Had a look around 12v and some 12v/240v systems they all seem to have a 10-15lt capacity and want a16-20a, 200w I imagine at 12v/200W it would be a bit of a draw to get it cooking probably a hour or more, a 240/1000W kettle takes long enough for just 1.5 lts, so certainly need heaps of storage or good sunshine ................................
Thankfully someone elsewhere did some maths and came up with this result ......................
QUOTE"
Using the Duoetto 10l unit it takes 2hr 15 mins to heat the water from 15C to 70C using 25A @ 12v therefore 56.75Ah. If you use 5l of that water then you will use approximately another 28.4Ah or 5.675Ah for every litre of hot water that you use. UNQUOTE"
Bit expensive on the battery I would think and if you used it a couple of times a day it you would certainly need a high recovery rate for the batteries, of course the time needed has so many variables, with temperature, cable loss its all ball park figures but still a lot of power and you wuldn't want to be using it a few times a day, 10lt isn't a great amount of water.... certainly a quick bird bath shower......... Possibly could be made into a portable unit , make a nice box for it, just need to be close to battery with direct connection with some 4 B&S cables for sure, short as possible ideally, tap into van water pump and lines ....
I haven't checked the figures but probably close, had a 12v kettle once in my truck, would hold 2 cups and even on 24v took ages to get to boil and had to keep the truck running or not enough juice in battery to start .if the water was cold .............
I reckon something like the Joocla Hot Tap Nomads kit is the way to go myself. .... portable but could be fixed, instant HW and is plug an play ........... not overly expensive ...... Im tempted to get one myself.................................
https://www.joolca.com.au/products/hottap-v2?variant=45054183702705