Posted by *nicksanspam* on December 6, 2006, 12:10 pm

*>> 160 NETSUN=SUN-SWNL-OWL+6*TA*64*UVG-(TMIN/2-TA)*64/RC'net sun (Btu/day)*

*>Nick, I believe the last term in line 160 above should be, *

*>"...-24*(TMIN/2-TA)*64/RC"...*

I think you are correct. Thanks :-) I'll fix that. I was wondering why raising

RC didn't raise the water temp much. With a warmer-than-room temp, the ceiling

seems like a good place for some extra insulation.

I also added lines 110 and 120 to the Liu and Jordon isotropic sky calc below

(which didn't change the answer, in this case.) This is described on pages

102-105 of the third (2006) edition of Duffie and Beckman's Solar Engineering

of Thermal Processes. It's a way to estimate how much sun falls on a south

wall (Rb = 5 times more beam sun, below), if we know how much falls on

the ground, eg from an Energy Plus weather stat file for Saskatoon.

10 SCREEN 9:KEY OFF:PI=4*ATN(1)

20 LDR+10/60'Saskatoon north latitude (degrees)

30 L=LD*PI/180'radians

40 DECD=-23'December declination (degrees)

50 DECCD*PI/180'radians

60 X=-TAN(L)*TAN(DEC)

70 HSR=-ATN(X/SQR(-X*X+1))+PI/2'sunrise hour angle (radians)

80 BETAD'vertical surface tilt (degrees)

90 BETATAD*PI/180'radians

100 X=-TAN(L-BETA)*TAN(DEC)

110 HSRP=-ATN(X/SQR(-X*X+1))+PI/2'sunrise hour angle (radians)

120 IF HSRP>HSR THEN HSRP=HSR'Hsrp is the min

130 NUM=COS(L-BETA)*COS(DEC)*SIN(HSRP)+HSRP*SIN(L-BETA)*SIN(DEC)

140 DEN=COS(L)*COS(DEC)*SIN(HSR)+HSR*SIN(L)*SIN(DEC)

150 RB=NUM/DEN'tilted surface to horizontal beam rad rat

160 RD=(1+COS(BETA))/2'tilted to horizontal diff rad rat

170 RHOG=.6'ground reflectivity

180 RR=RHOG*SIN(BETA/2)*SIN(BETA/2)'ground reflectance factor

190 IGLOH=1.007*317.1'global horizontal radiation (Btu/ft^2)

200 IDIFH=.472*317.1'diffuse horizontal radiation (Btu/ft^2)

210 IBEAMH=IGLOH-IDIFH'beam horizontal radiation (Btu/ft^2)

220 SS=RB*IBEAMH+RD*IDIFH+RR*IGLOH'south sun (Btu/ft^2-day)...

*>You don't seem to account for any heat to 'charge' the under-floor tank. *

I figure that's already accounted for, since most of the heat that leaks

from the tank moves up through the floor. Some leakage is desirable, since

that lowers the amount of heat the ceiling needs to provide, which lowers

the min usable ceiling water temp, so the cloudy-day store lasts longer.

It would also make sense to open a 2-watt motorized damper with a room

temp thermostat to let warm air flow up from the space between the top

of the tank and the bottom of the floor, instead of pumping water up

through the ceiling with more electrical power. A night/unoccupied setback

would also make sense, and a PV/battery-powered microcontroller.

*>With it in/under the floor, you would have to run the pump on sunny days to *

*>'charge' it, as well as on cloudy days to 'discharge' it.*

On an average day, the static ceiling mass would provide 100% of the heat

for the cube, so the pump would only run long enough to make up for the heat

leakage from the tank. The tank could also be heated with Big Fins or

fin-tube pipe in the sunspace, if the ceiling mass were not already there.

*>If it takes five days to 'charge' it for five cloudy days, wouldn't that*

*>about double the heat load on the sun space?*

Much less, IMO, because long strings of cloudy days are unlikely.

Less warmup time would be desirable for a portable cube.

