I'm looking to power my Raspberry Pi via rechargeable batteries, but I would like to know how long can it run with x number of batteries. I want to eventually be able to mount it outside and solar charge the batteries and then have the Raspberry Pi run whenever there is enough juice.
Here's a writeup using six aa:
In general I'd say 4 AAs is cutting it close. If they're rechargeable, they're actually only 1.2 V which adds up to 4.8 V. That doesn't even make the recommended 5 V cut-off. You can technically get away with using only 3.3 V to power the Pi, but then you loose all peripherals. Like USB, ethernet, and HDMI. Not so useful in most situations. (The weather balloon people are having a field day with it though!)
Using alkaline batteries, you get 6 V which is enough to power the Pi. Nominally you'd expect around 4 hours power with them (given a 500 mA draw of the Pi and a 2000 mAh capacity of the battery), but there's a catch. Alkaline batteries have a very steep initial power drop. They go from 1.5 V to 1.2 V very quickly, and then remain around 1.2 V for most the rest of their charge, before dropping off again. Ever wonder why rechargeable batteries were ever only 1.2 V? That quirk of alkaline battery chemistry is why.
So you really do need at least 6 AA batteries, no matter what. 6 AA batteries gets you probably between 5 and 7 hours of life. 8 AA batteries 8 to 10. The MoPi board is a convenient mechanism for hooking up the AAs nicely, and also lets the Pi know when the batteries are low so that it shuts down nicely. It also accepts dual power inputs, so you could potentially feed solar power directly into the Pi, as well as charging the batteries.