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re: one way to build a high-performance passive solar house 24 jul 1998 [i've corrected sunspace sizing and house thermal mass errors, and added some information about the effects of different sunspace temperatures.] step 1. gather some weather data. the most-difficult month for solar house heating is the one with the lowest ratio of average solar energy to indoor-outdoor temperature difference, ie the lowest amount of "sun per degree day." the long-term average outdoor temperatures near philadelphia, pa are 35.8 and 30.4 f (tb, in the calculation below) in december and january, with 900 and 1,000 btu/ft^2 of sun (ss, below) falling on a south wall on an average day. this makes january the worst-case month for house heating, with 1,000/(68-30.4) = 26.6 btu/f, vs 900/(68-35.8) = 28 in december. the national renewable energy laboratory's free "solar radiation data manual for buildings" (http://rredc.nrel.gov) has solar weather data for 239 us locations. nrel's phone number is (303) 275-4099. the average daily maximum temperature in january is 37.9 f in phila. nrel's manual says an average of 620 btu/ft^2 of sun per day falls on a horizontal surface, east and west walls receive about 420, and a north wall gets 190. how many cloudy days in a row, and what is the temperature then? in some places, cloudy days and nights are warmer than days and nights in sunny weather, because clouds act as insulation. nrel's tmy2 weather data or one of their 3 cd-roms might help answer this question. their cds ($130 each from orders@ncdc.noaa.gov) have 30 year's worth of _hourly_ solar weather data for 239 us locations. we might look for long low-temperature "cloudy degree-day" periods, or or do a simple computer simulation of a particular solar house design to estimate the interior temperature every hour for 30 years, or the total amount of backup heat required. then again, some people define a "solar house" as "one with no other form of heat." the issue then becomes comfort, vs "solar fraction." suppose our house is in a climate in which we expect at most 5 cloudy days in a row with 99% confidence, with an average outdoor temperature during those days of 30 f (-1 c)... step 2. gather some house data the thermal conductance of a house is the sum of each exterior surface area divided by its r-value, plus an effective conductance for air leaks. for example, a fairly airtight and very well-insulated 32'x32' (10mx10m) 2-story house with 2,048 square feet (190 m^2) of us r30 (metric r5.3) walls and 80 ft^2 of r4 windows (7.4 m^2 at 0.7 m^2c/w) and 1,024 ft^2 of r40 ceiling (95 m^2 at metric r7) and a natural air leakage rate of 0.3 house volume air changes per hour has a thermal conductance of about 1,968ft^2/r30 + 80ft^2/r4 + 1024ft^2/r40 + 30x30x16x0.3/55 = 164 btu per hour per degree f difference between indoor and outdoor temperatures (hc, below.) it needs about 164 btu or 48 watts to stay 68 f indoors when it's 67 f outdoors. the daily house heating energy needed is 24 (h) times the product of the thermal conductance of the house and the difference between the average indoor and outdoor temperatures. our example house needs about 24h(65f-30f)x164btu/h-f = 136k btu (eday, below) or 40 kwh to stay warm on an average january day, roughly equivalent to a gallon of oil. (the yearly energy needed to keep a house warm is 24 times the conductance times the number of heating degree days per year, 5,500 (f) for phila.) some of this energy comes from the occupants and their electrical usage. each person makes about 100 watts of heat power, and a kilowatt-hour is equivalent to 3,412 btu of heat energy. if our house has an average of 1 person inside and uses 500 kwh per month (an average of 694 watts) of electrical energy, it gains about 0.794x24 = 19 kwh or 65k btu/day (intheat, below) of heat from internal sources. sun also shines into house windows. if our house has equal window areas facing 4 compass directions, and they have 70% solar transmittance, it gains another 20ft^2x0.7x(1000+420+420+190) = 28k btu of solar heat (winheat) on an average january day. so we need 136k btu/day of heat, of which 65k comes from internal sources and 28k from windows, leaving an additional