Publisher’s version / Version de l'éditeur:
Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca.
Questions? Contact the NRC Publications Archive team at
PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the first page of the publication for their contact information.
https://publications-cnrc.canada.ca/fra/droits
L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB.
Building Research Note, 1982-03
READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE.
https://nrc-publications.canada.ca/eng/copyright
NRC Publications Archive Record / Notice des Archives des publications du CNRC :
https://nrc-publications.canada.ca/eng/view/object/?id=7e0854b4-4a20-475d-84a3-ee733bdd7369 https://publications-cnrc.canada.ca/fra/voir/objet/?id=7e0854b4-4a20-475d-84a3-ee733bdd7369
NRC Publications Archive
Archives des publications du CNRC
This publication could be one of several versions: author’s original, accepted manuscript or the publisher’s version. / La version de cette publication peut être l’une des suivantes : la version prépublication de l’auteur, la version acceptée du manuscrit ou la version de l’éditeur.
For the publisher’s version, please access the DOI link below./ Pour consulter la version de l’éditeur, utilisez le lien DOI ci-dessous.
https://doi.org/10.4224/40000529
Access and use of this website and the material on it are subject to the Terms and Conditions set forth at
Utilization of solar gain through windows for heating houses
Ser TFll
B92
ISSN 0701-5232 no. 184 c. 2 I-l C ? S
1
, , . . . . I..!. . . . . . . -. . . . . . , , . , , . . . . . - - * . . . . , , . . ... - ,. <. ,: , . . . 8UTILIZATION
OF
GALN THROUGH WINDOWS FORHEATXNG HOUSES
by
A N A L ~ Z E ~
-
S.A. Barakat and D.M. Sander
Division of Buildtng Research, National Research Council of Canada
UTILIZATION OF SOLAR GAIN
THROUGH WINDOWS FOR HEllTING HOUSESS .A. Earakat and D.M. Sander
The heating energy requirements for houses may be estimated by a slmple c a l c u l a t i o n using t h e concept o f a seasonal s o l a r utilization factor. Solar utilization factors were derived using an hour-by-hour computer stmulation with actual weather data f o r f l v e Canadian locations. These u t i l i z a t i o n factors are presented for various l e v e l s of thermal storage
as a function o f the r a t i o of seasonal solar gains to seasonal b u i l d i n g
loads. Curves are presented both for conditions a£ constant room
temperature and for temperature s w i n g s of 2.75 and 5.5 6 " . Experimental data obtained from the NRC Passive Solar Test Facility are shown t o
The need f o r a simple method t o estimate the heating energy requirements of houses is widely recognized. Such an es timatlag technique could be used for comparing a l t e r n a t i v e s in the design
process, and for evaluating house designs t o d e t e d n e their compliance with energy standards
.
An important component of t h i s method would be the estimation of the amount of solar energy collected through the windows of houses and
u t i l i z e d to offset heat l o s s e s . It has been shown1 that sourh-facing
double- and t r i p l e - g l a z e d windows can be net suppliers .of energy over the heating season for all locations In southern Canada, provided that a l l of the s o l a r gains are u t i l i z e d . In r e a l i t y , only a fraction of the
solar gains can be utilized. The magnitude of this fraction, which u i l l
be referred to as the utilization factor, depends upon several
parameters including the geographical location, the s i z e and type of
glass, the overall building heat loss, the thermal storage properties of
the house, and t h e allowable indoor temperature swing.
A number of methods2 9 n 4 have been developed to estimate the net
solar contribution t o space heating for direct-gain passive solar designs. One of the methods widely used in Canada and the USA 1s the solar load ratio (SLR) method developed by the toa Alamos Scientific
Laboratory. This method has been extensively applied t o a l l t y p e s of
buildings, deepf te the author's caution that "'the method is. not
applicable to the analysis of lcw-mass sun-t entpered buf l d i n g s "
.
