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Default An improved solar attic

When a local couple considered a "solar addition," it turned out the first
and second floor levels of the south wall were mostly shaded by evergreens,
including trees on the neighbors's property, but the roof had lots of sun.
It's about 20'x40' with a 4' high ridge running east and west. I suggested
removing the south roof and extending the north roof up to the south beyond
the ridge at the same angle to make a shed attic with an 8'x40' transparent
south wall. Soldier's Grove solar attics used blowers to move hot air down
to the building, but water is simpler and uses less power and makes heat
storage easier in a slow draindown system with an unpressurized heat storage
tank on the ground. The house has a gas furnace.

NREL says 1000 Btu/ft^2 falls on a south wall on an average 30.4 F January day
with a 37.9 max in Phila, so a $320 8'x40' Dynaglas wall would collect 900x8x40
= 288K Btu on an average day, or more, with a reflective deck to the south and/
or a reflective overhang (which could also prevent overheating in summertime.)

With 120 F water in an 800 Btu/h-F auto radiator and fan near the peak and
insulation under the roof, it might look like this, viewed in a fixed font:

--- 1/320
|---|--|-------www--- 34 F
--- |
288K/6h x
= 48K Btu/h |
w
w 1/800
w
|
|
|

120 F

Opening the circuit at x makes the solar (Thevenin) equivalent temperature
34+48K/320 = 184 F, like this:

1/320
184 F ---www---
|
x
|
w
w 1/800
w
|
|
|

120 F

.... which might collect (184-120)/(1/320+1/800) = 14.6K Btu/h or 87.8K Btu/day,
enough to make lots of hot water for showers (with a $60 300'x1" PE pressurized
pipe coil in the heat storage tank) and provide some space heat. The attic temp
might be 120+14.6K/800 = 138 F. We might also circulate some attic air through
a filter and the 2nd floor of the house.

This seems efficient, even if the upstairs needs little heat. A dark mesh
near the glazing (eg black aluminum window screen) with 70 F house air flowing
through it could greatly lower the heat loss by convection through the glazing,
as in a Scandinavian "breathing wall." With 70 F air near the glazing, we might
capture up to 288K-6h(70-34)320ft^2/R1 = 218.9K Btu on an average January day.
Polycarbonate blocks longwave IR, but there would still be radiation loss from
the mesh to the glazing.

http://www.cibse.org/pdfs/8cimbabi.pdf has an equation for the dynamic
metric U-value of a breathing wall, as corrected:

Ud = VRhoaCa/(e^(VRhoaCaRs)-1) W/m^2K, where

V is the air velocity in meters per second,
Rhoa is air density, 1.2 kg/m^3,
Ca is the air's specific heat, 1000 J/(kg-K), and
Rs is the wall's static thermal resistance in m^2-K/W.

Using V = 1/3600 (1 meter per HOUR :-), and Rs = 5.7 m^2K/W (a US R32 wall),
Ud = 0.058 W/m^2, like a US R98 wall. A more typical V = 10 meters per hour
makes Ud = 1.7x10^-8 W/m^2K, like a US wall with an R-value of 334 million :-)

If 1 meter per hour (0.0055 fpm) flows through 320 ft^2 of mesh, the total is
17.5 cfm... 100 lfm up into a 1' wide x 2x4 cavity 8' tall with a 0.29 ft^2
cross section (29 cfm per linear foot of wall) would not increase the glazing
loss much over still air. In that case, the total airflow would be 320x29
= 9300 cfm. So it looks like a wide range of airflow is possible, depending
on how much heat the house needs.

With no mesh and 2 glazing layers, eg sliding glass doors, we might have this:

2/320
Tsun ---www--- Tsun = 34+259K/6/(2/320) = 304 F.
|
x
|
w
w 1/800
w
|
|
|

120 F

..... which might collect (304-120)/(2/320+1/800) = 24.5K Btu/h or 147.2K
Btu/day with a 120+24.5K/800 = 151 F attic temp. (We datalogged 157 F in
December of 1995 in the sunspace of our phone-booth-size experiment at
Ursinus college.)

