Yeah, I do Ground Source Heat Pump calculations too. All Air Source Heat Pumps such as those on these water heaters require a large volume of constantly heated air that above their ‘Balance Point’. Because of such a small fan on the water heaters the balance point is pretty high at 50-60, but you don’t want it to operate at the balance point, it’s least efficient there as at that point it’s COP 1 or at 100% parity to resistance heat. You would want a heat source that is hotter to get the rated efficiency otherwise the compressor runs progressively harder to extract enough heat.

1kw = 3412 BTU, it takes 1 BTU to raise 1lb of water 1° F, 1 gallon of water roughly weights 8.33lbs. So, 8.33x50Gallons = 416.5 lbs of water x 73° rise to get to 120°F tap temp = 30404.5 BTU / 3412 BTU = 8.9kW input total the interval depends on the wattage rating of the water heater and usually is presented as a recovery time. But 30404.5 BTU needed, that is a lot of heat. Ground source heat pumps require acres and acres of tubing to collect that much heat and their COP is very high at like a 5 or more, water heaters are only a 2.2ish. So the house’s basement would have to be hundreds of feet deep or have a large footprint to collect that much heat or loose 30404.5 BTU on a consistent basis to be totally free of the water heater using the resistance coil. Unless the heat comes from the atmosphere outdoors it’s costing you something, somewhere to move into your space. Newer, REScheck compliant houses loose around 21000 BTU per hour, so at 30404 to totally negate the need for the water heater to not use the ‘backup’ resistance coil. Your furnace would be chugging hard produce those BTU’s and that energy use issn’t required to be on the Energy Star label and is what is costing you money in whatever fuel source it uses.