines show constant weight or constant battery capacity; following any particular line (or really, plateau; you can see these where lines kind of meet up) up or down the sizing diagram will show how required drag coefficient and range vary together for that weight or battery capacity. Put another way, for the chart of your intended vehicle class, simply find your required range and go up until you hit your desired weight or battery capacity; then, move left to find the required drag coefficient (or go the other way, drag coefficient to resulting range for a given weight or battery capacity).
 

Small Sedan

(56.2 in x 71.6 in x 183.6 in)

Small SUV

(62.8 in x 71.7 in x 175.8 in)

Midsize Sedan

(56.8 in x 72.5 in x 189.1 in)

Midsize SUV

(65.2 in x 73.7 in x 183.6 in)

Large Sedan

(57.3 in x 76.0 in x 198.8 in)

Large SUV

(67.8 in x 77.4 in x 196.3 in)

Discussion
 
These sizing diagrams could be used in more than one way.
 
First, of course, if I am interested in designing a new EV and have selected a size class (say, I want to design a midsize SUV), I can use this simple model to predict what sort of battery capacity I will need to satisfy a range requirement, and roughly how much the resulting vehicle should weigh. For example, if I want my midsize SUV to have a range of 320 miles, I can guess from the diagrams that it will need a battery capacity of around 90 kWh to achieve that at a drag coefficient of 0.30 (and a weight of 4800 lb), or 85 kWh if I can improve the drag coefficient to 0.25 (which reduces weight to around 4600 lb). As an initial approximation with no detailed design work, that seems like a pretty good guess in line with real vehicles in this size class—especially to define program requirements for a new vehicle. (Compare these predictions to the actual Chevrolet Equinox EV, a midsize SUV: 319 miles of range on 85 kWh at 4923 lb curb weight).
 
I could also use this to predict the result of aerodynamic modifications to an existing EV. My youngest brother and his wife have (almost) matching Tesla Model 3s; his is a 2018 Long Range RWD with an EPA range of 310 miles. If we wanted to improve that to 350 miles, by how much would drag need to be reduced? Following the line of constant weight or constant battery capacity on either of the Small Sedan diagrams from C_D = 0.23 and 310 mi until they cross the vertical line at 350 mi gives C_D = 0.18, or about a 20% reduction in drag. For a ballpark (and likely conservative) estimate, that seems realistic and in line with what I would expect based on engineering intuition—and as modifications are tried out, their actual effect on efficiency could be measured and used to refine this prediction. Of course, I could also run a sweep using the 2018 Model 3’s actual dimensions and get an even better (and likely closer to reality) estimate since I’ve already built the calculator, rather than use the generic Small Sedan dimensions (which differ slightly from the real Model 3). You could too (hey, I’m not giving everything away for free here).

2018 Tesla Model 3 Long Range RWD

Oh, fine—here you go.

 
Conclusion
 
Now that we’ve reached the end of the semester and I’ll actually have some free time, I’ll continue to modify this calculator to see if I can improve its accuracy. Specifically, I think it could be made better by introducing some method to account for regenerative braking and city driving rather than assuming a constant cruise (not that a constant cruise profile isn’t useful, as even EVs are used by some people for road trips—but city driving is more representative of the way our cars are regularly used on the whole. EPA combined ratings assume something like 55% city/45% highway driving). I might also try a vehicle buildup from scratch rather than seed, although that undoubtedly will be more complicated than what I’ve done already and may have to be built up component by component. But if it reduces bias in the results, it may be worth it. The model will still be wrong, but any way to make it less wrong warrants an attempt at least.