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Some modular sheds with solar closets
Looking for a nice Fall project?
How about an inexpensive, 100% solar heated shed for the back yard?
Below is a test box, a 4' x 4' "house" attached to a solar closet.
8'
R14
---------------.--------------- 30 F
| | |
| | |
| 70 F Vr Tw |
4' | | |
| "house" | solar closet |
| | |
------Vs------- ------Vc-------
| | | 4"
| Ts ggggggggggggggg
| sunspace | 4"
ggggggggggggggggggggggggggggggg
south
It could be built of 8 4' x 8' modular panels, each made from a 1 x 3
frame with a 4 x 8 sheet of Thermo-Ply attached to the inside face and
a 4 x 8 x 2" piece of Styrofoam cut to fit into the 1 x 3 frame. Thermo-Ply
is a 1/8" thick structural hardboard sheathing with one aluminized face
and one white face, that costs about 20 cents a square foot. It is made
by Simplex Corp at PO Box 10, Adrien, Michigan 49221 (517) 263-8881.
Such panels would have an R-value of 14. This would be a poorly-insulated
house, by today's standards. Each panel weighs 31 pounds, and can be
easily lifted by one person.
The sun shines in through the glazing over the air heater, which is
attached to the front of the solar closet, and a plastic film backdraft
damper Vc allows solar heated air to enter the closet and heat some 55
gallon drums full of water, when the passive air heater is warmer than
the drums.
The glazing could be Replex ((800) 726-5151) 20 mil flat, clear,
polycarbonate plastic, which comes in rolls 48" wide x 50' long,
and costs about $1.50/ft^2.
Vr is a $12 Leslie-Locke AFV-1B automatic foundation vent, available
>from Home Depot, attached to a rectangular hole at the top of the closet,
with its bimetallic spring reversed and adjusted so the louvers are
fully closed when the house is above 60 F. This will allow warm air
>from the solar closet to heat the house on a cloudy day. An open slot
at the bottom of the closet serves as the return air path.
Vs is another foundation vent, adjusted so the louvers are fully closed
at 70 F (or lower.) When the house temperature is less than 70 F, Vs will
open to allow sunspace air to warm the house. Vs has another plastic
backdraft damper in front of it so that air can only flow through Vs
>from the sunspace into the house, not in the other direction. (In this
4 x 8 structure, Vs may be closed most of the time, since the heat that
leaks through the inside west wall of the solar closet will keep the
"house" warm until the closet cools to about 120 F. Perhaps that inside
wall should have more insulation, or there should be another vent from
the house to the outside, that opens whenever the house air temperature
is more than 70 F.)
Steady-state performance
------------------------
It is interesting to calculate two temperatures above: Ts is the average
sunspace temperature when the sun is shining on an average day, and Tw is
the steady-state solar closet temperature after a string of average days,
with some sun. The sunspace in this scheme overheats to act as a parasitic
or slave heater, helping the solar closet achieve a higher temperature,
while the losses from the hot glazing on the solar closet make the air
in the sunspace hotter. The sunspace air is used to heat the house on
an average day, with some sun. (This is similar to "Khanh's Radically
New Approach to Increasing the Useful Output of a Flat-Plate Collector
Panel..." as described on pages 118-125 of William Shurcliff's 1979 book
_New Inventions in Low-Cost Solar Heating_, Published by Brick House,
except that not all the "slave heat" is lost to the outside world.)
With these assumptions:
1. The average wintertime outdoor temperature is 30 F;
2. On an average winter day, the sunspace receives 1000 Btu/ft^2 of sun
over 6 hours;
3. The average house temperature is 70 F, with no air infiltration or
internal heat generation;
4. The water and air in the solar closet and the passive air heater all have
the same temperature (approaching this requires careful design); and
5. Each layer of glazing has an R-value and solar transmittance of 1,
on an average winter day, the 8' x 8' sunspace would receive
(1) Eins = 8' x 8' x 1000 Btu/ft^2 = 64K Btu,
and this would be lost to the outside world through the sides and roof of
the structure as
(2) Eouts = 6 hours (Ts - 30) 64 ft^2/R1 Sunspace, daytime
+ 18 hours (70 - 30) 32 ft^2/R14 West sunspace, nightime
+ 18 hours (Tw - 30) 32 ft^2/R14 East sunspace, nightime
+ 24 hours (Tw - 30) 80 ft^2/R14 Solar closet, daily
+ 24 hours (70 - 30) 80 ft^2/R14 House, daily
--------------------------------
= 384 Ts + 178 Tw - 9736.
On an average winter day, the solar closet would receive
(3) Einc = 4' x 8' x 1000 Btu/ft^2 = 32K Btu,
and this would be lost through the outside world and the rest of the
house as approximately
(4) Eoutc = 6 hours (Tw - Ts) 32 ft^2/R1 To the sunspace, daytime
+ 18 hours (Tw - 30) 32 ft^2/R14 To the sunspace, nightime
+ 24 hours (Tw - 30) 80 ft^2/R14 To the outside, daily
+ 24 hours (Tw - 70) 32 ft^2/R14 To the house, daily.
--------------------------------
= -192 Ts + 425 Tw - 9188.
Setting (1) = (2) and (3) = (4), and adding (2) to (1) twice,
128K = 1,028 Tw - 28,112, so Tw = (128K + 28,112)/1,028 = 151.8 degrees F.
Substituting Tw back into (1), 64K = 384 Ts + 17,295, so Ts = 121.6 F.
So after a string of average days with some sun, the closet will be about
30 degrees warmer than the peak daytime sunspace temperature, but it will
stay at that temperature 24 hours a day, "just coasting," vs. the low-
thermal mass sunspace, which will get icy cold every night.
Cloudy-day performance
----------------------
On the first of several days with no sun, the structure will lose about
(2) Ens = 24 hours (70 - 30) 32 ft^2/R14 West sunspace
+ 24 hours (152 - 30) 32 ft^2/R14 East sunspace
+ 24 hours (152 - 30) 80 ft^2/R14 Solar closet
+ 24 hours (70 - 30) 80 ft^2/R14 House
---------------------------------
= 31,103 Btu.
