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APPENDIX D
APPLYING THE SIZING METHODS
D.O
THE DESIG
~~_.IGNMENT
The managE
~r
of a Daytona Beach oceanfront motel plans to install a
solar pool heatE
r with
a full-load capability, LPG-fired, backup heater
The motel is oW]
ed by a major chain which owns another motel in Ormond
Beach -- six mi
les north of the Daytona Beach site.
The buildings, site
layou t , pool size
and relative pool location and climate are almost identical
for the two
motels. Monthly LPG consumption figures for pool heating at
the Ormond Bea
That pool
h motel are available for the past six years.
does not have
Both ~1s are to be
kept
at a minimum
olar heater.
water temperature of 80F
The manage
~r of the Daytona Beach motel has two estimates from solar
contractors for
installed solar pool heaters. One contractor proposes to
use 2500 ft2 of
unglazed, flexible-mat collectors laid flat against the insu-
lated roof deck.
His bid for the installed system is $20 t 000.
The other
contractor plans
to use forty 4' x 10' flat black, insulated solar collectors
with
and
single-glass cover plates.
They
be
re to
opper passages
mounted facing
south at a 40 slope.
His bid is $25,600.
Neither contract
includes the LP(
It will be installed by the swimming pool
; backup heater
Bot}:
good reputations
ontracto~
contractors have
Both systems use
s;m;l;~r flow con
trol strategy (differentially controlled l~-hp booster pumps
and automatic valving)
Freeze protection is adequately provided in both
The chemical balance of the pool is carefully
the
ases
controlled so
contact of pool
water with the copper passages in the glazed collectors is
not seen as a problem
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Both contractors contend that their system represents the best return
on the initial in
vestment and the manager has asked you to help him decide
He has requested an estimate of monthly and
ontract to accept.
annual savings
based on average weather conditions and the history of
ed tor pool heating at the Ormond Beach motel Finally he
nergy consum~
has requested
that you advise his
construction foreman so that he can
effectively supe
rvise the installation
THE CALCULATIONS REQUIRED
D.l..1
STEP
Analyze the annual energy consumption of the Ormond
Beach pool
The average monthly energy consumption for pool heating at
the Ormond Bea
,ch motel is reported in Table D. 1
TABLE D.l
:)rmond Beach Motel Pool Energy Consumption
Month
Gal LPG
$/Mo
Energy Consupmtion
($l.20/gal)
B tu/Mo B u/Day
1,288,000
00
$ 720
38,640,000
$1620
350
86,940,000
2,804,516
1500
$1800
96,600,000 3,116,129
1455
$1746
93,702,000 3,346,500
450
$540
28,980,000 934,839
~
D.l.2
STEP 2:
Tabulate the Required Weather Data
$:r_EJ>~
Tabulate wind conditions using Table D. 2
D-2
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TABLE D.2
Site-specific Wind Conditions
Direction Site Wind Speed (in MPH) Rooftop Sp~ed (in l\'IPH)onth
51
from Table C .4, page C-13)
(site speed x [. 33 to
NW
4.4 - 6.65
3.3
NW
13.3
4.4 -
6.65
Jan
NE
4.5 - 6.9
3.'7
NNE
4.9 - 7.5
4.9
ssw
15.2
5.0 - 7.6
Because 160
0 ft2 to 2500 ft2 of collectors will be installed on the 5200
ft2 roof, which
is wind mapped in Figure C. 9 , some of the collectors will
as much as .5 times the
unobstructed wind speed.
Others
e subjected to
receive the
full protection afforded by the building and its parapet
)f roof top wind speeds is tabulated in Table D. 2
Their
hus, a range c
arithmetic averag;e will be used in subsequent calculations.
Tabulate daytime temperatures using information from the
TEP 2b
table on page E.10.
