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re: deployable doubt dispellers
18 mar 2006
the virtual 20' cube in rochester ny is now more of a virtual house.
the sizing calc below (based on an average december day) has twinwall
polycarbonate sunspace glazing and water shelves under the ceiling to
store heat from warm sunspace air on an average day and an air heater
inside the sunspace with some fin-tube pipe near the top to heat water
for showers and a large cloudy-day heat storage tank...
20 aceil=800:rceil=40'ceiling area (ft^2) and r-value
30 gceil=aceil/rceil'ceiling thermal conductance (btu/h-f)
40 awn=0:awe=24:aww=24:aws=48'n,e,w,s window areas (ft^2)
50 aw=awn+awe+aww+aws'total window area (ft^2)
60 rw=1/.25:rwall=34'window (1/u) and wall r-values
70 gwind=aw/rw'window thermal conductance (btu/h-f)
80 asg=240:gsg=.58:tsg=.8'sspace glazing area (ft^2) and u-value and solar xmsn
90 gsun=asg/(rwall+1/gsg)'nighttime sunspace conductance (btu/h-f)
100 wgain=.5*(160*awn+260*awe+250*aww+540*aws)'window solar gain (btu/day)
110 egain=226/27'indoor electrical use (kwh/day)
120 pgain=12*300'heat gain from 1 12h/day occupant(s) (btu/day)
130 igain=(wgain+3412*egain+pgain)'internal heat gain (btu/day)
140 perim1=120:perim2=80'1st and 2nd floor perimeters (ft)
150 awall=(perim1+perim2)*8-aw-asg'wall area (ft^2)
160 gwall=awall/rwall'wall thermal conductance (btu/h-f)
170 area1=800:area2=400'1st and 2nd floor areas (ft^2)
180 vol=(area1+area2)*8'volume of heated space (ft^3)
190 ach=.2:cfm=vol*ach/60'natural air leakage (cfm)
200 g=gceil+gwind+gsun+gwall+cfm'house thermal conductance (btu/h-f)
210 print"1000'conductances (btu/h-f):"
220 print"1010'ceiling","window","wall","air leaks","total"
230 print"1020'";gceil,gwind,gwall,cfm,g
240 tavg=29.1:tpek=35.8:tday=(tavg+tpek)/2'average dec outdoor temps (f)
250 ssgain=asg*tsg*540'sunspace gain (btu/day)
260 sigain=4*8*(.8*540-6*(70-tday)*gsg)'solar siding gain (btu/day)
270 gnosun=g-gsun'remainder of house (non-sunspace) conductance (btu/h-f)
280 snloss=18*(70-tavg)*gsun'sunspace night loss (btu/night)
290 nsnloss=24*(65-tavg)*gnosun'non-sunspace house loss (btu/day)
300 twi=47.6:twg=100:twh=110'incoming, gwhx and hot water temps (f)
310 dhw=50000!'water heating (btu/day from aug 2004 gas bill)
320 chw=dhw/(twh-twi)'hot water quantity (lb/day)
330 shwreq=chw*(twh-twg)'solar water heating requirement (btu/day)
340 print"1050'solar water heating:",shwreq,"(btu/day)"
350 netgain=ssgain+sigain+igain-shwreq-snloss-nsnloss'net gain (btu/day)
360 ts=tday+netgain/(6*asg*gsg)'daytime sunspace temp (f)
370 imass=2000'inherent structural thermal mass (btu/f)
380 nightheat=(70-60)*imass+.75*(igain)'heat supplied by mass and gains (btu)
390 shelfheat=snloss+.75*nsnloss-nightheat'heat supplied by shelves (btu)
400 n=4:ash=n*4*8'number of 4'x8' shelves and one-sided shelf area (ft^2)
410 t=1'initial shelf water depth (feet)
420 dloss=(60-(tavg-(tpek-tavg)))*g'dawn heat loss (btu/h)
430 tmin=60+dloss/(3*ash)'min water temp (f)
440 rc=62.33*t/3'time constant (hours)
450 tmax=ts+(tmin-ts)*exp(-6/rc)'dusk temp (f)
460 th=shelfheat/(ash*62.33*(tmax-tmin))'new water depth (feet)
470 if abs(th-t)>.01 then t=th: goto 440'iterate
480 print"1030'shelves","depth (in)","tmax (f)","tmin (f)","weight (lb)"
490 print"1040'";n,12*t,tmax,tmin,62.33*32*t
500 aah=8*12'air heater glazing area (ft^2)
510 ahgain=aah*.72*540-shwreq'air heater gain (btu/day)
520 tah=ts+ahgain/(6*aah)'air heater temp (f)
530 fah=64:gah=5*fah'air heater fin-tube (feet)
540 tcavg=tah-shwreq/(6*gah)'cloudy day tank temp on average day (f)
550 fcd=64:gcd=5*fcd:'cloudy-day fin-tube (feet)
560 closs=(70-tday)*g'cloudy daytime heat loss (btu/h)
570 tcmin=60+closs/gcd'min usable cloudy tank temp (f)
580 cgain=3412*egain+pgain'cloudy-day heat internal gains (btu/day)
590 cdheat=24*(62.5-tavg)*g+shwreq-cgain'cloudy-day heat required (btu/day)
600 tankcap=5*cdheat/(tcavg-tcmin)'cloudyr-ay tank heat cap (btu/f)
610 tankvol=tankcap/8.33'cloudy-day tank volume (gallons)
620 print"1080'tsunspace (f)","tairheat (f)","tcavg (f)","tcmin (f)"
630 print"1090'";ts,tah,tcavg,tcmin
640 print"1100'cloudy-tank volume:",tankvol,"(gallons)"
conductances (btu/h-f):
ceiling window wall air leaks total
20 24 37.17647 32 119.8946
shelves depth (in) tmax (f) tmin (f) weight (lb)
4 1.28014 95.51366 71.73969 212.7763
solar water heating: 8012.821 (btu/day)
tsunspace (f) tairheat (f) tcavg (f) tcmin (f)
97.21359 148.1025 143.9291 74.06889
cloudy-tank volume: 618.287 (gallons)
the program below prepares a "winter" file from nrel's rochester tmy2
(typical meteorological year) hourly weather data file, wban 14768.
