Not sure I understand your math. Remembering I'm not technically astute in the dark art of electricity.
If your inverter is say 90% efficient does that mean whilst its rated as 500w its actually only good for 450w?
How do you calculate start up power? I'm not familiar with this term.
Also, I guess my main question is what's wrong with buying a 1000w and be done with it?
Probably nothing, is the answer. Because, the US distributor's page is fairly direct...
The vaporizer is a 110 volt electrical appliance, 250 watts, 2.2 amps. Just plug it in to an inexpensive inverter, generator or use house current.
https://oxavap.com/product/provap-110-sidelinercommercial-vaporizer/
Not overly-informative, certainly doesn't suggest anything about being sensitive to clean output or start-up/inrush currents, but then I'm curious as to what could be in the provap black box to justify that price ?
Anyway, I would go for an Inverter Generator rather than an inverter.
The inverter is small and light, but you still need a battery.
An Inverter Generator otoh, is basically a generator which internally converts the AC it produces into DC, and then Inverts it back into a much cleaner AC output.
Very versatile, very useful piece of kit around the home. Not prohibitively heavy for lugging around the apiary, and obviously no need to lug a battery around when vaping.
That being said - this guy on youtube supplies the pro vap 220 in the UK and I found his video -
https://www.youtube.com/watch?v=7lWc4wU-9OY
He's using it with a Clarke inverter. It certainly looks like the 600 watt model from the Machine Mart website.
https://www.machinemart.co.uk/p/clarke-ci1200b-600w-power-inverter/
If that was recommended to him, as he says, then that seems a reasonable indication of what you need.
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A bit nerdy, but
very simplified FYI...
Start-up power refers to the huge inrush of current you get momentarily when you start up certain devices eg electric motors, transformers, pumps etc.
Perfectly normal, but often it's multiples of 'continuous current'. If the inverter can't manage that momentary load, it might shut down, or might damage either itself or the load device if it happens once too often. If it's borderline capable, it might reduce the output voltage.
It's not usual to expect the average punter to calculate/know the start-up power/surge power/power factor of a device, so to be very cautious, have the specs in hand and take them to the inverter shop.
Again, our man above seems to be using 600W capacity on advice, to power 250~275W load. Assuming no problems encountered, 1000W would seem to be very comfortable !
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'Pure sine-wave', and 'modified sine-wave', refer to the AC output waveform, a result of the technology that creates that sine wave. 'Pure sine-wave' (~ 90% efficiency iirc) is 'cleaner' power, whereas 'modified sine-wave' (~75% efficiency iirc)
will be less efficient in running motors etc, and yes, it's to be factored in as you did.
Also- standard words of theoretical caution here - 'modified'
may cause overheating and/or damage to sensitive electronics.
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Good luck with the purchase.