Using heat-loss-transmission from formulas and R-values of Materials for constant i came to this:
The heat transmission through a building wall or similar construction can be expressed as:
Ht = U A dt (1)
Ht = heat loss (Btu/hr, W)
U = "U-value" (Btu/hr ft2 oF, W/m2K)
A = wall area (ft2, m2)
dt = temperature difference (oF, K)
The U-value of a construction consisting of several layers can be expressed as
U = 1 / ∑ R (2)
U = Heat Transfer Coefficient (Btu/hr ft2 oF, W/m2K)
R = "R-value" - the resistance to heat flow in each layer (hr sq.ft oF/Btu, m2K/W)
R-values of common building materials
Gypsum Wallboard .6-.9
Fiberglass batts 3.1-3.3
Blown in fiberglass 2.2-4.1
Blown in cellulose 3.5-3.7
Polystyrene Board 3.7-4.2
Polyurethane Board 4.5-5.5
Polyiso board 5.5-7
Spray Polyurethane 4-6.3
So for my case without extra insulation U value would be:
1 / (1 * 1 + 5 * 3 + 1 * 1) = 0.059 (note that im converting cm to inches beacuse of table, 1 inch = 2.5 cm, took 1 for wood and 3 for fiberglass batts)
If I add extra 20cm of fiberglass wool:
1 / (1 * 1 + 5 * 3 + 1 * 1 + 8 * 3) = 0.024
With only 10cm of fiberglass wool:
1 / (1 * 1 + 5 * 3 + 1 * 1 + 4 * 3) = 0.034
My windows have U about 0.8, but I must consider much bigger area of the roof and much larger temperature difference there because tin will get much hotter during warm summer day. Lets look at UA for windows 0.8 * 15 = 12, for roof 0.059 * 40 = 2.4. If roof was warm as air than we would have no problem, question is can the temperature difference on roof surface be 5 times bigger than the one around windows? I think that this if this can happen sometimes, lets say my house is 22, air is 25 but roof heats to 40.
Conclusion, i will go for extra 20cm below the roof because wool is not so expensive, and then I will loose/gain more heat on windows than on the roof for sure. I think that 10cm would be also enough but this should also improve sound insulation a bit. But this extra layer has biggest impact only when roof is hot, in the winter i will lose 5 times more heat through windows than roof even if i don't add nothing. So cutting U for roof for half can decrease my bill maybe for 10%. I can't tell for sure but this could repay investment in year or two but only because i'm reconstructing drywall ceiling anyway. Otherwise it would repay in decades. I will try to match wall UA close to roof UA.
But I am not expert in construction, did I do the math and all conclusions right here??
Can someone with experience confirm this please??? If this is correct it will be much easier to decide where to invest more money in future.
Here is one sample example where U is similar for roof, but it has 0.3 for windows??
These are some better windows than mine or i have wrong number for mine windows.I have also forgot on floor looses.