for other locations, change 14768 in line 50 below to 13739 for phila,
24033 for billings, mt, and so on...
10 pi=4*atn(1):screen 9:key off:cls
20 line (0,0)-(639,349),,b:df=.434
30 for tr= 20 to 70 step 10'temp ref lines
40 line (0,349-5*(tr-10))-(639,349-5*(tr-10)):next
50 f$="14768.tm2"'nrel tmy2 file name (rochester)
60 open f$ for input as #1
70 open "winter" for output as #2
80 line input#1,s$'read header
90 city$=mid$(s$,8,25)
100 lat=val(mid$(s$,40,2))+val(mid$(s$,43,2))/60
110 lon=val(mid$(s$,48,3))+val(mid$(s$,52,2))/60
120 print#2,city$,lat,lon
130 gosub 190
140 pass=1
150 close #1
160 open f$ for input as #1
170 line input#1,s$'ignore header
180 gosub 190
190 for h=1 to 8760'hour of year
200 line input#1,s$
210 month=val(mid$(s$,4,2))'month of year (1-12)
220 if pass=0 and month<10 goto 610
230 if pass=1 and month=2 then end
240 wh=h+8760*pass
250 day=val(mid$(s$,6,2))'day of month
260 hour=val(mid$(s$,8,2))-.5'hour of day
270 n=h/24'day of year (1 to 365)
280 tdb=val(mid$(s$,68,4))*.18+32'dry bulb temp (f)
290 pset(df*(wh-8030),349-5*(tdb-10))
300 igloh=val(mid$(s$,18,4))*.317'global horizontal radiation (btu/ft^2)
310 print#2,month;day;hour;tdb;igloh;
320 idif=val(mid$(s$,30,4))*.317'diffuse horizontal radiation (btu/ft^2)
330 idir=val(mid$(s$,24,4))*.317'direct normal radiation (btu/ft^2)
340 l=pi*lat/180'phila latitude (radians)
350 t=hour'solar time (est)
360 x=-sin(pi*23.45/180)*cos(2*pi*(n+10)/365.25)
370 d=atn(x/sqr(-x*x+1))'sin^-1(x) = declination (radians)
380 w=2*pi*(t-12)/24'hour angle (radians)
390 x=cos(l)*cos(d)*cos(w)+sin(l)*sin(d)
400 thetas=-atn(x/sqr(-x*x+1))+pi/2'cos^-1(x) = sun zenith angle (radians)
410 x=cos(d)*sin(w)/sin(thetas)
420 if x^2 >=1 then phis=-1.570796327#:goto 440
430 phis=atn(x/sqr(-x*x+1))'sin^-1(x) = sun azimuth angle (radians)
440 for phipd=0 to 180 step 90'azimuth angle of plane (degrees)
450 phip=pi*phipd/180
460 x=sin(thetas)*cos(phis-phip)
470 thetai=-atn(x/sqr(-x*x+1))+pi/2'incidence angle to surface (radians)
480 if thetai>=pi/2 then thetai=pi/2
490 rhog=.2'ground reflectance
500 iglop=idir*cos(thetai)+idif/2+igloh*rhog/2'radiation on surface (btu/ft^2)
510 print#2,iglop;
520 'if phipd = 0 then pset(h-8030,349-iglop)
530 next phipd
540 phip=pi*270/180
550 x=sin(thetas)*cos(phis-phip)
560 thetai=-atn(x/sqr(-x*x+1))+pi/2'incidence angle to surface (radians)
570 if thetai>=pi/2 then thetai=pi/2
580 iglop=idir*cos(thetai)+idif/2+igloh*rhog/2'radiation on surface (btu/ft^2)
590 print#2,iglop
600 if hour=.5 then line (df*(wh-8030),349)-(df*(wh-8030),345)
610 next h
620 return
here are 362 worst-case hours ("winter2") from the winter file.
each line has month day hour and sun on the ground and 4 walls.