If a 4' x 4' x 8' solar closet contains 8 55 gallon drums full of water,
along with some cement blocks and plastic soda bottles, it might have a
thermal mass of 4647 Btu/F (see below) so on the first day with no sun,
the water temperature would decrease by about Ens/C = 6.5 degrees F. If
the closet lost heat at this rate every day until it reached a minimum
usable temperature of say, 80 F, (as the closet cools down, it actually
loses heat more slowly), it could provide useful heat for the "house"
for at least (152-80)/6.5 = 11 days in a row with no sun. Taking account
of the fact that the closet cools more slowly as time goes on, it should
provide heat for about 14 days without sun. Adding an extra layer of
2" Styrofoam to make all sides of the closet to make it an R24 box,
should extend the time it takes to cool to 80 F, while keeping the
"house" warm, to about 26 days:
10 '4' x 8' solar closet carryover
20 ' find steady-state closet temp
30 EINS=64000!'sunspace solar gain (Btu/day)
40 EINC=32000'closet solar gain (Btu/day)
50 CWS=18*32/24+24*80/24'sunspace Tw factor
60 CWC=6*32/1+18*32/24+24*80/24+24*32/24'closet Tw factor
70 CS=6*30*64/1+18*30*32/24+24*30*80/24'sunspace constant
80 CS=CS-18*(70-30)*32/14-24*(70-30)*80/14'more sunspace constant
90 CC=18*30*32/24+24*30*80/24+24*70*32/24'closet constant
100 TW=(EINS+2*EINC+CS+2*CC)/(CWS+2*CWC)'initial solar closet temperature
140 C=4647'thermal mass of solar closet (Btu/F)
150 CLOSS=24*(70-30)*32/14'constant daily west sunspace heat loss (Btu)
160 CLOSS=CLOSS+24*(70-30)*80/14'constant daily house heat loss (Btu)
163 PRINT " Temp at"
165 PRINT "Day end of day"
170 FOR D=2 TO 30 STEP 2'calc closet temp for 30 days without sun
180 TLOSS=24*(TW-30)*(32+80)/24'solar closet daily heat loss
190 HEATLOSS = CLOSS+TLOSS
200 TW=TW-2*HEATLOSS/C'new solar closet temperature
210 PRINT D,INT(TW+.5)
220 NEXT D
RUN
Temp (F) at
Day end of day
2 181
4 171
6 161
8 151
10 142
12 133
14 125
16 117
18 109
20 102
22 96
24 89
26 83
28 77
30 72
Larger sheds
------------
Each R14 4 x 8 panel loses about 2,200 Btu/day to the outside, which is
approximately the amount of heat one can collect from 3 ft^2 of sunspace
under the above conditions, approximating Philadelphia area weather in
December, so a larger shed, with N panels exposed to the outside air,
should have about N/10 panels with sunspace glazing, as a rule of thumb.
The 22,000 Btu/day needs to be collected over 6 hours, ie 3600 Btu/hour.
With 100 F air and a 70 F room, this requires an airflow rate of about
120 cfm, or an opening with area Av at the top and bottom of each 4 x 8
panel such that 120 cfm = 16.6 Av sqrt(8'(100-30)) (see appendix), ie
Av = 0.47 ft^2, so one 8" x 16" foundation vent per panel (0.89 ft^2)
may work.
Each panel loses about 12K Btu in 5 days, about the same as the heat
stored in half a 55 gallon drum full of water at 130 F, or 1/20 of a
4' x 4' x 8' solar closet module. So as another rule of thumb, for every
20 exterior panels used in the shed, one should include 1 4' x 4' solar
closet space, 8' high. On a cold winter night when it's -10 F outside,
the solar closet needs to provide about 3600 Btu/hour, to keep the shed
at 70 F, which it might do with an internal temperature of 100 F, with
one foundation vent, as above, or at 80 F with 3 foundation vents.
Below are some possible sheds, and their approximate characteristics:
10 'Modular solar closet compiler (MSCC)
20 PA=4*8'panel area (ft^2)
30 RP=14'R-value of panel
40 TIN=70'temperature inside shed (F)
50 TA=30'temperature outside shed (F)
60 SUN=1000'sun shining on south wall on an average 6-hour day (Btu/ft^2)
70 DPL=24*(TIN-TA)*PA/RP'daily heat loss from one panel
80 DPG=SUN*PA-6*PA*(TIN-TA)'average daily solar gain for a glazed panel