*>Is the ratio of sunny/cloudy days in Philadelphia about 50/50?*

Something like that. So cloudy day strings are like coin flips, 2 in a row

with probability 1/4, 3 with 1/8, 4 with 1/16, and 5 with 1/32th. For more

precision, we can do a simple simulation with TMY2 hourly weather data.

*>Granted, the ground is warmer, it isn't 70F.*

Deep ground is 54.3 F in Phila, and some ASHRAE people figure it's R10

for downwards heatflow. We might put 2" of foamboard under the 6'x6'x6"

tank and surround it with 1 foot of peat moss, with some deadmen under

the tank for wind overturning resistance. Stratification would help.

*>Anyway, all well and good if you want to live in an 8' cube with no windows *

*>or doors. A pair of St. Bernards' doghouse??*

With more insulation, they'd need no sun :-)

*>What about a 'practical' house, say a very modest 1200 sq ft single story*

*>with only a few windows, say 48 ft^2 of double glazed (that's about one*

*>double-hung window in each wall). And a paltry 2 air-changes per day.*

Sounds good to me. The new PA ICC building code finally allows building

a house with no windows (as they have always allowed for commercial

buildings), if someone wants to do that, with flat screen TVs and outdoor

cameras for views, CFs for light, insulated doors for fire escapes, and

an exhaust fan with a humidistat for ventilation. Windows and their framing

are expensive, and they can leak water and heat and bugs and burglars and

baseballs... 2ACHx1200ft^2x8'/24h/60m/h = 13 cfm sounds good for natural

air leakage.

*>Would such a 'practical' house still perform in the 'regional infestations *

*>of doubt'?? *

Sure, but it might never get built, if nobody believes it can heat itself,

inexpensively. Almost all architects and newspaper reporters and housing

developers around Phila seem firmly entrenched and espouse disbelief, with

little knowledge of basic physics.

*>What you've posted here has very little to do with heating what *

*>most people would call "a house". (even a dog house has a door)*

A door would be nice for serious doubters. And a small window, so crowds

can peer in to see that it's still 70 F on a big thermometer on a wall,

after a few cloudy 30 F days. I'd like to see "solar shrines" in public

places, eg the Franklin Institute, who are building an outdoor science

park with funding from McDonalds. I'd make them stark, pure science plays,

so people don't miss the point and start arguing about aesthetics.

Lots of people know how to make buildings pretty.

Nick

Posted by *daestrom* on December 6, 2006, 9:35 pm

<snip>

*>>You don't seem to account for any heat to 'charge' the under-floor tank.*

*> I figure that's already accounted for, since most of the heat that leaks*

*> from the tank moves up through the floor. Some leakage is desirable, since*

*> that lowers the amount of heat the ceiling needs to provide, which lowers*

*> the min usable ceiling water temp, so the cloudy-day store lasts longer.*

*> It would also make sense to open a 2-watt motorized damper with a room*

*> temp thermostat to let warm air flow up from the space between the top*

*> of the tank and the bottom of the floor, instead of pumping water up*

*> through the ceiling with more electrical power. A night/unoccupied setback*

*> would also make sense, and a PV/battery-powered microcontroller.*

What you seem to be describing are ways to get the heat *out* of the tank

and into the cube (sorry, I just can't bring myself to call what you're

heating (8' cube with no windows/doors) a 'house').

What I was referring to is that how does the tank get heated in the first

place? If it's from circulating water from the overhead storage, then your

calcs for the TS (temperature of the sun space) don't consider this.

If the house uses 'X' BTU/day, and the floor tank can supply heat for five

days, then it stands to reason that it holds '5X' BTU. So at the end of a

cloudy period, to 'recharge' the tank over the next five 'sunny' days, you

would need to put at *least* 'X' BTU into the tank each day (more,

considering any losses it has).

So to 'recharge' in five days, your system has to develop '2X' BTU/day. 1X

for heating the house, and 1X for dumping into storage. You have to get

those '5X' BTU from *somewhere* over some number of days, it isn't going to

'recharge' itself.