1 5 8.5 11.66 24.726 78.53785 9.129583 9.129583 85.46374
1 5 9.5 12.92 70.374 202.1037 12.74336 12.74336 148.7658
1 5 10.5 14.36 94.46601 161.2371 30.84408 30.84408 84.11995
1 5 11.5 15.62 114.437 180.4199 37.27918 37.27918 56.29107
1 5 12.5 17.06 100.172 96.7497 55.6245 49.32519 49.32519
1 5 13.5 17.42 97.002 139.1144 78.05207 35.85268 35.85268
1 5 14.5 17.6 73.544 123.799 96.11642 25.42338 25.42338
1 5 15.5 17.96 44.063 113.6599 123.81 12.64828 12.64828
1 5 16.5 17.24 11.729 16.84752 23.54156 6.244897 6.244897
1 5 17.5 16.7 0 0 0 0 0
1 5 18.5 15.98 0 0 0 0 0
1 5 19.5 15.98 0 0 0 0 0
1 5 20.5 15.98 0 0 0 0 0
1 5 21.5 15.98 0 0 0 0 0
1 5 22.5 15.98 0 0 0 0 0
1 5 23.5 15.98 0 0 0 0 0
1 6 .5 15.98 0 0 0 0 0
1 6 1.5 17.06 0 0 0 0 0
1 6 2.5 17.96 0 0 0 0 0
1 6 3.5 19.04 0 0 0 0 0
1 6 4.5 19.76 0 0 0 0 0
1 6 5.5 20.3 0 0 0 0 0
1 6 6.5 21.02 0 0 0 0 0
1 6 7.5 22.28 .9510001 1.066952 .5705999 .5705999 1.381782
1 6 8.5 23.72 18.703 22.752 10.1123 10.1123 24.04432
1 6 9.5 24.98 30.432 20.25946 17.7837 17.7837 19.5655
1 6 10.5 26.24 48.501 31.47705 28.4666 28.4666 29.69874
1 6 11.5 27.68 57.06 36.34515 33.7605 33.7605 34.10436
1 6 12.5 28.94 64.351 40.977 38.23839 37.8181 37.8181
1 6 13.5 29.3 60.23 37.57801 36.44666 35.6625 35.6625
1 6 14.5 29.66 43.112 26.54027 26.26304 25.5502 25.5502
1 6 15.5 30.02 30.115 18.27957 18.30125 18.069 18.069
1 6 16.5 29.66 8.876001 5.3256 5.3256 5.3256 5.3256
1 6 17.5 29.3 0 0 0 0 0
1 6 18.5 28.94 0 0 0 0 0
1 6 19.5 28.94 0 0 0 0 0
1 6 20.5 28.94 0 0 0 0 0
1 6 21.5 28.94 0 0 0 0 0
1 6 22.5 29.3 0 0 0 0 0
1 6 23.5 29.66 0 0 0 0 0
1 7 .5 30.02 0 0 0 0 0
1 7 1.5 29.3 0 0 0 0 0
1 7 2.5 28.76 0 0 0 0 0
1 7 3.5 28.04 0 0 0 0 0
1 7 4.5 26.96 0 0 0 0 0
1 7 5.5 26.06 0 0 0 0 0
1 7 6.5 24.98 0 0 0 0 0
1 7 7.5 24.62 1.902 1.1412 1.1412 1.1412 1.1412
1 7 8.5 24.44 18.703 11.2218 11.2218 11.2218 11.2218
1 7 9.5 24.08 44.697 27.06548 26.8182 26.8182 26.99653
1 7 10.5 24.98 61.498 37.1722 36.8988 36.8988 37.01091
1 7 11.5 26.06 73.227 44.35154 43.7777 43.7777 43.85418
1 7 12.5 26.96 82.103 49.2618 49.2618 49.2618 49.2618
1 7 13.5 26.96 68.472 41.35656 41.19532 41.0832 41.0832
1 7 14.5 26.96 59.279 35.81461 35.74576 35.5674 35.5674
1 7 15.5 26.96 35.821 21.4926 21.4926 21.4926 21.4926
1 7 16.5 26.06 8.876001 5.3256 5.3256 5.3256 5.3256
1 7 17.5 24.98 0 0 0 0 0
1 7 18.5 24.08 0 0 0 0 0
1 7 19.5 23.72 0 0 0 0 0
1 7 20.5 23.36 0 0 0 0 0
1 7 21.5 23 0 0 0 0 0
1 7 22.5 22.64 0 0 0 0 0
1 7 23.5 22.28 0 0 0 0 0
1 8 .5 21.92 0 0 0 0 0
1 8 1.5 21.2 0 0 0 0 0
1 8 2.5 20.66 0 0 0 0 0
1 8 3.5 19.94 0 0 0 0 0
1 8 4.5 19.58 0 0 0 0 0
1 8 5.5 19.4 0 0 0 0 0
1 8 6.5 19.04 0 0 0 0 0
1 8 7.5 19.04 1.585 1.280405 .9509999 .9509999 1.492708
1 8 8.5 19.04 18.703 18.98735 10.5878 10.5878 19.89165
1 8 9.5 19.04 48.501 62.43346 22.91909 22.91909 51.47656
1 8 10.5 19.4 75.763 65.67029 40.5443 40.5443 50.86708
1 8 11.5 19.58 89.394 83.20006 45.0774 45.0774 50.1676
