Inverters of different sizes from various Manufacturers have their 'standby' or 'quiescent' current draw, and it
tends to increase with Inverter Output capacity. Other 'phantom loads', like TT Propane Detectors or lil Power Supplies and Chargers, are also becoming more widely understood as loads not to be ignored when calculating power requirements.
A 1,500 Watt Wally World Heater indicated 5,100 BTU output. So, your ~200 Watt Heater would output 680 BTUs at 100% efficiency [theoretical]. Only an empirical test will tell if that's enough and if it's practical, energy use-wise.
I'm a big fan of Insulation, so I'd do what you can in that regard. Then, shift from theoretical discussion - which will only get you in the ballpark anyway - to a practical test setup. Hook up your lil Heater, and borrowed other stuff via a temp Power Strip, and see how it does in Real World conditions in your Driveway with variables like Bedding or a BTU- producing Dog in place. Outside the TD, hook up a few Spotlights, or some other load, the same total wattage as the 115 VAC Fridge of interest. Flick them on once, then off, for ~1/2 hour for each on/off condition to simulate the ~50% duty cycle of a chilled-down Fridge. I strongly suspect you'll rediscover what's already known: 115 VAC Fridges, Hairdryers and Heaters really suck down the Inverter input Amps, even over the short time periods calculated accurately above. I was surprised and educated the other day to learn that 3-way Fridges use ~Amps to operate their internal cutover electronics that auto-switch optionally between energy types. On Big Rigs trying to Boondock efficiently on Solar, it turns out the Leveling Jack Sensors are always on and consuming ~Amps. Not a direct TD concern, but insightful. Lil 'gotchas' abound.
As mentioned above, Inverter losses and phantom loads likely will be known only when you grab that 'Kill-A-Watt' and Voltmeter and check Battery condition for yourself in drawdown scenarios. Then, you can tweak your setup to achieve the desired performance. As I read this Thread, part of the meandering is in trying to supply well-intentioned numeric answers based, in part, on non-numeric inputs like 'run very rarely' or 'reasonable'. G.I.G.O..
One fellow I just read was a big fan of pricier AGM Batteries, due to the ability to slam more Amps into them during the charge cycle. His 'vision', and experience, was to use a High Output Alternator in his Expedition Rig, or TV, to achieve short charge cycles [~1/2 hour] that Solar Panels or a Genny couldn't achieve; not even close. He got me to re-thinking my future design... I've also bookmarked a lil Project where a Lawn Mower Engine [not designed for long duty cycles] directly runs a typical 37 Amp Delco Alternator w/built-in Regulator for charging. The trick is add a better Muffler to achieve Honda Generator-type low dB levels [<60 dBs].
One Big Rig Owner cited his direct experience to claim he got ~4 years life from paralleled +12 VDC Deep Cycle Batteries. If he discharged them below 50% 'too often', the life dropped to 2 years. This is not inconsistent with other data I've read. Going to +6 VDC Golf Cart Batteries in Series/Parallel, he got ~6 years life. So, he was a devotee of using +6 VDC Golf Cart Batteries. As the Masthead of a lil CO Mountain Town Newspaper says: 'You hear what you want to hear. You see what you want to see'. So true.
These folks linked below have some good observations. Also, Off Grid Solar/Alt. Energy Geeks have reasons to run the numbers exhaustively. So, along with the Mr. Solar Website above, check those Alt. Energy Resources on line. They will have answers for things like Fridge start-up draw, and long term effects of exceeded 50% drawdown, or if Heaters/Hair Dryers are practical. My own bias is to skip most conversion inefficiencies, like Inverters and 115 VAC -> DC Adapters, and run things directly. My Cellphone optionally runs/charges off a +5 VDC USB Port. There are AA Battery Chargers, and all sorts of neato things, now running off of USB efficiently [1 Amp max. per the latest USB Spec]. Not to mention integral USB outputs now on higher-end Charge Controllers...
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