*>>With it in/under the floor, you would have to run the pump on sunny days *

*>>to*

*>>'charge' it, as well as on cloudy days to 'discharge' it.*

*> On an average day, the static ceiling mass would provide 100% of the heat*

*> for the cube, so the pump would only run long enough to make up for the *

*> heat*

*> leakage from the tank. The tank could also be heated with Big Fins or*

*> fin-tube pipe in the sunspace, if the ceiling mass were not already there.*

Now you're speculating about a different design, putting the storage in the

sun space. If the storage is 'discharged', do you think it would 'recharge'

fully in one day? If not, what's heating the cube while the storage is

'recharging'?

*>>If it takes five days to 'charge' it for five cloudy days, wouldn't that*

*>>about double the heat load on the sun space?*

*> Much less, IMO, because long strings of cloudy days are unlikely.*

*> Less warmup time would be desirable for a portable cube.*

*>>Is the ratio of sunny/cloudy days in Philadelphia about 50/50?*

*> Something like that. So cloudy day strings are like coin flips, 2 in a row*

*> with probability 1/4, 3 with 1/8, 4 with 1/16, and 5 with 1/32th. For more*

*> precision, we can do a simple simulation with TMY2 hourly weather data.*

On sunny days the energy collected in the sunspace would just 'break-even'

to maintain cube temperature, but nothing left to go into storage. On

cloudy days, energy would come from storage. But with no excess energy on

sunny days, the storage would soon be depleted and not replenished.

Your sun-space has to collect *more* than what is just needed to maintain

the cube temperature. The excess is what goes into the storage. If the

amount of energy collected is only *slightly* more than the cube's heating

requirements, it may take many sunny days to 'recharge' the storage. And

each cloudy day in between sunny days just drains the storage again.

*>>Granted, the ground is warmer, it isn't 70F.*

*> Deep ground is 54.3 F in Phila, and some ASHRAE people figure it's R10*

*> for downwards heatflow. We might put 2" of foamboard under the 6'x6'x6"*

*> tank and surround it with 1 foot of peat moss, with some deadmen under*

*> the tank for wind overturning resistance. Stratification would help.*

*>>Anyway, all well and good if you want to live in an 8' cube with no *

*>>windows*

*>>or doors. A pair of St. Bernards' doghouse??*

*> With more insulation, they'd need no sun :-)*

*>>What about a 'practical' house, say a very modest 1200 sq ft single story*

*>>with only a few windows, say 48 ft^2 of double glazed (that's about one*

*>>double-hung window in each wall). And a paltry 2 air-changes per day.*

*> Sounds good to me. The new PA ICC building code finally allows building*

*> a house with no windows (as they have always allowed for commercial*

*> buildings), if someone wants to do that, with flat screen TVs and outdoor*

*> cameras for views,*

Nah, not a chance. Besides, that's a constant electrical drain. Although

windows do lose heat in the winter, they are useful in many ways. For other

seasons, ventilation. Additional solar gain. Mental health. An above

ground, windowless house would never catch on.

*>>Would such a 'practical' house still perform in the 'regional infestations*

*>>of doubt'??*

*> Sure, but it might never get built, if nobody believes it can heat itself,*

*> inexpensively.*

What do you mean by 'sure'? That a 1200 ft^2, four window, low-leakage

house could be built? I have no doubt.

But would a south-facing wall/sunspace, with overhead and underfloor storage

keep such a house 70F in a 30F winter? That I doubt. The windows and

air-changes would add a significant heating and storage requirement.

*Thats* the question I was asking, "Would such a house still perform [with

your sunspace/storage idea]?"

daestrom

Posted by *nicksanspam* on December 6, 2006, 11:13 pm

*>>>You don't seem to account for any heat to 'charge' the under-floor tank.*

*>>*

*>> I figure that's already accounted for, since most of the heat that leaks*

*>> from the tank moves up through the floor...*

*>What I was referring to is that how does the tank get heated in the first *

*>place? If it's from circulating water from the overhead storage, then your *

*>calcs for the TS (temperature of the sun space) don't consider this.*

I disagree. The tank loss heats the cube. Try mentally drawing a box around

the cube and balancing the solar energy that enters with the heat energy

that leaves.