1 8 12.5 19.94 97.319 115.6677 51.34473 41.43189 41.43189
1 8 13.5 19.58 112.218 144.5825 86.19238 45.45778 45.45778
1 8 14.5 19.4 68.155 76.52848 64.28863 32.33399 32.33399
1 8 15.5 19.04 33.919 29.62897 30.79042 18.9249 18.9249
1 8 16.5 17.42 5.389 5.049526 6.326246 3.074899 3.074899
1 8 17.5 15.62 0 0 0 0 0
1 8 18.5 14 0 0 0 0 0
1 8 19.5 13.64 0 0 0 0 0
1 8 20.5 13.28 0 0 0 0 0
1 8 21.5 12.92 0 0 0 0 0
1 8 22.5 14.9 0 0 0 0 0
1 8 23.5 17.06 0 0 0 0 0
1 9 .5 19.04 0 0 0 0 0
1 9 1.5 19.4 0 0 0 0 0
1 9 2.5 19.58 0 0 0 0 0
1 9 3.5 19.94 0 0 0 0 0
1 9 4.5 21.02 0 0 0 0 0
1 9 5.5 21.92 0 0 0 0 0
1 9 6.5 23 0 0 0 0 0
1 9 7.5 24.98 0 0 0 0 0
1 9 8.5 26.96 8.559 6.234627 4.976899 4.976899 6.373759
1 9 9.5 28.94 22.19 14.97004 12.997 12.997 14.42619
1 9 10.5 30.02 73.861 59.99554 40.3541 40.3541 48.44024
1 9 11.5 30.92 76.714 75.42444 37.62789 37.62789 42.6845
1 9 12.5 32 86.858 96.09641 46.74127 39.11779 39.11779
1 9 13.5 29.3 67.204 59.59585 44.99608 34.7749 34.7749
1 9 14.5 26.78 65.302 75.17882 62.82557 30.30519 30.30519
1 9 15.5 24.08 33.919 33.42665 35.1322 18.1324 18.1324
1 9 16.5 22.64 3.487 2.0922 2.0922 2.0922 2.0922
1 9 17.5 21.38 0 0 0 0 0
1 9 18.5 19.94 0 0 0 0 0
1 9 19.5 19.22 0 0 0 0 0
1 9 20.5 18.68 0 0 0 0 0
1 9 21.5 17.96 0 0 0 0 0
1 9 22.5 17.96 0 0 0 0 0
1 9 23.5 17.96 0 0 0 0 0
1 10 .5 17.96 0 0 0 0 0
1 10 1.5 18.32 0 0 0 0 0
1 10 2.5 18.68 0 0 0 0 0
1 10 3.5 19.04 0 0 0 0 0
1 10 4.5 19.4 0 0 0 0 0
1 10 5.5 19.58 0 0 0 0 0
1 10 6.5 19.94 0 0 0 0 0
1 10 7.5 19.94 .317 .1902 .1902 .1902 .1902
1 10 8.5 19.94 12.046 7.6968 7.069101 7.069101 7.768201
1 10 9.5 19.94 45.331 29.09809 26.8816 26.8816 28.49098
1 10 10.5 19.94 45.648 28.16168 27.0718 27.0718 27.52146
1 10 11.5 19.94 58.328 35.28282 34.9968 34.9968 35.03515
1 10 12.5 19.94 69.42301 41.93981 41.69215 41.6538 41.6538
1 10 13.5 20.3 64.351 39.54181 38.90182 38.4521 38.4521
1 10 14.5 20.66 45.014 27.2546 27.18726 27.0084 27.0084
1 10 15.5 21.02 27.896 16.99733 17.0453 16.5791 16.5791
1 10 16.5 20.3 9.51 5.706001 5.706001 5.706001 5.706001
1 10 17.5 19.76 0 0 0 0 0
1 10 18.5 19.04 0 0 0 0 0
1 10 19.5 17.96 0 0 0 0 0
1 10 20.5 17.06 0 0 0 0 0
1 10 21.5 15.98 0 0 0 0 0
1 10 22.5 14.9 0 0 0 0 0
1 10 23.5 14 0 0 0 0 0
1 11 .5 12.92 0 0 0 0 0
1 11 1.5 12.92 0 0 0 0 0
1 11 2.5 12.92 0 0 0 0 0
1 11 3.5 12.92 0 0 0 0 0
1 11 4.5 13.64 0 0 0 0 0
1 11 5.5 14.36 0 0 0 0 0
1 11 6.5 15.08 0 0 0 0 0
1 11 7.5 17.06 1.585 .9510001 .9510001 .9510001 .9510001
1 11 8.5 19.04 15.85 9.51 9.51 9.51 9.51
1 11 9.5 21.02 38.357 23.2601 23.0142 23.0142 23.1932
1 11 10.5 22.1 54.524 43.73963 29.8614 29.8614 35.60037
1 11 11.5 23 54.841 46.24183 29.1006 29.1006 31.40359
1 11 12.5 24.08 88.76 81.83446 49.687 44.69699 44.69699
1 11 13.5 24.08 76.39701 67.79425 51.20267 39.4982 39.4982
1 11 14.5 24.08 53.89 41.51027 38.37128 29.9565 29.9565
1 11 15.5 24.08 25.36 16.35991 16.53236 14.899 14.899
