The smaller generator on it's own does not put out enough amperage to start the air conditioner. The inverter is a 3,500 watt unit, so it does not have a problem with the starting current. Most things with a heavy load do not run constantly. Air conditioner compressors, refrigerators etc come on and off. So my idea was to use a small generator and charger to recharge the battery when these things cycled off. When they came back on, the battery and inverter would handle the initial load. The battery and inverter would act like a shock absorber for the moments of heavy loads. If I wasn't running a heavy load, I would not need to run the generator but maybe once a day, maybe less. (the house battery also charges from the truck if I go somewhere). I may also go with solar panels to handle light loads.
The generator is an inverter type, so once the heavy load shut down and the battery was full, it would idle down. These small generators can run all day on less than a gallon of gas. Some days it is worth $3 to stay cool all day. If I were to get a generator that could handle an air conditioner all on it's own, we are looking at burning twice the gasoline, (with a lot more noise). It would have to be at least a 1,500 watt generator, and I don't know if any idle down feature would react quick enough for an A/C unit compressor start. So I might have to run it on high speed constantly.
If my present 800 watt generator really did put out 800 watts continuous, the system would work. It puts out 700 watts continuous, (and only 800 for a very short time). The charger pulls a little more than the 700 watts, so to protect itself, the generator shuts down. I could probably use a 40 amp charger and it might work. 40 amps at 12 volts is 480 Watts. The running A/C uses 555, so with the a/c running, 75 watts, (6.25 amps), would be coming out of the battery. A single battery might not be able to handle this for too long.
Because it is such a balancing act,( air conditioner usage, battery charger input and output, generator output), I decided to go with a generator rated at 1,200 watts peak, and a constant 1,000 watts, ( this also would also be too small to run an air conditioner on it's own). Later if I decided that I needed a 55 or 60 amp battery charger, it should handle that as well. Because it is an inverter type generator, and does not drive the A/C unit directly, an idle down feature can be used.
So in brief, I am trying to run heavy loads with a generator that would normally be way too small. The low fuel usage is a plus, but the lower noise from these small generators is what I was really after. The size of the generator is calculated by the average amount of power the load uses during the day, (including the time it is shut off). Because all the 120volt loads come off of the inverter, I don't need to flip switches if I don't really need the generator. It is all kind of automatic. Should I run the battery low, the generator can bring it back up in short order.