The objective of t h l a study was to develop a method for quantifying
the useful solar gain through windows t h a t would apply t o a l l types of
houses in all climatic regions of Canada. S i n c e the scope of this
method w a s not to be limited to passive solar houses, i t was necessary to consider solar heat gains through a l l windows (not only those facing south), as well a s houaea with different amounts of thermal masg. The
most important a p p l i c a t i o n of t h i s methad, however, w f l l be the
evaluation of energy consmp t i o n i n the lightweight wood-f rame houses prevalent in Canada. In a d d i t i o n , it was deemed desirable t o base the method on seasonal rather than monthly coasmption t o make it easier to
estimate, the seasonal heating energy required for a hauae. This
seasonal approach has, in fact, r e s u l t e d i n a calculation procedure that is only slightly more dffficult to apply than the degreeday method.
This Note describes the development of the method and presents the solar u t i l i z a t i o n factors for various amounts of t h e m 1 storage and for three values of indoor temperature swing.
INSTANTANEOUS HEAT BALANCE
The instantaneous (hourly) heat balance for a house is given by:
where h = instantaneous heating required,
It = instantaneous hear l o s s due t o transmfssion through
exterior w a l l s , windows, c e i l i n g s , etc.
,
1, = instantaneous heat l o s s due to a i r change with outdoors
( i n f i l t r a t i o n -t ventilation), L
l b = instantaneous below-grade heat loss,
gi = instantaneous heat gain from i n t e r n a l sources ( l i g h t s ,
equipment, people, etc. )
,
g,
-
instantaneous s o l a r heat gain through windows.There will be times when the gains exceed the L o s s e s . Under these
c o n d i t i o n s the excess heat w i l l be stored In the mass of trhe roam,
causing the roam temperature to rise. In order to prevent the room
temperature from rising above an acceptable l i m f t , t h e excess heat gain must be eliminated, This may be done by closing the b l i n d s , opening the
windows, or operating a ventiSatfon or a i r c o n d i t f o n i n g system. A
portion of the stored heat will become a v a i l a b l e a s useful heat once the room temperature drops to the t h e m s t a t setting. The remainder of t h e
stared heat w f l l have been wasted in t h e form of increased transmission
heat loss through the walls due to t h e rise Tn room a i r temperature.
SEASONAL
HEAT
BALANCEThe heat balance equation may be written for a longer time period, such as the heating season, by i n c l u d i n g a utilization f a c t o r to account for the usable portion of fnternal and solar gains.
where H = total heating required
for
season,Lt = seasonal t o t a l of heat losses due t o transmission through
exterior w a l l s , windows, c e i l i n g s , etc.
,
La
= seasonal total of heat losses due t o indoor-outdoor a i r exchange ( i n f i l t r a t i o n+
ventilation),Lb = seasonal t o t a l below-grade heat loss,
GI = seasonal total of heat gains from internal sources
lights, equipment, people, etc.),
6, = seasonal total
of
solar heat gains through windows, rii = a t l l i z a t l w factor for gnternal g a i n s ,UTILIZATION OF INTERNAL
GAINS
S i n c e , in most situations, the internal gaina arc small relatcve to
t h e sum of loss term (less than 2 5 x 3 , a u t i l i z a t i o n factor of one may be assumed.
UTILIZATION
OF S O U RW I N S
It has been found that the solar utilization factor can be expressed
as a function of t w o normalized parameters, namely the "gain-load ratio"
(GLR) and the "thermal mass-gain ratio" (PER). The gain-load ratio is
defined as:
GLR = Gs
'
t + La + Lb
-
q i G iThe gafn-load ratio is the ratio of the solar gain through windows to the net heating l o a d , where the n e t heating laad is the amount a5
heating energy required, in the absence of solar g a i n a , to maintain the room temperature at the heating thermos t a t setting.
This gain-load r a t i o d i f f e r s from the solar load ratio (SLR) as defined in Reference 2 in that the GLR includes heat losses through the windows while the SLR does not. Moreover, the GLR includes solar gaina
through a l l the windows, not only those
f
acfng south.For locations in southern Canada, a house b u i l t ta pre-1975
standards would have a GLR of less than 0,2, while a well-insulated
passive salar house (with a south-facing window area equal t o 20% of the floor area) would have a GLR in t h e order of 0.4 to 0-6.
