h a l f b a k e r yRecalculations place it at 0.4999.
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Breezeblocks <link> have holes in them to reduce weight/cost while maintaining structural strength. When the blocks are put together to make a wall their holes line up, forming vertical squared-off tubes.
Insulation is often poured into the tubes to give the wall better insulating qualities: cement
is pretty poor in that regard.
You don't get any better than a vacuum for insulation. Nor cheaper.
_________
How to install a vacuum insulation layer ?
- When the wall is completed, but before putting something on top of it, drill a few internal-internal holes inside the top level of bricks to join all the airspaces together.
- Once the wall has been topped with something airtight, drill the hole for the airpump.
Temporarily using a high-pressure pump, pressurize the wall to a few bar with smoke. Make any repairs necessary to fill in the most obvious microgaps evidenced by stains on the wall surface, then pressurize it again with a magic nanovapour that will solidify after a while when it dries, to fill in the non-obvious cracks.
Then seal or paint the surface as desired (or just leave it alone; there won't be that much difference).
Lastly, install the sensors (wall-vacuum, inside-temperature, outside-temperature), pump and display/control unit.
Done. It may take awhile for the pump to evacuate the whole wall from scratch.
As the years go by, if the pump starts running too often, repeat the initial pressure test and repair. If it runs all the time then you have a crack in the wall that should be looked at.
So, to recap, for a couple creds a year in kWh, wall insulation that is cheaper up front than any other form, guarantees no seepage (unless you've forgotten to plumb out the airpump's condenser), and notifies of any structural damage.
----
notes:
It's a given that blocks specially designed will perform the best, but even bog-standard cement blocks should work.
The same could be done for roofs, using terracotta round pipes (lighter than cement blocks).
breezeblocks, cinderblocks, whatever...
http://en.wikipedia...ncrete_masonry_unit
the kind with big stacking holes in them. [FlyingToaster, Oct 11 2012]
r-values for perlite loosefill insulation added to breezeblocks
http://www.schundler.com/rvalues.htm
[FlyingToaster, Oct 12 2012]
EPS Concrete Block Insulation
http://www.universa...lock-insulation.php
[xaviergisz, Oct 12 2012]
Thermal Resistance Circuits
http://web.mit.edu/.../notes/node118.html
[xaviergisz, Oct 12 2012]
[link]
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I don't think it would make much difference to the total thermal conductivity of the wall. I reckon a more significant factor in the thermal conductivity of the wall is due to the concrete itself. I think a more effective solution would be to make the bricks in halves and connect with a thermal barrier material. I'd be interested to see the maths. |
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(courtesy of Schundler Company <link>)
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8" thick breezeblocks, with/without a perlite loosefill core:
- lightweight: R goes from 2.86 to 9.07
- heavyweight: goes from 2.21 to 5.06
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perlite has an R-value of 2.7/in. |
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So what are the values going to be when the core-fill has an R-value of 50/in. ? |
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//connect with a thermal barrier material// then your wall falls over because it isn't structurally strong enough. But sure, build two walls and stuff hay bales or aerogels in between: nothing wrong with that: bit expensive if you ask me. |
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The maths is too hard for me, since I don't think you can ignore how much heat is 'channeled' from the outside face of the wall through the connecting perpendicular pieces. If it were just 'additive' maths then I agree the type of insulation makes a large difference. |
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Edit: Note that I'm making a comparison between bricks with different types of insulation (foam vs vacuum). Obviously a brick with insulation is much better than a brick without. |
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I'm not sure if the thermal barrier approach would work. Note however that the perpendicular connecting part of the brick does not need to be as strong as the load bearing part. I can imagine the connecting part being made of something with good tensile strength and good insulation properties such as kevlar. |
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If the ribs (your "perpendicular connective pieces") take up 1/5 of the cross-sectional space of each brick then the square footage of a wall, for all intents and purposes, can be seen mathematically as 1/5 pure concrete, and 4/5 concrete-encapsulated insulation. |
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And while you can't do much about 1/5 of the wall, there really is no question as to what the best insulation is for the other 4/5. |
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I don't think you can simplify the maths to say that since only 1/5 of the cross sectional space is concrete therefore it only contributes 1/5 to the thermal conductivity. |
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To take an extreme example, what if the concrete was replaced with an extremely good thermal conductor, e.g. iron. Would the type of insulation in the gaps make a huge difference? |
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Obviously concrete is not as good a conductor as iron but its not a great insulator either, so an accurate mathematical model is somewhere in between the two extremes. |
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I do see your point: it doesn't matter how well insulated the wall is if the window's open. |
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But if you had say a 10 foot section of wall, would you rather have 10 foot of iron, or 2 feet of iron and 8 foot of decent insulation, or 2 feet of iron and 8 foot of perfect insulation. |
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I don't know. This idea reminds me of the lighter-than-air ideas using a vacuum enclosed within a structure rather than helium in balloons - possible but not practical. |
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yes, but if the structure could handle it then we'd all be driving vacuum dirigibles. |
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Let's start with a solid concrete brick with an R-value of 1. |
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Now if we hollow it out so the crossribs only take up 1/5 of the space, then fill the hollows with vacuum (R-infinity), we get an R value of 5. Filling the spaces with an R20 insulation gives an overall R-value of 4.13333. |
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So the vacuum delivers a 20% performance increase over a costly'ish insulation core. |
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Mind you this was a pretty crude, probably inaccurate calculation based only on math. |
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Both of our links (insulation mfr's) show a greater increase for insulation, so using their math there should be even more for using a vacuum. |
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I just realised the maths isn't actually very hard.
