Problem is if you are using Michigan 45F input water, it will only heat a small amount of water to 105F. If you are camped in Florida with 65F or 75F water, then it can heat a lot of water and take a decent shower.
With 45F water, then less than 1 gallon per minute flowrate, as you increase flow, it will get cooler. WWorking from a water pump is even more difficult, say it is to warm, you must increase the flow rate or try to add some cold water. If to warm, you must slow the flow rate, so that the 45F water spends more time in the heater to reach 105F. If you slow the water to slow (on the pump) it will perhaps overheat or the pump will cycle off or something, and you will get cold water for a few seconds.
You are much better off using a regular 6 gallon tank. You could also use a electric option, increasing the BTU input a little bit while plugged in at a campground.
That said, I did buy a L5 tankless water heater. It hooks up to my garden hose, and I used it to warm he water going into my 100 gallon fresh water tank, in the winter. I would have 45 - 50F water, and at best might gget a 3-4 minute shower. By warming the water to 85F, and pumping from the fresh water tank (I have a 5.7 GPM Variable speed pump) I could take a 15 minute shower with the 6 gallon hot water tank.
The L5 is a portable water heater, I hung it from my steel bike rack, next to my fresh water filler. It is 39,000 Btu's per hour. So it can heat 5 liters per minute by about 60F (or 45 - 105F). (1.25 gallons per minute). It was only $120 or so at Amazon.com
They also sell a L10, rated around 60,000 Btu's per hour for about $200. The RV water heaters - I do not know what BTU the tankless is, and if it is variable gas input or not.
The normal 6 gallon tank that I have is 8,800 Btu's per hour. 10 gallon models are closer to 10,000 Btu's per hour. Most will have a 800 watt electric heat option - about 2,800 Btu's per hour. You can run both at the same time when you have the electric option.
Many conserve water while showering by lathering up, then shut off the shower water at the valve in the handle. This allows the heater to warm the water further, while you use the washcloth. Then they rinse. It is a more effective way to shower with less water. So called 'Navy Shower' because fresh water is a limited while out at sea. It also conserves space in the grey tanks too.
While dry camping, I normally will transfer some shower water from my tub into the nearby toilet. This is because for whatever reason, I have a 42 gallon grey tank and 59 gallon black tank. Fresh is 100 gallons. I use a dishpan that is almost as wide as my tub, and I can quickly transfer all but 1" of the water in 3 scoops. Or with just a shower pan, standing in a dishpan you might collect say 1/4 the water?
Also if you do dishes in a dishpan, you can toss that out on the grass, just like all the tent campers do.
Have fun camping!
Fred.
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Porsche or Country Coach!
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