Calculating and deciding on thermal insulation for an energy-efficient house

We have talked in the previous article about the basics of building energy efficient houses.
Today I wanted to get deeper in science and try to make you understand why a huge part of future savings could come from a very efficient insulation system. Or as my father says: "A house should be a habitation machine".

Let's talk a little about heat loss. We have covered it superficially in the previous article, now I will try to discuss the science behind it, helping to understand why and how much insulation is enough, while still not spending a fortune.

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How can we calculate the heat loss?

The overall heat loss is calculated by adding all the ways in which a house can exchange energy with the environment. Transmission through walls, windows and doors, but also through floor, roof and through ventilation or infiltration. If you want to skip the definition, you can jump straight to the comparison of conductivity in common materials. Therefore, the formula is:

H = H_t + H_v+H_i

H is the total energy loss (measured in Watts - W)
H_t is the energy being lost through diffusion through walls, windows, doors and roof (W)
H_v and H_i are the energies lost through ventilation and infiltration, also measured in Watts.

In order to determine the energy lost in transmission through walls, windows, doors and roof, we can calculate:

H_t = A * U (t_i - t₀)

A = surface area being exposed in square meters
U = overall transmission coefficient. This is the most important factor in choosing building materials and insulations. It is measured in (W/m²K - Watts per squared meter multiplied by Kelvin)
t_i and t₀ are the inside and outside air temperatures (in degrees Celsius)

In order to determine the heat loss through roofs, the same calculation is applied, with the mention that in practice there is a coefficient of 1.10 and up to 1.20 of increased radiance in roofs. Another mention is the fact that in determining the heat loss through floors, the t₀ is the temperature of the ground, which is usually warmer than the sample taken at the depth of the foundation in an empty place.

The influence of wall thickness

The heat transmission coefficient drops by the thickness of the wall. So, in practice we would have:

U = 1 / ( 1/ C_i + x₁/k₁ + 1 / C₀)

C_i is the interior wall surface conductance expressed in W/m²K
x is the material's thickness in meters, k is the thermal conductivity
C₀ exterior wall surface conductance.

There is also loss of heat energy by ventilation and infiltration, which is harder to pinpoint and to be measured. We will only focus on the building insulation since is not in the scope of this article to cover habits, but they also play an important part in having an energy efficient house.

Comparison of building materials

I have used the table the engineeringtoolbox to pull out the usual materials and their conductivity levels. They have an impressive list of materials so if you don't find what you seek here, you will find it there. The cost is added by me, I have used informative values as the price will probably vary a little across the world because of regulations, availability and such:

Material	Thermal Conductivity	Price
Brickwork	0.6 - 1.0	Low
AAC	0.25 - 0.3	Low
Thermo Brick	0.15	Low
Cement, mortar	1.73	Low
Concrete	0.4 - 0.7	Low
Silica aerogel	0.02	WOW
Glass wool	0.04	Medium
Polystyrene, expanded	0.03	Low
Polystyrene, extruded	0.035	High
Gypsum board	0.17	Medium
Hardboard	0.15	Medium
Air, atmosphere (gas)	0.0262	Free
Fiberglass	0.04	Medium
Cork	0.07	Medium
Plywood	0.13	Low
Rubber	0.045	High
Tar	0.19	Low
Wood or Timber	0.17	High
Chrome Nickel Steel	16.3	Low
PVC solid	0.19	High
PVC window frames	0.16	High
Aluminium window frames	0.12 - 0.14	High
Wood window frames	0.16	High
Diamond	1000	WOW

Readers! Come back, I can also show it graphically!

So what does the table show us? Aside from the fact that building your walls out of silica aerogel or solid diamonds is not practical in terms of cost, or insulation AND cost ( in the case of diamonds). It shows us the best materials to build with the lowest cost involved.

After not being able to find a copyright free image of a simple wall sandwich, I had to create my own. It's better this way as I can show you the exact layout that I have found to work best.

• The first mortar layer is to cover the spaces between bricks vertically and horizontally. It is also used in places where the bricks had to be scooped into, in order to place the electricity cables.
• The polystyrene adhesive is placed in clustered blobs, this saves material and keeps air inside which helps with the insulation.
• The polystyrene blocks are made of expanded polystyrene not extruded because of the very similar coefficients. As a drawback this type of polystyrene is not waterproof so extra waterproofing is necessary in the outer shell. The blocks are held in place by the plastic bolts which hug them all the way to the brick. Only used as a backup in case the adhesive fails.
• Another thin layer of mortar to allow the placement of the fiberglass net. This will prevent parts of the insulation to fly off in case of high level winds.
• A last very thin layer of mortar to smooth everything out and reduce the porosity of the wall in order to reduce the amount of the more expensive paint and primer.
• A very thin layer of paint primer. It usually comes in the color of the external paint to allow for a uniform color.
• External finish. Recent research made a class of rubber paints that still allow the masonry to breathe and conduct humidity to the outside while being perfectly waterproof from the outside.