The thermal mass-gain r a t i o is d e f i n e d as:
MGR
=
c/&
(4 )where @
-
= thermal capacity of the bullding interior(MJI K),
g, = average hourly solar gain for season (MJ/hr)
(g,
= Gs/hours in heating season).The thermal capacity, C, ia calculated as the '"effective mass" of
the buildfng m l t i p l l e d by its specirk heat. The effective mass is the
mass actually available to store heat as a result of d i r e c t solar gains or of close contact with the room a i r so that any change in the room a i r
temperature affects the mass temperature. This normally Includes she mass i n s i d e the insulating layer of the walls and ceilings, but excludes
the exposed concrete of unfnsulated basement w a l l s and floors.
The mass-gain ratio reflects the thermal storage characteristics of
the b u i l d i n g as well as the area, type and orientation of the glazing.
T y p l c a l houses of lightweight construction with window areas equal to 10
to 20% of the floor area have a mass-gain ratio of approxdmately I hr/K.
The medium and heavy canstructions described in Table 'L have mass-gain
ratios of approximately 3 and
7.5
h r / K , r e s p e c t i v e l y , These mass-gain ratios increase as the window area decreases and v i c e versa.FTguses 1 Eo 3 show the seasonal solar utilization factor plotted
against the GLR for various values of MGR. F i g u r e 1 i s based on the
assmaption that the room temperature is maintained constant, while
Figures 2 and 3
are
for cases in which room temperature rises of 2.75and 5.5 Go, respectively, are permitted. The development of t h e s e solar
utilization factors is described in the followfng section.
COMPUTER
SIMJIATION
The solar u t i l i z a t i o n curves shorn Zn Figures 1 to 3 were d e r i v e d
from a large number of computer simlations. To produce these curves,
the computer program perfarma hour-by-hour calculations, using measured
weather data for an actual year, to determine heat gains and losses, the
heating energy required t o maintain room temperature at the thermostat
s e t t k n g , and the room temperature resulting from excess heat gains. The
solar radiation incident on glazed surfaces is calculated from hourly values of measured horizontal radiation using the correlation developed by ~ a y ~ . The solar gain is calculated by applying the transmissfoa
characteristics for standard glass and the shading coefficient of the
appropriate glazing type6.
The thermal storage effects are simulated according to the ASHRAE t h e m 1 response method7. The response factors e v e n in the A S H M
Handbook, however, are not approprtate far the type of construction u s e d in houses. Consequently, for t h i s study, new values corresponding to
three different w e i g h t s sf house coastruction (light, medium and heavy) were obtalned u s h g the reom thermal response factor p r o g r a d . For reference purposes, very heavy construction was defined by the
coefficients given in t h e A S B W Handbook. In addition, the thermal response factors of the three weights
of
house construction wereconfitmed experimentally in the NRC p a s s i v e test f acf lityg
.
The construction features of each house weight are described in Table 1.HOUSE MODELS
Twenty house models, each a t h a different l e v e l of insulation so as
t o p r o v i d e a wide range o f gain-load ratios, were d e f i n e d ; their windaw
area w a s fixed in order to maintain a coaatant'maas-ga3n ratio. Each model was shmlated f o r five locations representing different Canadian climatic regions: Vancouver ( B . C . ) , Summerland (B.C.), Edmonton
(Ut a. )
,
Ot taw& (Qnt.1
and Halifax (N.S .).
Thf s procedure w a s repeatedfor each af the constructions described i n Table I, as well as for an i n f i n i t e l y light construction established f o r reference purposes.
