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I gave this some further thought overnight and I reckon you could build a heat store that you then store your water in or over. The theory is a heat absorbent surface, ie a solar panel that passes warmed air through a substrate such as pumice which has a high surface area and is therefore absorbent. The heat is then released by means of vents. This will depend on the amount of radiant heat you get in your chosen location, but assuming it is cold but clear and not grey and cloudy (like gloomy old Devon)then you should be on to a winner.
I can’t think where you would get plans for this idea but there must be info on the net somewhere as the idea is not a new one. In fact it isn’t that far removed from the Roman underfloor heating system, the difference being you use solar radiation instead of a couple of slaves feeding a fire.
If you maintain a temperature of just above freezing then the water will stay liquid. It takes a sustained period of cold to start the icing process, however once ice crystals have formed then you are in trouble as the whole process is speeded up. This is why you need to protect all parts of the system, pipework, pumps, inlets etc.
The best policy is to store larger amounts of water as the heat exchange required to lower to freezing point is greater and so the process will take longer your water will stay wet through all but the longest coldest spells. Again it shouldn’t be too difficult to do some basic maths to calculate the volume of water and the heat used etc. I am no mathematician so can’t help here but any keen physicist at your local university should have the ability to work this out, it is all known physics as water is the basis of a lot of known data for temperature calculation. Hence why zero Celsius is freezing point.
It would probably pay to have a separate tank over the main tank that acts as a filling reservoir so the cold incoming water is separated from the main store until it is heated (superficially) to the ambient temperature in the store. This system is the same as in a Fortic tank used in some central heating systems. If the incoming supply is particularly cold it could be possible to pass it through a heating jacket or an old radiator that would use solar heat to raise the temperature to a suitable level. Again a bit of maths is what you need here.
Anyway, I hope this assists you in thinking your problem through. Good luck, Love & Light, Phil.
Oh and as a bit of data regards volumes of water gathered from rain. I live in Devon England and we have regular winter rainfall and some summer rains . I gather my water from a 81m square roof (9×9) filter it to 0.25mm through a Wisy vertical filter (which i could show you how to make one, I paid over £100 for mine….pah, live & learn).
The water is allowed to settle in a 1500l tank then pumped to 2x1500l tanks using a swimming pool pump run from battery/solar/inverter and controlled by a relay and float level system that my friend made for me ( a NAND gate I think).
I never drop far below a total of 3000 litres and I use a washing machine and flush toilet. I am very conservative with water use and at the moment I have no shower and instead wash from a bucket, but this is only a temporary arrangement. However 2 gallons (10litres) is adequate for a shower and you really don’t need to shower every day unless it is hot and you are dirty. As for dish washing, well those machines are a pointless piece of junk for lazy people seeing as I can wash all my plates, pots and cutlery in three bowls of water in less than half an hour. Hey stop me here I’m ranting……..