1 11 16.5 23.72 4.438 2.826035 2.934538 2.6628 2.6628
1 11 17.5 23.36 0 0 0 0 0
1 11 18.5 23 0 0 0 0 0
1 11 19.5 23 0 0 0 0 0
1 11 20.5 23 0 0 0 0 0
1 11 21.5 23 0 0 0 0 0
1 11 22.5 22.64 0 0 0 0 0
1 11 23.5 22.28 0 0 0 0 0
1 12 .5 21.92 0 0 0 0 0
1 12 1.5 22.64 0 0 0 0 0
1 12 2.5 23.36 0 0 0 0 0
1 12 3.5 24.08 0 0 0 0 0
1 12 4.5 24.08 0 0 0 0 0
1 12 5.5 24.08 0 0 0 0 0
1 12 6.5 24.08 0 0 0 0 0
1 12 7.5 23.72 1.585 .9510001 .9510001 .9510001 .9510001
1 12 8.5 23.36 14.582 9.424281 8.5907 8.5907 9.52474
1 12 9.5 23 36.455 22.94207 21.7145 21.7145 22.61043
1 12 10.5 23.72 48.501 29.75737 28.9421 28.9421 29.28004
1 12 11.5 24.26 63.4 38.32534 38.04 38.04 38.07842
1 12 12.5 24.98 66.887 41.2418 40.00733 39.8152 39.8152
1 12 13.5 24.98 65.302 39.56612 39.24803 39.0227 39.0227
1 12 14.5 24.98 58.645 35.27393 35.20773 35.0285 35.0285
1 12 15.5 24.98 32.968 19.98907 20.01438 19.7808 19.7808
1 12 16.5 24.26 9.193 5.5158 5.5158 5.5158 5.5158
1 12 17.5 23.72 0 0 0 0 0
1 12 18.5 23 0 0 0 0 0
1 12 19.5 23 0 0 0 0 0
1 12 20.5 23 0 0 0 0 0
1 12 21.5 23 0 0 0 0 0
1 12 22.5 22.64 0 0 0 0 0
1 12 23.5 22.28 0 0 0 0 0
1 13 .5 21.92 0 0 0 0 0
1 13 1.5 21.92 0 0 0 0 0
1 13 2.5 21.92 0 0 0 0 0
1 13 3.5 21.92 0 0 0 0 0
1 13 4.5 22.28 0 0 0 0 0
1 13 5.5 22.64 0 0 0 0 0
1 13 6.5 23 0 0 0 0 0
1 13 7.5 23.72 3.487 2.0922 2.0922 2.0922 2.0922
1 13 8.5 24.26 23.458 14.28275 14.0748 14.0748 14.30856
1 13 9.5 24.98 56.109 33.9105 33.6654 33.6654 33.84478
1 13 10.5 26.06 74.495 45.08125 44.5385 44.5385 44.76404
1 13 11.5 26.96 85.273 51.73374 51.16381 51.16381 51.24073
1 13 12.5 28.04 87.809 52.81185 52.56537 52.5269 52.5269
1 13 13.5 28.04 45.331 31.3571 28.18627 25.9306 25.9306
1 13 14.5 28.04 71.00801 96.28086 78.177 28.65679 28.65679
1 13 15.5 28.04 36.772 65.10101 71.50357 13.97969 13.97969
1 13 16.5 27.32 14.899 19.18325 26.77858 7.988396 7.988396
1 13 17.5 26.78 0 0 0 0 0
1 13 18.5 26.06 0 0 0 0 0
1 13 19.5 26.78 0 0 0 0 0
1 13 20.5 27.32 0 0 0 0 0
1 13 21.5 28.04 0 0 0 0 0
1 13 22.5 28.4 0 0 0 0 0
1 13 23.5 28.58 0 0 0 0 0
1 14 .5 28.94 0 0 0 0 0
1 14 1.5 28.94 0 0 0 0 0
1 14 2.5 28.94 0 0 0 0 0
1 14 3.5 28.94 0 0 0 0 0
1 14 4.5 28.22 0 0 0 0 0
1 14 5.5 27.68 0 0 0 0 0
1 14 6.5 26.96 0 0 0 0 0
1 14 7.5 26.96 .634 .3804 .3804 .3804 .3804
1 14 8.5 26.96 17.118 10.89322 10.2708 10.2708 10.97287
1 14 9.5 26.96 39.625 24.83986 23.6165 23.6165 24.5144
1 14 10.5 27.68 47.55 41.30137 25.043 25.043 31.81666
1 14 11.5 28.22 86.224 68.57505 46.6624 46.6624 49.62752
1 14 12.5 28.94 100.172 102.8482 54.37561 46.78919 46.78919
1 14 13.5 28.94 80.518 62.07062 51.64188 44.1898 44.1898
1 14 14.5 28.94 56.743 50.72783 45.07649 29.4493 29.4493
1 14 15.5 28.94 31.383 27.66031 29.02542 17.0863 17.0863
1 14 16.5 27.68 12.997 23.99868 36.08822 6.371695 6.371695
1 14 17.5 26.24 0 0 0 0 0
1 14 18.5 24.98 0 0 0 0 0
1 14 19.5 23.9 0 0 0 0 0
1 14 20.5 23 0 0 0 0 0
