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A method for estimating the utilization of solar gain through windows
Sander, D. M.; Barakat, S. A.
https://publications-cnrc.canada.ca/fra/droits
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https://nrc-publications.canada.ca/eng/view/object/?id=afe21835-251a-4420-ad8d-400692f10c00 https://publications-cnrc.canada.ca/fra/voir/objet/?id=afe21835-251a-4420-ad8d-400692f10c00Ser
TH1
N21d
no.
1163
National Research
Conseil national
c . 2
1
Council Canada
de
recherches Canada
BLDG
A METHOD FOR ESTIMATING THE UTILIZATION OF
SOLAR GAIN THROUGH WINDOWS
by
D.M. Sander and S.A. Barakat
ANALYZED
Reprinted from
ASHRAE Transactions 1983
Vol. 89, Part 1A, p. 12
-
22
DBR Paper No. 1163
Division of Building Research
On p e u t , p a r un s i m p l e c a l c u l , e s t i m e r l 1 6 n e r g i e n'ecessaire au c h a u f f a g e d e s h a b i t a t i o n s e n f a i s a n t a p p e l b l a n o t i o n d e
f a c t e u r s s a i s o n n i e r s d ' u t i l i s a t i o n d e l ' g n e r g i e s o l a i r e d e r i v 6 s d'une s i m u l a t i o n s u r o r d l n a t e u r q u i t i e n t compte, chaque h e u r e , d e s donn'ees & t 6 o t o l o g i q u e s de cinq v i l l e s du Canada. Ces f a c t e u r s d ' u t i l i s a t i o n s o n t pr'esent'es pour d i v e r s nlveaux de s t o c k a g e thermique comme une f o n c t i o n du r a p p o r t d e s a p p o r t s s a l s o n n l e r s de c h a l e u r s o l a i r e b l a charge s a i s o n n i s r e du
bbtiment. Les courbes s o n t t r a c k s pour d e s temperatures i n t ' e r i e u t e s c o n s t a n t e s e t d e g & a r t s d e t e m p e r a t u r e d e l ' o r d r e d e 2,75OS pt. de 5;5aC'. Les dinn'ees e x p e r i m e n t a l e s , obtenues d e l ' i n s t a l l a t i o o d ' e s s a l d e c h a u f f a g e s p l a i r e p a s s i f , corrqspondent aux d o n n k ' s c s l c u l 6 e s b p a r t l r des f a c t e u r s
No.
2736
A Method for Estimating the Utilization
of Solar Gain through Windows
D.M. Sander
S.A. Barakat
ABSTRACT
The h e a t i n g energy requirements f o r houses may be e s t i m a t e d by a simple c a l c u l a t i o n u s i n g t h e concept of s e a s o n a l s o l a r u t i l i z a t i o n f a c t o r s d e r i v e d from hour-by-hour computer s i m u l a t i o n of a c t u a l weather d a t a f o r f i v e Canadian l o c a t i o n s . These u t i l i z a t i o n f a c t o r s a r e presented f o r v a r i o u s l e v e l s of thermal s t o r a g e a s a f u n c t i o n of t h e r a t i o of s e a s o n a l s o l a r g a i n t o s e a s o n a l b u i l d i n g load. Curves a r e p r e s e n t e d f o r c o n d i t i o n s of c o n s t a n t room temperature and f o r temperature swings of 2.75OC and 5.5OC. Experimental d a t a o b t a i n e d from t h e P a s s i v e S o l a r T e s t F a c i l i t y a r e shown t o agree w i t h c a l c u l a t i o n s u s i n g t h e u t i l i z a t i o n f a c t o r s .
