check my math for slab heat loss?
Trying to decide between R22 and R33 options of under slab insulation for my workshop. After trying a couple of web based calculators that spat out nonsense numbers, I decided to do it the manual way:
q=U*A*dt
I saw that in several places, so it seems legit.
My numbers:
area = 1800 sq ft = 167 sq m
dt = 14degC (assumed 46degF ground temp at edge of zone 5 and 6)
(Yes, I do plan on maintaining a 22degC or 72degF room temperature in there. It’s likely to become an ADU in the future.)
insulation R22 or R33 (2 vs 3 layers) = 0.256W/m2K or 0.170Wm2K
presumed, average electrical rate = $0.15
cost of insulation $2000 per layer
number of heating days guessed at 180 per year
(I’ve ignored the cooling season; while it may seem like I’ll be losing cooling capacity, the majority of our cooling load is latent heat so extra sensible cooling is at best superfluous, and at worst detrimental)
results
heat loss for 2 layers = 14*167*0.256 = 600W
heat loss for 3 layers = 14*167*0.170 = 400W
difference = 200W
annualized savings = 200W * 24 hours * 180 days = 864kWh
heating with a mini-split effectively drops that by at least half, to say 400kWh
cost of 400kWh = $60
simple payback = $2000 / $60/yr = 33 years
Does that appear to be correct?
The big variable is the cost of electricity, which could be wildly different. I’m probably on the high side, given that a pretty big chunk of heating will probably occur during off-peak hours. Moneywise it doesn’t appear to make any sense. Is there any argument for comfort?
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Replies
I think you’ll never notice a difference. Insulation can be a terrible investment past pretty low levels.
The math checks out.
You may even be overstating the savings, ground is notoriously hard to model. The question is whether the soil down there will stay at 47F, or over time, as the house above is kept at a steady 72F, will the ground warm up? There's reason to believe that might happen but it's something that you really can't model.
I think framing it as "will it stay at 47F" is beginning with a false premise. Without the building there, the ground isn't going to be 47F. It's going to be more like 20F. Deeper down it's 47F, and that pretty much sets the ceiling for how warm it can get, ignoring active heating from the building. Sure, the heat you put into the building is going to warm up the soil somewhat, but you've already paid for that heat. You're not getting it back, it's going to spread out into the virtually infinite heat sink of soil around it.
I probably was overestimating the savings, and even at that I can see it's not worth it.
It might be 20F in winter, but in summer it would be close to the average air temperature. 47F is just the average annual air temperature. With a building protecting the soil from cold air, the soil under the center of the space will eventually be close to room temperature and relatively consistent year-round. Near the edges of the building, the soil will track more closely with air temperature.
A 33 year simple payback is pretty long, a 3% simple ROI. It's not as bad as some ROIs, such as for replacement windows, but not the best either. I would treat is as a comfort issue; in a house I might consider the higher R-value but for a workshop I would not.
Trevor,
Much of the comfort issues around slabs are due to their high conductivity. Especially in a shop where it is unlikely you will be working in socks, I'm sure there is no difference between the two levels of insulation.
Try the math for R4 for a better ROI.
Walta