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### Hybrid Solar Electric Cars : Refueling With The Sun

#### What if you could charge an electric car simply by parking it in the sun?

What if you could charge an electric car simply by parking it in the sun? I’ve been keenly interested in the Tesla Model S, and was curious if it would make sense to incorporate solar cells into the vehicle body. I did the math on this, and was a bit surprised at the results.

Using the Tesla Model S as an example, I estimated how much upward facing surface area is available for solar cells (about 6 square meters, assuming solar cells are crammed into every available space, plus another 2 to 4 square meters if the side panels are also lined with solar cells, also useful for collecting light when the sun is low in the sky). I used 8 square meters as an estimate of how much space is available including both upward and side facing solar surfaces.

Some readers commented that the area estimate is a bit high. I assumed that designers would be aggressive in maximizing the usable solar area.

Average solar insolation at sea level is 850 Watts per square meter. The most efficient solar cells that are commercially available convert 24% of this energy into electricity. Most of the southwestern US receives about 5.5 to 6 sun-hours per day on average. With that, we can estimate the power production of the vehicle integrated array by multiplying collecting area, efficiency and sun-hours to get between 9 and 10 kilowatt hours per day.

If we use higher efficiency solar cells (the current record is about 40% efficiency), we could boost this to almost 17 kilowatt hours per day. (Ultra efficient cells like this are quite expensive, and are currently limited to special applications such as powering space vehicles, however they’re coming down in price).

Output could be boosted by placing a flat, slide out solar panel or trailer in the space above or below the battery tray. This would slide out into a parking space behind the vehicle, and would double the collecting area and therefore daily charging potential (it would be straightforward to make this an expandable panel, like a dining room table, so it could be stowed compactly, but span out to cover a standard parking space, and maybe also pivot to the optimal collecting angle).

This is also an easy way to add solar to a car without embedding solar cells in the car body, perhaps a good first step (embedding solar cells in the car body involves a lot of design and technical tradeoffs whereas the solar trailer is easy, and it would be protected in its storage space).

The Model S consumes about 0.28 kilowatt hours per mile, so a vehicle mounted solar array would generate an average of about 35 miles per sunny day or 12,700 miles per year (using modules rated at 24% efficiency), well in line with average commute distances.

Note: this is a rough estimate, based on annual averages. Actual output will vary depending on the time of year, weather conditions, vehicle geometry, etc. So treat this as a rough estimate. Your milage may vary, as they say.

There are a number of benefits to integrating solar power into an electric vehicle, among them:

Range extension : driving range could be extended 10 to 15% with a vehicle like the Model S.

Low carbon power : when recharging an electric vehicle, you’re drawing from carbon fueled power plants. By enabling the vehicle to generate most or all of its power via integrated solar panels, you can further reduce your carbon footprint.

Off grid charging : wherever there is sunlight, you have a charging station. Next time you go on a weekend camping trip, you can pick up 50 to 100 miles of range just by parking your car in a sunny location.

It would also be interesting to find out if its possible for the Model S to operate in a slow speed, low acceleration solar only mode. Aerodynamic drag increases in proportion to velocity cubed. Acceleration could be limited to match the power output of the solar cells. Not a sporty ride, but if you can pull out your solar trailer and limp along to the nearest charging station or power outlet, its better than calling a tow truck.

What do the economics look like? At an average of 9-10 kilowatt hours per day, the vehicle would generate roughly \$1.00 worth of electricity per day that would otherwise be purchased from the grid (I assume \$0.10 per kilowatt hour as a rough number, about right for the California market). At current solar cell prices, it’s cheaper to buy electricity from the grid, however prices continue to drop rapidly, so by the time something like this reaches the market, that may change.

As an option, its pretty attractive for the reasons mentioned earlier. Being able to charge your car by simply parking it in the sun would be super convenient. Add the peace of mind of knowing that if you run out of juice, you can recharge anywhere or limp along to the nearest power source, and that seems like an option many EV owners would go for.

The math looks interesting today, and should only improve, for example when ultra high efficiency solar cells become cost effective, or new lithium-sulfur batteries slash vehicle weight and power requirements.

The important point is that it’s not necessary to design a car that runs solely on solar power, but simply generates enough power on average, to offset typical daily use. Then all you’d need to do is park your car in the sun to keep it topped up and ready to go (and tap into the grid only when you need to).

Performance Estimates Recap

Model S covered with 24% efficient cells (Sun Power used as example), approx 8 square meters of usable solar surface area via combination of upward and side facing surfaces, 5.5 to 6 sun hours per day. 9 to 10 kilowatt hours charge per day, 32 to 35 miles per day, approx 12,500 miles per year.

Pull out, expandable solar trailer, sized to cover a standard, small parking space (8' by 18', or approx 13 square meters). 14.5 to 16 kilowatt hours per day, 52 to 57 miles per day, approx 20,000 miles per year.

Combined solar-hybrid vehicle and pull out solar trailer. 23.5 to 26 kilowatt hours charge per day, 84 to 92 miles per day, approx 32,500 miles per year.

Q: How did you calculate the surface area of the vehicle?

I used specs from Tesla Motors to get the physical dimensions of the vehicle (roughly 5 meters long by 2 meters wide). I subtracted a meter from the vehicle length to account for windows (in fact there are solar coatings for windows that are 10% efficient, but I treated the windows as unusable space. I assumed that at least part of the door and side panels could be covered in solar cells. So I went with 8 square meters is a safe estimate for the available area (adjust your estimates as desired). If a manufacturer actually builds this, they’ll almost surely adjust the geometry to maximize usable area.

Q: How did you calculate the power output and daily range potential?

This is pretty simple to do. The Earth’s surface receives, on average 850 Watts per square meter. The National Renewable Energy Laboratory publishes maps that depict solar insolation in terms of sun hours per day or kilowatt hours per day. Most of California gets 5.5 hours/day on average. To calculate average daily output, multiply surface area by 0.85 by solar cell efficiency (24% for the best Sun Power modules) and then by sun hours per day. That works out to 9 kilowatt hours per day.

The Tesla Model S consumes 0.28 kilowatt hours per mile, so that works out to 32.14 miles.

Q: How can you increase charging potential further.

There are three ways to do this. One is to modify the vehicle geometry to maximize surface area (make it a bit wider and/or longer), not much room to work with there. Another is to use ultra high efficiency solar cells, such as those used in satellites (expensive, but they’ll get cheaper). The simplest way is to store a removable solar panel or trailer that slides out from a compartment above the battery pack (which runs along the entire length of the underside of the car). Then when you park your car, you’d pull this out into the space behind you. This would double the collecting area and therefore charging potential (to about 60 miles a day, 80-90 miles per day if vehicle and trailer based charging is in use, more than most people drive).

Q: Wouldn’t the car get incredibly hot?

No more so than a car with a dark colored paint job (a black car converts nearly 100% of the light striking it into heat). On a hot sunny day, you could remotely turn on your A/C before you head to the car. The energy cost of running the A/C for a few minutes to cool the car down will be covered by the power generated by the solar cells if the system is designed right. The system could also run a simple fan to vent outside air to prevent overheating.

Q: Solar panels are fragile, this can’t be done, hand wave, hand wave, hand wave.

This article is about back of the envelope calculations to show that this can be done, not a proposal for a specific implementation of the idea. There would be lots of technical and design considerations to deal with in building an actual vehicle (such as what type of coating to use to protect solar cells), but the basic math in terms of how much power can be generated and the driving distance that equates to is sound and is derived from solar modules that are shipping commercially today. A pull out solar trailer is probably the place to start with the Model S as it sidesteps the issues associated with integrating solar cells into the vehicle body.