# Optimize insulation cost / benefit

I have roof made by scheme from images. Both should be same, just different angle. I have 20cm of space yet to fill. How can I calculate conductivity in W/m2K if i fill missing 20cm of space with 20cm of mineral wool or if i fill just 10cm and leave 10cm of air. I would like to know this because i want to know heat loss ratios between walls, roof and windows to rationally spend same amount of money to get best insulation for my house. Maybe ill leave this empty and buy better windows, or maybe take thicker insulation for walls. Notice that some insulation already exists, 12 cm of glass wool and 2 x 2.5cm of wood. My question is about remaining 20 cm of space.

[Update] Several facts that matter here, this object is in Croatia, see temperature graph below. It will serve for 4-seasonal living, insulation required to keep heating bill lover in winter and to prevent heating during summer when temperatures can be sometimes 35-40 Celsius.

Where are you located and is this for a 4-season living space?

You want to insulate your ceiling to keep the warmth in (if in a climate with a heating season) or keep the heat out (if in a climate with a longer cooling season). Assuming you are in a region where you need to heat your house.

You will lose more heat through an uninsulated ceiling than you could ever recover through better wall insulation or better windows.

Make sure you extend your insulation over the exterior walls to the edge, otherwise you will lose a lot of heat through the corners at the exterior wall.

• I have update missing info in question. Notice that ceiling is already insulated with several layers, my question is about remaining 20cm which can be empty or isolated or partially isolated. As roof is of tin, although it is ventilated, you can expect high temperature there during warm summer day. – watbywbarif Jan 11 '15 at 17:56

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)

where

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)

where

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
Material    R/inch
Masonry/Stone/Brick/Glass   .1-.3
Wood    .9-1.3
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.

• As far as I know U depends on humidity so I guess you need to take that into account. I'm not an expert though but have read that in a book by Jerzy Zembrowski (bdb.com.pl). – Marcin Zawiejski Feb 20 at 9:28