1 14 21.5 21.92 0 0 0 0 0
1 14 22.5 19.94 0 0 0 0 0
1 14 23.5 17.96 0 0 0 0 0
1 15 .5 15.98 0 0 0 0 0
1 15 1.5 18.68 0 0 0 0 0
1 15 2.5 21.38 0 0 0 0 0
1 15 3.5 24.08 0 0 0 0 0
1 15 4.5 24.08 0 0 0 0 0
1 15 5.5 24.08 0 0 0 0 0
1 15 6.5 24.08 0 0 0 0 0
1 15 7.5 23.72 .317 .1902 .1902 .1902 .1902
1 15 8.5 23.36 12.997 8.419151 7.7982 7.7982 8.501076
1 15 9.5 23 33.285 20.7894 19.8125 19.8125 20.53165
1 15 10.5 23 72.593 67.90038 37.0573 37.0573 49.94211
1 15 11.5 23 87.809 87.40825 42.22439 42.22439 48.35425
1 15 12.5 23 90.662 87.82219 49.75361 43.7777 43.7777
1 15 13.5 22.28 104.61 140.5403 81.33593 38.83248 38.83248
1 15 14.5 21.74 85.907 144.0851 113.1585 26.65968 26.65968
1 15 15.5 21.02 52.622 117.9352 131.648 14.93068 14.93068
1 15 16.5 18.32 12.046 32.56771 51.68226 5.008592 5.008592
1 15 17.5 15.62 0 0 0 0 0
1 15 18.5 12.92 0 0 0 0 0
1 15 19.5 14 0 0 0 0 0
1 15 20.5 14.9 0 0 0 0 0
1 15 21.5 15.98 0 0 0 0 0
1 15 22.5 14.36 0 0 0 0 0
1 15 23.5 12.56 0 0 0 0 0
1 16 .5 10.94 0 0 0 0 0
1 16 1.5 11.66 0 0 0 0 0
1 16 2.5 12.2 0 0 0 0 0
1 16 3.5 12.92 0 0 0 0 0
1 16 4.5 11.66 0 0 0 0 0
1 16 5.5 10.22 0 0 0 0 0
1 16 6.5 8.959999 0 0 0 0 0
1 16 7.5 10.58 2.219 4.069766 1.014399 1.014399 6.204218
1 16 8.5 12.38 23.775 50.92946 10.46099 10.46099 56.43663
1 16 9.5 14 58.962 100.9546 22.22168 22.22168 80.36186
1 16 10.5 17.42 101.757 162.0322 34.26768 34.26768 87.79176
1 16 11.5 20.66 93.832 115.0019 38.38869 38.38869 48.81027
1 16 12.5 24.08 77.982 62.8388 44.45371 41.5587 41.5587
1 16 13.5 25.34 66.887 67.64957 46.78406 31.73169 31.73169
1 16 14.5 26.78 66.887 63.84694 55.95936 33.63369 33.63369
1 16 15.5 28.04 26.945 21.45337 22.33171 15.0575 15.0575
1 16 16.5 28.04 10.144 7.854993 9.207159 5.927899 5.927899
1 16 17.5 28.04 0 0 0 0 0
1 16 18.5 28.04 0 0 0 0 0
1 16 19.5 28.94 0 0 0 0 0
1 16 20.5 30.02 0 0 0 0 0
1 16 21.5 30.92 0 0 0 0 0
1 16 22.5 31.28 0 0 0 0 0
1 16 23.5 31.64 0 0 0 0 0
1 17 .5 32 0 0 0 0 0
1 17 1.5 33.98 0 0 0 0 0
1 17 2.5 35.96 0 0 0 0 0
1 17 3.5 37.94 0 0 0 0 0
1 17 4.5 37.94 0 0 0 0 0
1 17 5.5 37.94 0 0 0 0 0
1 17 6.5 37.94 0 0 0 0 0
1 17 7.5 37.58 1.902 1.1412 1.1412 1.1412 1.1412
1 17 8.5 37.4 15.85 10.17526 9.351499 9.351499 10.29092
1 17 9.5 37.04 30.749 19.1792 18.4494 18.4494 18.99006
1 17 10.5 37.76 39.942 24.50452 23.9652 23.9652 24.19179
1 17 11.5 38.3 61.815 37.62194 36.772 36.772 36.88794
1 17 12.5 39.02 62.449 37.75269 37.50805 37.4694 37.4694
1 17 13.5 39.02 61.498 37.3906 36.92174 36.5818 36.5818
1 17 14.5 39.02 47.55 29.10099 28.9123 28.3715 28.3715
1 17 15.5 39.02 30.432 18.2592 18.2592 18.2592 18.2592
1 17 16.5 38.3 11.412 6.8472 6.8472 6.8472 6.8472
1 17 17.5 37.76 0 0 0 0 0
1 17 18.5 37.04 0 0 0 0 0
1 17 19.5 37.04 0 0 0 0 0
1 17 20.5 37.04 0 0 0 0 0
1 17 21.5 37.04 0 0 0 0 0
1 17 22.5 36.68 0 0 0 0 0
1 17 23.5 36.32 0 0 0 0 0
1 18 .5 35.96 0 0 0 0 0
1 18 1.5 36.32 0 0 0 0 0
1 18 2.5 36.68 0 0 0 0 0