solar heating requirement of 136k-65k-28k = 43k btu (sday) on an average january day. the inherent thermal mass of a house can store solar heat on an average day, if it is allowed to cool at night. if our house has 4x32x16 = 2,048 square feet of external walls and another 1,024 ft^2 of internal walls and 3x1,024 ft^2 of ceiling and floors, ie 6,144 ft^2 of surface, all covered with 1/2" drywall or something with equivalent heat capacity (1/2 btu/f-ft^2), the total capacity of the house is 6,144x0.5 = 3,072 btu/f, ie it can store 3,072 btu per degree f. with a 10 f day/night temperature swing (eg 70 f during the day and 60 f at night, it can store 30,724 btu (swingheat, below.) with a few more internal walls, this house wouldn't need any extra overnight heat on an average january day. (1) after a house is 100% solar heated, the next largest energy need is often hot water. suppose our house needs enough hot water for 4 10-minute showers per day, heating 3 gallons of water per minute from 60 f to 110 f. heating a pound of water 1 f takes 1 btu, so we need 4x10mx3gpmx8lb/gal(110f-60f) = 48k btu/day (watheat) for hot water. step 3. solar closet sizing. we need 43k btu of additional solar heat on an average january day. a sunspace keeping our house warm for 6 hours can supply 6/24(43k) = 11k btu, which leaves 32k, of which the house itself can store and supply 30.7k, leaving about 2k. adding another 48k btu for heating water makes a total of 50k btu/day (escuse.) suppose that comes from a "solar closet" inside the sunspace, ie a box full of sealed containers of water completely surrounded by insulation, with a solar air heater over its insulated south wall. the water is heated by solar warmed-air from the air heater. the sun doesn't shine on the water containers. solar closets live inside sunspaces, but they have their own glazings and air circulation. sunspace air never mixes with closet air. solar closets need to be fairly airtight. air leaks between the sunspace and the outdoors are less important. the closet air heater glazing might be replex's (800) 726-5151 clear flat polycarbonate plastic, which has a 10 year guarantee and costs about $1.25/ft^2 ($13/m^2) and comes in long rolls 49 inches wide by 0.02 inches thick. rimol greenhouse systems at (603) 425-6563 (nh) sells it for $250/roll + $10 ups. it can be cut with scissors. suppose we design the closet so the water inside is 130 f after a long string of average days. each square foot of its glazing gains 810 btu of sun per day, if it's not shaded much by the sunspace. with r20 south wall insulation behind the glazing, it loses about 6h(130f-100f)1ft^2/r1 to a 100 f sunspace during the day plus 18h(130f-30f)1ft^2/r21 at night, for a net gain of about 540 btu/day (scnet.) storing 50k btu/day of sun takes about 50k/540 = 90 ft^2 of closet glazing (agc.) a 1 cfm airstream with a 1 f temperature difference carries about 1 btu/h (1 m^3/s with a 1 c difference carries about 1 kw), so "charging" the closet heat battery with air that enters 10 f warmer than air that leaves (to keep the air heater cool and efficient) requires an airflow of about 50kbtu/6h/10f = 830 cfm. "discharging" the closet at night or on cloudy days takes about (136k-65k)btu/24h/10 f = 300 cfm (scdcfm.) our house needs 5(136k-65k) = 356k btu (ecl) or 104 kwh to stay warm for 5 cloudy days in a row. if the closet water starts out at 130 f (54 c), and it keeps the house warm until it cools to, say, 80 f (27 c), then the closet needs 356kbtu/(130f-80f) = 7.1k btu/f of thermal capacity (cc), eg about 7,100 pounds of water. the closet thermal mass also needs sufficient area to allow heat to flow efficiently between the air and the water through the container surface. having 10x thermal mass surface than glazing surface allows heatflow with a low air-water delta-t: if each square foot of glazing collects 540 btu over 6 hours, ie 90 btu/h, which flows into 10 ft^2 of container surface with a slowly-moving air film thermal conductance of 1.5 btu/h-f, dt = 90/(10x1.5) = 6 f, by "ohm's law for heatflow." we could increase thermal mass surface by using more drums, or putting hollow concrete blocks under the drums (each 8x8x16" block adds 6 ft^2 and 5 btu/f.) in that case, we might well draw air