90 PRINT "1000'"
100 PRINT"Daily panel loss (Btu): "; INT(DPL+.5)
110 PRINT"Daily glazed panel gain (Btu):"; INT(DPG+.5)
120 PRINT"
130 PRINT" matl SS Closet percent min # days"
140 PRINT" Size NP NRP NGP NSC Cost temp temp floorsp carryover"
150 PRINT"
160 FOR W=20 TO 32 STEP 4'width of shed
170 FOR L=W TO W+8 STEP 4'length of shed
175 N=N+1
180 NPP = 2*(L/4+W/4)'number of perimeter panels
190 NPPC=6+3+16+6'cost of perimeter panel, including battens
200 NRP=INT(L*W/32+.5)'number of roof panels
210 NP =INT(NPP+NRP+.5)'total number of exterior panels
220 NGP=INT(NP/10)+1'number of sunspace panels required
230 NSC=INT(NP/20)+1'number of 4' x 4' x 8' solar closet modules
240 TCOST=INT(NP*NPPC+NRP*.28*32+NGP*32+NSC*32+.5)'materials cost
250 EINT=SUN*PA*NGP'solar heat received by glazed panels
260 EOUTF=18*(TIN-TA)*NGP*PA/RP+24*(TIN-TA)*PA*(NP-NGP)/RP-6*30*NGP*PA
270 TS=INT((EINT-EOUTF)/(6*NGP*PA)+.5)'average daytime sunspace temp
280 EINS=SUN*PA*NSC'sun falling on solar closet
290 EDEN=6*NSC*PA+18*NSC*PA/RP+24*NSC*48/RP+24*(NSC+1)*PA/RP
300 EOUTF=NSC*(6*TS*PA+18*TA*PA/RP+24*TA*PA/RP+24*TIN*(NSC+1)*PA/RP)
310 TC=INT((EINS+EOUTF)/EDEN+.5)'steady-state solar closet temperature
320 ENS=24*(TIN-TA)*NP*PA/RP'energy lost during a day without sun
330 EST=NSC*4647*(TC-80)'useful energy stored in solar closet
340 CAR=INT(EST/ENS+.5)'number of days without sun supported
350 PCT =INT(100*NSC*16/(L*W)+.5)
360 PRINT W;"X";L;TAB(17);NP;TAB(21);NRP;TAB(26);NGP;TAB(31);NSC;TAB(36);TCOST;
370 PRINT TAB(42);TS;TAB(48);TC;TAB(56);PCT;TAB(65);CAR
380 NEXT L
390 NEXT W
400 PRINT
RUN
Daily panel loss (Btu): 2,194
Daily glazed panel gain (Btu): 24,320
matl SS Closet percent min # days
Size NP NRP NGP NSC Cost temp temp floorsp carryover
8 X 8' 10 2 2 1 424 142 164 25 18
8 X 12 13 3 2 1 526 125 157 17 13
8 X 16 16 4 2 1 628 108 149 13 9
12 X 12 17 5 2 1 668 102 146 11 8
12 X 16 20 6 3 2 834 123 176 17 20
12 X 20 24 8 3 2 976 108 169 13 16
16 X 16 24 8 3 2 976 108 169 13 16
16 X 20 28 10 3 2 1118 93 162 10 12
16 X 24 32 12 4 2 1292 108 169 8 12
20 X 20 33 13 4 2 1331 105 167 8 11
20 X 24 37 15 4 2 1473 94 162 7 9
20 X 28 42 18 5 3 1719 104 181 9 15
24 X 24 42 18 5 3 1719 104 181 8 15
24 X 28 47 21 5 3 1901 92 175 7 13
24 X 32 52 24 6 3 2115 100 179 6 12
28 X 28 53 25 6 3 2155 99 178 6 12
28 X 32 58 28 6 3 2337 89 173 5 10
28 X 36 64 32 7 4 2623 95 188 6 14
32 X 32 64 32 7 4 2623 95 188 6 14
32 X 36 70 36 8 4 2877 100 191 6 13
32 X 40 76 40 8 4 3098 91 186 5 12
Some sketches of larger sheds
-----------------------------
12'
-------.-------.------- 30 F
| |
| |
| 4' |
8' . 70 F ---Vr--.
| | |
| 4'| 157 F |
| | |
-------.--Vs---.---Vc--
| | | 4"
| 125 F ggggggg
| | 4"
ggggggggggggggg
24'
-------.-------.-------.-------.-------.------- 30 F
| |
| |
| |
. .
| |
| |
| |
16'. 70 F .
| |
| 8' |
| |
. ---Vr--.---Vr--.
| | |
| 4'| 169 F |
| | |
-------.-------.---Vs--.---Vs--.---Vc--.---Vc--
| | | | 4"
| 108 F ggggggg ggggggg
| | 4"
ggggggggggggggggggggggggggggggg
28'
---.---.---.---.---.---.--- 30 F
| |
. .
| |
. .
| |
24'. 70 F .
| |
. .
| 12' |
. .-Vr.-Vr.-Vr.
| 4'| 175 F |
---.---.-Vs.-Vs.-Vc.-Vc.-Vc
| | | | | 4"
| 92 F ggg ggg ggg
| | 4"
ggggggggggggggggggg
36'
---.---.---.---.---.---.---.---.---.---.---.--- 30 F
| |
. .
| |
. .
| |
. .
28'| 70 F |
. .
| |
. .
| 16' |
. -Vr.-Vr.-Vr.-Vr.
| 4'| 188 F |
---.---.---.---.---.-Vs.-Vs.-Vs.-Vc.-Vc.-Vc.-Vc
| | | | | | 4"
| 95 F ggg ggg ggg ggg
| | 4"
ggggggggggggggggggggggggggg
Air heater performance
----------------------
Below is a small theoretical air heater exploration...
10 'Some simplified solar air heater calculations, with radiant heat loss.
20 ' (in a linear model, the collector heat loss only depends on the
30 ' air temperatures, not on the collector plate area...)
