# Heating a pool with a roof

Posted by nicksanspam on June 8, 2006, 9:54 am

Based on average monthly Phila weather data, it looks like the local YMCA
might save 30% of the indoor pool heating bill over 9 months of the year
by trickling about 50 gpm of pool water over the bare standing seam roof
during the day, and maybe preheat water for showers in summertime.

A transparent roof cover might triple the savings.

30 DATA 30.4,37.9,620,1000,0.0025
40 DATA 33.0,41.0,870,1080,.0027,42.4,51.6,1200,1070,.0036
50 DATA 52.4,62.6,1520,950,.0050,62.9,73.1,1760,830,.0080
60 DATA 71.8,81.7,1940,790,.0111,76.7,86.1,1890,820,.0133
70 DATA 75.5,84.6,1710,940,.0130,68.2,77.6,1380,1070,.0104
80 DATA 56.4,66.3,1020,1150,.0070,46.4,55.1,680,900,.0048
90 DATA 35.8,43.4,530,900,0.0032
100 P87=EXP(17.863-9621/(460+87))'87 F sat air vapor pressure ("Hg)
110 P85=EXP(17.863-9621/(460+85))'85 F vapor pressure near pool ("Hg)
120 APd00'indoor pool area (ft^2)
130 AR0*51.5/COS(SLOPE)'main roof area (ft^2)
140 TR0'roof water temp (F)
150 P100=EXP(17.863-9621/(460+100))'100 F sat vapor pressure ("Hg)
160 GP=1.58'gas price (\$/therm)
170 FOR MONTH = 1 TO 12
190 TN=TA-(TM-TA)'average daily min temp (F)
200 TW=TN+.7*(87-TN)/2'indoor R2 window surface temp (F)
210 TDP=TW+5'max indoor dew point to avoid night condensation (F)
220 PA=EXP(17.863-9621/(460+TDP))'indoor vapor pressure ("Hg)
230 PLOSS\$*100*AP*(P85-PA)/100000!'daily pool heat loss (therms/day)
240 RH0*PA/P87'/max indoor RH to avoid night condensation (%)
250 SUN=HSUN*COS(SLOPE)+SSUN*SIN(SLOPE)'Btu/ft^2 of roof
260 PO).921/(1+.62198/W)'outdoor vapor pressure ("Hg)
270 RGAIN=AR*(SUN-6*100*(P100-PO))/100000!'roof gain (therms/day)
280 IF RGAIN<0 THEN RGAIN=0'roof loss vs gain
290 PRINT MONTH,RH,PLOSS,RGAIN
300 IF RGAIN>PLOSS THEN RGAIN=PLOSS'more gain than loss
310 TGAIN=TGAIN+RGAIN'yearly savings (Btu)
320 NEXT
330 SAVINGS0*GP*TGAIN'yearly savings (\$/year)
340 PRINT SAVINGS

Month  max RH        pool loss     roofgain
(%)           (therms/day)  (therms/day)

1      28.26181      132.3402      0
2      29.71948      129.3945      6.165614
3      36.07612      116.5486      24.38077
4      44.4258        99.6752      40.49223
5      56.31135       75.6563      54.99459
6      68.96872       50.0776      68.24747
7      77.52261       32.7915      69.73278
8      76.03465       35.7985      62.59364
9      64.44674       59.2159      44.37123
10     48.99176       90.4481      22.22977
11     40.05736      108.5032      0
12     32.07007      124.6443      0

Yearly savings: \$4755.71

Nick

Posted by nicksanspam on June 9, 2006, 9:49 am

A single cover (eg 2 \$00 32'x100' pieces of polyethylene greenhouse film
with a 5-year guarantee) might save 22% more for pool heating, or 63% more,
if we preheat water for showers. The calc below assumes the roof evaporates
enough water to make up for the heat loss from the cover to the outdoors,
with condensation under the cover and minimal water loss.

160 GG=7'glazing conductance to outdoor air (Btu/h-F-ft^2)
170 K10/GG'constant...
220 TD=TA+(TM-TA)/2'average daytime temp (F)...
290 K2=K1*P100+460+TD'constant
300 TGQ0'initial glazing temp estimate (R)
310 TG=K2-K1*EXP(17.863-9621/TG)'glazing temp (R)
320 IF ABS(TGL-TG)>.01 THEN TGL=TG:GOTO 310'iterate
330 RGAINW=AR*(.9*SUN-6*(TG-460-TD)*GG)/100000!'roof gain (therms/day)
340 IF RGAINW<0 THEN RGAINW=0'roof loss vs gain
345 IF RGAINW>PLOSS THEN RGAIN=PLOSS ELSE RGAIN=RGAINW'more gain than loss
350 PRINT 440+MONTH;"'";TAB(12);PLOSS,RGAIN,RGAINW
380 TGAIN=TGAIN+RGAIN'accumulate savings
390 TGAINW=TGAINW+RGAINW
400 NEXT
410 SAVINGS0*GP*TGAIN'yearly savings (\$)
420 SAVINGSW0*GP*TGAINW'yearly savings with DHW (\$)
430 PRINT SAVINGS,SAVINGSW

Month   pool loss     roofgain      roofgain w/ DHW
(therms/day)  (therms/day)  (therms/day)

1       132.3402      0             0
2       129.3945      11.61019      11.61019
3       116.5486      31.94458      31.94458
4        99.67521     51.02791      51.02791
5        75.65631     67.52151      67.52151
6        50.07769     50.07769      82.37038
7        32.79157     32.79157      84.81842
8        35.79851     35.79851      77.58797
9        59.21592     58.5638       58.5638
10       90.4481      34.43198      34.43198
11      108.5032      6.749671      6.749671
12      124.6443      0             0

Yearly savings:

no cover             cover         cover+DHW

\$4755.71            \$8036.53     \$4014.09

Nick