INTRODUCTION
The need f o r a simple method of e s t i m a t i n g t h e h e a t i n g energy requirements of houses i s widely recognized. Such a technique could be used f o r comparing a l t e r n a t i v e s i n t h e d e s i g n p r o c e s s and f o r e v a l u a t i n g house d e s i g n s t o determine t h e i r compliance w i t h energy s t a n d a r d s . An i m p o r t a n t component would be t h e e s t i m a t i o n of t h e amount of s o l a r energy c o l l e c t e d through t h e windows s f houses and u t i l i z e d t o o f f s e t h e a t l o s s e s . It h a s been shown t h a t south-facing double- and t r i p l e - g l a z e d windows c a n be n e t s u p p l i e r s of energy d u r i n g t h e h e a t i n g s e a s o n f o r a l l l o c a t i o n s i n s o u t h e r n Canada, provided t h a t a l l of t h e s o l a r g a i n s a r e u t i 1 i z e d . l I n r e a l i t y , however, i t i s p o s s i b l e t o u s e only a f r a c t i o n of t h e s o l a r gains. The magnitude of t h i s f r a c t i o n , which w i l l be r e f e r r e d t o a s t h e u t i l i z a t i o n f a c t o r , depends upon s e v e r a l parameters i n c l u d i n g g e o g r a p h i c a l l o c a t i o n , s i z e and t y p e of g l a s s , o v e r a l l b u i l d i n g h e a t l o s s , thermal s t o r a g e p r o p e r t i e s of t h e house, and t h e allowable indoor temperature swing.
A number of methods have been developed t o e s t i m a t e t h e n e t s o l a r c o n t r i b u t i o n t o s p a c e h e a t i n g f o r d i r e c t - g a i n p a s s i v e s o l a r d e ~ i ~ n s . ~ - ~ One t h a t i s widely used i n Canada and t h e USA i s t h e s o l a r l o a d r a t i o (SLR) method developed by t h e Los Alamos S c i e n t i f i c Laboratory.
It h a s been a p p l i e d e x t e n s i v e l y t o a l l t y p e s of b u i l d i n g s , d e s p i t e t h e c a u t i o n t h a t " t h e method i s n o t a p p l i c a b l e t o t h e a n a l y s i s of low-mass sun-tempered buildings."
It was t h e o b j e c t i v e of t h e p r e s e n t s t u d y t o develop a method of q u a n t i f y i n g t h e u s e f u l s o l a r g a i n through windows t h a t would be a p p l i c a b l e t o a l l t y p e s of houses i n a l l c l i m a t i c r e g i o n s of Canada. A s t h e scope of t h e method was not t o be l i m i t e d t o passive s o l a r houses, i t was n e c e s s a r y t o c o n s i d e r s o l a r h e a t g a i n s through a l l windows ( n o t only t h o s e f a c i n g s o u t h ) a s w e l l a s houses with d i f f e r e n t amounts of thermal mass. The most i m p o r t a n t a p p l i c a t i o n , however, w i l l be t h e e v a l u a t i o n of energy c o n s ~ m p t i o n i n t h e l i g h t w e i g h t wood- frame houses p r e v a l e n t i n Canada. I n a d d i t i o n , i t was deemed d e s l r a b l e t o base t h e method on s e a s o n a l r a t h e r t h a n monthly c o n s m p t i o n t o make i t e a s i e r t o e s t i m a t e t h e s e a s o n a l h e a t i n g energy r e q u i r e d f o r a house. This s e a s o n a l approach h a s , i n f a c t , r e s u l t e d i n a c a l c u l a t i o n procedure only s l i g h t l y more d i f f i c u l t t o apply t h a n t h e d e g r e e d a y method.
This paper d e s c r i b e s t h e development of t h e method and p r e s e n t s t h e s o l a r u t i l i z a t i o n f a c t o r s f o r v a r i o u s amounts of thermal s t o r a g e and t h r e e v a l u e s of indoor temperature swing.
D.M. Sander and S.A. Barakat, D i v i s i o n of B u i l d i n g Research, N a t i o n a l Research Council of Canada, Ottawa.
TBE
OTILIZAT3[0N FACTOR CONCEPT Instantaneous Heat BalanceThe instantaneous (hourly) heat balance for a house is given by: h = l t
+
1,+
lb-
gi -gswhere
h = instantaneous heating required
It
= instantaneous heat loss due to transmission through exterior walls, windows, ceilings, etc.1, = instantaneous heat loss due to air change with outdoors (infiltration plus ventilation)
lb = instantaneous below-grade heat loss
gi = instantaneous heat gain from internal sources (lights, equipment, people, etc. )
gs = instantaneous solar heat gain through windws
There will be times when gains exceed losses. Under these conditions, the excess heat will be stored in the mass of the room, causing the room temperature to rise. In order to prevent it from rising above an acceptable limit, the excess heat gain must be eliminated. This may be done by closing the blinds, opening the windows, or operating a ventilating or air-conditioning system. A portion of the stored heat will become avatlable as useful heat when the room temperature drops to the thermostat setting. The remainder of the stored heat will have been wasted in the form of increased transmission heat loss through the walls owing to the rise in room air temperature.