A heating thermostat setting of 21°C was assumed. Since occupant preference would determine the allowable rise fn room temperature, three different assumptions were considered; namely, a constant room
temperature, and two allowable rises in room temperature, one of
2-75 C O , and t h e other of 5.5 C a m In t h i s simulation I t was a l s o
assumed that the roam temperature was prevented from rfsfng above the
SEASONAL
SOLAR
UTILIZATIONThe heatlng seasan for a l l l o c a t i o n s was assumed to last from October t o A p r i l inclusive. The seasonal values f o r she solar
utilization factor, the gain-load r a t i o , and the mass-gain ratio were determined for t h i s time period. Following t h i s , curves of the s o l a r utilfzation factor as a function aE the GLR were obtained for each of the l i g h t , medium, heavy, and very heavy constructions (MGR equal t o 1.0, 2 . 6 , 7.2, and 14.0, respectively) uslag the method of least
squares. Figures I to 3 w e r e then obtained by interpolation between
these curves for ocher values of the MGR. The data and corresponding
curve fits are p r e s e n t e d in Appendix A.
The in£ormation contained in t h e utilization factor curves can a l s o be presented as the ratio of purchased heating energy t o load (purchased Heating Fraction), or alternatively, as the ratio of solar contribution
ta l o a d (Solar Heating Fraction)* Curves presenting the data in both of
these forms are given in Flgures 4 to
6.
In addition to seasonal values, calculations can a l s o be performed using solar u t i l i z a t i o n factors on a monthly b a s i s , This is discussed
in Appendix B.
4, COMPARISOH UITB EXPEISlMllTAL DATA
The measured energy consumption for the NRC passive test units
d u r i n g the 1981-82 heating seasonlo, was compared wkth the corresponding consumption calculated using t h e solar utilizatfon factor concept.
The NRC t e s t facilkty1l, described in Reference 11, congists of four 2-room t e s t units and four single-roomunfts. Three of the f a r 2-room units (Units 1, 2 and 3) are of the direct-gain type and differ only in
their thermal mass: U n i t 1 Ss classified a s l i g h t ; Unit 2, aa medium;
and Unit 3 as heavy construction (see T a b l e I). The south room of each
unit has a south-facing window with a 2.6 m2 glass area: t h e n o r t h room
has a 1 m2 window f a c i n g north. The four single-room u n i t s have the
same thermal mass as Unit 1. Each u n i t has a 2.6
d-
window facing oneof the cardinal directions.
The 2-room units were operated in two modes, which were alternated every two weeks. In the f i r s t mode each unit was monitored as two
separate rooms; in the second, air was circulated between the south and north to-, and the whole unit was treated as a single space. A L l the rooms were operated with an allowable indoor
air
temperature swing of 7c",
The solar gain values were obtained by measuring the solarradiation on the vertical surfaces. The load values were determined by
multiplying the heat loss caefficfent by the sum of the differences
between the heating set point and the measured outdoor temperature.
The comparison between the measured and the calculated energy
consumptions i s presented In Table I1 for both modes of operation.
F i g u r e 3 by interpolating between t h e curves for the appropriate value of the MGR. The calculated values show close agreement w i t h the
measured results; the mafinasm difference between the calculated and measured space heating energy is less than 52.
5 .
USE
AND LPaTATIONSThe use of solar u t i l i z a t i o n factor curves t o estimate the heating energy requirement of houses is d e s c r i b e d i n d e t a i l in Reference 12.
The s t e p s involved can be summarized as follows:
-
calculate each of the lass and gain components of Equation 2,- calculate the GLR from Equation 3 ,
-
calculate the MGR from Equation 4 (or assume 1 for standardl i g h t w e i g h t construction),
- obtain the u t i l i z a t i o n factor corresponding ts the GLB and MGR by i n t e r p o l a t i o n from Figure 1, 2 or 3 (depending on the desired allowable temperature rise),
-
substitute t h i s utilization factor i n t o Equation 2 to obtain theheating energy requirement.
The u t i l i z a t i o n factors presented here are based upon a number of
assmnptions, some of which impose l i m i t a t i o n s on t h e use of t h e factors.
These utilization factors apply only to sfmple direct-gain buildfngs
that do not use night: i n s d a t l o n systems on the windows. They should
not be used for mass-walls, attached sunspaces, or systems utilizing
a c t i v e thermal storage.
