No need to be condescending, here are my "armchair calculations"
Spacing of holes gives you thermal capacity, surface area gives you thermal conductivity.
1" pipe has an outside diameter of 1.3"
1/2" pipe 0.84", so a 1/2" pipe loop has 29% greater surface area.
Cast iron has a thermal conductivity of 55 W/m K
Polyethylene pipe 0.5
Modelling conductivity of dirt is vary difficult, a static number for wet clay soil is about 1.5
Either way, the 200' per ton is a vary inaccurate estimate.
Keep in mind, I was thinking 640' of pipe for 3 ton would work, but it's pretty easy to measure inlet and outlet temp on the heat pump and decide if you need more.
A pump and dump system is definitely more efficient, cheaper, and easier to install. Unfortunately the property doesn't already have a well (municipal water).
We haven't yet decided if we're going to live here long term, or sell it in a few years (if say I need a bigger shop). So I wanted the system to be more idiot proof, needing to descale the heat exchange every fall isn't something that helps sell a house. But I don't mind doing it for myself.
But a better option might be to just convert the heat pump to air source as an AC only system before selling. I would be keeping the natural gas furnace as the auxiliary anyway.
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