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November 20, 2014


Mobile Devices
Nadim Maluf

I am sure many have wondered about the possibility of pasting a solar cell on the back of their mobile device to charge their battery. The idea is elegant but, it turns out, is not terribly practical. We will go through the analysis together.

First, let’s establish the practical size of a solar cell that could reasonably fit on our mobile device. For the sake of simplicity, I will assume that we can somehow glue and connect one such cell on the backside of our mobile device. The table below provides the approximate dimensions of common mobile smartphones.

Next, let’s examine the power flux from the sun; in other words, how much solar energy one would reasonably expect to receive. Again, I will simplify. I will assume sunny days and the surface is perpendicular to the sun rays.

The Earth receives from the Sun radiation at approximately 1,340 Watts for each square meter of surface (W/m2). This is called the solar constant. For comparison, it is about as much radiating power as you will get in your microwave oven. But that’s in space, right at the edge of our atmosphere. By the time the radiation reaches the surface of our planet, it is now down to an average of approximately 340 W/m2, or less than ¼ of its value in space. The table above calculates the average amount of power that this hypothetical solar cell will deliver to the mobile device, again, assuming a sunny day — once again, this means outside, in direct sunlight with your mobile device facing perpendicular to the sun rays.

The math tells that we should not expect more than 2 to 5 Watts of peak available charging power. In reality, once your mobile device is indoors or in the shade, or worse yet, in your pocket or purse, that amount of energy will drop by a factor of 100 or even more.

So, remaining optimistic, and willing to sit in direct sunlight while my mobile device charges, how long would it take to charge each of these mobile devices given this amount of solar charging power? The following table calculates these approximate times to full charge (100%). On average, it takes about 4 to 5 hours of charging. On the positive side, you will walk away with a nice tan!

Of course, the question can be posed a little differently: How much surface area would one need in order to charge their device using a solar cell in a reasonable amount of time? Assuming that somehow this solar cell can be mounted outside in direct sunlight and a charging wire can be brought inside, and assuming again that you are willing to charge your device exclusively during the peak day hours near noon, then one requires a surface area about 200 to 300 cm2, or a square roughly about ½ to ¾ foot on each side.

I will leave you with some food for thought. The power levels available from a solar cell are about the same as the power levels that one gets from wireless charging pads. In other words, if you put your mobile device on a wireless charging pad, it will take 4 to 5 hours to charge your device. Of course, you are not tanning at the same time, but it is awfully slow! Now why is it that fast charging is not yet a standard?

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