Table D.3
Daytime Temperature Data
Month
Tar
( 2"'4fij
npa Day time Mean
r Average mean + 5OF)
Daytona 24hr Average
Max Mean
Nov
Dec
Jan
Feb
Mar
71.2
65.8
65.8
65.8
71.2
74.8
69.8
68.8
69.3
14.6
68.2
59.5
57.9
58.8
64.6
D-3
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'eather data does not appear in Appendix E
Thus, data
aytona w
Jacksonville
h the most similiar weather should be chosen
or the city wi
mri is too hot. Gainesville is mlaDd and north of Daytona so
s too cold., Mt
Tampa appears to be a good choice.
TemperatuJ
:'e data for Daytona Beach is available from NOAA (see page
idress) and is tabluated in the right hand two columns of
-7 for the ac
Table D.3 Th1
correlation between the calculated daytime average temper-
ature for Tamp.
a and the average of measured mean and high temperat~res
tor Daytona Be~ch is good.
Tabulate monthly available insolation data using the table
TEP 2c
on page E-10
TABLE D.4
Insolation Data (tor Tampa)
Average B ultt2 .
ay
(Horizontal)
Average B tu/ft2 . day
South facing-, 400 slope
Month
1913
1722
1799
1870
1939
Nov
Dec
Jan
Feb
Mar
1314
1112
1204
1439
1756
In this case. too. we will select Tampa weather data because it is the
city with availa
Lble insolation data listed in Appenidx E whose climate most
found in Daytona Beach..
esembles that
We now have tabulated the weather data that we will use to calculate
the two solar pool heating systems which require evaluation
he output of
performance
of
the
competing
.l..3
STEP 3
the
thermal
stimate
solar systems
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STEP 3a
collector performance
data for
the
collectors
ssemble
under consideration
Performance
data for both the glazed and unglazed collectors under
evaluation have
been made available by the two competing solar contractors
~d in Figure D.l
nd are presentE
1.00
.80
.80
.70'
.80
.50
.40
.30
.20
.10
Unglazed Perf
" 8 .808 3.60
,-Low temperatl
ormance Equation:
: .
< 3 MPH
I
'
ure rating: aeo BTU/Ft2.0ay
Glazed Performance Equation:
.,. .72 -1.003 : .
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TABLE D.S
Unglazed Collector Output
(Btu/tt2.day)
Corrected Collector Output
Wind
Speed
Temp/lnsol from Wind Speed
Correction Table Correction
from Fig. D.2 from
(A.S) (A.6)
~~
Fig.(5.3)
80-71 = 9
80-66 = 14
80-66 = 14
80-66 = 14
80-71 = 9
1314
1112
1204
1439
1756
5.5
5.5
5.7
6.2
6.3
700
380
450
630
1080
Nov
Dec
Jan
Feb
Mar
785*
500(A.5)
580(A.5)
750(A.5)
1110*
lues from Figure A.5 (AT = 14) and Figure A.6 (AT = 5) is used
a AT of goF.
*Average of va
to approxmate
The dotted lines on Figures A. 5 and A. 6 trace the rerating path for
a 860 B u/ft2 .
standard-Florida-day unglazed collector through the nomo-
graphs for No~
The same proce-
ember temperature/insolation conditions.
.propriate nomographs is used for .each month during which
ure, using aJ:
pool heating is
expected to be required.
The dotted lines on Figure 5. 3 indicate the path through the
785 B u/ft2 . ay rating (the modified
speed
correctic
.n nomograph tor a
ctor rating, obtained by averaging values from AT = 14 and
November colle-
Table D. 6 lists the monthly output. of
T = 5 temp/iI
lsolation nomographs)
the 2500 ft2
I1nglazed-mat-type system which has been proposed
collector output has been multiplied by the nwnber of days
redicted daily
and by the appropriate system correction factor, .95 (from
n each month
Table 5.4), wh:
ich corresponds to 0 slope and no heat exchanger
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Therma
. Table D.6
1 Output of Unglazed Solar Pool Heating System
System Correction
Factor
Collelation rate = 1600 Btu/ft2 -day -- the predicted perform-
t of 14, inS(
rhe same situation holds for all the pool heating months in
nce improves
this sample problem but certainly not for all months, locations and winter
weather condition:
in Florida.