through the blocks with fans, since moving air at v mph past a rough surface raises the thermal conductance to 2 + v/2 btu/h-f, which lowers the needed surface. a 10'x4" pvc pipe threaded through block holes adds 10 ft^2 and 50 btu/f, at a cost of about $6, including 2 end caps and a #3 rubber stopper. we can increase container surface by using smaller containers. plastic soda bottles might lose 10% of their contents each year by moisture vapor transmission. milk jugs are easier to support and hold more water per cubic foot, and their cross-linked polyethylene walls have about half the vapor transmission of pet soda bottles. recycled 5 gallon plastic pails (about 1'tall x 1'diam.) with tight-fitting lids are easy to ship, since they nest... a 2' high x 3' diameter 55 gallon drum has about 25 ft^2 of surface. a 1 gallon plastic milk jug (about 15 cents each, new, with a screw top, or 50 cents, already filled with water) is about 6" square x 10" tall, with about 2 ft^2 of surface. we might use d drums and j jugs on shelves. with 90 ft^2 of glazing, the surface requirement is 900 ft^2 < 25d + 2j, and we need 7,100 < 55x8d + 8j for thermal mass. combining constraints, 7,100 - 4000 < 55x8d - 100d, so we might use 10 drums and 330 jugs on 4x4'shelves made from 12 4' 1x3s on 4" centers screwed to 2 4' 2x4s on 4' centers, which in turn rest on concrete blocks. supporting the shelves with 2x4 posts instead leaves more room for 36 jugs on each 4'x4' shelf. with 8x8x12" = 0.44 ft^3/jug, we need 147 ft^3 for 330 jugs and another 10x2x2x3'= 120 ft^3 for 10 drums. we might use 2 8x8' single pane sliding glass doors to make a 16' wide x 8' tall x 4' deep 512 ft^3 closet with a 4'x4' area for 8 drums stacked 2-high over a 2' high x 10' long shelf made with 3 layers of 15 hollow blocks on 1' centers threaded with 18 10'x 4" pipes, and a 4x6' area for 6 shelves holding 324 jugs, made with 36 $1 12' 1x3s on 4" centers screwed to 18 4' 2x4s, and an empty 4x6' section that might be used for a clothesline or a sauna with a small woodstove with a double-wall condensing air-air heat transfer chimney with a 50 cfm fan blowing outside air down between concentric fluepipes for burning junk mail, letters from congressmen, and press releases announcing amazing new price breakthroughs in photovoltaic technology. or, we might put a $900 90 pound 1500 w gasoline-powered honda generator that also makes 7.5 kw of heat in that part of the closet, with a $40 nighthawk digital co monitor and an air-liquid exhaust gas heat exchanger and a small exhaust fan to create negative air pressure in the closet, when the generator is running with the vents to the house closed. we might charge a couple of sears diehard batteries with 5-year guarantees using a couple of $300 todd engineering b-series 30 amp 24v chargers with lifetime guarantees, and the batteries might be connected to a $3k trace 4024 inverter that makes the meter go backwards when the generator is running, and also serves as a ups for occasional short term power. (if this were my only source of power, i'd have a spare honda, and maybe about 8 deep-cycle batteries and a few pv panels.) this arrangement of drums and pipes and blocks and jugs gives 8x55x8 +18x50+45x5+324x8 = 7,237 btu/f of capacity and 12x25+18x10+45x6+324x2 = 1,478 ft^2 of surface for 128 ft^2 of glazing. the closet needs about 10' of fin tube pipe near the ceiling to heat water for showers via a thermosyphoning water loop through a large conventional water heater on the floor above, with a heating element that rarely turns on, or about 4 10x4" pvc pipes near the ceiling with a smaller water heater above (and maybe a liner and float valve near the floor of the closet, in case of pipe leaks.) the closet has 2 air loops, one for charging, which circulates air between the closet and its air heater during the day at 50k/6h = 8.3k btu/h (sccflow), and one for discharging, which circulates air between the house and closet on a cloudy day at 71k/24 = 3k btu/h (scdflow.) the closet charging loop might use a $100 differential thermostat or a $6 thermostat in a glazed box controlling 2 $60 36 watt 10" diameter grainger 4c688 560 cfm cooling fans, which have a 149 f upper operating temperature spec. making 830 cfm of airflow in