How do we calculate it?

By using the previous formula we can just input the different materials from the insulation sandwich.

U = 1 / ( 1/ C_brick + x_brick/k_brick + x_mortar / k_mortar + ..._{(all the other layers)} ..+ 1 / C_external)

For example the U-value of the previous system would be lower than 0.203 W/m²K, which is pretty low, even without taking into consideration the subsequent layers of mortar. See my calculation on Google's Calculator.

I could make a quick PHP(programming language) calculator to be available from my server to help with anyone wanting to calculate their own building solutions and coefficients, perhaps in a future article I could link to it, this is what happens when scientists go #homesteading :D.

Roof Insulation

Similar to the walls, under the sheets of metal roofing there must be a waterproof membrane and a structure to hold either polystyrene or the most common fiberglass wool or basaltic wool sheets. The most inexpensive way is to lift the wool and then while holding it in place to use metallic wire over previously nailed screws.

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Then it can be encompassed in gypsum boards, seams covered in elastic tape and smoothed out using very fine mortar, sandpapered and then painted ( with an elastic paint to prevent cracking due to inevitable temperature changes or roof deformation due to heavy snow weight).
Below you even have a video which shows the procedure of properly insulating a roof (posted under a Creative Commons Licence).

Foundation Insulation

The foundation can be insulated by either using a mix of tar liquid layer or as a solid membrane before pouring the concrete plates, or if a lighter structure is used, perhaps by simply inserting extruded dense polystyrene under the leveling mortar. This is placed just before the wood flooring or the ceramic tiles. Below is another example of cellulose insulation. Cellulose is recycled so it has very little cost, but the cost of transport or pumps is strictly related to nearby production facilities:

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Windows and Doors insulation

An important part of the insulation system is the ability to find a balance between the window surface of the house, the factor that gives a house light and coziness, and the heat loss that follows those surfaces.

Wood is the most used material for building windows and doors but there are other options such as Aluminium or PVC (Polyvinyl chloride). They are sometimes much more cheaper and they revolve around using air chambers to break the cold bridges. Steel resistance elements are incorporated at greater dimension window frames and the efficiency and price is balanced. There are 3 chamber entry level products which are very cheap and there are 7 or 8 chambers premium products that also offer superior soundproofing and performance. The finishing color palette is diverse, with the least expensive being the white one and the most expensive ones being the ones with wood insertions or wood texture. Plus, they don't have to be repainted or reconditioned and they have close to the house's lifetime guarantee.
As for the window pane, all of the modern window frames come with a triple window pane, although the improvements over the two window pane models is marginal. The sandwich is usually 4-15-4 (two 4mm window panes with a 15mm air(or another inert gas) inside them for added efficiency),and 4-15-4-15-4 for triple pane).

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Below you have an example of a house using PVC gutters and downspouts, fascia, decorative imitation "half-timbering", windows, and doors. Design is not an issue problem and the suppliers have catalogs which allows a practically limitless offer.

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In the end

The research available right now means that it is now more affordable than ever to build reduced carbon footprint houses, or find a balance between reduced footprint, cost and energy use, which inevitably lowers the lifetime carbon footprint of the household.

There is a lot to say or ask or study in this field, so I am open to discussing about the techniques, the science and even alternative insulation options like organic materials, straw or cork, to only name a few. There were also many project which involved the use of used tires, soil insulation or even PET bottles(Polyethylene terephthalate or plastic bottles as we commonly know them). The options are limited only by our imagination and I think that we could and should be able to reduce our energy consumption and I will cover this in one of the future articles on green power generation and reducing waste, perhaps even to zero.

Further reading and sources:
https://wienerberger.co.uk/about-us/porotherm-versus-other-building-materials https://www.thenbs.com/knowledge/what-is-a-u-value-heat-loss-thermal-mass-and-online-calculators-explained https://www.engineeringtoolbox.com/thermal-conductivity-d_429.html - this is an amazing portal that taught me a lot of what I needed to know to build everything. https://www.theseus.fi/bitstream/handle/10024/24695/Chaykovskiy_German.pdf?sequence=1