RamlinChet, John R, et. al,
Completing the corrected calc above for required Ah from the battery:
One gallon of water from 40° F to 110° F would require 583 BTU.
1 BTU equals 0.000293 KWh. 1 KWh at 12.8 v equals 78.125 Ah
So 583 BTU equals 0.17089 KWh and 0.17089 Kwh equals 13.351 Ah at 12.8 v.
Therefore to heat 5 gal of water 70 deg F requires 66.754 Ah of battery (or solar) power.
Note there is no time factor in these calcs except for Ah. So in order to calculate the amps needed to heat 1 gal of water in one minute we need to multiply Amp hours by 60 to get amps per minute.
The result is 13.351*60 = 801.46 Amp*min. You are not going to be able to provide that much current without melting wires.
6 gauge wire can handle about 55 amps. So the fastest you could heat 1 gal 70 F using 12.8 V with 6 gage wire is about 805 A*min/55 A = 14.64 minutes if I did the calculations correctly.
That is not fast enough for a tankless shower.
So as has already been concluded using a 12 v system to power a tankless water heater unit for showering is not going to work in practical terms.
I suppose with a large enough battery bank and an appropriately sized inverter it would be possible to use a 120v tankless shower in a camper (RV or boat). However, the efficiency of the electrical conversion is only around 50%.
0.17089 Kwh at 120 v equals 1.424 Ah or about 85 Amin
Factoring in the electrical conversion gives 1.5*85 Amin = 128 Amin
As a check I looked up electric tankless units and I find that "the average electric tankless water heater needs at least 120 amps to operate".
If the heating was cut back to say 1/2 gal per min the current required would drop to about 60 amp which may be feasible using 4 ga wire.
One gallon of propane provides about 91,500 BTU = 27 KWh of electricity. It is hugely more efficient to heat water with it.
Diesel has a higher energy density than propane and (ignoring smell and other reasons people don't like diesel) it is a more efficient fuel for heating. Indeed, 1 gallon of diesel produces about 137,381 BTU = 40.26 KWh.
It appears to this is why all the water heaters use diesel or propane.
Edited by ckent323, 27 November 2021 - 08:39 PM.