Hi,
If you are plugged in, then the trailer 45 amp 'converter/charger' will keep the batteries full.
If not plugged in then the tow vehicle #12 wire through 45 feet of wire, then a connector or two, it will barely charge at 15 amps, probably more like 10 amps. 1/2 hour = between 5 and at the very most 10 amp hours of power to the battery.
Your RV will be consuming 35 amp hours a day, not including lights or anything but the refrigerator, CO and propane detectors. If you do not have a generator, or 120 volt shore power, the battery will be dead in about 48 hours.
Hooking up the truck to jumper cables, letting them sit and charge the battery for about 1/2 hour, then start the engine and let it run about 1/2 hour, then let it sit another 1/2 hour to finish charging, you might get say 35 amp hours into a very low group 27 battery. If the battery is 105 AH capacity, you probably can never exceed 35 amps per hour into the battery (without getting the battery very hot). Even with 4 golf cart batteries, and 440 amp hours of total capacity, I can only charge at about 45 amps per hour while warming the batteries, and they must be charging at around 14.4 volts to stay at 45 amps (10% of my total battery capacity).
You will be best off with a pair of golf cart batteries (total of about 220 amp hours at 12 volts), second best is a pair of group 27 batteries (about 200 amp hours total at 12 volts). The advantage of golf cart batteries is that you have much more water in the battery, it will run cooler, last longer (like 13 years in my case) and be much more tolerant to not keeping the battery full of water each month.
The worst thing for battery life is leaving them discharged a few days - longer will compound the damage to the point they will never work again. Second worst thing for your battery is dry cells. This can lead to warped plates, and shorted cell. Overheating a battery due to quickly charging it, or running low on water can also warp the plates = new battery time.
You can get really long battery life by installing a solar panel or two. Because you will be consuming 35 amp hours daily just to run the CO meter, propane detector and refrigerator, those will use all the power that one 120 watt panel can make in one day.
SunELec.com They sell panels for about $1 per rated watt.
You can install those panels with 6" long 2" angle aluminum mounts. 3 holes 3/16" for #10 screws into the roof, and 5/16" hole for the panel bolt - 1/4-20 bolt and nylo nut that will not vibrate off, and takes time to remove, something someone trying to steal one will not have!
#10 direct burial wire is UV rated, can run from the panels to the refrigerator vent, and down to the controller, then on to the battery. It is pretty simple to install.
100 watts would be the minimum I would recommend, but 200 watts is much better, and will keep up with your usage. If you want to use a inverter to run a laptop, and watch a DVD, it will only use about 20 watts, and is easy to do with a portable 100 watt - 200 watt inverter. Costco used to sell a Colman 500 watt inverter for $40.
I installed some extra cigarette lighter receptacles in my RV (Radio shack) or your local auto parts store. I used #10 wire and 20 amp fuse.
Have fun camping!
Fred.
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