We might start by drilling holes from the inside of the attic with a long bit
near the ridge next to the present rafters, then Sawzall a rafter-size piece
of roof from the outside and slip a 12' 2x6 into each hole parallel to the
rafter and bolt the bottom foot to the rafter, then build the new roof, then
remove the old one (or not) and build the wall...

I bought a used 1984 Dodge Omni automobile radiator for $35. We might attach
a $50 Lasko 2470 cfm 90 watt window fan to it... 800/5 = 160' of fin-tube pipe
with no fan would cost about $320. I like that better, since it is simpler and
uses less electrical energy and the fan may not last very long over 100 F. (My
640 ft^2 Dynaglas solar attic has a $433 2764 cfm 275 W Swedish Multifan with
special ball bearings and lubricant rated for 311 F.)

Nick

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tom
 
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Default An improved solar attic

Good thinking! Tom

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Default An improved solar attic

When a local couple considered a "solar addition," it turned out the first
and second floor levels of the south wall were mostly shaded by evergreens,
including trees on the neighbors's property, but the roof had lots of sun.

It's about 20'x40', with a 4' high ridge running east and west. I suggested
removing the south roof and extending the north roof up to the south beyond
the ridge at the same angle to make a shed attic with an 8'x40' transparent
south wall. Soldier's Grove solar attics used blowers to move hot air down to
the building, but water is simpler and pumps use less power and make heat
storage easier in a slow draindown system with an unpressurized heat storage
tank on the ground. The house has a gas furnace.

NREL says 1000 Btu/ft^2 falls on a south wall on an average 30.4 F January day
with a 37.9 max in Phila, so a $320 ($0.02 per peak watt :-) 8'x40' Dynaglas
corrugated polycarbonate wall would collect 900x8x40 = 288K Btu on an average
day, or more, with a reflective deck to the south and/or a reflective overhang
(which could also prevent overheating in summertime.)

With 120 F water in an 800 Btu/h-F auto radiator and fan near the peak and
insulation under the roof, it might look like this, viewed in a fixed font:

--- 1/320
|---|--|-------www--- 34 F
--- |
288K/6h x
= 48K Btu/h |
w
w 1/800
w
|
|
|

120 F

Opening the circuit at x makes the solar (Thevenin) equivalent temperature
34+48K/320 = 184 F, like this:

1/320
184 F ---www---
|
x
|
w
w 1/800
w
|
|
|

120 F

.... which might collect (184-120)/(1/320+1/800) = 14.6K Btu/h or 87.8K Btu/day,
enough to make lots of hot water for showers (with a $60 300'x1" PE pressurized
pipe coil in the heat storage tank) and provide some space heat. The attic temp
might be 120+14.6K/800 = 138 F. We might also circulate some attic air through
a filter and the 2nd floor. The present furnace might spread the heat around
the house.

This seems efficient, even if the upstairs needs little heat. A dark mesh
near the glazing (eg black aluminum window screen) with 70 F house air flowing
through it could greatly lower the heat loss by convection through the glazing,
as in a Scandinavian "breathing wall." With 70 F air near the glazing, we might
capture up to 288K-6h(70-34)320ft^2/R1 = 218.9K Btu on an average January day.
In full sun, with 225x340 = 76500 Btu/h entering and (70-34)320 = 11520 leaving
the attic, one attic temp upper limit would be 120+(76500-11520)/800 = 201 F.
Polycarbonate blocks longwave IR, but there would still be radiation loss
from the mesh to the glazing.

http://www.cibse.org/pdfs/8cimbabi.pdf has an equation for the dynamic
metric U-value of a breathing wall, as corrected:

Ud = VRhoaCa/(e^(VRhoaCaRs)-1) W/m^2K, where

V is the air velocity in meters per second,
Rhoa is air density, 1.2 kg/m^3,
Ca is the air's specific heat, 1000 J/(kg-K), and
Rs is the wall's static thermal resistance in m^2-K/W.

