#45: The Math of Charging Your Phone

This is mark Joseph “young” blog entry #45, on the subject of The Math of Charging Your Phone.

I once had a charger for my phone that I could plug into the cigarette lighter outlet (now called “power outlet”) of a car.  I used it sometimes when I would leave the house and then discover my phone was dying, or when I was headed to a convention and knew I was not going to be in the hotel room long enough or frequently enough to support the battery, or when the wires on the one in the house came loose and I couldn’t justify buying another house charger right away.  I don’t use it now because the lighter outlet in the one car we still have on the road broke.  However, I’m given to understand that newer cars are more and more coming equipped with USB ports for the specific purpose of charging cell phones or powering similar equipment, and people are doing this far more.

So of course now someone has come along and said that we shouldn’t do that because it’s contributing to an environmental disaster.

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He’s not a nutcase.  He’s an automotive electronics engineer, retired.  In general, he makes a good point; but in making it, he does a few things that create a misleading result.  We will get to the good point eventually here.

He begins his calculation by estimating that a smartphone requires 4.8W (four and eight-tenths watts) to recharge.  That’s fascinating, because Universal Serial Buss (USB) ports don’t deliver that much.  All USB ports deliver five volts (5V).  The common USB 1.0 and USB 2.0 ports are limited to a maximum of five hundred milliamps (500mA), or half an amp.  That means maximum output is two and a half watts (2.5W).  The newer USB 3.0 ports can deliver nine hundred milliamps (900mA), nine tenths of an amp, which comes to a maximum output of four and a half watts (4.5W).  You can’t get as much as he says the phone draws from a USB port.  We might presume that the ports in a car, not being directly tied to a computer, might have higher current capabilities, but the way USB works, the connected device controls the current flow (amperage) and thus the total power (wattage), and the smartphone is not going to assume the port can provide more than specifications dictate.

Our author gets his number not from what USB ports provide but from the amount required to charge the phone from completely dead to fully charged.  It might take a long time to do that on a trickle charge, but he’s right to the degree that if you are completely charging your phone from nothing, you’re going to use that much power to do it.  But then he assumes that you get that 4.8W in one hour, from which he calculates that this will cost you 0.03 (zero-point-zero-three, or three one hundreds) of a mile per gallon.  That’s not negligible–it’s about half a football field per gallon, a bit more than the distance around the high school track on a ten gallon tank–but if you’re getting thirty miles per gallon, it’s point one percent (0.1%), one part in one thousand.  He then multiplies that by the three trillion road miles traveled by all United States drivers in a year assuming an average velocity of thirty miles per hour, and comes up with one hundred million gallons of gasoline spent to charge phones.  That’s two hundred million dollars.  It also produces as much greenhouse gas as burning nine hundred forty-five million pounds of coal.

The article does make one excellent point:  It will cost you thirty times as much to charge your phone on your car’s engine as it will to charge it on your house current.  That’s because electric companies don’t use gasoline engines to generate electricity, but go for the least expensive options at all times, and automobiles are designed to be efficient transportation, not efficient electrical generators.  It will cost you about two cents an hour to charge your phone in your car, about six one-hundreds of a cent for the same hour of charging at home.  It will cost you, personally, even less to charge it in your hotel room if you’re on the road.  Car chargers should be the backup option, not the primary choice.

On the other hand, he’s using the phantom of big numbers to frighten us.  It is reminiscent of the famous “National Geographics Disaster” covered thoroughly (and facetiously) in The Journal of Irreproducible Results, in which scientists jokingly calculated the long-term consequences of the fact that the relatively heavy National Geographic Magazine is never scrapped but rather stored in growing piles in basements and garages, such that in millions of years the accumulated weight would cause continents to buckle and sink.  Because we’re multiplying that tiny two cents an hour by three trillion miles of driving, of course we get a huge number.  If all of that charging was shifted to wall outlets, the cost would still be over six million dollars–a lot less than two hundred million, but still one of those huge frightening numbers.  The amount of power we’re talking about for one phone is still a very small amount.  Your car stereo probably draws several times that.  If you don’t have the new light-emitting diode (LED) or similar high-technology low-power headlights, they almost certainly do.  Besides, even were you to leave your phone connected to the charger for every minute that you drive, one of the functions of USB charging systems is that when the device is fully charged it stops drawing power.  So if in that first hour of driving your phone is fully charged, it doesn’t charge more until you’ve used it.  It’s absolutely foolish to imagine that we are, or ever will be, charging our cell phones every mile that we drive.  We charge them until they tell us they’re charged, then we put them away until we notice that they’re getting low again.  The scary numbers are inflated by this critically unreal assumption.

So do the reasonable thing and charge your phone from less expensive more environmentally sound wall current instead of the power system of a gasoline engine, but don’t obsess over the number of charging ports in new vehicles.  Driving is already an expensive environmentally unsound convenience.  Using the charging ports in the car is another one, a far less one on the grand scale of things and one which can more easily be replaced by something better.  Do so when you can.

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