*>If the house uses 'X' BTU/day, and the floor tank can supply heat for five *

*>days, then it stands to reason that it holds '5X' BTU.*

Sure.

*>So at the end of a cloudy period, to 'recharge' the tank over the next five*

*>'sunny' days, you would need to put at *least* 'X' BTU into the tank each day*

Sure, if you wanted to recharge the tank completely in 5 days,

after 5 cloudy days in a row, but is that a requirement?

*>So to 'recharge' in five days, your system has to develop '2X' BTU/day. 1X *

*>for heating the house, and 1X for dumping into storage. *

Sure, in the above scenario, which is unlikely to be required.

*>>>With it in/under the floor, you would have to run the pump on sunny days *

*>>>to charge' it, as well as on cloudy days to 'discharge' it.*

*>>*

*>> On an average day, the static ceiling mass would provide 100% of the heat*

*>> for the cube, so the pump would only run long enough to make up for the *

*>> heat leakage from the tank. The tank could also be heated with Big Fins or*

*>> fin-tube pipe in the sunspace, if the ceiling mass were not already there.*

*>Now you're speculating about a different design, putting the storage in the *

*>sun space...*

No. Just moving the small solar collector from the ceiling to the sunspace,

with the cloudy-day tank still under the floor. In that case, we forget

the ceiling mass and its louvers and add enough higher temp isolated mass

to store overnight heat (eg 200 lb of water cooling from 150 to 80 F) in

a small closet near the south wall.

*>If the storage is 'discharged', do you think it would 'recharge' fully*

*>in one day?*

Probably not. Then again, it doesn't have to.

*>On sunny days the energy collected in the sunspace would just 'break-even' *

*>to maintain cube temperature, but nothing left to go into storage.*

Nonono. That's what happens on an average vs sunny day. We can model solar

weather as binary coin flips with cloudy (no sun) and sunny (2X sun) days

or as ternary coin flips with cloudy and average (1X) and sunny (2X) days.

*>Your sun-space has to collect *more* than what is just needed to maintain *

*>the cube temperature.*

No... It costs nothing to maintain part of the cube at a higher temp, if

the heat that leaks from that part heats the cube. If sun were to shine

in through a window and heat some water inside several nested aquaria to

100 F, that wouldn't change the amount of solar heat the cube needs to

stay 70 F on a 30 F day.

*>What do you mean by 'sure'? That a 1200 ft^2, four window, low-leakage *

*>house could be built? I have no doubt.*

I agree. A larger solar house has more available heat storage volume, with

a lower surface to volume ratio. It's harder to build small solar houses.

A 2' D-cube would be almost impossible, even with R40 per inch evacuated

aerogel insulation. We might have a contest with a prize for the smallest

D-cube.

*>But would a south-facing wall/sunspace, with overhead and underfloor storage *

*>keep such a house 70F in a 30F winter?*

No problem, if it is well-designed.

Nick

Posted by *jgraber* on December 7, 2006, 1:05 am

nicksanspam@ece.villanova.edu writes:

*> *

*> >>>You don't seem to account for any heat to 'charge' the under-floor tank.*

*> >>*

*> >> I figure that's already accounted for, since most of the heat that leaks*

*> >> from the tank moves up through the floor...*

*> >*

*> >What I was referring to is that how does the tank get heated in the first *

*> >place? If it's from circulating water from the overhead storage, then your *

*> >calcs for the TS (temperature of the sun space) don't consider this.*

*> *

*> I disagree. The tank loss heats the cube. Try mentally drawing a box around*

*> the cube and balancing the solar energy that enters with the heat energy*

*> that leaves.*

Nick, you keep talking about tank heat loss.

Daestrom keeps asking about tank heat gain,

but you dont answer much.

*> >If the house uses 'X' BTU/day, and the floor tank can supply heat for five *

*> >days, then it stands to reason that it holds '5X' BTU.*

*> *

*> Sure.*

*> *

*> >So at the end of a cloudy period, to 'recharge' the tank over *

*> >the next five 'sunny' days, you would need to put *

*> >at *least* 'X' BTU into the tank each day.*

*> *

*> Sure, if you wanted to recharge the tank completely in 5 days,*

*> after 5 cloudy days in a row, but is that a requirement?*

Yes.