40 '
50 'Assumptions: uniform air and plate temperatures inside collector
60 ' shadecloth has 2 ft^2 heat xfr area/ft^2 surface area
70 ' rough plate surfaces, smooth glazing surfaces
80 ' all absorptivities and emissivities = 1
90 ' shortwave glass transmission = 1
100 ' longwave glass transmission = 0
110 ' no back or edge losses
120 '
130 ' Model: large air gap
140 ' /
150 ' | shadecloth / | outside air
160 ' |<-absorber plate->| | temp at Ta = 80 F
170 ' | with area | | moving at 0 mph
180 ' | Ap (ft^2) and | |
190 ' | temp Tp (R) | | <--Io = 147 Btu/hr/ft^2 lw rad
200 ' | | | from 80 F surround
210 ' | Tp | Tp | Tg
220 ' | |<----------|------Is= 300 Btu/hr sw rad
230 ' | ^ | | from sun
240 ' | | | | Ugo
250 ' | airspeed V | |---www--- Ta (R)
260 ' | | |
270 ' | air temp | | 1 ft^2 glazing
280 ' | Tc (R) | | with temp Tg (R)
290 ' | Up | | Ugi |
300 ' |--www-------------|------www--|
310 ' | | |
320 ' | Ir--> | <--Ig | Ig--> lw heat radiated
330 ' | lw heat | | from glazing
340 ' radiated by
350 ' plate to glazing
360 '
370 'at equilibrium,
380 ' (1) Is - Ir + Ig - (Tp-Tc)UpAp = 0, for the plate surface, and
390 ' (2) Io + Ir - 2Ig - (Tg-Tc)Ugi - (Tg-Ta)Ugo = 0, for the glazing
400 '
410 B=1.74E-09'Boltzman's constant
420 IS = 300'Btu/ft^2/hour peak sun input
430 UGI = 3/2'U-value of glazing to slow-moving inside air
440 UGO = 3/2+0/5'U-value of glazing to fast-moving outside air
450 TA = 460 + 80'outside air temperature (R)
460 IO = B*TA^4'rad from outside world to glazing
470 FOR AP = 1 TO 5 STEP 2'collector plate area (ft^2)
480 PRINT INT(AP/2);"shadecloth layers"
490 FOR V=0 TO 4 STEP 2'air velocity in mph
500 UP = 2 + V/2'U-value of surfaces exposed to air
510 FOR TCC=80 TO 140 STEP 20'solar closet air temp (F)
520 TC=460+TCC'solar closet air temp (R)
530 TP = 600'initial guess at Tp (R)
540 TG = 500'initial guess at Tg (R)
550 IG = B*TG^4'heat radiated by glazing in each direction
560 TPL=TP'overall last Tp
570 GOSUB 700'determine new Tp
580 TGL=TG'overall last Tg
590 GOSUB 750'determine new Tg
600 IF ABS(TP-TPL)>1 OR ABS(TG-TGL)>1 THEN GOTO 560
610 EFF = 100*((TP-TC)*UP*AP+(TG-TC)*UGI)/IS'solar collection efficiency
620 PRINT TAB(2);"V = ";V;" ";"Tc =";TCC;TAB(22);"Tp =";INT(TP-459.5);
630 PRINT TAB(33);"Tg =";INT(TG-459.5);TAB(44);"EFF =";INT(EFF+.5);"%"
640 NEXT TCC
650 PRINT
660 NEXT V
670 IF V < 4 THEN PRINT #1
680 NEXT AP
690 END
700 IR = B*TP^4'heat radiated by absorber plate to glazing
710 TPH = TC + (IS-IR+IG)/(UP*AP)'solving (1) for Tp
720 TP = TP + .1*(TPH-TP)'adjust Tp
730 IF ABS(TP-TPH)>1 GOTO 700' stop when Tp converges to 1 degree F
740 RETURN
750 IG = B*TG^4'heat radiated by glazing in each direction
760 TGH = (IO+IR-2*IG+TC*UGI+TA*UGO)/(UGI+UGO)'solving (2) for Tg
770 TG = TG + .1*(TGH-TG)'adjust Tg
780 IF ABS(TG-TGH)>1 THEN GOTO 750'stop when Tg converges to 1 degree F
790 RETURN
RUN
0 shadecloth layers
V = 0 Tc = 80 Tp = 176 Tg = 105 EFF = 76 % |
V = 0 Tc = 100 Tp = 189 Tg = 115 EFF = 67 % | No fan...
V = 0 Tc = 120 Tp = 203 Tg = 125 EFF = 58 % |
V = 0 Tc = 140 Tp = 216 Tg = 135 EFF = 48 % |
V = 2 Tc = 80 Tp = 153 Tg = 98 EFF = 82 %
V = 2 Tc = 100 Tp = 169 Tg = 108 EFF = 73 %
V = 2 Tc = 120 Tp = 184 Tg = 118 EFF = 63 %
V = 2 Tc = 140 Tp = 199 Tg = 129 EFF = 54 %
V = 4 Tc = 80 Tp = 139 Tg = 94 EFF = 86 %
V = 4 Tc = 100 Tp = 156 Tg = 104 EFF = 76 %
V = 4 Tc = 120 Tp = 172 Tg = 115 EFF = 67 %
V = 4 Tc = 140 Tp = 188 Tg = 125 EFF = 57 %
It looks to me that a fan might increase the efficiency of an air
heater with no mesh absorber, ie a box with a black surface inside,
with air flowing between the glazing and the surface, by a few percent
(48-->57% at 140 F), but when you add a mesh absorber, with air flowing
through the absorber, the fan only seems to help by 2 or 3%:
1 shadecloth layers
V = 0 Tc = 80 Tp = 122 Tg = 89 EFF = 89 % <--
V = 0 Tc = 100 Tp = 140 Tg = 100 EFF = 80 % |
V = 0 Tc = 120 Tp = 157 Tg = 110 EFF = 70 % |
V = 0 Tc = 140 Tp = 175 Tg = 121 EFF = 60 % <--|-- the fan
| doesn't
V = 2 Tc = 80 Tp = 109 Tg = 86 EFF = 91 % | help
V = 2 Tc = 100 Tp = 128 Tg = 97 EFF = 82 % | much
V = 2 Tc = 120 Tp = 146 Tg = 107 EFF = 72 % | here
V = 2 Tc = 140 Tp = 164 Tg = 118 EFF = 62 % | |
| |
V = 4 Tc = 80 Tp = 102 Tg = 85 EFF = 92 % | |
V = 4 Tc = 100 Tp = 121 Tg = 95 EFF = 83 % | |
V = 4 Tc = 120 Tp = 140 Tg = 105 EFF = 73 % | |
V = 4 Tc = 140 Tp = 159 Tg = 116 EFF = 63 % <--|---
|
|
2 shadecloth layers |
|
V = 0 Tc = 80 Tp = 107 Tg = 86 EFF = 91 % <-----additional
V = 0 Tc = 100 Tp = 125 Tg = 96 EFF = 82 % layers of
V = 0 Tc = 120 Tp = 144 Tg = 106 EFF = 72 % mesh don't
V = 0 Tc = 140 Tp = 162 Tg = 117 EFF = 62 % seem to
help much
V = 2 Tc = 80 Tp = 98 Tg = 83 EFF = 91 % either
V = 2 Tc = 100 Tp = 117 Tg = 94 EFF = 83 %
V = 2 Tc = 120 Tp = 136 Tg = 104 EFF = 73 %
V = 2 Tc = 140 Tp = 155 Tg = 115 EFF = 63 %
V = 4 Tc = 80 Tp = 93 Tg = 83 EFF = 91 %
V = 4 Tc = 100 Tp = 113 Tg = 93 EFF = 81 %
V = 4 Tc = 120 Tp = 132 Tg = 103 EFF = 73 %
V = 4 Tc = 140 Tp = 151 Tg = 114 EFF = 62 %
How long will it take a solar closet to charge up?