ou~ut
of glazed collectors does not require correction for wind
speeds
likely
to be encountered during periods of operation in Florida
Table D.9 lists
the predicted monthly output of the 1600 ft2 glazed
collector system ~
Ihich has been proposed
D~8
1913
1722
1799
1870
1939
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Table D.9
Thenr tal Output of Glazed Solar Pool Heating System
(Btu x lO6/month)
System
Output
Nov
Dec
Jan
Feb
Mar
61.9
55.1
57.5
54.2
65.5
.95
.95
.95
.95
.95
58.8
52.4
54.6
51.5
62.2
In this
the appropriate system correction factor is .95 (from
ase
Table 5.~).
This is a more favorable system factor than that assigned to
a horizontal surf
'ace
because the collector slope (30) improves the collec-
The incident angle of the incoming radiation is near 300
ion geometry.
(o : l~s) during
winter collection hours The incident angle on a horizon-
tal surface durin:
g win ter collection hours is 30 (or more)
Table D .10 tabulates the monthly energy requirements of the pool and
the energy predi
lcted to be available from the glazed pool heating system.
Poo]
Table D .10
Energy Requirements/Glazed System Output
(Btu x 106/month)
Pool
Requirt
(Table
Savings
($)
~ment
~
Cost
~
onth
Available
from
Solar System
Nov
Dec
Jan
Feb
Mar
38.6
86.9
96.6
93.7
29.0
58.
52.
54.
51.
62.
720
975
1016
958
540
4209
720
1620
1800
1746
540
6426
*Cannot aU be used
D-9
(30)
(31)
(31)
{28)
(31)
8*
4
6
5
2*
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D.2 STEP 4
C_9_r1~~~EHE ECONOMICS OF BOTH PROPOSED SYSTEMS
Under
the
assumed
weather conditions,
characteristics and
ystem
both
systen1S offer an equally good return on initial investment
about
15%.
The
actual
figures are:
3178/20000
= 15.9% for the unglazed
system and 4209/
The portion of the
26500 = 15.9% for the glazed system.
annual pool heati
ng load is: 3162/ 6426 = 49% in the case of the unglazed
collectors and 42
09/6426 = 65% in the case of the more expensive array of
FSEC suggests a solar fraction range of roughly. 5 - .8
lazed collectors
(50%-80%) as heir
kg cost effective for solar' service or domestic water heat-
It fairly may
be argued that pool heating should not be
ystems
limited to the smme range of solar fractions.
~ether such ar~ents are
valid or invalid, both systems are reasonably close to the suggested range.
STEP 5 COMPARE CALCULATOR (APPENDIX F) WITH NOMOGRAPH
(APPENDIX A) RESULTS
Table D-ll
gives monthly inputs and outputs for the unglazed collec-
ideration as calculated using Program
"A" for a HP 15C
ors under cons:
calculator
INSOLATION WIND
~Btu/ft2day) ~)
ONTH TO of t.
1
71 80
66 80
66 80
66 80
71 80
Nov.
Dec.
Jan.
Feb.
Mar.
1314
1112
1204
1439
1756
5.5
5.5
5.7
6.2
6.3
3.6 x 1.2*
= 4.32
3.6 x 1.2 = 4.32
3.6 x 1.22 = 4.40
3.6 x 1.28 = 4.60
3.6 x 1.29 = 4.65
.808
.808
.808
.808
.808
737
444
506
653
1055
*Wind speed modifiers
ed annual solar savings using the calculator program equalhe predict
$3178
LlSing the nomographs--very close agreement
s
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A similar
malysis
for the glazed collector array under consideration
shows
a differen
ce of less than 1%
It should
be noted that the comparisons are for collectors with first
order
thermal performance equations, either exactly like (unglazed) or
very close to (2
~lazed) those for which the nomographs were derived
The
agreement will n.01 be this close if the thermal performance equations vary
substantially from
808 - 3.60 (t. - t ) (unglazed)
1 a
r
1}
s
67 - 1.03 (ti -.ta) (glazed)
I
tt
=
D.4
UNCERTA J
~rI~S ASSOCIATED WITH USING "AVERAGE" VALUES
If January
consisted of 31
equally
days with 66F average
unny
ture, actual solar heater performance would closely follOW
aytime tempera
the calculated p
,erfonnance. Its more likely however,
that some January
days will be clo
,udy, some clear, some unseasonably warm and some cold.