There has to be some recharge requirement,

otherwise, we can assume the heat tank is charged at the beginning

of the winter, and once we have 5 cloudy days, the heat tank

is discharged and useless for the rest of the year.

If the recharge rate is less than the depletion rate,

then this design does not fulfill the design goal

in any location where there are more cloudy days than sunny days.

So a complete recharge in 5 days sounds like the minimum requirement.

What is the ratio of cloudy days to sunny days in Philly?

What is the rate at which the heat tank can be recharged on a sunny day?

*> >So to 'recharge' in five days, your system has to develop '2X' BTU/day. 1X *

*> >for heating the house, and 1X for dumping into storage. *

*> *

*> Sure, in the above scenario, which is unlikely to be required.*

How do you calculate it is an unlikely requirement?

*> >>>With it in/under the floor, you would have to run the pump on sunny days *

*> >>>to charge' it, as well as on cloudy days to 'discharge' it.*

*> >>*

*> >> On an average day, the static ceiling mass would provide 100% of the heat*

*> >> for the cube, so the pump would only run long enough to make up for the *

*> >> heat leakage from the tank. The tank could also be heated with Big Fins or*

*> >> fin-tube pipe in the sunspace, if the ceiling mass were not already there.*

I'll parse that as agreement.

*> >If the storage is 'discharged', do you think it would 'recharge' fully*

*> >in one day?*

*> *

*> Probably not. Then again, it doesn't have to.*

If you dont permit 1 sunny day to recharge for 5 cloudy days,

then what do you permit?

*> >On sunny days the energy collected in the sunspace would just 'break-even' *

*> >to maintain cube temperature, but nothing left to go into storage.*

*> *

*> Nonono. That's what happens on an average vs sunny day. We can model solar*

*> weather as binary coin flips with cloudy (no sun) and sunny (2X sun) days*

*> or as ternary coin flips with cloudy and average (1X) and sunny (2X) days.*

You are the model guy Nick. Can you do better than coin flip for

modeling the frequency and run-length of cloudy days in Philly,

by using some weather/insolation database?

*> >Your sun-space has to collect *more* than what is just needed to maintain *

*> >the cube temperature.*

*> *

*> No... It costs nothing to maintain part of the cube at a higher temp, if*

*> the heat that leaks from that part heats the cube. If sun were to shine*

*> in through a window and heat some water inside several nested aquaria to*

*> 100 F, that wouldn't change the amount of solar heat the cube needs to*

*> stay 70 F on a 30 F day.*

You missed the point again Nick.

By this point, I'm beginning to think it is deliberate.

On a cloudy day, there is no solar gain, so all the heat comes

from the tank, right?

On an Average day, the solar gain equals the loss,

so there is no net change in the heat tank, right?

On a sunny day (only), the heat tank charge can be increased, right?

How much more energy is available on a sunny day,

than on an average day, that can be used to recharge,

so we can tell how many days it takes to recharge after 5 cloudy days.

*> >What do you mean by 'sure'? That a 1200 ft^2, four window, low-leakage *

*> >house could be built? I have no doubt.*

*> *

*> I agree. A larger solar house has more available heat storage volume, *

*> with a lower surface to volume ratio.*

Lets check the surface to volume ratio. Ok, thats right.

Dcube has 6x8x8 surface to 8x8x8 volume = 3:4 = 0.75 ratio

A 42x42x8 house has 42x42x2+42x8x4= 3108 surface to 42x42x8 volume = 0.22 ratio

What about the ratio of collector surface vs the entire surface?

Dcube 8x8x8 = 1/6 = 0.167

42x42x8 house = 42x8/3108 = 0.11, a smaller ratio, so even average days

will draw down the heat store,

and more Sunny days will be required to recharge it,

unless the design parameters like R value are change to compensate.

