**Editor’s Note: EarthTechling is proud to repost this article courtesy of Do The Math. Author credit goes to Tom Murphy, an associate professor of physics at University of California, San Diego.**

If you like the sun, and you like cars, then I’m guessing you’d love to have a solar-powered car, right? This trick works well for chocolate and peanut butter, but not so well for garlic bread and strawberries. So how compatible are cars with solar energy? Do we relish the combination or spit it out? Let’s throw the two together, mix with math, and see what happens.

**What Are Our Options?**

Short of some solar-to-liquid-fuel breakthrough—which I dearly hope can be realized, and described near the end of a recent post—we’re talking **electric cars** here. This is great, since electric drive trains can be marvelously efficient (ballpark 85–90%), and immediately permit the clever scheme of regenerative braking.

Obviously there is a battery involved as a power broker, and this battery can be charged (at perhaps 90% efficiency) via:

- on-board internal combustion engine fueled by gasoline or equivalent;
- utility electricity;
- a fixed solar installation;
- on-board solar panels.

Only the final two options constitute what I am calling a solar-powered car, ignoring the caveat that hydro, wind, and even fossil fuels are ultimately forms of solar energy. The last item on the list is the dream situation: no reliance on external factors other than weather. This suits the independent American spirit nicely. And clearly it’s possible because there is an annual race across the Australian desert for 100% on-board solar powered cars. Do such successful demonstrations today mean that widespread use of solar cars is just around the corner?

**Full Speed Ahead!**

First, let’s examine the requirements. For “acceptable” travel at freeway speeds (30 m/s, or 67 m.p.h.), and the ability to seat four people comfortably, we would have a very tough job getting a frontal area smaller than 2 m² and a drag coefficient smaller than *c*_{D} = 0.2—yielding a “drag area” of 0.4 m². Even a bicyclist tends to have a larger drag area than this! Using the sort of math developed in the post on limits to gasoline fuel economy, we find that our car will experience a drag force of *F*_{drag} = ½*ρc*_{D}*Av*² ≈ 250 Newtons (about 55 lbs).

Work is force times distance, so to push the car 30 meters down the road each second will require about 7,500 J of energy (see the page on energy relations for units definitions and relationships). Since this is the amount of energy needed each second, we can immediately call this 7,500 Watts—which works out to about ten horsepower. I have not yet included rolling resistance, which is about 0.01 times the weight of the car. For a super-light loaded mass of 600 kg (6000 N), rolling resistance adds a 60 N constant force, requiring an additional 1800 W for a total of about 9 kW.

What can solar panels deliver? Let’s say you can score some space-quality 30% efficient panels (i.e., twice as efficient as typical panels on the market). In full, overhead sun, you may get 1,000 W/m² of solar flux, or a converted 300 W for each square meter of panel. We would then need 30 square meters of panel. Bad news: the top of a normal car has well less than 10 square meters available. I measured the upward facing area of a sedan (excluding windows, of course) and got about 3 m². A truck with a camper shell gave me 5 m².

If we can manage to get 2 kW of instantaneous power, this would allow the car in our example to reach a cruising speed on the flats of about 16 m/s (35 m.p.h.). In a climb, the car could lift itself up a grade at only one vertical meter every three seconds (6000 J to lift the car one meter, 2000 J/s of power available). This means a 5% grade would slow the car to 6.7 m/s, or 15 miles per hour—in full sun. Naturally, batteries will come in handy for smoothing out such variations: charging on the downhill and discharging on the uphill, for an average speed in the ballpark of 30 m.p.h.

So this dream of a family being comfortably hurtled down the road by real-time sun will not come to pass. (Note: some Prius models offered a solar roof option, but this just drove a fan for keeping the car cooler while parked—maybe simply offsetting the extra heat from having a dark panel on the roof!) But what of these races in Australia? We have real-live demonstrations.

## Garfield Lawrence, Sr.

This is an excellent introductory article that covers all the basis for an in depth analysis of the choices that we have to make. The decisions that we have to make are complicated but must be done to improve the country’s infrastructure for support of the transportation sector. I agree that the economics behind the scientific calculations may seem disappointing now, but the “economies of scale” should take care of the higher costs in the future. At a certain point in time we will have to address this issue head on. It’s a lot better to do these calculations now and make the hard decisions while we have a little time instead of waiting until the last minute and acting in panic mode. I hope our leaders are paying attention to this upcoming problem with a solution in mind.