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I'm going on a road trip and will be sleeping in the bed of the truck at night. I want to be able to have a fan running during this time. I have a couple old car batteries sitting around, and I was thinking I could charge them up before I leave home, and then use them to power the fan at night. The engine will not be running when I am using the fan, and I don't want to drain the battery that's used for starting the engine. The thought is that I get a power inverter so that I get 120 VAC out to power typical AC desk fans (the smaller the better).
I want to calculate how long a battery can power such a fan.
Let's say the fan is a 120 V, and on the "Low" setting consumes 30 W. Let's say the battery is a 600 CCA, 12 V, lead-acid car battery, with a 50 Ah capacity (20 Ah Rate).
How can I calculate the time that the battery will last? I know that the power rating of the fan can give the current used (P=IV), and the capacity of the battery can tell me how long at whatever current (Capacity = Amps*hours). But I don't know which voltage to use (12 or 120), or how to incorporate the inverter or the part about the 20 Ah Rate.
I'm also open to other ideas for running a fan with the engine off.
Another additional thought is to connect the battery in parallel to the truck's battery and that way it would be charging when I drive during the day, but the batteries are different capacities, and I don't know if there would need to be other hardware to prevent my truck battery from being drained. If this can't be done then I will just drain the battery and when it's dead, I'll just have to wait to get back home to charge it.