Article 27749 of sci.energy: Xref: freenet.victoria.bc.ca sci.energy:14042 sci.engr.heat-vent-ac:1827 alt.energy.renewable:1953 alt.architecture.alternative:653 alt.solar.thermal:20 Path: freenet.victoria.bc.ca!holly.softwords.bc.ca!news.bctel.net!kryten.awinc.com!netnet2.netnet.net!news.sprintlink.net!tank.news.pipex.net!pipex!news.mathworks.com!uunet!in1.uu.net!newsfeed.pitt.edu!dsinc!news.ee.vill.edu!not-for-mail From: nick@vu-vlsi.ee.vill.edu (Nick Pine) Newsgroups: sci.energy,sci.engr.heat-vent-ac,alt.energy.renewable,alt.architecture.alternative,alt.solar.thermal Subject: Some modular sheds with solar closets Date: 14 Sep 1995 02:13:27 -0400 Organization: Villanova University Lines: 1150 Message-ID: <438h67$bdi@vu-vlsi.ee.vill.edu> NNTP-Posting-Host: vu-vlsi.ee.vill.edu 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