Looking at your math someone told me it requires 4000 BTU of heat per 100 square foot is that wrong?
Which would equate to almost 400000 BTU’s that did seem crazy though in. 2000 sq for home.
The volume or floor area have nothing to do with heat loss.
Heat loss is primarily a function of the area of the exterior surfaces of the house, the temperature difference from indoors to outdoors, and the R-value of the different surface types (eg: code-min low-E windows are about U0.35. R=1/U and U= 1/R, so you're looking at R2.9 for the windows, whereas a 2x4/R13 wall comes in at about U0.08-U0.01, or R10-ish after factoring in the thermal bridging of the framing, and adding in the R-values of the wallboard siding, sheathing.) The basic formula is:
U-factor x surface area x temperature difference= BTU/hour
For the interior design temperature 68F is code minimum, but people often use 70F. For an outside design temperature it's best to use the 99th percentile temperature bin for the local weather history, referred to as the "
99% outside design temperature". Of the 8760 hours in a year, only 1% of all hours (about 88 hours) are colder than the 99th percentile bin. Some will use the 99.6th percentile bin, which is a few degrees colder, but there are only 35 hours out of a year that are cooler than that. In NC the 99% outside design temps range from about 15F in some of the mountainous areas, to the high 20s along the coast. If your 99% outside design temperature is, say 23F and you're designing to 68F indoors, that's a 45F temperature difference, and that what you would use for a temperature difference in the heat-loss formula.
All surface types (roof, walls, doors, windows foundations etc) all have different U-factors, so those areas all all measured up and applied separately, on a room-by-room basis. The ceiling under a heated space doesn't have a heat loss, nor does a floor over a heated (or at least insulated and enclosed space like a basement that stays over 60F even without directly heating it.)
Air infiltration is another factor that needs consideration, and is hard to estimate accurately. The cubic feet per hour and thermal mass of air by volume and temperature difference math is the same as in the hot-air heating example above, only you're using the design temperature difference and a WAG on the actual air leakage (most software grossly overestimates infiltration losses on newer tighter houses.)
Then, start subtracting off all of the internal heat sources, such as the 24/7 plug loads such as refrigerators, DVRs & cable boxes, etc. and subtract off 230BTU/hr per sleeping human.
More can be found
here.
Even though heat loss is not a function of floor area, at a temperature difference of 45 degrees most
tight 2x4 framed houses with R38 in the attic will have a load/area ratio of between 10-15 BTU/hr, and 2x6/R19-ish houses would come in around 8-11 BTU/hr per square foot of conditioned floor area. So for a 2000 square foot house expect the load numbers to come in at about 20,000 BTU/hr @ +23F outdoors, 68F indoors give or take 3000 BTU/hr. Even pretty crummy 2-ton heat pumps have that much capacity, ergo the mystery of why FOUR tons of heat pump can't keep up in your house without engaging the heat strips. Something is really
wrong with either the system design/duct layout, or the refrigerant charge on the heat pumps, or the house is just plain leakier than you think it is (or all of the above.) But using a BTU/hr per square foot of conditioned space is a truly lousy way to estimate heat load, with room-by-room exceptions to the average that can be well over 2x the average.
The labeled heating efficiency of heat pumps is expressed as HSPF (heating season performance factor), the units of which are BTUs per watt-hour (x 1000= BTU /kwh.) The lowest legal HSPF efficiency for heat pumps of a decade ago was about 7, or 7000 BTU/kwh. Best in-class newer cold climate ductless heat pumps can deliver twice that much. Oversizing the heat pumps gives more capacity at cooler temps, but reduces the as-used efficiency due to excessive cycling during periods of low to moderate heat load. It takes about 8-10 minutes of run time for the heat pump to hit it's steady state efficiency for the real time indoor & outdoor conditions, and if it's satisfying the thermostat in 15 minutes, most of the run time was at lower efficiency. Every spin-up of the compressor uses some amount of power that you never really get back, so the total number of cycles as well as the duty-cycle matter.
To compare costs, use the nameplate HSPF on the heat pumps and your local electric rates to come up with the cost of what it takes to put a million BTUs (MMBTU) into the house. A condensing boiler like the NCB 240 delivers about 87,000 BTU/gallon of propane into the house, so it takes ~11.5 gallons per MMBTU, then multiply by the price/gallon to come up with $$/MMBTU. Even in high priced electricity markets it's usually cheaper to go with heat pumps than propane. And if the efficiency problem is the duct design and air leakage, using the same system for heating would suffer the same efficiency losses with hydro-air propane as it does with the heat pumps.
Outdoor wood boiler can definitely deliver the heat, and can often be cheap to operate where scrap wood is cheap/free, but the are a very substantial local air pollution source, much more so than EPS rated wood stoves. To minimize the pollution with a wood boiler requires loading up only enough fuel so that it will burn completely before the boiler's temperature limits are reached, which requires either a lot of smaller loads/burns, or a large buffer tank of water for thermal mass to keep the temperature from being reached quickly.
Don't just dive into a hydro-air design project until you calculate the heat loads, and figure out why the heat pumps aren't keeping up, have verified the air tightness of the house, the ducts, and the balance of the duct design, or you'll end up where you started. A 2-tube hand held manometer with 0.01 water inches resolution can be had for $50-150, and can be used to track down room-to-room pressure differences, and room to outdoor pressure differences. An Energy Star house would have pressure deltas no greater than 0.012", but for retrofit fixing getting to at least under 0.03" would be a good starting point. This may require a lot of duct-boot sealing and creating bigger return paths for doored off rooms that have only supply ducts, but it's usually possible to get to reasonable balance without tearing the whole house apart.
For using a NCB240 or wood boiler for supplementary heat or even as a standalone system it's better to just skip the highly suspect ducts and install heat emitters in all the rooms you care about. Fin-tube baseboard is pretty cheap, and if you calculate the room by room heat loads, if you use a ratio of 350BTU /hr of design load for every foot of running baseboard you would be able to run in condensing mode most of the time, and set the outdoor reset curves (which adjusts the water temp at the boiler in response to outdoor temperature) to ensure that is going to work. The minimum burn rate of the NCB240 is about 17,000 BTU/hr, and it'll deliver 95% efficiency when the boiler output is about 125F, a temperature at which fin tube baseboard is delivering about 200 BTU/hr per linear foot. To keep it from short-cycling itself into lower efficiency/higher maintenance it's best to install at least 17,000/200= 85 feet of baseboard per zone. You can cheat that a bit, but if you go too far it will be doing 10+ ignition cycles per hour, with burn times measured in 10s of seconds, all of which is lousy for system efficiency and the longevity of the boiler.
