What, I'm not allowed typos?
Make that 60F-9F= 51F in 'merican math...
If you use base 65F it gives you a lower constant, but 5 more heating degrees, call it 56F heating degrees between the outside design temp and the heating/cooling balance. Using the higher heating degree base results in a lower implied heat load overall, and we're trying to find a reasonable estimate of the upper bound of what it really is.
If you use overnight setbacks the average room temp is lower, and the heat load lower, which also shifts the heating/cooling balance point lower. Also, in post 1990 homes base 60F is closer to reality as the heating/cooling balance point for most houses. Base 65F was a reasonable model for 1950s houses with 2x4 framing, R13-R20 in the attic and clear-glass storm windows. Base 60F is closer to the mean for house built with 2x6/R19 and U0.35 low-E windows (or U0.50 sealed clear glass double-panes), and R30-R38 in the attic.
The reason you do the math on the mid-winter big bills rather than the whole year or some other random month is that the error introduces by other burners becomes much smaller. If you did the same math on your May or June bill you'd be off by quite a bit. Solar heat gain also introduces an error in the other direction, offsetting the other-appliances' fuel-use error, and the solar gain in winter is much smaller than the spring/fall seasons, which also reduces the magnitude of the error. For the January/February bills your space heating use it BY FAR the elephant in the fuel-use menagerie- the others are all mouse or kitten sized uses. Hot water use is usually the second biggest but you use the dryer & hot water in summer too- the 11 therms in July is a single digit percentage of the 278 therms on the February bill. In practical terms the solar gain & other uses error ends up being in the statistical noise. The exact time of day of the meter reading can introduce an error that big, but all of those factors don't add up to 10% of the calculated load number.
For Pembroke +10F for is about right for the 99th percentile temperature bin- close enough to the real design temp for sizing a boiler. That makes it 50F heating degrees.
The 278 therms burned over 29 days (696 hours) is 39,942 BTU/hr average input, and at 80.4% efficiency is indeed 32,114 BTU/hr out at an average temp of +16.4F. Assuming a balance point of 60F that's (60F - 16.4F= ) 43.6 heating degrees, and a constant of 32,114/43.6= 737 BTU/degree-hour. For a design temp of +10F, or 50F heating degrees, the implied load is then 36,850 BTU/hr
If one assume a balance point base of 65F, an average temp of 16.4F is then 48.6 heating degrees, and a constant of 32,114/48.6= 661 BTU/degree-hour. The design temp of +1oF it's 55F heating degrees below the base temp, for an implied load of 661BTU/degree-hour x 55F= 36, 355 BTU/hr.
That's about 500BTU/hr below the implied temp when using base 60F, but still the same ball park. The heat output of two sleeping humans is about 500 BTU/hr. But really, the heat load on the boiler is about 36-37K, not the contractors' calculated 50K- 58K. If you project down to -10F for 70F heating degrees (base 60F), the heat load at -10F is 70F x 737 BTU/degree-hour- 51,590 BTU/hr finally hitting the range of their calculated numbers at
much higher temps. While it might hit -10F during a Polar Vortex event in Pembroke, it might not be that low again within the lifecycle of a boiler, and even with a 50K-in/45K-out boiler you still wouldn't get very cold at -10F- the 6590 BTU/hr shortfall at 5AM on the coldest day of the decade is only about 2000 watts- a single 1800 Watt space heater and leaving the TV and a few lights on (or firing up the gas fireplace) would cover the difference if you really needed to.
Now, regarding the min-fire output an short cycling on zone calls...
Fin tube
baseboard puts out about 550-600 BTU/hr per running foot an an average water temp of 180F. But to get condensing efficiency out of a condensing boilers requires that the water entering the boiler be 125F or lower, otherwise the heat exchanger will be above the dew point of the gas exhaust gas and any condensation will be in the flue, where it won't be transfering heat into the heating system. In practical terms an average water temp of 120F or lower is required to get you into the mid-90s or higher, which means a boiler output temp of 125F or lower. At an average temp of 120F fin tube baseboard only emits about 200 BTU/hr per running foot. So at condensing temps your zone radiation can only emit:
1st Floor: 81 feet x 200 BTU/hr = 16,200 BTU/hr
2nd Floor: 67 feet x 200 BTU/hr= 13,400 BTU/hr
Basement: 19 feet x 200 BTU/hr= 3800 BTU/hr
Note, the output of the fin-tube of your first & second floors 29,600 BTU/hr which is about 80% of your design temp load, so if you tweak in the temperature settings you will be able to get condensing efficiency nearly all of the time, and you can actually hit the 95% as-used AFUE range.
The basement zone calling for heat on it's own is going to short cycle on zone calls with any of those boilers since it's emittance is a small fraction of the min-fire output. But it's probably used much less often so it's not going to impact you average efficiency or the boiler's life, if you size the boiler such that calls for heat from the other zones are very long, all but guaranteeing that a call for heat from the basement zone will overlap with a call from one or more of the other zones.
A boiler with a min-fire output of 15,000 BTU/hr or less will do OK (note, that's
not the ALP-105, but the ALP-080 is). Something with an even lower minimum firing rate would be even better. The GWM-0751IE has an output of about 14K, but the GWM-050IE's output is about 9.5K, and would be MUCH better matched to your radiation, since it'll modulate rather than cycle on/off. It's good for 46K out at max fire, which is well above your design heat load, but will start losing ground a bit when temps drop below 0F. It'll work, but not with much margin.
Something like the
HTP EFT-55 would be a better fit, since it can deliver over 50K at full bore, giving you some sub-zero margin, and has a min-fire output of about 12K, which gives it some modulating room in the condensing temperature range with your radiation. Another good fit is the
Lochinvar WH-055 , which delivers ~52K at high-fire, but modulates down to ~10K. Push back on your Lochinvar guy- see if he'll quote you on the WH-055, and call HTP and get them to recommend a local contractor who installs Elite series boilers. Either one of those are pretty much a slam-dunk for your load and radiation parameters. DON'T let anybody talk you into a bigger boiler than that- you have your gas fireplace as auxilliary backup for temps below the 99% outside design temp, and The EFT-55 or WH-055 output specs slightly exceed even your contractor's Manual-J load calc @ +9F, which is good enough.
You can run the fuel use/load numbers on a few other winter-month billing periods too. Most of them should be in the same ball-park, but there will be variances attributable to hot water & dryer use in a family of four. Unless you were actually not heating the place, that biggest-use bill is going to be the best model of your actual heat load, and it's probably still slightly higher than reality. Your existing boiler is almost 3x oversized for the load, leading to cycling losses and overheating the boiler-room type efficiency hits. With a right-sized condensing boiler the boiler room will no longer be the warmest place in the house, and that's a GOOD thing.