Seasonal Heat Balance
The heat balance equation may be written for a longer time period, such as the heating season, by including a utilization factor to account for the usable portion of internal and solar gains.
where
H = total heating required for season
Lt = seasonal total of heat losses due to transmission through exterior walls, windws, ceilings, etc.
La seasonal total of heat losses due to indoor-outdoor air exchange (infiltration plus ventilation)
Lb = seasonal total belw-grade heat loss
Gi = seasonal total of heat gains from internal sources (lights., equipment, people, etc. )
Gs = seasonal total of solar heat gains through windows
n i
= utilization factor for internal gainsns
= utilization factor for solar gainsUtilization of Internal Gains. Since, in most situations, the internal gains are small relative to the sum of loss terms (less than 25%), a utilization factor of one may be
assumed.
Utilization of Solar Gains. The solar utilization factor can be expressed as a function of two normalized parameters, namely, the "gain-load ratio" (GLR) and the "thermal mass-gain ratio" (MGR). The gain-load ratio is defined as:
GLR
-
Ir sLt + L a
+
Lb-
niGiThe gain-load ratio is the ratio of the solar gain through windows to the net heating load, where the net heating load is the amount of heating energy required in the absence of solar gains to maintain the room temperature at the heating thermostat setting.
This gain-load r a t i o d i f f e r s from t h e s o l a r l o a d r a t i o (SLR) a s d e f i n e d i n Ref 2 i n t h a t t h e GLR i n c l u d e s h e a t l o s s e s through t h e windows w h i l e t h e SLR does not. Moreover, t h e GLR i n c l u d e s s o l a r g a i n s through a l l t h e windows, n o t o n l y t h o s e f a c i n g south.
For l o c a t i o n s i n s o u t h e r n Canada, a house b u i l t t o pre-1975 s t a n d a r d s would have a GLR of l e s s t h a n 0.2, w h i l e a w e l l - i n s u l a t e d p a s s i v e s o l a r house ( w i t h a south-facing window a r e a e q u a l t o 20% of t h e f l o o r a r e a ) would have a GLR on t h e o r d e r of 0.4 t o 0.6.
The thermal mass-gain r a t i o i s defined a s :
MGR =
c/zs
where
C
-
= thermal c a p a c i t y of t h e b u i l d i n g i n t e r i o r (MJ/ K)gs = average h o u r l y s o l a r g a i n f o r s e a s o n ( W / h ) (gs = Gs/hours i n h e a t i n g season)
Thermal c a p a c i t y , C , i s c a l c u l a t e d a s t h e " e f f e c t i v e mass" of the b u i l d i n g m u l t i p l i e d by i t s s p e c i f i c h e a t . The e f f e c t i v e mass i s t h e mass a c t u a l l y a v a i l a b l e t o s t o r e h e a t from d i r e c t s o l a r g a i n s o r c l o s e c o n t a c t w i t h room a i r , s o t h a t any change i n t h e room a i r
temperature a f f e c t s t h e mass temperature. T h i s normally i n c l u d e s t h e mass i n s i d e t h e i n s u l a t i n g l a y e r of t h e w a l l s and c e i l i n g s b u t excludes t h e exposed c o n c r e t e of u n i n s u l a t e d basement w a l l s and f l o o r s .
The mass-gain r a t i o r e f l e c t s t h e thermal s t o r a g e c h a r a c t e r i s t i c s of t h e b u i l d i n g a s w e l l a s t h e a r e a , t y p e , and o r i e n t a t i o n of t h e g l a z i n g . T y p i c a l houses of l i g h t w e i g h t c o n s t r u c t i o n w i t h window a r e a s e q u a l t o 10% t o 20% of t h e f l o o r a r e a have a mass-gain r a t i o of
approximately 1 h/K. The medium and heavy c o n s t r u c t i o n s d e s c r i b e d i n Tab. I have mass-gain r a t i o s of approximately 3 and 7.5 h / ~ , r e s p e c t i v e l y . These mass-gain r a t i o s i n c r e a s e a s t h e window a r e a d e c r e a s e s and v i c e v e r s a .