the closet seems hard to do with natural convection. closet discharging might use natural convection with a foamboard damper attached to a honeywell 6161b1000 damper actuator motor that uses 2 watts of electrical power, only when moving (for a cop of over 10,000, with a 5% duty cycle) in series with a heating thermostat. with an airflow of 16.6 av sqrt(hxdt) = 148 av cfm, (using one chimney formula, with h=8' and dt=10 f), we need a damper area av = 3k/(148x10) = 2 ft^2 near the closet top and bottom. or, the closet might be part of the airflow path of a forced air electric resistance heating system with a heating element that very rarely turns on. the closet might be used for summertime cooling, if it isn't used as a water heater. (2) july is the warmest month in philadelphia, with a 24-hour average temp of 76.7 f, average daily min/max of 67.2/86.1 and a humidity ratio of 0.0133, corresponding to a dew point or shaded pond temperature of about 65 f. cooling a 7,237 btu/f closet and house to 70 f at night with outdoor air and closing the house up during the day while circulating air through the closet makes about 16h(81-70)164 = 29k btu plus 43k of internal heat gain, raising their temperature (29k+43k)/(7,237+3072) = 7 f by the end of the day. step 4. sunspace sizing. on an average january day with an average amount of sun, the sunspace supplies about 6 hour's worth of house heat (about 11k btu) and it also warms the mass of the house (30.7k btu) and provides the energy that the closet supplies to the house on an average night, ie it provides all the extra solar heating energy needed (sday) by the house on an average day, beyond internal house heat gain and sun that shines in windows, and it also provides the energy used by the closet for water heating. each square foot of sunspace glazing gains about 900 btu/day (ssgain.) if the daytime sunspace temperature is 100 f, it loses 6h(100-30)1ft^2/r1 = 180 btu/day (ssloss.) our sunspace needs about 180 ft^2 of glazing (ags.) it might be 8' tall x 24' long. lowering the sunspace temperature makes it more comfortable and raises its solar collection efficiency, but it also raises the daytime sunspace- house airflow requirement and closet glazing loss and required closet glazing area. with an 80 vs 100 f sunspace and a 130 f closet, each square foot of closet glazing still gains 810 btu/day and loses about 90 btu at night, but it loses about 6(130-80)1ft^2/r1 = 300 vs 180 btu during the day, for a net gain of 420 btu/day, so collecting 43k btu requires about 43k/420 = 117 ft^2 of closet glazing, less than above. the sunspace might also have a transparent roof and endwalls, with the roof shaded in summertime. this would collect more winter sun. (3) the sunspace airflow loop needs to circulate air through the house at 43k/6h = 6.9k btu/h (sscflow.) this requires about 230 cfm with a 100 f sunspace and 30 f delta t, or 690 cfm with an 80 f sunspace and 10 f delta t. we might use grainger's 4ch71 $26 20" window box fan to move 2,100 cfm of 80 f sunspace air while consuming 87 watts. it might be in series with a cooling thermostat in the sunspace and a heating thermostat in the house, or we might use natural convection, if we had larger air passages or a higher sunspace temperature or a taller sunspace. natural airflow increases with the square root of the height. the energy crafted homes spec says: "for optimal heat flow into the house from the sunspace, install sliding or french doors between the two. natural air flow through an open door can be as high as 1000 cfm... most effective if a complete loop through the house is possible. two-story sunspaces can be tremendously effective at heating a house for this reason." a two-story sunspace probably needs no fan. it might operate automatically with a damper motor in series with two thermostats that opens and closes a clear plastic damper in an upstairs window, with air returning to the sunspace via a downstairs window with a plastic film backdraft damper. to move 230 cfm by natural convection, a 16' tall 100 f sunspace needs 16.6 av sqrt(16x(100-70)) = 230. this makes vent area av = 0.6 ft^2 or 91 in^2, less than the size of a window, and doubtless an underestimate, since that formula came from chimneys with