Water – How to heat a bathtub when the water heater isn’t doing enough

Without natural gas or propane, your only source of heat is electricity. Electric tankless water heaters would probably require a new circuit to be run. Here's a table of typical power and wire requirements:

http://www.rheem.com/documents/rte-13-tankless-electric-spec-sheet

The smallest unit they recommend for a shower is the RTE13 which takes 13 KW or 54A@240V. This requires #6 wire. If your incoming temp is 40F and desired out temp is 110F, you need 70F of temp rise and the RTE13 will provide 1.27 GPM.

Many people think they want tankless because the mfg tell them tankless is more efficient. There is some truth to this for gas fired water heaters but in the case of electric water heaters, the difference in efficiency is very small.

Years ago I had one of the first high efficiency gas boilers. It supplied an air-handler for heat and a heat exchanger for hot water. Because back then this kind of boiler would breakdown about 2 or 3 times a year, I installed backup electric heat in the air-handler and a backup electric 30 gallon hot water tank.

I plumbed the hot water tanks in parallel with separate valves to both and normally just kept all valves open and the breaker off to the electric tank until needed. It was amazing how the two tanks acted as one with just gravity flow for one tank to heat the other. If I hadn't experienced it for many years I wouldn't believe it could work so well.

If you added a small electric tank, you'd increase the amount of stored hot water to buffer the times of high usage. And you wouldn't even have to run electric to it, but if you did you'd also have electric auxiliary hot water.