I have an AutoCraft Marine / RV 12-Volt Deep Cycle Battery, Group Size 27, 600 CCA. I hooked the battery up to the inverter with a short piece of #6 wire and plugged in my Frigidaire FFRA05L1R1, 5000 btu window shaker. It fired right up. It is rated at450 watts.
The inverter has an auto cutoff at 10.6 volts. I ran it on max cool with the fan on high until the inverter kicked off. It ran about an hour. This is what the calculated run time is according to this online calculator (VERY COOL....you must try it!) http://www.donrowe.com/power-inverter-f ... m#how_long
I like it COLD in my TD. Like...I have to use a comforter to keep from being cold when I am sleeping. When I have shore power, I run the thing on MAX everything. It gets damn cold in there and I LOVE it.

Using that battery, I would need 7.5 batteries in parallel to run the AC the way I like it for 8 hours.
Resolution? Shore power. I basically have a monster inverter that will be WAY under utilized.