I think you are going to have to consider yourself a pioneer here and do your own testing. Even in the RV/camper world, recirculating showers are quite rare, probably because of filtering complexities. Folks just tend to accept either the navy shower or the large tanks or the frequent fill up.
OTOH, I don’t see why your question cannot be addressed by folk who don’t recirculate. You need to heat a couple gallons of water. It doesn’t matter whether you navy shower with it or recirculate it for a longer shower.
Heating one gallon of water by 1 degree F requires 2.42 Wh. Plug in the specs of your heat source, and you should be able to calculate time required, which will obviously vary with the starting temperature of the water.
I know many people in the van world. I don’t know anybody who heats water with 12V. If you have access to AC where you stop, a Sous Vide functions as a convenient, compact, efficient temperature-controlled electric heating element. On average, it takes me about 15-20 minutes to heat 2.5 gallons to our preferred 105°.
OTOH, I don’t see why your question cannot be addressed by folk who don’t recirculate. You need to heat a couple gallons of water. It doesn’t matter whether you navy shower with it or recirculate it for a longer shower.
Heating one gallon of water by 1 degree F requires 2.42 Wh. Plug in the specs of your heat source, and you should be able to calculate time required, which will obviously vary with the starting temperature of the water.
I know many people in the van world. I don’t know anybody who heats water with 12V. If you have access to AC where you stop, a Sous Vide functions as a convenient, compact, efficient temperature-controlled electric heating element. On average, it takes me about 15-20 minutes to heat 2.5 gallons to our preferred 105°.