1) Good HVAC designers don't "estimate" loads - we calculate them. Two ways do do this: Either pay a competent HVAC designer to run the calculations or for $50 download Don Sleeth's HVAC calc software - its a $400 package but for $50 you get a 30 day license tailored for homeowners. The process is a bit tedious - need size and energy specifications for every door, window, exterior wall, ceiling, etc. Doing it yourself lets you experiment with different construction choices and determine the impact on load.
Getting someone to do it is not easy - many, if not most 'typical' HVAC contractors can't or won't do them, preferring instead to rely on antiquated rules of thumb for sizing that nearly always result in mis-sized, underducted , uncomfortable, and / or inefficient systems.
The calculations, in order, are:
Manual J - whole building heating and cooling loads
Manual D - loads for each room / zone - necessary to determine required airflows and thus duct sizes
Manual S - matches systems to load AND local conditions - tonnage ratings are nominal only and vary widely in actual application.
2) Drilling and system installation costs are highly localized. Critical to your quest will be locating a competent, experienced local installer. Start at the IGSHPA website. Make sure any perspective installer has happy homeowners as references. You do NOT want to be serial number one for a newcomer in this field unless you have enough electrical, HVAC, and plumbing knowledge and experience to materially participate in the project.
3) Vertical vs horizontal loops - this refers to orientation of tubing in closed loop systems. Vertical typically involves several boreholes each hundreds of feet deep. Advantages are access to more even deep earth temperatures (higher efficiency results), relatively little disruption of surface land (don't have to dig up whole yard). Disadvantage - cost of vertical well drilling likely higher than horizontal trenching.
Horizontal - long trenches are dug and plastic tubing is placed in the trenches either in several parallel paths or in 'slinky' format. Ground temps aren't as favorable near the surface, and tears up a bunch of land - gotta consider driveways, other buried utilities, septic drainfields, etc. Horizontal systems are generally cheaper to install since trenching is much creaper than vertical well drilling.
4) Infloor radiant will almost certainly be more expensive up front - Forced air can handle both heating and cooling, infloor radiant does heating only. (In theory, infloor tubing can cool as well, but this is tricky and not for the faint of heart). From what I understand, nothing beats the comfort of infloor radiant heating, and it can be more efficient than forced air - lower heating temperatures needed can increase system efficiency, though I doubt the savings would ever amortize the increased cost of infloor.
Lastly, if you surf here you'll note enthusiastic advocates for certain types of systems - I'm not going down that road here, other than to reiterate that everything depends on a competent local installer. If you are A) actually serious about doing this and B) gifted with multiple competent installers in your area, each with different design ideas and proposals, come on back with their specifics and we'll help you choose...
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