Using V = 1/3600 (1 meter per HOUR :-), and Rs = 5.7 m^2K/W (a US R32 wall),
Ud = 0.058 W/m^2, like a US R98 wall. A more typical V = 10 meters per hour
makes Ud = 1.7x10^-8 W/m^2K, like a US wall with an R-value of 334 million :-)

If 1 meter per hour (0.0055 fpm) flows through 320 ft^2 of mesh, the total is
17.5 cfm... 100 lfm up into a 1' of 2x4 cavity 8' tall with a 0.29 ft^2 cross
section (29 cfm per linear foot of wall) would not increase the glazing loss
much over still air. In that case, the total airflow would be 40x29 = 1160 cfm.
With no water flow, we'd have something like this:

Ta = 70+I/1160 = 95 F.
|
1/320 | 1/1160
184 F ---www-------www--- 70 F
I --

I = (184-70)/(1/320+1/1160) = 28.6K Btu/h.

It looks like a wide range of airflow is possible, depending on how much
heat the house needs.

With no mesh and 2 glazing layers, eg sliding glass doors, we might have this:

2/320
Tsun ---www--- Tsun = 34+259K/6h/(2/320) = 304 F.
|
x
|
w
w 1/800
w
|
|
|

120 F

..... which might collect (304-120)/(2/320+1/800) = 24.5K Btu/h or 147.2K
Btu/day with a 120+24.5K/800 = 151 F attic temp. (We datalogged 157 F in
December of 1995 in the sunspace of our phone-booth-sized experiment at
Ursinus college.)

We might start by drilling holes from the inside of the attic with a long bit
near the ridge next to the present rafters, then Sawzall a rafter-size piece
of roof from the outside and slip a 12' 2x6 into each hole parallel to the
north rafter and bolt the bottom foot to the rafter, then build the new roof,
then remove the old one (or not) and build the wall...

I bought a used 1984 Dodge Omni automobile radiator for $35. We might attach
a $50 Lasko 2470 cfm 90 watt window fan to it... 800/5Btu/h-F-ft = 160' of
fin-tube pipe with no fan would cost about $320. That's simpler, it uses less
electrical energy, and the fan may not last very long at 151 F. (My 640 ft^2
Dynaglas solar attic has a $433 2764 cfm 275 W Swedish Multifan with special
ball bearings and lubricant rated for 311 F.)

Nick

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The Real Bev
 
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Default An improved solar attic

No it's not.

See the problem?

--
Cheers,
Bev
++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++
Is it sick to think that 'Commando' is a really fun movie?
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Default An improved solar attic

The Real Bev wrote:

No it's not.


The solar attic is not improved?

See the problem?


No.

Nick



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Logan Shaw
 
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Default An improved solar attic

Jeff Thies wrote:
I'm reading this from alt.solar.thermal, and I have no idea what you are
talking about.


That shouldn't make a difference. As far as I can tell, every article
in this thread, including the article that started it, and everything
that Bev said and that she was responding to, has been posted in
alt.solar.thermal.

What I do know is that not including *any* of the thread (see your
original post in this thread) is abysmal usenet practice. Why Nick even
responded is beyond me.


If you think that's not a good thing, then it might be interesting to
take a look at the message Bev responded to. If you do, you will
notice that that message didn't quote any context either. I wonder
if that might even be related to Bev's point.

- Logan
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The Real Bev
 
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Default An improved solar attic

Logan Shaw wrote:

Jeff Thies wrote:
I'm reading this from alt.solar.thermal, and I have no idea what you are
talking about.


That shouldn't make a difference. As far as I can tell, every article
in this thread, including the article that started it, and everything
that Bev said and that she was responding to, has been posted in
alt.solar.thermal.