the perfonnance of both solar system and may cause major
his will aft ect
differences
If half of
the month has 55F average daytime temperatures and half
the month
has
75F
temperatures the monthly
verage daytime
daytime
average will reI
nain at about 66F
It may
be interesting to calculate
changes in the
January
contribution of the two solar systems when ad-
justed on the b asis of half a month of each of the new temperature pro-
files
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75 F
(AT:5)
55 F
(6.T = 25)
unglazed output
820 Btu/ft2 -day
200 Btu/ft2.day
ating modified
(from Figure
[or temp/ingot
~.6 or A.4)
90 Btu/ft2.day
ating modified f
(from Figure 5
~or wind speed
.3)
725 B u/ft2 . day
85 = 3.0
5 = 23.9
31 x 90 x 2500 x
2
31 x 725 x 2500 x
-2
half month outpu
(Btu x 106)
t
Total = 26.0
So the out]
put of the unglazed system drops 21% and becomes very
unbalanced with
respect to time of mon h
55 F
5 F
lazed output
1065
ating modified
(from Figure
ror temp/insol
~.13 or A.1 .)
1260
95 = 29.7
31 x
1065
x
1600 x
95
= 2
31 x 1260 x 1600 x
2
half month outpu
(Btu x 106)
.t.:
""2
Total = 54.8
;>ut of the system remains about the same and is reasonably
o the out]
well balanced wi1
h respect to time of month
rIONSHIP BETWEEN SYSTEM SIZE AND ENERGY AND
.S THERELA1
DOLLAR SAVINGS
orthy that in November and March both proposed solar pool
t is notew
produce more energy than the Ormond Beach pool used
heating systems
Yet during December, January and February both
uring those months
The selection of an economically op timized
n is required.
roduce less tho
system must takl
e the following factors into account
er square fo?t of solar heating systems tends to rise as the
he cost p
This is because certain costs -- engineering and
system size is reduced.
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ove~head, controllers,esign, company
valves and supply lines -- do not
decrease linearly
with a reduction in system size
Additionally
the fraction of
the thermal load carried by the solar
(solar
does
increase linearly with
ystem
fraction) collector
ot area
Witness Novembe
and March when a system twice as large as those pro-
posed
would
For these and otherontribute no extra
usable energy
reasons, a syste:
m that meets about 50% - 80% of the annual thermal load is
in a size and co;
st range that maximizes return on the buyer's investment
Another imJ:
ortant fact is apparent from a close examination of tables
D.7 and D.I0 The maximum ~ at which either solar system can con-
tribute energy d
luring the period when it is needed is about 2 million Btu
on a clear,
seasonally
temperate day.
During and immediately after a
during which the motel-sized pool may lose 5-6 million
evere cold snal=
Btu/day, the LPG-fired heater will have be used to maintain a comfortable
pool temperature
Such heaters are able to supply the pool with heat at
the rate
of 200,0
100 o 600,000 B tu per hour (depending on their size) on a
If an unseasonable cold snap occurs in November or
4-hour-a-day basis.
March,
some LPG utilization
be
during those
osts may incurred even
months which on
a 3D-day basis have excess solar heating capacity avail~
able
Thus,
caution must be exercised in predicting the dollar savings
that will result f]
Those savings are effectedom solar pool heating system.
~rns
as well as by
monthly
average conditions
y weathe~ patte
Fortuna tely swimming pools have high thermal storage capacity and
may be heated to 50
-
7F over the minimum acceptable temperature with-
out causing use A 50,000 discomfort.
gal pool has a thermal storage
capacity of 432,
)00 Btu per of and thus can maintain a minimum tempera-
ture
of 80F (ai
.ded by normal daily solar system input) through several
days of
cold weather
in November or March if preheated to say 87F
D-13
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