The Woods: Battery life calculation help, because I am bad at maths and electrons
Obviously I'll have some real world numbers soon, but I'm sitting here waiting for my second train out of Secaucus to Harriman and am topping off the Lenovo X300's battery from the Brunton Solo 15, and it got me thinking: how many times could I do this if the Solo 15 wasn't getting recharged from solar?
Then I realized you guys are smarter than I am, so I stopped trying to figure it out and thought I'd just Lay-Z-Web it.
Here's the specs for the X300's 3-cell battery: 11.2 V dc, 2.44 Amp/Hr,
And for the Solo 15:
# Peak Power = 77 Watts, Nominal Power = 39 Watts, Total Power = 154 Watt Hours
# Storage: 12 Amp Hours @ 12.8 volts
# Max Output: 14.6 Volts
# Max Power: 77 Watts
So I looked at the amp/hour and thought, okay, about six times. And maybe that's right. Remember: I'm dumb as a shed. So dumb I'm not even sure that's the right metaphor. Or if that's a metaphor or a simile. See?
Keep in mind, because I couldn't find a car charger for the X300, I'm going out of a DC Solo 15 into an AC inverter, then back out to the standard AC/DC adapter, so there's got to be some loss in there. But I'm not interested in exact numbers, really, just a general idea. And even more important, what the probably simple equation that I'm too dopey to understand might be.
Okay, I better pack up. My train is coming soon.

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Watt-hours = volts * amp-hours
In the case of the solo 15, 12.8 volts times 12 amp-hours is 153.6 watt-hours. Hence the stated 154 watt-hours.
And the X300 battery is 11.2 * 2.44 = 27.328 watt-hours.
I'm not familiar enough with inverters to guess at the loss incurred there, or in the X300's power supply and charging system, but a 100% efficiency calculation would get you 5.62 charges.
Looks like inverters and AC adapters can get up to around 90% efficiency. So... 4.5-ish charges maybe. Conservatively, 4. If the computer isn't drawing power while it's charging.
And just to add my two bits - for an inverter you're looking at a 10 to 20% power loss, depending on the model. So that'll decrease you're on time by a not insignificant amount.
It's a metaphor. To make it a simile, you would need to say "I am dumb like a shed."
As for the maths, I may be less helpful.