“Be kind, for everyone you meet is fighting a hard battle” - Often attributed to Plato but likely from Ian McLaren (pseudonym of Reverend John Watson)

Saturday, August 10, 2019

Solar energy is GREAT but...

Image credit: 4Patriots, LLC
As is pretty clear from previous posts (and despite my current vehicle, airplane, and travel itinerary), I'm a very big fan of renewable energy. And thus, also a fan of solar power. But sometimes solar isn't appropriate for a particular application. To the left is a collage from 4Patriots, LLC, let's see if this device is in the "inappropriate" category.

This is a charger for such electronics as cell phones, tablets, etc. Is this an appropriate application? Lithium ion battery in the device is specified on the advertising web site as storing 8,000 mAh (milliamp hours) or 8 amp hours. The solar array is specified as delivering 1.5 watts.

Let's first see if the 1.5 watts is reasonable. To do so, we'll need to estimate the size. Using the measuring tool in Tracker Video Analysis and Modeling Tool, I estimate that there is an area of about 0.0068 m^2 of solar cells. This is actually generous as I've used to whole area of the face of the charger with the cells. And, during bright sunlight at my location if I hold the device facing the sun I can count on about 350 w/m^2 over the course of a day of actual insolation. Let's give the solar cells an estimated efficiency of 18% (again, generous) and figure the charging can take place at the rate of 350*.18*0.0068=0.42 watts. Well, if we use a full 1000 watts/m^2, we get 1.22 watts. I'd say that the 1.5 specification is an exaggeration at best.

Well, let's go with the 1.2 as a compromise between the 1.5 watts claimed and the 0.42 watts by my best estimate. And let's think about an iPhone 8, standard model. Such a phone has a battery capacity of 1.821 amp hours at 3.7 volts. This means it will deliver 1.821 amps at 3.7 volts for 1 hour, or 3,600 seconds. Since volts * amps is watts, we have 6.7377 watts. Since joules of energy are the same as watt seconds, we can use 3,600 seconds * 6.7377 watts to determine that the iPhone 8 battery stores 24,256 joules. Charging at 1.2 watts, or 1.22 joules/second, we find that it will take 24,256 joules/1.2 watts = 20,213 seconds or 5.6 hours to go from complete discharge to full charge.

Of course, if you're in the middle of nowhere with no other way to charge your phone and you're completely discharged, you won't need to wait for 100% charge to use your phone. Below is a graph of time needed as a percentage of charge from complete discharge. You can click on it to enlarge. Keep in mind that this is specific to the iPhone 8, other phones with different (and typically larger) batteries will be different. The new Samsung Galaxy Note 10+, for example, will carry a 4,300 mAh battery pack, well over twice as large as that in the iPhone 8, and the Apple iPhone XS Max sports a 3,174 mAh battery pack. And, of course, charging is a non-linear process so don't use this as a "to the minute" guide. It's more of a very best case scenario.



Still, this is actually a lot better than I'd anticipated when I started. It would take about an hour to go from complete discharge to 20%, certainly enough to make a few calls or send some texts. Of course it assumes perfect efficiency in the charger circuit but the efficiency is likely to be fairly high. Even if we use the low end estimate for the area of the solar array, the device will still give usable energy in a not too extreme amount of time, though if we use the more conservative estimates for insolation and charging on a state of the art, top of the line phone, we'd be looking at something more like 7 hours to go from complete discharge to 20%. Nevertheless, unlike the two previously published posts I linked above, this seems to be a good use of a small solar panel.

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