fewer turns in the airpath. our house might have a dramatic 16' high x 12' wide x 12' deep (5x5x4m) lean-to sunspace made from standard commercial greenhouse components, including 4 $35 24'-long curved galvanized pipe bows on 4'centers, with more pipes for ground stakes, and a pressure-treated perimeter board for the foundation, and carpeting or shredded wood playground mulch over black plastic film on the ground. the sunspace glazing might be bayer's (412) 777-3837 dureflex urethane film, which costs about 35 cents/ft^2. it's about as clear as plastic food wrap and comes in 15' wide rolls with a 10 year guarantee. frugal people might make $3 bows on 4' centers from 2 $1 12' 1x3s bent to an 8' radius with 1x3 spacer blocks and deck screws every 2' to hold them together. the bow bottoms can be sandwiched around a horizontal 1x3 near the ground which is bolted through the treads of used tires filled with soil to make planters inside the sunspace. (my local garage pays people $1.25 each to take away tires. my zoning board defines a building as "any structure permanently attached to the ground.") a $10 12x16' piece of 4 year cloudy (and private) greenhouse polyethylene film could be held to the bottom 1x3 with a cedar or poly-film-covered 1x3 cap strip and deck screws, with the excess draped onto the ground and covered with gravel to make a walkway and air seal, and keep the ground near the sunspace warmer and drier. nick 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.edyou computer simulation and modeling. high performance, low cost, solar heating and cogeneration system design. bsee, msee. senior member, ieee. registered us patent agent. web site: http://www.ece.vill.edu/~nick notes: (1) for this to work, the thermal mass of the house has to be exposed to direct sun through windows or circulating house air. a couple of low rectangular 100 gallon water tanks near the bottom of some south windows would add about 1,600 btu/f to the thermal mass of the house. a strawbale house with 1,024 ft^2 of walls with 2" of plaster inside could store about 4k btu/f. a house might have a concrete floorslab placed over 4" pvc drainpipes, with insulation under the slab, with a fan pulling warm air through the pipes. concrete has a heat capacity of about 25 btu/ft^3 (about twice that of drywall by volume.) a house with a 1,024 ft^2 x 6" slab could store 1,024x0.5x25 = 13k btu/f. a house with 4 32' x 8' tall x 8" thick concrete basement walls with exterior insulation and an 8" concrete basement floor with insulation beneath could store (512x4+1024)8/12x25 = 51k btu/f. making the walls hollow block with a capacitance of about 5 btu/ft^2 and making the floor 4" thick lowers this to 2048x5+1024x8/12x25 = 27k btu/f. more thermal mass in a house means better summertime cooling and less closet glazing and airflow and thermal mass surface... (2) sloped vs vertical glazing is better for year-round water heating, and if the closet doesn't have to heat water, the glazing and airflow requirements are greatly reduced, so this might be a completely passive system with airflow by natural convection, and the sunspace and closet could be shaded and cooler in summertime. one might use a sunspace or attic with a steep south transparent roof to make a water heater with something like zomeworks' big fins, which are dark-painted aluminum extrusions that clip tightly on to copper pipes. they have no glazing or insulation, but that's ok in a sunspace or attic, with an insulated tank above. the copper pipes do need to be protected from freezing. (3) one way to enhance sunspace solar collection efficiency and keep most of it cooler during the day is to hang some sort of dark porous screen over back wall, spaced away from the wall, and let house air flow out into the space between the screen and the sunspace glazing, then rise up and move from south to north through the screen, then pass back into the house from the space between the screen and the house wall. this can (a) keep most of the solar-warmed air away from the cool sunspace glazing, (b) increase the solar absorbing surface, which lowers the surface temperature and reduces reradiation loss, (c) reduce reradiation loss from the house wall, by blocking some of the longwave ir radiation