--------------------------------------------------
If it is fully discharged to a minimum usable temperature of 80 F, it looks
like a solar closet will take about 20 days to charge back up to 130 F:
10 'solar closet simulation, with natural convection
20 C=4647'thermal mass of solar closet (Btu/F)
30 TA=70'ambient temp of closet surroundings (F)
40 SUN=32*1000/6'solar input (Btu/hr)
50 TW=80'initial water temp (F)
60 Q=300'initial assumption for airflow (cfm)
70 SAR=(32*3+16)/14'back loss factor
80 PRINT"Day Tw airflow Tmax Tmin"
90 FOR DAY=1 TO 20
100 BOXLOSS=(TW-TA)*SAR*24+(TW-30)*32/14*18'daily heat loss from solar closet
110 HTRLOSS=(TW+DT/2-TA)*32/1'air heater loss (Btu/hr)
120 DT=(SUN-HTRLOSS)/Q'delta T from solar input
130 QL=Q'last estimate of Q
140 Q=94*SQR(DT)'new estimate of Q
150 IF ABS(QL-Q)/Q>.01 GOTO 110'iterate until < 1% change
160 NTU=539*1.5/Q'heat exchange xfr units per p. 3-4 of 1993 ASHRAE HOF
170 EFF=1-EXP(-NTU)'heat exchanger effectiveness
180 TMAX=TW+DT/EFF'max air temp entering closet
190 TMIN=TMAX-EFF*(TMAX-TW)'min air temp leaving closet
200 DTG=TMAX-TMIN'delta T of air through closet
210 SGAIN=6*Q*DTG'daily solar gain
230 PRINT DAY;TAB(12);INT(TW+.5);TAB(17);INT(Q+.5);
232 PRINT TAB(26);INT(TMAX+.5);TAB(33);INT(TMIN+.5)
235 TW=TW+(SGAIN-BOXLOSS)/C'new water temp (F)
240 NEXT DAY
Day Tw airflow Tmax Tmin
1 80 349 95 82
2 85 344 100 87
3 90 342 105 92
4 95 336 109 96
5 99 335 113 100
6 102 332 116 104
7 106 327 119 107
8 109 324 122 110
9 111 322 124 112
10 114 320 126 115
11 116 318 129 117
12 118 317 130 119
13 120 315 132 121
14 122 313 134 123
15 123 312 135 124
16 125 311 136 126
17 126 310 138 127
18 127 308 139 128
19 128 307 140 129
20 129 307 141 130
Will this make the shed 100% solar heated? I don't know. A simulation
with hourly weather data over a few years would answer this question.
One way to build an R14 4 x 8 panel
-----------------------------------
The panels might look like this: 1 Styrofoam 1
x ------------ x
s are 1/2" x 2" foam strip spacers 3s s s3
---Thermo-Ply---
(white side)
Find a 4' x 8' flat surface to work on.
Cut 2 46.5" pieces off of a 1 x 3, and combine them with 2 8' 1 x 3s to make
a 4 x 8' frame of 1 x3s joined along the 2.5" edges, with 2 2 1/2" drywall
screws and some adhesive in each corner.
Put a bead of adhesive along the .75" top edge of the 1 x 3 frame, and
place the Thermo-Ply on top of the frame, white side up, aluminized side down.
Screw on the Thermo-Ply with 1 drywall screw every 16" around the frame.
Make and stack up some more frames on top of this one.
Allow the adhesive to dry.
Cut a 1 1/2" strip off the short edge of the Styrofoam.
Cut 3 strips off long edge of Styrofoam, each 94.5" x 2" x .5".
Glue 2 of the 94.5" strips flat, along the long edges of the printed
side of the piece of Styrofoam.
Cut 2 44" pieces off the other 94.5" strip.
Glue the 44" strips flat along the short edges of the piece of Styrofoam.
Glue the small remainder of the last 94.5" strip onto the middle
of the Styrofoam.
Place the large piece of Styrofoam into a 1 x 3 frame, with the
spacers against the Thermo-Ply.
After assembly, the Thermo-Ply will be on the inside of the shed and the
Styrofoam will be on the outside.
Glazed panel construction
-------------------------
Front panels for solar closets may be made as above, substituting 1 x 10s
for the 1 x 3s, and adding a diagonal layer of 80% black greenhouse
shadecloth a few inches south of the Styrofoam, and a layer of flat
polycarbonate glazing 9.25" in front of the Thermo-Ply sheet, as
sketched below.
Glazed sunspace panels may be conveniently made with a layer of flat
polycarbonate glazing attached to a 1 x 3 frame with some 1/16" thick
x 3/4" or 1 1/2" wide x 96" aluminum batten strips, with no foam or other
sheathing on the frame. The sunspace panels would sit on an extension of
the 2 x 4 foundation boards, about 16" from the front of the solar closet
panels, and they could be covered and supported on the tops and sides
by a 16" strip of plywood or exterior flakeboard, as shown below. The
EPDM rubber roof should cover the top of the plywood.