What I do know is that not including *any* of the thread (see your
original post in this thread) is abysmal usenet practice. Why Nick even
responded is beyond me.


If you think that's not a good thing, then it might be interesting to
take a look at the message Bev responded to. If you do, you will
notice that that message didn't quote any context either. I wonder
if that might even be related to Bev's point.


Gee, ya think?

First it was "sigh September again." Then it was "Oh Lord, another AOL
newbie." Now it's "Oh Lord, another Google goober." Wonder what will be next
and how much worse it will be...

--
Cheers,
Bev
---------------------------------------------------------------------
"If the Eskimos have a thousand different words for "snow," does this
mean the French have a thousand different words for "surrender?"



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Jeff Thies
 
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Default An improved solar attic

snip

That shouldn't make a difference. As far as I can tell, every article
in this thread, including the article that started it, and everything
that Bev said and that she was responding to, has been posted in
alt.solar.thermal.


Actually no...

What I do know is that not including *any* of the thread (see your
original post in this thread) is abysmal usenet practice. Why Nick
even responded is beyond me.



If you think that's not a good thing, then it might be interesting to
take a look at the message Bev responded to. If you do, you will
notice that that message didn't quote any context either. I wonder
if that might even be related to Bev's point.


What we have here is one of those rare quirks in usenet. Each message
has an identifier that is randomly generated. This is usually unique
because of the large number of possibilities, but as luck would have it,
in this case it was not.

Reading here in alt.solar.thermal, Nicks post was the start of a new
thread, not a follow up.

Since '95, I've seen this only once before... Caused a stir then also!

Where are you reading from???

Cheers,
Jeff


- Logan

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Logan Shaw
 
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Default An improved solar attic

Jeff Thies wrote:
What we have here is one of those rare quirks in usenet. Each message
has an identifier that is randomly generated. This is usually unique
because of the large number of possibilities, but as luck would have it,
in this case it was not.

Reading here in alt.solar.thermal, Nicks post was the start of a new
thread, not a follow up.


I'm not following you, but it's no big whoop either way. From where
I stand, it seems like Bev responded to someone named "tom" who wrote
a message whose body was just this one line:

Good thinking! Tom

And, unless Usenet has mangled the posting badly, he was not starting
a new thread, because his posting has a References: line. And Bev
was replying to him.

But, I don't see much point in pressing the issue, since Usenet is
fairly chaotic sometimes, and not everybody always sees the same set
of articles in the same order. Sometimes articles never even make
it to certain sites, etc., etc.

Where are you reading from???


misc.consumers.frugal-living.

- Logan
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Default An improved solar attic

The Real Bev wrote:

... Losers who quote NOTHING of the post to which they're replying have
nothing at all to say worth reading because they aren't smart enough to
let the readers know what they're talking about.


Thanks for explaining. Abby and m Ransley sometimes do this. It can be
an interesting puzzle with a solution. Other times, a complete mystery.
Amusing cluelessness.

No it's not.

The solar attic is not improved?


I imagined you meant the original attic wasn't solar, so the new design was
not an "improvement." I meant that it seemed to be an improvement compared
to the 20 or so solar attics built in Soldier's Grove, WI about 25 years ago
when that sensible little town turned down $6 million from the Army Corps of
Engineers to build dikes and moved its commercial district uphill (after too
many Kickapoo River floods) and then passed a law saying all new commercial
buildings must be at least 50% solar-heated (see the Solar Today story at
http://www.ece.villanova.edu/~nick, if you like.) Most of their large empty
solar attics have sloped glazing with a large blower moving hot air down
to the lower part of the building and a motorized damper to keep building air
from rising back up into the cold attic at night, but that uses big ducts
and lots of electrical power, and it's hard to store heat from warm air.
Some buildings store no solar heat. Others store heat in rock beds, hollow
floors, and shelves of canned goods in the IGA supermarket.