The calculation method assumes that a l l of the loss components can
be offset by solar gains whenever and wherever the latter occur, T h i s is a valid assumption for small open spaces or when farced a i r
c i r c u l a t i o n is provided; however, if an area (such as a basement or a north-facing room) is remote from or thermally separated from the
windows providing the solar gains, the loss from such an area should not
be included in the "load" used to calculate the gafn-load ratio.
Furthermore, the mass i n t h i s area s h o u l d not be included in the
calcuZatZons 05 the
K R ,
These considerations are especially importantwhen estimating the energy requirements of houses with zone-controlled heaters.
It should be noted that the accuracy of the heating energy estimate
is more dependent on t h e calculatfon of heat losses and gains than ft is
upon the limitations of the solar utilization curves themselves. The
heat l o s s and gain calculations must allow for factors such as the
w i n d m s by trees, buildings, overhangs, etc. ; the use of b l i n d s and
drapes by the occupant; and the correct estimation of a seasonal average
air change rate.
One should a l s o keep in mind that the u t i l i z a t i o n factors p e r m i t
calculation
of
heating energy on the assumption that the designer has providedsome means
t o limft the risein roam
temperature. A t highgain-load ratios, it is qugte p o s s i b l e t h a t problems with interior
comfort could arfse as a result of overheatfng and glare.
Despite a l l the indicated limitations, the solar utflization factor
does provide a simple method f a r calculating the contribution of solar
heat gains for direct-gain p a s s i v e 6019s designs a5 well as for houses
Barakat, S.A. Solar Heat Gains Through Windows in Canada, National Research Council
of
Canada, Divisionof
Building Research,NRCC 18674, O t t a w a , 1980.
Wray, W.O. Design and Analysis of Direct Gain Solar Heated Buildings, Los Alamos Scientific laboratory,
LA-8885-HS,
1981.Cuplf nakas
,
E .L. Residential Passive Solar Heating: Review ofDevelopment of D e s i g n M d s , Report t o Ministry of Energy, Provlnce of Ontarfa, February 1980.
Monsen, W.A., S.A. K l e i r i , and WmA. Becknun, PredictZng of Direct
Gain Solar Heating System Perf ormanee, Solar Energy, Vo2. 27,
NO. 2, pp- 143-947, 1981.
Ray, J. A Study 05 Shortwave Radiation of Nonhorizontal Surfacee, Canadian C l Z m a t e Centre Report 79-12, Atmospheric Enviranment Service, Downsvfew, Ont., 1979.
ASHRAE Handbook of Fundamentals, Chapter 26, American Society of Heating, Refrigeration and M r Conditioning Engineers, New York,
1977
ASHRAE Handbook of Fundamentals, Chapter 2 2 , American S o c i e t y of Heating, Refrigeration and
Air Conditioning
Engfneers, New York,1977.
Hitalas, G.P. Room Thermal Response Factors (in progress), Barakat, S.A. and D.M. Sander. Thermal Response of Houses (in progress)
.
B a r a b t , S.A. DBR/NRC Passive Solar Test Facility, 1980181 Thermal Performance (in progress),
Barakat, 5-A. A Canadian F a c i l i t y for Investigating Passive Solar Heating, presented at International Spmpasim on Experimental
Research with Passive Solar Houses, Nice, France, December 1980.
Sander, D.H, et al. A Simple Method of Estimatfng Heating Requirements of Houses (in progress).
HOUSE WEIGHTS FOR COMPUTER SIMULATION Light Medium Heavy V e v heavy Thermal Capacity
MI
*Km2
floor area 0.060 0.153 0.4156
.a10 DescriptionStandard frame construction, 12.7 mm
gyproc w a l l s and c e i l i n g s , carpet over
wooden floor.
as above, but 50.8 mm gyproc
walls and
25.4 mm gyproc c e i l i n g .
fnterior wall finish of 101.6 mm brick,
12.7 m, gyproc ceiling, carpet over wooden floor.
very heavy comcercf a1 off ice b u i l d i n g ,
Appendix A
The data points obtained for Edmonton, Ottawa, and Halifax produced well-defined curves of solar u t f lfzation factor versus GLR f o r l i g h t , medium, heavy, and very heavy constructions (BGR equal to 1.0, 2.6, 7.2
and 14.0 hr/K, respectively),
as
w e l l as for the zero-mass case. Theroot mean square
(rms)
error between these data p o i n t s and the curve f i tis less than 0.015. The data and corresponding curve f i t s are
illustrated in Figures Al t o A 3 for light, medium and heavy cons trucrioas only.
