Have you tested the monitors connected to an inverter? Cheap (< $X000) inverters will produce a crappy AC signal. Some (most?) electronics don't like that.
I would recommend getting a
deep cycle battery. They are designed to provide less amps, but over a longer time.
Make sure you disconnect your auxiliary battery from the main battery when the engine is off. If your relay is not automatic, you must be very diligent to turn it off every time. Every time a
starting battery "dies" it damages it: it will hold less charge each time and eventually be useless.
We would need some more numbers from a specific battery (There should be a couple aH ratings.) and the dropout voltage for the inverter you are using to convert "car" electricity to "house" electricity.
The relay could be as big as you can afford. If it is ever "on" when you turn the starter, it could see a large amount of current pass through it which would destroy a smaller relay.
Or, you could size the relay to handle 31.9 amps + a bit more and just plan to replace the relay if you ever fry it by leaving it connected during startup.
The power you listed is the "average" power. There will be spikes of larger current draw, but for computer monitors it shouldn't be too big of a problem. (It's more of a problem for large stereo guys.) I assumed up to 50 amp spikes below.
If the car is running and your relay is "on":
- The alternator will be charging both of the batteries at the same time. It will charge the one with less charge more until it catches up and they're voltage is the same.
- The load will be drawing current from both batteries.
If the relay is off when you start the car, the starter will only pull from the main battery.
But, when you flick your keys to the "Start" position, you are also turning on everything in the car. Meaning: if you wire the relay to turn on when the car turns on, your auxiliary battery will supply charge to your starter. This could be bad if you get a
deep cycle battery for your auxiliary battery.
Deep cycle batteries are not designed to supply such a large amperage at a time. When the two batteries are connected in parallel (as you describe), it's not guaranteed that your main battery will be doing most of the work.
There would be (almost) no way to power the load from only the auxiliary battery while also charging the battery. (I say almost because it would be absolutely prohibitively expensive.)
Between auxiliary battery and load:
- I'd recommend AWG 8 wire which is rated for 73 amps.
- I started at AWG 14 for 32 amps.
- You listed the "average" power. I added a buffer for spikes up to 50 amps so we're at AWG 10.
- I added a buffer because your run will probably be a little further than 3', but not by much so we're at AWG 8 for 73 amps.
- You could even go bigger if you don't mind the cost, but that's my calculation for the minimum.
Between auxiliary battery and main battery:
- Big. You want to be able to not burn the wire if you ever accidentally have the relay "on" when you start the vehicle. I once used 0000 AWG for a stereo. That was a bit ridiculous and I don't recommend it (There were so many installation issues!), but you get the point.
- When a wire burns is a function of both time and amperage. If you pull a large amount of current (e.g. 700 amps), but for a very short time (< 7 seconds), you can use a wire that is much smaller than a wire that could handle that amperage continuously.