As to "improvements," this newer design might have a higher solar collection
efficiency, with cool air next to the glazing losing less heat to the outdoors.
It might also collect and store heat in water, which requires less electrical
power and makes for easier heat storage and water heating for showers, and
the glazing is vertical, which allows an overhang for summer shading to avoid
overheating and extend the glazing lifetime and make more of the attic space
useful for people. Corrugated greenhouse polycarbonate glazing (eg "Dynaglas")
has largely replaced the fiberglass glazing used in Soldier's Grove, since it
costs less and installs easier and lasts longer, with no maintenance. My roofer
neighbor envied my solar roof as he watched it go up in a day or so in 4'x12'
sheets, with no sheathing, felt or shingles. It costs less than a normal roof.

Nick

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Abby Normal
 
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Default An improved solar attic

I apologize, for suggesting Nick could be the Rocket



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Default An improved solar attic

Abby Normal wrote:

wrote:


The Real Bev wrote:

... Losers who quote NOTHING of the post to which they're replying have
nothing at all to say worth reading because they aren't smart enough to
let the readers know what they're talking about.


Thanks for explaining. Abby and m Ransley sometimes do this...


Are you sure you are not Rod 'the Rocket' Speed's alter ego?


Yes. Rod is often correct, but I reluctantly killfiled him
because he is sooo obnoxious.

Nick

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daestrom
 
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Default An improved solar attic


"Jeff Thies" wrote in message
ink.net...
snip

That shouldn't make a difference. As far as I can tell, every article
in this thread, including the article that started it, and everything
that Bev said and that she was responding to, has been posted in
alt.solar.thermal.


Actually no...

What I do know is that not including *any* of the thread (see your
original post in this thread) is abysmal usenet practice. Why Nick even
responded is beyond me.



If you think that's not a good thing, then it might be interesting to
take a look at the message Bev responded to. If you do, you will
notice that that message didn't quote any context either. I wonder
if that might even be related to Bev's point.


What we have here is one of those rare quirks in usenet. Each message has
an identifier that is randomly generated. This is usually unique because
of the large number of possibilities, but as luck would have it, in this
case it was not.

Reading here in alt.solar.thermal, Nicks post was the start of a new
thread, not a follow up.

Since '95, I've seen this only once before... Caused a stir then also!


I don't think it is all that hard to replicate. Nick could have just
*added* alt.solar.thermal to his reply. Change the 'subject' line, and in
some groups it looks like a reply to some previous message with the subject
line changed, but in a.s.t it looks like a new thread.

Perhaps Nick felt the subject was applicable to a.s.t ?? That's the only
group in this reply that I read, but I left the others in, in case someone
is reading it from another.

daestrom


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John P.. Bengi
 
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Default An improved solar attic

Who really cares except the whiny, bitchers?

Maybe they can learn to use their browser killfilters
to block the thread or block the poster or block their
mouths instead of whining about Nick looking at them
funny.

****ing babies!

"daestrom" wrote in
message
...

I don't think it is all that hard to replicate. Nick

could have just
*added* alt.solar.thermal to his reply. Change the

'subject' line, and in
some groups it looks like a reply to some previous

message with the subject
line changed, but in a.s.t it looks like a new

thread.

Perhaps Nick felt the subject was applicable to a.s.t

?? That's the only
group in this reply that I read, but I left the

others in, in case someone
is reading it from another.

daestrom




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The Real Bev
 
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Default An improved solar attic

Logan Shaw wrote:

Jeff Thies wrote:
Where are you reading from???


misc.consumers.frugal-living.


Me too. Not many of us left. I think I'm going to bail...

--
Cheers, Bev
================================================== ===========
My house isn't a pigsty, it's an Immunity Enhancement Center.
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The Real Bev wrote:

Jeff Thies wrote:
Where are you reading from???


misc.consumers.frugal-living.