4' 4'
--------------|1|1|----------------|1|1|-------------------|1|p| -- 0"
foam |x|x| foam |x|x| foam |x|l|
--------------|3|3|----------------|3|1|-------------------|1|y| -- 2.5"
|p|1x3| 1 x 3 |0| 1 x 3 |0|w|
|l| | | | | |o|
|y|1| shadecloth | | shadecloth | |o|
|w|x| | | | |d|
|o|3| | | | | |
|o|--------------------| |-------------------| | | -- 6.75"
|d| 1 x 3 | | 1 x 3 | | |
| |--------------------| |---------------------| | -- 9.25"
| | no glazing --- glazing ---| |
| | Al Al| |
| | | |
| | | |
| | | |
| |1|----------------|1|1|-------------------|1| | -- 13.5"
| |x| |x|x| |x| |
| |3|----------------|3|3|-------------------|3| | -- 16"
----- glazing ----- glazing -----
Al Al Al
It would look something like this from the west side:
0" 2.5" 6.75" 9.25" 13.5" 16"
| | | | | |
-------------------------------------------------
| p l y w o o d |
-------------------------------------------------
| 1 x 3 | .| 1 x 3 | | 1 x 3 |
|-------| |-------| |-------|
. . | | | |
. 1 . | 1 | s | 1 | s
Vc . x . 8" | x | o | x | u
. 3 . . | 3 | l | 3 | n
. ----- . | | a | | s
| | | | r | | p
| f | s | | | | a
| o | h | | c | | c
| a | a . | | l | | e
T| m | d | | o | |
h| | e | | s | | g
e| | c | | e | | l |
r| | l | | t | | a
m| | o. | | | | z 8'
o| | t | | g | | i
-| | h | | l | | n |
P| | | | a | | g
l| | | | z | |
y| | . | | i | | south-->
| | | | n | |
| | | | g | |
| | | | | |
| | | | | |
| f | | | | |
| o |1|. | | | |
| a |x|. | | | |
| m |3|. | | | |
|------ |. | | | |
. . | | | |
. . | | | |
8". .Vc | | | |
. . | | | |
. . | | | |
|-------| |-------| |-------|
| 1 x 3 | | 1 x 3 | | 1 x 3 |
-------------------------------------------------
| p l y w o o d |
-------- -------------------------------------------------
pressure-treated 2 x 4 |
----------------------------------------------------------
pressure-treated 2 x 4 |
-------------------------------------------------------------------------
Solar closet construction
-------------------------
It is important that the thermal mass in the solar closet be large and
thermally conductive, and have a large surface area compared to the glazed
area of the closet, so that the sun-warmed air is not much warmer than the
thermal mass. It is also important that the airflow path through the thermal
mass have a large cross section, at least, say, 5% of the glazed area of
the closet, so that air flows freely and with a large volume through the
closet by natural convection. Section A of the diagram below shows an open
area for vertical airflow, Av, of approximately
Av = 4'x 4' - 4 pi (23"/2')^2/144 - 25 pi ((4.25"/2)^2)/144 = 2 ft^2,
which is about 6% of the glazed area of the closet.
The diagram below shows several kinds of water containers and materials
with various sizes in inches, weights in pounds, thermal masses in Btu/F
and surface areas in ft^2.
appr approx spec ther surf
Container size # weight heat mass area location
55 gal drum 23 D 8 450 1 3,600 200 D
(plastic) x 35 H
2 liter bottle 4.25 D 150 4.2 1 630 136 B, around drums
(plastic) x 12 H 36 151 33 on top
Blocks 8 x 8 24 30 0.16 115 120 C
(cement) x 16
1 liter bottle 3 D 72 2.1 1 151 50 b
x 11 H --------
Totals 4647 539
4'
----------|-----------|-----------|---------- --96"
| |
| |
| |
A-| - - - - - - - - |---cross section A
| B B B B B B B B B B B B |
-------------------------------------------------86"
| | | |
| | | |
| | | |
| | | |
| | | |
- | | -
| | | |
| | | |
| D | | D |
| | | |
| | | |
- | | -
| | | |
| | | |
| | | |
| | | |
| | | |
8' =---------------------------------------------=--51"
| C | C | C |
| | | |
| b b b | b b b | b b b |
|---------------------------------------------|--43"
| | | |
- | | -
| | | |
| | | |
| | | |
| | | |
| | | |
- D | | D -
| | | |
| | | |
B-| - - - - | | - - - - |---cross section B
| | | |
| | | |
- | | -
| | | |
|---------------------------------------------|--8"
| C | C | C |
C-| | | |---cross section C
| b b b | b b b | b b b |
-----------|----------|----------|----------- --0"
| | | | | | | |
--- --- --- ---
^--- 2 pressure-treated 2 x 4s laid flat on ground
Cross section A, showing the top of the solar closet, with 4 vertical
drums supporting 36 horizontal 2 liter bottles, with an optional fan
blowing room air in at the top of the closet, so that warmer air will
flow out of the bottom of the closet:
-----------|----------|----------|-----------
| . . . | (fan?) | . . . |
| . ----------- . |
| . . . . |
| .B B B B B B. .B B B B B B . |
|. . . .|
-. D . . D .-
|. . . .|
| .B B B B B B. .B B B B B B . |
| . . . . |
| . . . . |
| . . . . . . |
- -
| . . . . . . |
| . . . . |
| . . . . |
| .B B B B B B. .B B B B B B . |
|. . . .|
-. D . . D .-
|. . . .|
| . . . . |
| . . . . |
| . . . . |
| p l a s t i c f i l m d a m p e r |
----------|-----------|-----------|----------
Cross section B, showing 4 drums and 25 vertical 2 liter bottles
surrounding the drums:
-----------|----------|----------|-----------
| B . . . B B . . . B|
| . . B . . |
| . . . . |
| . . . . |
|. . . .|
-. D . . D .-
|. . . .|
| . . . . |
| . . . . |
| . . B . . |
| B . . . B B . . . B |
- B B B B B -
| B . . . B B . . . B |
| . . B . . |
| . . . . |
| . . . . |
|. . . .|
-. D . . D .-
|. . . .|
| . . . . |
| . . . . |
| . . B . . |
|B . . . B B . . . B|
----------|-----------|-----------|----------
Cross section C, showing the lower part of the solar closet with an optional
charging fan and 12 blocks supporting 4 drums (36 1 liter soda bottles, not
shown, are lined up with the 3 north-south-running holes of each block):
(plastic film damper, if a discharge fan is used)
-----------|----------|----------|-----------
|---------------------------------------------|--46"
| C . | C . | C . |
| . | . . | . |
| . | . . | . |
|---------------------------------------------|--38"
------------D---------------------D--------------36"
|.C | C . . | C .|
| . | . . | . |
| . | . . | . |
|---------------------------------------------|--28"
| . . . | | . . . |
- | | -
| . . . | | . . . |
|---------------------------------------------|--22"
| C. | C . . | C . |
| . | . . . |
|---------------------------------------------|--14"
------------D---------------------D--------------12"
|.C | C . . | C .|
| . | . . | . i
|---------------------------------------------|--4"
| . ----------- . |
| . . . | (fan?) | . . . |
----------|-----------|-----------|----------
p l a s t i c f i l m d a m p e r
This closet has 539 ft^2 of thermal mass surface area exposed to solar
heated air, ie about 17 square feet of thermal mass per square foot of
glazing. So if the passive air heater were 100% efficient, and the solar
closet were collecting 100% of the 300 Btu/ft^2/hour of energy falling
on it in peak sunlight, the air in the closet might be 300/17 = 18 F
warmer than the thermal mass. The drums used are made of plastic, with flat
bottoms, so they can conduct heat away from the cement blocks, which
act as fins for the drums. The vertical plastic bottles will be a tight
fit, so they will be in thermal contact with the drums as well.