*> >But would a south-facing wall/sunspace, with overhead and underfloor storage *

*> >keep such a house 70F in a 30F winter?*

*> *

*> No problem, if it is well-designed. Nick*

Circular definition alert.

--

Posted by *nicksanspam* on December 7, 2006, 11:29 am

*>nicksanspam@ece.villanova.edu writes:*

*>> *

*>> >>>You don't seem to account for any heat to 'charge' the under-floor tank.*

*>> >>*

*>> >> I figure that's already accounted for, since most of the heat that leaks*

*>> >> from the tank moves up through the floor...*

*>> >*

*>> >What I was referring to is that how does the tank get heated in the first *

*>> >place? If it's from circulating water from the overhead storage, then your *

*>> >calcs for the TS (temperature of the sun space) don't consider this.*

*>> *

*>> I disagree. The tank loss heats the cube. Try mentally drawing a box around*

*>> the cube and balancing the solar energy that enters with the heat energy*

*>> that leaves.*

*>Nick, you keep talking about tank heat loss.*

*>Daestrom keeps asking about tank heat gain...*

The tank won't need much heat, since it only needs to provide heat on

cloudy days, ie it is rarely used. We might pump tank water up through

the ceiling to keep the tank hot. Or heat it with Big Fins or fin-tube

in a sunspace, or use a closet with some overnight heat storage mass.

If the natural tank heat loss heats the cube on an average day, that

loss is automatically included in the average-day solar heating budget.

*>> >If the house uses 'X' BTU/day, and the floor tank can supply heat for five *

*>> >days, then it stands to reason that it holds '5X' BTU.*

*>> *

*>> Sure.*

*>> *

*>> >So at the end of a cloudy period, to 'recharge' the tank over *

*>> >the next five 'sunny' days, you would need to put *

*>> >at *least* 'X' BTU into the tank each day.*

*>> *

*>> Sure, if you wanted to recharge the tank completely in 5 days,*

*>> after 5 cloudy days in a row, but is that a requirement?*

*>Yes.*

Why?

*>There has to be some recharge requirement, *

Sure.

*>otherwise, we can assume the heat tank is charged at the beginning *

*>of the winter, and once we have 5 cloudy days, the heat tank *

*>is discharged and useless for the rest of the year.*

If it takes 2 average weeks to recharge, how much does that lower

the maximum solar heating fraction?

*>If the recharge rate is less than the depletion rate,*

*>then this design does not fulfill the design goal*

*>in any location where there are more cloudy days than sunny days.*

*>So a complete recharge in 5 days sounds like the minimum requirement.*

You might think harder about this. What is "the depletion rate"? How often

do strings of 5 cloudy days occur? This is like "the gambler's ruin," with

a little gain, vs even odds.

*>What is the ratio of cloudy days to sunny days in Philly?*

About 1:1.

*>What is the rate at which the heat tank can be recharged on a sunny day?*

About twice the average-day rate.

*>> >So to 'recharge' in five days, your system has to develop '2X' BTU/day.*

*>> >1X for heating the house, and 1X for dumping into storage. *

*>> *

*>> Sure, in the above scenario, which is unlikely to be required.*

*>How do you calculate it is an unlikely requirement?*

Cloudy days are like coin flips. Long strings are unlikely. You might try

this: Flip a coin 365 times. Add 2 to the heat store if it comes up heads.

Subtract 1 every day (or 0.8, if you want to be more conservative) to heat

the house. Limit the store to 5 days max. If it contains no heat, add 1

to the yearly backup fuel bill...

*>> >If the storage is 'discharged', do you think it would 'recharge' fully*

*>> >in one day?*

*>> *

*>> Probably not. Then again, it doesn't have to.*

*>If you dont permit 1 sunny day to recharge for 5 cloudy days,*

*>then what do you permit? *

... 5 or 6 average vs sunny days for a complete recharge seems to work well.