Me too. Not many of us left. I think I'm going to bail...


We might discuss the economic and technical aspects, vs "You must be crazy
to think that will work," "Your computer can't even make Pi," "Your attic
can't work, because you haven't installed enough heat pumps," and so on.

Dynaglas polycarbonate costs $1/ft^2. Installing a 4'x12' panel takes 10
minutes. It lasts 20 years but might go longer with a sloped reflective
overhang for less summer sun and more winter sun. Shingles cost about
$0.30/ft^2, plus $0.10 for felt plus $0.50 for OSB? So materials are
a wash, but there's a large labor savings. How much? The solar heat is
worth about $1/ft^2 per year.

How much heat will a dark absorber lose to cold glazing by radiation?
How can we make a dark mesh that will work with a 1-10 meter per hour
face velocity? Black aluminum window screen costs about 25 cents/ft^2
in 4' rolls, but its pneumatic resistance is likely too low. Typar is
cheap, about 10 cent/ft^2 IIRC, but its pneumatic resistance is high.
How about poking some holes in Typar? How many? How big?
Would a geotextile material work better?

http://www.reemay.com Typar comes in wide rolls, eg 9'x111.1'. It's porous,
0.0032L/s-m^2 at 75 Pa, ie 0.00063 cfm/ft^2 at 0.3" H20, eg 0.2 cfm for
an 8'x40' wall, and charcoal on one side. It lasted 5 years on a south wall
of my house, exposed to the weather, but it has a lifetime guarantee :-)

Nick



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Typar is cheap, about 10 cent/ft^2 IIRC...

.... $145 for a 9'x100' roll.

but its pneumatic resistance is high. How about poking some holes in Typar?
How many? How big?


If 1 cfm = 16.6Asqrt(HdT) = 16.6Asqrt(dP) in a 1' chimney with a 1 F temp diff
and dP = 0.075x(1/460-1/461) = 3.54x10^-7 psi and a 0.01"H20 fan pressure makes
dPf = 3.61x10^-4 psi, it might push 0.01 cfm through an A ft^2 hole in a 1 ft^2
surface if 0.01 = 16.6Asqrt(dPf/dP) = 531A, so A = 1.88x10^-5 ft^2, ie 0.0027
in^2, ie a 0.059 inch diameter hole, about 1/16".

So we might put up an 8'x40' 32 cfm Typar wall with 2x4 studs on 4' centers and
poke big nailholes on a 1' grid from the south. With luck, the edges will open
more at higher flows, keeping the pneumatic resistance low. A layer of black
window screen might make it last longer and reduce the heat loss by radiation.

Nick

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Typar is cheap, about 10 cent/ft^2 IIRC...

... $145 for a 9'x100' roll.

but its pneumatic resistance is high. How about poking some holes in Typar?


If 1 cfm = 16.6Asqrt(HdT) = 16.6Asqrt(dP) in a 1' chimney with a 1 F temp
diff and dP = 0.075x(1/460-1/461) = 3.54x10^-7 psi and a 0.01"H20 fan makes
dPf = 3.61x10^-4 psi, it might push 0.01 cfm through an A ft^2 hole in
a 1 ft^2 surface if 0.01 = 16.6Asqrt(dPf/dP) = 531A, so A = 1.88x10^-5 ft^2,
ie 0.0027 in^2, ie a 0.059 inch diameter hole, about 1/16".

So we might put up an 8'x40' 32 cfm Typar wall with 2x4 studs on 4' centers
and poke big nailholes on a 1' grid from the south...


Oops. That's a 3.2 cfm wall. For 32 cfm, we might poke 0.59" holes, or
0.29" pencil-sized holes with 0.04 "Hg. For uniform air distribution,
we might make the pneumatic resistance of the mesh large compared to
the pneumatic resistance of the stud cavity.