Assembling sheds
----------------
Put two layers of pressure-treated 2 x 4s flat on the ground, to make an
8' x 12' frame, on top of some level crushed stone.
Place a 2 x 4 under the bottom edge of each panel, with the 4' outside
edge of the panel resting along the outside edge of the 2 x 4, and attach
the 2 x 4s to the 1 x 3 bottom of each frame with a drywall screw every
12". Tilt up the frames onto the layer of 2 x 4s on the ground, and screw
the top layer of 2 x 4's to the bottom layer, on the inside of the shed.
When this is done, the inside of the shed should have an 1" lip of 2 x 4
showing on the ground.
To join two frames along a wall, attach the vertical edges of the frames
with a 1 x 3 battens on the inside and the outside of each frame, using a
drywall screw every 16":
1 x 3 1 x 3 corner detail 1 x 3
1 1 - Styrofoam- 1 1 -Styrofoam-1
x x x x x
3 3s s s3 3 Thermo-Ply-3 1 x 3 1
---.---Thermo-Ply---.-- 1 x 3 x
1 x 3 1 x 3 | | 3
Cut one 8' pressure treated 2 x 4 into several pieces.
Lay two pieces flat on the ground diagonally inside the SW, NE and NW corners
of the shed, and put a 55 gallon drum on top of the two pieces, with the
outside edges of the drum resting on the inside edges of the two 2 x 4s
under the corner panels. Fill the drums with water and cap them.
Roof details
------------
If the shed is constructed to have a interior dimensions that are
exact multiples of 4' and 8', and the roof panels are 4' x 8', the
roof panels should rest on top of the 1 x 3 horizontal battens on the
inside top edge of the wall panels (which would be screwed on edgewise
to the roof, as in the above corner detail.) The walls would extend
out 2 1/2" from the roof on every side, and the outside wall battens
would extend another 3/4". A large single piece of EPDM rubber would
overlap this joint where the walls meet the roof, and it would be
attached to the walls 3 1/4" below the top of the roof:
Place more panels on the roof, and cover the roof with a large single
piece of EPDM rubber roofing material (which costs about 30 cents/ft^2
and comes in rolls 20' wide.) Put some old tires on top of the rubber
to keep it in place and reduce summer heat gain and lend an attractive
"alternate energy" look to the shed.
Tack the edge of the roof rubber over the 1 x 3 horizontal battens on
the outside of the wall panels.
Paint all the exposed battens and Styrofoam with latex paint. Steve
Baer says that latex-painted foam will last practically forever outside.
Appendix
--------
Thermo-Ply is hard to find. It is strong and inexpensive, and made from
100% recycled fibers, but it also shrinks and delaminates unhappily if it
gets wet or hot, or both. One might also use thin plywood or flakeboard
for the 4 x 8 panels, with 3" vs 2" Styrofoam, or Thermo-Ply with two
polyethylene faces instead of the poly/foil-faced kind which is harder
to find. To this one might add a layer of 4' wide, double-sided "builder's
foil" such as the "Super R Radiant Barrier" (ES302--48" x 125' for $125)
sold by Jade Mountain at (800) 449-6601 or Innovative Insulation at
(800) 825-0123. With a 1/2" spacer in the center of the panel, between
the plywood and the foil, and a 1/2" spacer strip around the edge of the
panel, between the foil and the foam, a plywood/foil/foam panel should
have an R-value of about 16. One could also use thicker foam and wider
panels to get more insulation value.
Houses with better insulation require fewer sunspace and solar closet
modules. A house with an average exterior insulation value of R24
would only require about N/20 sunspace panels and N/40 solar closets,
if it had N exterior 4' x 8' panels, in the Philadelphia area.
A real house built this way might use drywall on the inside of the panel
(which would add some desirable thermal mass to the house, for overnight
heat storage), with more another vertical support in the middle, and
diagonal galvanized metal strips for cross-bracing each panel. It might
still use aluminum foil as additional insulation and a vapor barrier,
with beadboard or Styrofoam in the middle of the panel, and stucco,
Dri-Vit, or Flexlite on the outside. Or the foam might be covered with
T-111 or a thin sheet of galvanized metal or vinyl siding.