1 18 3.5 37.04 0 0 0 0 0
1 18 4.5 38.3 0 0 0 0 0
1 18 5.5 39.74 0 0 0 0 0
1 18 6.5 41 0 0 0 0 0
1 18 7.5 41.72 2.219 1.3314 1.3314 1.3314 1.3314
1 18 8.5 42.26 15.85 9.715386 9.51 9.51 9.745148
1 18 9.5 42.98 41.527 25.00046 24.7577 24.7577 24.93815
1 18 10.5 44.06 62.766 37.6596 37.6596 37.6596 37.6596
1 18 11.5 44.96 69.42301 41.93665 41.6538 41.6538 41.69249
1 18 12.5 46.04 73.861 44.59944 44.3553 44.3166 44.3166
1 18 13.5 44.78 66.887 40.40133 40.24566 40.1322 40.1322
1 18 14.5 43.34 53.89 32.41815 32.356 32.1755 32.1755
1 18 15.5 42.08 18.703 11.2218 11.2218 11.2218 11.2218
1 18 16.5 40.64 11.095 6.657 6.657 6.657 6.657
1 18 17.5 39.38 0 0 0 0 0
1 18 18.5 37.94 0 0 0 0 0
1 18 19.5 37.04 0 0 0 0 0
1 18 20.5 35.96 0 0 0 0 0
1 18 21.5 35.06 0 0 0 0 0
1 18 22.5 35.42 0 0 0 0 0
1 18 23.5 35.6 0 0 0 0 0
1 19 .5 35.96 0 0 0 0 0
1 19 1.5 35.6 0 0 0 0 0
1 19 2.5 35.42 0 0 0 0 0
1 19 3.5 35.06 0 0 0 0 0
1 19 4.5 34.7 0 0 0 0 0
1 19 5.5 34.34 0 0 0 0 0
1 19 6.5 33.98 0 0 0 0 0
1 19 7.5 33.98 2.536 1.5216 1.5216 1.5216 1.5216
1 19 8.5 33.98 19.337 11.80701 11.6022 11.6022 11.83765
1 19 9.5 33.98 43.429 26.14113 25.8989 25.8989 26.07958
1 19 10.5 33.26 65.302 39.1812 39.1812 39.1812 39.1812
1 19 11.5 32.72 73.544 44.1264 44.1264 44.1264 44.1264
1 19 12.5 32 79.884 48.05426 47.81065 47.7719 47.7719
1 19 13.5 33.08 85.907 105.1852 64.25841 34.26769 34.26769
1 19 14.5 33.98 77.982 122.0816 97.52248 25.23318 25.23318
1 19 15.5 35.06 58.011 133.1444 151.1249 14.04307 14.04307
1 19 16.5 33.44 15.216 49.7723 82.01438 5.484086 5.484086
1 19 17.5 31.64 0 0 0 0 0
1 19 18.5 30.02 0 0 0 0 0
1 19 19.5 28.4 0 0 0 0 0
1 19 20.5 26.6 0 0 0 0 0
1 19 21.5 24.98 0 0 0 0 0
1 19 22.5 24.26 0 0 0 0 0
1 19 23.5 23.72 0 0 0 0 0
1 20 .5 23 0 0 0 0 0
1 20 1.5 22.28 0 0 0 0 0
1 20 2.5 21.74 0 0 0 0 0
1 20 3.5 21.02 0 0 0 0 0
1 20 4.5 21.02 0 0 0 0 0
1 20 5.5 21.02 0 0 0 0 0
1 20 6.5 21.02 0 0 0 0 0
1 20 7.5 24.08 3.17 7.126154 1.267998 1.267998 11.42546
1 20 8.5 26.96 20.605 41.0968 9.034491 9.034491 46.04781
1 20 9.5 30.02 37.406 27.0514 21.4926 21.4926 25.65353
the simulation below has 3 capacitors: the inherent mass of the 1200 ft^2
house (2k btu/f); the shelf capacitance, 1200 pounds of water in flat poly
film ducts on 2 stacks of 3 4'x8' shelves under the ceiling; and an 86" diam
x 4' tall 957 gallon stss heat storage tank with a copper coil heat exchanger
for 100% solar space heat and close to 100% solar hot water in december,
with no evacuated tubes nor antifreeze. and no pvs nor milk-based paints
nor bicycle racks, and a low leed score :-)
the frugal electrical use is 227 kwh/month. there's a good greywater
heat exchanger. the shelf and tank caps grew from the sizing calc during
the simulation, which doesn't assume any beneficial tank stratification
nor explicitly use the shelf and fin-tube conductances, but it looks good
and allows margins for those conductances.