These figures also show that the solar utilization factara obtdned for Vancouver and Slrmmerland, B-C. are sorpewhat Imer than those f o r t h e other locations. This was attributed to the cheracteristfcs of the climatic pattern for the West C o a s t redon. Vancouver weather hae long,
cloudy and relatively cold periods with intermittent short, avmy and
wanner periode. Even with high levels of thermal storage, the bu'klding laad during such warm, sunny periods is very small, causing the excess gains to be eliminated once the room temperature has risen to the allowable lidt. Consequently, the u t i l i z a t i o n factor is reduced.
Although the curves shown in Figures 1, 2 and 3 are directly
applicable t o t h e type of climate found in most of Canada, they w i l l
overestimate the ~ o l a r u t i l i z a t i o n for reglaas with very overcast winter
conditions. This Indicates that another parameter may be needed t o account for climatic varfations. Further study la necessary t o i d e n t i f y this parameter and the corresponding correction. In any case, the
maximum error in the utilization factor is only about .08, even for
Vancouver, which probably t y p i f i e s the extremz
of
t h i s type of winterweather far Canada. For a house H t h a G L R ' o f 0.6, this would cause a
Appendix B
Calculations may be performed usgng solar u t i l i z a t i o n on
a
monthly rather than on a seasonal basis. The values of the solar u t i l i z a t i o n factor and the gain-load ratios for each =nth of the heating season for all f i v e locations are plotted in Figures El to B 3 , together with t h e curve showing seasonal solar u t i l i z a t i o n . Since the monthly utilization factors do not d i f f e r greatly from those for seasonal u t i l i z a t i o n , t h em
error between the monthly data points and the curves, being in she order o f 0.05, the seasonal utilizatfon factor curves of Figures 1 t o 3could be a p p l i e d an a monthly basis.
The scatter cf pofnts is considerably greater for monthly values than for seasonal values. This may be partfally explained by t h e fact that the value of the MGR varies from month to month. In addition, the
influence of the monthly climatic variation m ~ t be considered, as well
as the effect
of
carry-over of stored energy in heavy constrzrctioas from one month to the next. A l l t h e s e factors may lead t o significaat errors i n estimating the solar contribution for a particular month.0 0.2 0,4 0.6 0.8 1.0 1 2 1.d 1.6 1.8 ZO 2.2 2.4 L 6 2.8 3.0 GLR lab L I G H T C Q N S T R U C T I O N IMGR.11 GLR I b l MEDIUM CONSTRUCTION (MGR= 2.6) 0 I l l l l l l l l r l 1 1 1 0 0.2 0.4 O.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2 2 , L 4 2 6 2.8 3.0 GLR I c l H E A V Y C O M S T R U C T ION IMGR ' 7.2) F I G U R E 8 . 1 MONTHLY V A L U E S OF S O L A R U T l L l Z A T l O M
I. 0 0.8 0.6 P" 0.4 a. 2 0 GPR l a ) L t G H T C O N S T R U C T l O N ( M G R 11 1.0 0.8 0.6 F" 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1.0. t 2 1.4 1.6 1.8 2.0 2.2 2.4 26 2.8 3.0 G L R ( b l M E D I U M C O N S T R U C T I O N (MGR
-
2 . 6 1 1.0 0.8 0.6 F" 11.4 0.2 GLR ( c l H E A V Y C O N S T R U C T I O N ( M C R 7.2) FIGURE 8 . 2GLR l a ) LLGHT C O N S T R U C T l O W IMGR = 11 GLR I b l MEDIUM C O N S T R U C T I O N ( M G R . 2.6) GL R ( c l H E A V Y C O N S T R U C T I O N lMGR