Thermal conductivity is calculated in the same way
that electrical resistivity is calculated, i.e. circuits in
series and parallel. |
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I'll get around to plugging the numbers in later. |
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OK, I've had a crack at the calculations. I have
derived my
calculations from the information in the "thermal
resistance circuits" link. |
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I assumed: each rib was 1/5 width of the block face,
the
ribs are 5 times as long as wide, ribs and block face
had
same width, and the following thermal conductivities
in
W/mK:
concrete=1.1
insulation foam=0.04
insulation vacuum=0.007
and setting A and L to 1 |
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Results:
The thermal resistance R in m²K/W is:
for the bricks filled with foam, R=4.33
for the bricks filled with vacuum, R=4.79 |
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Not a big difference, but someone should check my
results. |
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hmm... I didn't bother with the series bit first time around. |
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Say a brick of 0.2R/in. substance, 8x8x15" with 3 1" ribs per brick, and faces 1" thick. (so we retain the "1/5th of the brick cross-section is rib" thing) |
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If the brick were solid it would have an R-value of .2 * 8, or 1.6. |
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Vacuum I think has pretty close to infinity R-value: WP lists a value range for "vacuum panels" which includes framing and internal membranes. In a real vacuum you'd only get radiative heat loss. |
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given that, the brick's R-value would consist of the 2 faces (2 * 0.2 = 0.4) plus the stuff in the middle which consists of 1/5 of (6" of brick = 1.2) combined with 4/5 of infinity, so that gives an R value of 6 for a total of 6.4 |
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Using "home foam" with an R-value of 4 we add the faces (still 2 * .2 = .4) to the middle (1/5 has an R value of 1.2, 4/5 has an R-value of 24, so that gives... 5) to get 5.4. |
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so vacuum gives a 20% increase in R-value. |
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I think your brick is too thick. |
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OK, you can recalculate for a thinner brick. |
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I was using the following formula: |
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R_total = R_concreteface + 1/(1/R_concreterib +
1/R_insulation) + R_concreteface |
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where R=L/kA, L=thickness of each part, A is the area
(since the brick is an extruded form the area is essentially
the width of each part). |
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I set the rib length to be 5 times the concrete face
thickness. The insulation is 4 times the width of the rib. |
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I can calculate for thermal conductivities of the solids (and
the vacuum), but I can't figure out how to take into account
the higher thermal conductivity of air due to convection. |
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hmm... I think the middle bit of your formula needs to be reinverted after the inverted elements are added together. [edit: okay, but now you have to account for 1/5 and 4/5 unless that's already done] |
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the depth of your brick would be 1 + 5 + 1 units ? (pretty close to mine of 1 + 6 + 1). |
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Also what unit measurement is the "1.1" for concrete ? so I can sub that into my equation. I was using an R-value of .2/inch for brick, though .08/inch for poured concrete might have been more accurate. |
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I used a similar formula using R-values only: |
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Given that substance R-values are in "per inch":
concrete
fill-substance(s)
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then the component R-values are the substance R-values multiplied by the component depth
face
rib
fill
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so the total of the brick would be:
serial addition of (face, (parallel-operation-of 1/5 rib, 4/5 fill), face). |
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I'm responding via my phone at
the moment so I can't provide a
full explanation of my
calculations. |
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I did all calculations in SI units.
The values I used are thermal
conductivity, typically denoted k
or kappa. |
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I could very easily have made a
mistake in the calculations - all
done while keeping my two sons
entertained. |
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Yes, total depth of brick in my calculations is 1+5+1. |
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hmm... however "air-entrained concrete" is listed as having an R-value of 3.90/inch: using different fill materials makes quite a difference . . . |
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Foam
3.9 + (inverse(1/5 x inverse(6 x 3.9) + 4/5 x inverse(6 x 4.0)) + 3.9 which yields
R-value of 31.68 |
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Vacuum
3.9 + (inverse(1/5 x inverse(6 x 3.9) + 4/5 x inverse(6 x infinity) + 3.9 yields
R-value of 124.8 |
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which is rather impressive. Of course that's also based on the assumption that they make cinderblocks out of the stuff with that R-value, that the cinderblocks can be used for more than decoration, and that you'd be using air-entrained mortar as well. |
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Why not fill the voids with a large cell foam
inflated with Argon? |
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you mean the large voids in the cinderblock ? or make it "argon-entrained concrete". |
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We're using different values and units so its not surprising
we're getting different results; we're out by at least an
order of magnitude which indicates we've got very
different assumptions. |
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In your calculations you use an R value for air-entrained
concrete of which is almost the same as the R value of
your insulation. I don't think this is a fair value since air-
entrained concrete is (presumably) not load bearing. |
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I was basing my calculations on the concrete being 25
times more thermally conductive than the insulation. |
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My calculations using the Wikipedia R-value for "poured concrete"(0.08) for the brick substance came up with only a 5% gain of vacuum over the poured foam (compared with 10% for yours). |
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Using their R-value for "brick" (0.2), I got the 20% figure of my Oct12 anno. |
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I don't doubt that the R-3.9/inch air-entrained concrete, which produced the mind-boggling R-125 figure using a vacuum fill (Oct13), is comparatively crap for load-bearing, but even if it could only handle its own weight vertically as well as the 14psi from the sides, it'd make a brilliant (if somewhat ugly) very cheap cladding wall. |
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