According to [1], the battery in my iPhone XS has a capacity of 2658 mAh. That means it can deliver 2658 mA for one hour. Or 1329 mA for 2 hours. And so on. Current times time is a unit of energy, the energy with which the battery is filled. With that capacity I normally just about get through my iPhone day, although sometimes I top up in the car in between when I listen to audiobooks. My usage statistics are up next. So if I want to recharge this battery, I need around 2700 mAh from my power bank. But that is not the whole truth, because charging is not perfect. That means you have to put more energy into the battery than you can take out of it afterwards. According to [2] the charging efficiency is about 80%, so I have to put in 2700 mAh / 0.8 = 3375 mAh. And because everything is always worse than you think, we carry on with 3500 mAh.
And if the whole thing is to work sustainably, I have to top up that much from the power bank every day. Furthermore, I also have to fill the power bank with just as much from the solar panels every day. This charging process again has only 80% efficiency. So I need 3500 mAh / 0.8 = 4375 mAh from the solar panels. Here we can now round down and continue with 4300. That is how much I need from the panels, every day. According to the manufacturer the gizmo delivers 1000 mA in full sun. To generate 4300 mAh with that it takes about 4.5 h. Currently that will be hard, because the sun rises at about 8 o'clock and sets again at 16:30 … so there are only … 8.5 hours in between, and not all of them at full strength, and I am not always at the window or outside. According to the gizmo's manual the 1000 mA is reached at 25,000 lux. Lux is a unit of illuminance, see [3]. There you also learn that in summer at noon there are about 130,000 lux, in winter at noon about 20,000 lux, and an overcast winter day offers 3,500 lux. Argh. On a bad winter day when the panels are always in the light, but it only has 3,500 little lux, I would get just
3500/25000 × 1000 mA × 8 h = 1120 mAh from the panels and thus only 1120 mAh × 0.8 (power bank) × 0.8 (phone) = 716 mAh into the phone. That is 28% of a charge … oh dear.
Time to save! We'll see. However, the gizmo does have 25,000 mAh of capacity, so with three good days I could get myself through a bad one 🙂
[1] https://9to5mac.com/2020/04/16/iphone-battery-life-compared/
[2] https://www.macwelt.de/news/iPad-und-iPhone-Die-richtige-Stromversorgung-fuer-unterwegs-finden-9033105.html (archived copy; in German)
[3] https://en.wikipedia.org/wiki/Illuminance