Power on the Go

Recharging a Laptop on the Go

For a few years now, I’ve had a Noovoo AC Power Bank (claims to be 20100mAh with 60W output and 72.36Wh) (no longer available; newer version). It’s ... Fine. Gets the job done. Can recharge an ancient MacBook Air. Takes a while to recharge with the bundled AC adapter (3-4 hours with the bundled 19V 1.6A charger). The capacity isn’t really 20100 mAh (more like 15,000 mAh usable, according to this review - but the math isn’t sourced; internally, it uses 3x 6700mAh 3.7v batteries). The form factor is awkward. But I have it, and it works.

I covet the Omni 20+, but $249 is a bit steep...

Basically, I want something that can recharge a MacBook Air 11" at least once, on the go, without being a hassle to lug around in a backpack.

Novoo has a more squared-off Portable Laptop Charger, but it seems like it would be almost as awkward as what I’ve currently got. There’s also this Novoo Portable Laptop Charger with a claimed 40,000 mAh capacity, but at $140 it’s getting up there, too. (Does have the option of a 4-hour solar recharge, though, with additional hardware (reported to work) (or even a smaller unit?). Apparently.) Then there’s the no“er” name brand options (Novoo has been around long enough I guess it’s not really “no name” anymore?), like this thing from SinKeu. Which also used to be (?) available in a kit with this 40W SinKeu solar panel. (Solar recharge isn’t a requirement, but it’s kind of a cool thing to toy with mentally. For those camping trips I don’t take, the Burning Man weeks I don’t do anymore, or the societal breakdown that certainly is never going to happen.)

Of course, if I finally get out of the dark ages and move to something that charges over USB-C (like the 2015+ MacBook), this becomes largely moot ...

Pondering.

Battery Capacity: Running the Numbers

Speaking of the math, I decided to dig into things. I’m guilty of being lazy: “20100 mAh capacity, my laptop has a ~6000 mAh battery, I should be able to recharge it 3x!” (Er, well, if I was going DC-to-DC I might expect that; through an AC socket, to an AC adapter, to the laptop’s DC input, not so much. Turns out even that’s way oversimplified, and not even close to how any of this works.)

Converting Stored Energy to Output Capacity

First, terms: A watt hour is a measure of electrical energy equivalent to a power consumption of one watt for one hour. If a computer uses 45 watts an hour, it will consume a 90 Wh power supply in 2 hours (assuming 100% efficiency, which, well, see below.)

Okay. Watt hours (Wh) = [battery capacity (mAh) x battery voltage (V)] / 1000.
Using the Novoo AC Power Bank I have, ((6700 mAh x 3 batteries) x 3.7 V) = 74.37 Wh, which is pretty close to what Novoo claims (72.36 Wh).

To charge a standard 5V USB device (not a 9V fast charging system), the battery voltage has to be converted (3.7V → 5V). This isn’t lossless, but assuming it was:

Output capacity (mAh) = [ battery capacity (mAh) x voltage (V) ] / charging voltage (V).

So (20100 mAh x 3.7V) / 5V = 14874 mAh. We’ve already lost 25% of the rated storage capacity.

Also, (a) the battery quality and age will decrease the stated storage capacity, and (b) the voltage conversion will generate some heat (the Joule effect), which is electrical capacity that’s not being delivered to the device being charged.

A good quality battery pack with good electronics might be close to 90% efficient. Let’s ball park it at 85%. 

Stored energy: (20100 x 3.7V) / 1000 = 74.37 Wh
Usable energy: 74.37 Wh x 0.85 = 63.22 Wh
Output Capacity @ 5V: (63.22 Wh / 5V) x 1000 = 12643 mAh (~63% of advertised storage capacity)

Meanwhile, if you want to test the capacity of a bank at 5V, found this nugget: “[C]onnect a 5 ohm resistor to the 5 volt output. That will draw 1000 mAh. Time how long it lasts before the power bank shuts off. If it lasts 10 hours, you will know you gotten 10,000 mAh at 5 volts.” If you really want to get crazy about things, do an actual instrumented run with something like this USB load tester.

Determining Charges per Device

Now, the device being charged will have similar inefficiencies built in. Again, we’ll ballpark at 80%. (This is assuming DC charging, e.g., over USB. Introducing an AC adapter into the mix is a whole other thing.)

We’ll use an iPhone 6s with an aftermarket 1715 mAh 3.82V battery (6.55 Wh).
Power needed to recharge: (1715 mAh x 3.82V) / 0.80 = 8189 mWh = 8.19 Wh.
Guesstimating here, 1715 / 0.80 = 2144 mAh, which goes into 12643 about 5.9 times.

So, that Novoo should recharge the iPhone 6 5 times fully with enough juice left over to almost charge it fully one last time.

But What About an AC Adapter?

I started down this rabbit hole pondering a solution to recharge a laptop while away from mains power, like, at Disneyland. Or camping. I meant camping.

An Apple MagSafe2 power supply is a switching power supply. (A 60W charger is producing 16.5V at 3.6A.) We’ll call the Apple power supply about 85% efficient. Running off of the more or less unlimited power available from the wall, that’s whatever. Assuming it’s delivering 45W it’s probably drawing 53W, which will give it about 1 hour 11 minutes before it’s depleted the Novoo.

The MacBook’s stock battery is a 50 Wh unit at 7.3V (6850 mAh). An iFixit replacement is spec’d at 54.4 Wh and 7.6V, for 7160 mAh. (The math checks out, see above.) Accounting for energy loss in the conversion, we’ll need 68 Wh to fully charge the laptop once, or 1 hour 30 minutes. So a brand new, pristine condition, Novoo 20100 mAh power bank should be able to take the Air from 0% to about 78% before it’s as dead as a Monty Python parrot. (Complicating this math a bit further, I believe the Apple will slow the charging rate once the battery’s above 80%, very common with Lithium Ion batteries.)

Not great, not terrible. One of these days I’ll do the math to see what capacity I’d actually need to fully recharge the device.

Getting rid of the intermediate AC conversion would probably get me there. The earliest (cheapest) MacBook 2015 has an aftermarket battery of 39.7 Wh (5260 mAh at 7.55V) and charges via 30W USB-C. A 10500 mAh battery pack should be able to fully charge it at least once? Wonder what this Anker would do...

More on Watts

I feel like I should have more of a handle on this stuff than I do (I’ve only been playing - key word, playing - with electronics since getting a 160-in-One Electronic Project Kit as an xmas gift one year, I was no older than 8?). But here goes.

Watts is a simple formula, “West Virginia,” W = V(A). So if you have a 5 volt device slurping 2 amps of current, you’re consuming 10 watts. A 10 Wh power source (with 100% efficiency) will provide 1 hour of operation (or charging) of that 10W consumer. Watt is a rate used to measure power, Watt Hour is an amount (of storage, and/or of total consumption).