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On most of our Mayfly sensor stations, We use the 3.5W panel from Voltaic, and it’ll charge a brand new battery just a few hours in full sun. When you buy a new Lipo, it should already be at least 50% charged, so you won’t be starting from zero. And you should avoid totally discharge a battery because that will damage it and shorten it’s lifespan or kill it entirely. So there should never be a time where you need to charge a fully-depleted Lipo. If this happens often then you need to change your circuit or increase your battery capacity. Our datalogger stations use sleeping routines, sensor switching, and other smart power management tricks to allow them to run for weeks even without sunlight, so on a normal day they need about a half hour of sun to charge the battery after being in the dark overnight.
The charge regulator on the Mayfly circuit board has a maximum output of 500mA, so even if you put a large 6-watt panel on the Mayfly, it’s still not going to charge it any faster since you’re limited by the 500mA charge regulator. But in areas with lots of shade, using a large shaded 6-watt panel can give you the same results as using a smaller panel in full sun.
The yellow LED on the Mayfly indicates that the battery is actively being charged. Once the battery is fully charged, that LED goes out and there’s no other indication that the battery is full. The Mayfly can sample the input Lipo battery voltage on analog input A6 so you can print it to the serial monitor or write it to the card or whatever. There’s an example sketch on how to do that here: https://envirodiy.org/mayfly/software/battery-measurement/ If you’re needing to know Lipo battery voltages often and when not connected to a Mayfly, then there are small Lipo voltmeters you can get, just be sure to observe polarity since many of them have reversed pins on the JST-2.0 jacks.
And yes, the Mayfly will charge your battery even if the power switch is turned off. You can also charge a Lipo battery by connecting the microUSB cable of the Mayfly to your computer or just use a regular phone charger.