...2021 Mazda CX-5...to move into. I have a storage space...a a cooking area for bulk meals.
I guess I need a pretty decent power inverter to run out of my back 12v supply. And does a rechargeable large battery make sense?
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a)
Yes!, an auxiliary ('house') battery bank makes sense for your purpose.
And most batteries are rechargeable, so that is one less thing to consider.
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I would strongly recommend *AGAINST* one of those silly all-in-one boxes generically known as a 'solar generator'.
Those goofy contraptions are designed for and marketed to the Carhartt-beanie crowd.
If any part of the box goes TU (toes up), the entire thing is worthless.
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(This forum has several threads about 'solar generator' failures, and failures of the manufacturer to warranty the darn things, then you are out major fedbux... and have to begin again from the beginning.)
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Instead, be modular and resilient:
Get a couple AGM or LiFePo4 batteries -- these are your bank.
Get a 2,000-Watt pure-sine inverter from Harbor Freight -- this operates your 120vdc appliances.
Get an isolator -- your starting battery is charged first, then your house batteries are charged second to ensure you are always able to start the vehicle.
On the farm, I built this system in each of our delivery trucks.
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If any part of my system goes TU, I can quickly and easily plug in another unit, and I am instantly up and running.
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Another benefit to my system:
The components are readily available at auto-parts stores, hardware stores, and Harbor Freight stores.
The 'solar generator' business seems to be primarily mail-order, so any adjustments require shipping the deely-bobber back to the manufacturer, and then, you get to wait.
Meanwhile, your whole shootin' match is dead in the water.
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b)
Unless you are married to your little station-wagon, I think you might be better served with a van or truck-camper.
For us, we need someplace to stand while getting dressed.
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re : 'stealth'
In most urban paradises, so many people live in vehicles, nobody much cares anymore.
Unless you go major sideways, nobody will notify LawEnforcementOfficials.
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An aside:
In Boise v., the 9th Circuit judge ruled the bureaucrats cannot 'churn' street-campers unless adequate off-street housing is available.
[This's my understanding and my opinion.]
That ruling applies to all the western states, and may be quoted in other regions.
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San Diego, California, Dave is a full-time live-aboard in his van.
He hangs his photovoltaic panels all over his rig, plus sets them on the lawn next to the sidewalk.
Like us in our rig, Dave ignores the entire concept of 'stealth'.