Figs. 1 t o 3 show t h e seasonal s o l a r u t i l i z a t i o n f a c t o r p l o t t e d a g a i n s t t h e GLR f o r v a r i o u s v a l u e s of MGR. Fig. 1 i s based on t h e assumption t h a t t h e room temperature i s
maintained c o n s t a n t , while Figs. 2 and 3 a r e f o r c a s e s i n which room temperature r i s e s of 2.75OC and 5.5"C, r e s p e c t i v e l y , a r e permitted. The development of t h e s e s o l a r u t i l i z a t i o n f a c t o r s w i l l be d e s c r i b e d .
DEVELOPMENT OF SOLAR UTILIZATION CURVES Computer S i m u l a t i o n
The s o l a r u t i l i z a t i o n curves shown i n Figs. 1 t o 3 were derived from a l a r g e number o f computer s i m u l a t i o n s . The computer program performed hour-by-hour c a l c u l a t i o n s , u s i n g measured weather d a t a f o r an a c t u a l y e a r , t o determine h e a t g a i n s and l o s s e s , t h e h e a t i n g energy r e q u i r e d t o m a i n t a i n room temperature a t t h e t h e r m o s t a t s e t t i n g , and t h e room
temperature r e s u l t i n g from excess h e a t g a i n s . The s o l a r r a d i a t i o n i n c i d e n t on g l a z e d s u r f a c e s
i s c a l c u l a t e d from h o u r l y v a l u e s of measured h o r i z o n t a l r a d i a t i o n u s i n g t h e c o r r e l a t i o n developed by S o l a r g a i n i s c a l c u l a t e d by a p p l y i n g t h e t r a n s m i s s i o n c h a r a c t e r i s t i c s f o r
s t a n d a r d g l a s s and t h e shading c o e f f i c i e n t of t h e a p p r o p r i a t e g l a z i n g type.6
The thermal s t o r a g e e f f e c t s a r e s i m u l a t e d according t o t h e ASHRAE thermal response
method.' The r e s p o n s e f a c t o r s g i v e n i n t h e ASHRAE Handbook, however, a r e n o t a p p r o p r i a t e f o r t h e type of c o n s t r u c t i o n used i n houses. Consequently, f o r t h i s s t u d y new v a l u e s
corresponding t o t h r e e d i f f e r e n t w e i g h t s of house c o n s t r u c t i o n ( l i g h t , medium, and heavy) were obtained u s i n g t h e room thermal response f a c t o r program. For r e f e r e n c e purposes, v e r y heavy c o n s t r u c t i o n was d e f i n e d by t h e c o e f f i c i e n t s g i v e n i n t h e ASBRAE Hafidbook. In a d d i t i o n , t h e thermal response f a c t o r s of t h e t h r e e weights of house c o n s t r u c t i o n were confirmed
e x p e r i m e n t a l l y i n t h e NRC p a s s i v e t e s t f a c i l i t y . The c o n s t r u c t i o n f e a t u r e s of e a c h house weight are d e s c r i b e d i n Tab. 1.
Houee Models
Twenty house models, each with a d i f f e r e n t l e v e l of i n s u l a t i o n s o a s t o provide a wide range of gain-load r a t i o s , were defined; t h e window a r e a was f i x e d i n order t o maintain a constant mass-gain r a t i o . Each model was simulated f o r f i v e l o c a t i o n s r e p r e s e n t i n g d i f f e r e n t Canadian c l i m a t i c regions: Vancouver (B.C.)
,
Summrland (B.C.),
Edmonton (Alta. ),
Ottawa (Ont.), and Halifax (N.S.). This procedure was repeated f o r each of t h e c o n s t r u c t i o n sdescribed i n Tab. I, a s w e l l a s f o r an i n f i n i t e l y l i g h t c o n s t r u c t i o n e s t a b l i s h e d f o r r e f e r e n c e purposes.