*>> >On sunny days the energy collected in the sunspace would just 'break-even' *

*>> >to maintain cube temperature, but nothing left to go into storage.*

*>> *

*>> Nonono. That's what happens on an average vs sunny day. We can model solar*

*>> weather as binary coin flips with cloudy (no sun) and sunny (2X sun) days*

*>> or as ternary coin flips with cloudy and average (1X) and sunny (2X) days.*

*>You are the model guy Nick. Can you do better than coin flip for *

*>modeling the frequency and run-length of cloudy days in Philly,*

*>by using some weather/insolation database?*

Sure. A simulation using NREL's Phila TMY2 hourly measured weather data file.

*>> ... It costs nothing to maintain part of the cube at a higher temp, if*

*>> the heat that leaks from that part heats the cube. If sun were to shine*

*>> in through a window and heat some water inside several nested aquaria to*

*>> 100 F, that wouldn't change the amount of solar heat the cube needs to*

*>> stay 70 F on a 30 F day.*

*>You missed the point again Nick. *

*>By this point, I'm beginning to think it is deliberate.*

You might think harder about this :-) If sun shines in through a window

and heats a black spot on the floor to 100 F, that does not increase

the amount of heat the cube needs to stay 70 F on a 30 F day...

*> On a cloudy day, there is no solar gain, so all the heat comes*

*>from the tank, right? *

Right (in this simple model, with no internal heat gains.)

*> On an Average day, the solar gain equals the loss,*

*>so there is no net change in the heat tank, right?*

I think we need a little tank gain on an average day.

*> On a sunny day (only), the heat tank charge can be increased, right?*

On a sunnier or warmer than average day, when there is excess solar heat.

*>How much more energy is available on a sunny day, *

*>than on an average day, that can be used to recharge,*

About 2:1, on a clear day.

*>so we can tell how many days it takes to recharge after 5 cloudy days.*

What's the requirement, 1/(1-0.82) = 5.6 days, as in the calc below?

Perhaps that depends on economics.

*>> ... A larger solar house has more available heat storage volume, *

*>> with a lower surface to volume ratio.*

*>Lets check the surface to volume ratio. Ok, thats right.*

*>Dcube has 6x8x8 surface to 8x8x8 volume = 3:4 = 0.75 ratio*

*>A 42x42x8 house has 42x42x2+42x8x4= 3108 surface to 42x42x8 vol = 0.22 ratio*

Counting the floors, which I ignore. How about a 24' cube?

*>What about the ratio of collector surface vs the entire surface?*

*> Dcube 8x8x8 = 1/6 = 0.167*

*> 42x42x8 house = 42x8/3108 = 0.11, a smaller ratio, so even average days*

*>will draw down the heat store, *

*>and more Sunny days will be required to recharge it,*

*>unless the design parameters like R value are change to compensate.*

Different sizes and shapes need different R-values. Is that surprising?

Nick

20 N0000!'simulate days

30 FRAC=.82'house heat/average day gain fraction

40 FOR SMAX=2 TO 8'store size (days)

50 HEAT=0:STORE=SMAX

60 FOR FLIP=1 TO N

70 IF RND>.5 THEN STORE=STORE+2'sunny day

80 STORE=STORE-FRAC'heat house

90 IF STORE>SMAX THEN STORE=SMAX'store smax days

100 IF STORE<0 THEN STORE=0:HEAT=HEAT+FRAC'purchase heat

110 NEXT FLIP

120 HEATFRAC=HEAT/N'non-solar heat fraction

130 COINFRAC=2^-SMAX'coin flip estimate

140 PRINT SMAX,HEATFRAC,COINFRAC,HEATFRAC/COINFRAC

150 NEXT SMAX

store size non-solar coin-flip fraction

(days) fraction fraction ratio

2 .1333603 .25 .5334413

3 7.934428E-02 .125 .6347543

4 5.306072E-02 .0625 .8489715

5 3.220179E-02 .03125 1.030457

6 2.200014E-02 .015625 1.408009

7 1.580112E-02 .0078125 2.022543

8 1.066005E-02 3.90625E-03 2.728973

>> 160 NETSUN=SUN-SWNL-OWL+6*TA*64*UVG-(TMIN/2-TA)*64/RC'net sun (Btu/day)>Nick, I believe the last term in line 160 above should be,>"...-24*(TMIN/2-TA)*64/RC"...