there's 32 ft^2 of solar siding and 240 ft^2 of twinwall polycarb passive
sunspace glazing (5 4'x12' thermaglas panels) with 144 ft^2 of one-layer
polycarb higher temp air heater glazing inside the sunspace in a barra-like
system with a kind of thermal cogeneration and 64' of fin-tube inside
the air heater glazing with a small pump and a differential thermostat.
on an average day, sunspace air naturally thermosyphons up through a one-way
plastic film damper into the shelf space under the ceiling and down through
a vertical duct on the inside of the insulated south wall of the house and
back into the lower part of the sunspace. when the house needs heat and
the shelf space is warm, a fan near the floor pulls air out of the duct
and into the room. another small pump moves tank water up through some
fin-tube inside the house on a cloudy day.
the lowest temp in the weather file is -3 f. rochester ny is a hard climate,
colder than phila, with half the sun, about 500 btu/ft^2 on a south wall on
an average december day. the min tank temp is 82 f on 1/15 at 9:30 am, when
the outdoor temp is 23 f. the room temp setpoint is 70 f for 8 hours per day
and 50 f otherwise, altho it rarely cools to 50 by dawn. the room temp is
allowed to overshoot to 74 f during the day, which helps. reducing the room
mass would allow it to cool more quickly at night and reduce the required
tank and shelf sizes. so would zoning, eg closing bedroom doors during the
day or automatically turning heat off when rooms are unoccupied. lines 20
and 30 below adjust the graphic display. line 145 sampled the cap temps on
1/5 during a longer simulation, which were set to those temps at the start
of this shorter simulation using the winter2 file.
10 cls:screen 9:line (0,0)-(639,349),,b
20 tmax=100:v=350/tmax'vertical scaling
30 hs=100:he=330'start and end display hours
40 for tr=10 to 50 step 10'plot temp ref lines
50 line (0,349-v*(tr))-(639,349-v*(tr)):next
60 gcloud=120'cloudy day house conductance (btu/h-f)
70 cr=2000!'room capacitance (btu/f)
80 tr=50.58'initial room temp (f)
90 cs=1200'6-shelf capacitance (btu/f)
100 ts=86.85'initial shelf temp (f)
110 ct=957*8.33'tank capacitance (btu/f)
120 tt=115.84:ttmin=1000'initial tank temp (f)
130 open "winter2" for input as #1:line input#1,h$
140 input#1,month,day,hour,ta,sh,ss,sw,sn,se
145 if month=1 and day=5 and hour=9.5 then print tr,ts,tt
150 gsun=120-240/(34+1/.58)'sunny day house conductance (btu/h-f)
160 ssgain=.8*240*ss-(ts-ta)*.58*240'sunspace solar gain (btu)
170 if ssgain<0 then ssgain=0:g=gcloud else g=gsun'sunspace dampers closed
180 sigain=.9*32*ss-(tr-ta)*32'solar siding gain (btu)
190 if sigain<0 then sigain=0'no heat from solar siding
200 if hour<9 or hour>17 then trs=50 else trs=70'room temp setpoint (f)
210 wgain=.5*(24*se+48*ss+24*sw)'solar gain from windows (btu)
220 ir=wgain+sigain+1440-(tr-ta)*g'net heat into room (btu)
230 tr=tr+ir/cr'find new room temp (f)
240 if tr>74 then tr=74'limit upper room temp (f)
250 if tr>trs then is=0:it=0:goto 330'room needs no heat :-)
260 rheat=(trs-tr)*cr'required room heat (btu)
270 if ts |
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