Nick

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Jeff Thies wrote:

Typar is cheap, about 10 cent/ft^2 IIRC... For 32 cfm, we might poke
0.59" holes, or 0.29" pencil-sized holes with 0.04 "Hg.


What's wrong with felt or multiple layers of black screen (could be
fiberglass). Seems to me that you don't want much distance between
holes. Surely the thermal conductivity of Typar is not that great.


The tiny airflow (32 cfm for an 8'x40' wall) just provides insulation,
eliminating convection heat loss from the mesh to the glazing, as in
a Scandinavian breathing wall. The fin tubes collect the heat, which
moves from the south to the north side of the Typar by conduction and
up to the fin tubes by convection.

Nick



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http://www.cibse.org/pdfs/8cimbabi.pdf has an equation for the dynamic
metric U-value of a breathing wall, as corrected:

Ud = VRhoaCa/(e^(VRhoaCaRs)-1) W/m^2K, where

V is the air velocity in meters per second,
Rhoa is air density, 1.2 kg/m^3,
Ca is the air's specific heat, 1000 J/(kg-K), and
Rs is the wall's static thermal resistance in m^2-K/W.

Using V = 1/3600 (1 meter per HOUR :-), and Rs = 5.7 m^2K/W (a US R32 wall),
Ud = 0.058 W/m^2, like a US R98 wall. A more typical V = 10 meters per hour
makes Ud = 1.7x10^-8 W/m^2K, like a US wall with an R-value of 334 million :-)

But less air saves more energy, if outdoor air flows in through the wall with
no heat exchanger: with 0 C outdoors and 20 indoors and a square meter of R5.7
wall losing 20Ud = 24000V/(e^(6840V)-1) watts and V m^3/s flowing in through
the wall requiring 1200V = 20Ud watts of warming, V = ln(21)/6840 = 0.000445
m/s, ie 1.6 m/h is optimal, and the wall loses 0.534 W, with a 1m^2x20K/0.534W
= R37 effective metric R-value, ie US R213 :-)

How does this compare with ASHRAE's 15 cfm per occupant fresh air standard?

Nick

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http://www.cibse.org/pdfs/8cimbabi.pdf has an equation for the dynamic
metric U-value of a breathing wall, as corrected:

Ud = VRhoaCa/(e^(VRhoaCaRs)-1) W/m^2K, where

V is the air velocity in meters per second,
Rhoa is air density, 1.2 kg/m^3,
Ca is the air's specific heat, 1000 J/(kg-K), and
Rs is the wall's static thermal resistance in m^2-K/W.

Using V = 1/3600 (1 meter per HOUR :-), and Rs = 5.7 m^2K/W (a US R32 wall),
Ud = 0.058 W/m^2, like a US R98 wall. A more typical V = 10 meters per hour
makes Ud = 1.7x10^-8 W/m^2K, like a US wall with an R-value of 334 million :-)

But counting air heating energy, the total is 1200VdT(1+1/e^(1200VRs)-1),
which increases with airflow. If 30 cfm of 0 C outdoor air flows through
4000 ft^2 of metric R7 (US R40) exterior surface in a typical 40'x60'x8' US
house with no heat exchanger and warms to 20 indoors, V = 3.8x10^-5 m/s, with
0.914 W/m^2 of air heating. The walls and ceiling (eg 8" fiberglass with 9"
TGI joists and studs) would lose 0.914/(e^1200V7-1) = 2.4 W/m^2h, for a total
of 3.31 W/m^2, ie metric R6 or US R34, including fresh air heating as needed,
with (68-32)4000ft^2/R34 = 4235 Btu/h at 30 cfm. This would only work well
in an extremely airtight house.

In which case, maybe it's better to take the R40 with simpler non-breathing
walls losing (68-32)4000ft^2/R40 = 3600 Btu/h and add an 80% air-air heat
exchanger (eg some bidirectional breathing walls) losing about 0.2x30(68-32)
= 376, for a total of 3976 Btu/h.

Nick

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