as it travels back out the sunspace, and (d) absorb some of the visible light that is reflected from the house wall. greenhouse shadecloth (about 15 cents/ft^2) can be used for a screen. so can dark window screen. of course the part of the house wall that is covered by the sunspace needs no additional heat during the day, and the part of the wall that is covered by the closet doesn't need heat at night either. the calculation below ignores this. 10 'step 1. weather data 20 tb=30.4'24-hour average winter monthly temperature (f) 30 tm=37.9'average daily maximum winter temperature (f) 40 ss=1000'average daily sun that falls on a south wall (btu/ft^2) 50 'step 2. house data 60 hc=164'thermal conductance of house (btu/h-f) 70 thd=70'daytime house temperature (f) 80 thn=60'nighttime house temperature (f) 85 tha=(thd+thn)/2'average house temperature (f) 100 eday=24*(tha-tb)*hc'average house heating energy need (btu/day) 110 intheat=65000!'house heat from internal sources (btu/day) 120 winheat=28000!'average solar heat through windows (btu/day) 125 tswing=thd-thn'day/night temperature swing for house (f) 130 chouse=3072'house thermal capacity (btu/f) 140 tss=80'average daytime sunspace temperature (f) 150 tcl=130'average solar closet temperature (f) 160 sday=eday-intheat-winheat'average solar heating need (btu/day) 170 print"average solar heating need (btu/day):",sday 180 watheat=48000!'water heating load (btu/day) 190 'step 3. solar closet sizing 200 swingheat=chouse*tswing'day/night house heat storage (btu) 205 if swingheat>.75*sday then swingheat = .75*sday 210 escuse=.75*sday-swingheat+watheat'useful closet heatflow (btu/day) 220 scgain=.81*ss'average solar closet gain (btu/ft^2-day) 230 scloss=6*(tcl-tss)+18*(tcl-tb)/21'closet loss (btu/ft^2-day) 240 scnet=scgain-scloss'average net closet gain (btu/ft^2-day) 250 agc=escuse/scnet'closet glazing area (ft^2) 260 print"closet glazing area (ft^2): ",agc 270 sccflow=escuse/6'closet charging heatflow (btu/h) 280 scccfm=sccflow/10'closet charging airflow (cfm) 290 print"closet charging airflow (cfm): ",scccfm 300 scdflow=(eday-intheat)/24'closet discharging heatflow (btu/h) 310 scdcfm=scdflow/10'closet discharging airflow (cfm) 320 print"closet discharging airflow (cfm): ",scdcfm 330 ecl=5*(eday-intheat)'5-cloudy day heating need (btu) 340 cc=ecl/(tcl-80)'closet thermal capacity (btu/f) 350 print"closet thermal capacity (btu/f): ",cc 360 scms=10*agc'closet thermal mass surface (ft^2) 370 print"closet thermal mass surface (ft^2): ",scms 380 d=int((cc-4*scms)/340)'number of closet drums 390 j=int((scms-25*d)/2)'number of closet jugs 400 if j<0 then j=0 410 print"closet drums/jugs (55 gal/1 gal): ",d;"/";j 420 d=int((cc-5*scms)/315)'number of closet drums 430 p=int((scms-25*d)/10)'number of closet pipes 440 if p<0 then p=0 450 print"closet drums/pipes (55 gal/10'x4 in.):",d;"/";p 460 'step 4. sunspace sizing 470 essuse=.25*sday+swingheat'useful sunspace heatflow (btu/day) 480 ssgain=.9*ss'average sunspace solar gain (btu/ft^2-day) 490 td=(tb+tm)/2'average daytime temperature (f) 500 ssloss=6*(tss-td)'average sunspace heat loss (btu/ft^2-day) 510 ssnet=ssgain-ssloss'average net sunspace gain (btu/ft^2-day) 520 ags=(sday+watheat)/ssnet'sunspace glazing area (ft^2) 530 print"sunspace glazing area (ft^2): ",ags 540 sscflow=essuse/6'sunspace heatflow (btu/h) 550 ssccfm=sscflow/(tss-70)'sunspace airflow (cfm) 560 print"sunspace airflow (cfm): ",ssccfm run with a 100 f sunspace... average solar heating need (btu/day): 43185.6 closet glazing area (ft^2): 91.19829 closet charging airflow (cfm): 827.82 closet discharging airflow (cfm): 296.6066 closet thermal capacity (btu/f): 7118.56 closet thermal mass surface (ft^2): 911.983 closet drums/jugs (55 gal/1 gal): 10 / 330 closet drums/pipes (55 gal/10'x4 in.): 8 / 71 sunspace glazing area (ft^2): 180.6013 sunspace airflow (cfm): 230.6467 with an 80 f sunspace... closet glazing area (ft^2): 116.9709 closet thermal mass surface (ft^2): 1169.709 closet drums/jugs (55 gal/1 gal): 7 / 497 closet drums/pipes (55 gal/10'x4 in.): 4 / 106 sunspace glazing area (ft^2): 145.9203 sunspace airflow (cfm): 691.94 notice that closet glazing and sunspace airflow increased and sunspace glazing decreased as sunspace temperature decreased. |