The edges of the panel sheathing should be beveled at 45 degrees, if
the panels are to fit together at corners exactly on 4' x 8' centers,
in a completely modular way.
One might well increase the amount of insulation on the solar closet walls,
especially the east wall, by gluing on another Styrofoam panel to the outside
of that wall. One might also increase the roof insulation level, by laying
more beadboard or Styrofoam on top, under the rubber, or putting some
fiberglass insulation up under the rafters with curved wires.
Plastic soda bottles are good water containers to use in a solar
closet, because they have a large surface-to-volume ratio, vs eg 55
gallon drums, however they have some drawbacks: they require a support
structure; they become weak and shrink at temperatures above 130 F;
and they are time-consuming to fill.
Greenhouse shadecloth is cheap, about 15 cents per square foot from
Stuppy (800) 423-1512, for 80%-absorbing, porous, black, polyethylene
shadecloth, but it too has drawbacks: it shrinks about 20% at 212 F,
although it stays fairly strong. Other "transpired absorbers" might be
a layer of 50% black shadecloth behind a layer of 50% green shadecloth,
for aesthetics. Or black aluminum window screen or painted black metal
lath. Simply painting the Styrofoam black would probably not be a good
idea, because it might melt.
Other things that may melt include the plastic flap dampers Vc, inside
the solar closet. It is a good idea to use a high temperature, lightweight
plastic for the dampers, such as 1 mil Tedlar film.
Suppose there is more than one solar closet module, as in the 28' x 36'
structure above, and there is a fin-tube pipe, say 20' long, near the
ceiling of the closet to make hot water in a conventional water heater
with an insulated tank above the closet, using a convective water loop.
Then, in order to maximize the solar hot water fraction provided by the
closet during cloudy weather, one might build the internal (north-south)
closet partitions every 4', and set the Vr vents on the east side of the
building to open at a higher temperature than the ones in the middle,
so that the closet module temperatures are stratified, ie the modules
near the center of the building are progressively warmer than the eastern
one. Then cold water could enter the eastern closet module, and be
progressively preheated until it leaves the western one, leaving to
circulate back to the water heater above the closet at a high temperature,
even after several cloudy days. Two additional solar closet modules,
beyond the N/20 rule of thumb above, should supply close to 100% of the
hot water needs of a house, as well as the space heating needs of the
house, even during long periods of cloudy winter weather.
Interior ground stakes could be used instead of 55 gallon drums at the
corners of the shed, to hold it down in the wind. A suitable ground stake
might be a 3' long, 1" diameter galvanized pipe with a lag bolt into
one of the pressure treated 2 x 4s on the ground.
The sunspace could be a lean-to sunspace, instead of shallow glazed panels,
extending out from the front of the structure. This might work better
thermally, and it might be easier to build, and provide a place to grow
plants or store things, or put a reflector in front of the solar closet,
that stays clean, out of the weather. It would also probably cost more,
and it would have larger thermal losses, since it would have a larger area
exposed to the cold outside air. A taller sunspace would naturally go along
with making the roof higher in front and pitching it back from south to
north, (a shed roof) instead of making it flat.
As a less expensive alternative, the sunspace glazing might be 3-year
poly greenhouse film, which costs about 5 cents per square foot, and
comes in very large sheets. It is easily attached with aluminum
extrusion clamps, and takes about a hour to change, every 3 years. It
is recyclable.
The tires on the roof might contain dirt, and the roof itself might
have 2-3" of dirt on top, which would require that it be stronger.
Two-story structures lose less heat per square foot of floorspace than
one-story structures, since they have better surface to floorspace-volume
ratios. And for the same solar area, a taller sunspace or solar closet,
eg a two-story version, should work better than a wider one, since there
would be more convective airflow. According to one approximate formula, the
natural airflow in a chimney is Q = 16.6 Av sqrt(H*dT), where Q is in cfm,
Av is the vent area at top and bottom in ft^2, H is the chimney height
in feet and dT is the difference (F) between the air temperature at the
top and bottom of the chimney (sqrt means "square root," above.) To find
the amount of airflow in a sunspace, one can use the facts that full sun
adds about 300 Btu/ft^2/hr of heat through the glazing to the sunspace,
some of which heat passes back out of the glazing, and 1 Btu can heat
55 ft^3 of air 1 degree F.
One might use a fan and thermostat or differential or setback thermostats
in lieu of the foundation vents and plastic film dampers. This would allow
more precise temperature control. A suitable fan might be the $60 Grainger
4C688 10" fan, which has a free air delivery of 540 cfm at 36 watts at
110 VAC, with a maximum temperature rating of 149 F. The fans could also
be PV-powered, with a 12 V battery for the solar closet discharge fan,
so it can run at night.
Another interior venting alternative is to make the interior closet
doors and sunspace panels open gradually and automatically, or have
the panels swivel on a horizontal axis, halfway from top to bottom,
using some sort of motor with a leadscrew and thermostat.
Disclaimers
-----------
I've haven't built one of these yet...
These sheds are fairly flammable. One needs to be careful about fires inside.
Larger roofs need rafters, posts, or loadbearing walls under the roof panels.
These structures may not comply with local code requirements, but being
sheds, they may not have to. I believe they do comply with BOCA code
insulation requirements, if you count the solar heating, as the code allows.
Note
----
Villanova has recently discontinued all alt newsgroups, so if you see
this cross-posting in alt.energy.renewable, alt.architecture.alternative,
or alt.solar.thermal, and you post something about it there, that is
not crossposted to sci.energy or sci.engr.heat-vent-ac, I won't see it.
I would appreciate feedback though, so feel free to send comments by
email. I would be especially pleased if some people were to build some
of these solar closets or sheds, soon, and I'd be pleased to help with
that effort in any way that I can.
Nicholson L. Pine System design and consulting
Pine Associates, Ltd. (610) 489-0545
821 Collegeville Road Fax: (610) 489-7057
Collegeville, PA 19426 Email: nick@ece.vill.edu