I donít know. Have spent several seasons in tropics. Seems we use a lot of hot water. Use it to wash greasy dishes. When showering in the morning or evening like water temperature the same as body temperature. Tank water is colder. After diving get cold so a hot shower is nice.
Also think never have enough electricity because always can use extra fresh water. If tanks are full itís time to turn on the TV or computer or charge all the devices.
Guess for me and I think most this whole discussion seems off target.
Know Iím not a full time live aboard but Iím am 7-8/12 month one. Only times Iíve had ďspareĒ power to think about doing this is the rare windy and sunny days when I donít have another need or desire. Would look forward to comments from others if they are in the same boat😀.
We spend all of our time in the tropics and can relate our experience for comparison. We have 700W of solar lying flat on the hardtop. We used to have FLA batteries, but installed lithium batteries 1.5yrs ago. We consume ~150Ah/day at anchor and ~250Ah/day on passage. With the FLA batteries, the solar got them back to 100% SOC every day at anchor if it was greater than 50% sunny. In accomplishing this, only ~150-200W of solar was available as excess during the afternoon absorption tail-off charging.
December and January are the tough months if above ~18N because of shortened daylight. Closer to the equator, it is 12hrs of daylight year round. In the Bahamas, with full sun every day in Dec/Jan, we would struggle to get the FLA bank to 100% SOC, with no solar to spare. In the summer above 18N, we had lots of excess solar and could easily heat water with it through a tank element. At the equator (where heat works against solar), it averaged as above - 150W or so to spare. Not much.
Lithium batteries completely changed everything. First, they never need to be fully charged, and are more happy operating in partial discharge states, so there is no pressing need to get them back to full charge regularly. One can use electricity for other things instead of charging any time one wants.
Second, in charging by solar, they act like an additional panel was added. Two things responsible for this - they take all the charge the panels give with no absorption tail-down, so the efficiency is almost 100%, and second, they charge a full volt lower than FLA, which allows an MPPT controller to turn that spare voltage into amperage - another 10-15% jump in output.
700W of solar has now gone from just meeting our needs to more than we need. We now run our AC powered watermaker off the inverter/batteries, as well as our 1500W water heater. The AC power on the boat is left on all of the time, with the device chargers always sucking from it. The generator hardly ever gets used anymore - only if several contiguous full rainy days.
BTW, Outbound, consider using an electric kettle instead of your water heater tank for hot dish water. We recently got one ($20 Walmart). It heats 1.5L of water to boiling in ~2 minutes, and only consumes 5Ah of battery (through the inverter) in doing so.
Getting back to the thread title, it is possible to regularly have hot water with minimal excess solar, if the system is managed well. If the hot water tank is well-insulated, and heated to temp by motoring or otherwise, then all one needs is to replace the smaller amount of heat that is lost through the insulation, as well as the smaller amount of new water that is brought in during use. Not the entire 6 gallons from cold every day. Just a bit of excess solar makes this possible, assuming one does not use the full 6 gal tank every day.