A heating thermostat s e t t i n g of 21°C was assumed. A s occupant preference would determine t h e allowable r i s e i n room temperature, t h r e e d i f f e r e n t assumptions were considered, namely, a constant room temperature and two allowable r i s e s i n room temperature, one of 2.75'C and t h e o t h e r of 5.5OC. In t h i s simulation i t was a l s o assumed t h a t t h e room temperature was
prevented from r i s i n g above t h e allowable l i m i t by v e n t i l a t i o n using o u t s i d e a i r . Seasonal S o l a r U t i l i z a t i o n
The h e a t i n g season f o r a l l l o c a t i o n s was assumed t o c o n s i s t of t h e months October t o A p r i l , i n c l u s i v e . Seasonal v a l u e s of s o l a r u t i l i z a t i o n f a c t o r , gain-load r a t i o , and mass-gain r a t i o were determined f o r t h i s time period. Curves of s o l a r u t i l i z a t i o n f a c t o r a s a f u n c t i o n of GLR were obtained f o r each of l i g h t , medim, heavy, and very heavy c o n s t r u c t i o n s (MGR e q u a l t o 1.0, 2.6, 7.2, and 14.0 h/K, r e s p e c t i v e l y ) using t h e method of l e a s t squares. The d a t a
p o i n t s obtained f o r Edmonton, Ottawa, and H a l i f a x produced well-defined curves of s o l a r I u t i l i z a t i o n f a c t o r a g a i n s t GLR f o r a l l cases. The r o o t mean square (rms) e r r o r between t h e s e i d a t a p o i n t s and curve f i t i s l e s s than 0.015. Data and corresponding curve f i t s , f o r l i g h t ,
1
medium, and heavy c o n s t r u c t i o n s only, a r e i l l u s t r a t e d i n Figs. 1 t o 3. Figs. 4 t o 6 were thenobtained by i n t e r p o l a t i o n between t h e s e curves f o r o t h e r v a l u e s of MGR.
I
The s o l a r u t i l i z a t i o n f a c t o r s obtained f o r Vancouver and Summerland, B.C., a r e somewhatlower than those f o r t h e o t h e r l o c a t i o n s . This was a t t r i b u t e d t o t h e c h a r a c t e r i s t i c of t h e c l i m a t i c p a t t e r n of t h e West Coast region. Even f o r Vancouver, however, which probably t y p i f i e s t h e extreme of t h i s type of w i n t e r weather f o r Canada, maximum e r r o r i n u t i l i z a t i o n f a c t o r i s only about 0.08. For a house with a GLR of 0.6, t h i s corresponds t o a maximum e r r o r of 5X i n e s t i m a t i n g h e a t i n g energy requirements.*
The information contained i n t h e u t i l i z a t i o n f a c t o r curves can a l s o be presented a s t h e r a t i o of purchased h e a t i n g energy t o l o a d (Purchased Heating Fraction) o r a s t h e r a t i o of s o l a r c o n t r i b u t i o n t o load (Solar Heating Fraction). Curves presenting t h e d a t a i n t h i s form a r e given i n Figs. 7 t o 9. In a d d i t i o n t o seasonal v a l u e s , c a l c u l a t i o n s can a l s o be performed using s o l a r u t i l i z a t i o n f a c t o r s on a monthly basis.8
COMPARISON WITH EXPERIMENTAL DATA
The measured energy consumption f o r t h e NRC passive t e s t u n i t s during t h e 1981-82 h e a t i n g season was compared with t h e corresponding c o n s m p t i o n c a l c u l a t e d using t h e s o l a r u t i l i z a t i o n f a c t o r concept. The NRC t e s t f a c i l i t y 9 c o n s i s t s of four two-room t e s t u n i t s and four s i n g l e - room u n i t s . Three of t h e f o u r two-room u n i t s ( U n i t s 1, 2, and 3) a r e of t h e d i r e c t - g a i n type and d i f f e r only i n t h e i r thermal mass: Unit 1 i s c l a s s i f i e d a s l i g h t , Unit 2 a s medium, and Unit 3 a s heavy c o n s t r u c t i o n ( s e e Tab. 1 ) . The s o u t h room of each u n i t h a s a south-facing window with a 2.6 m2 g l a s s area; t h e north room has a 1 m2 window facing north. The f o u r s i n g l e r o o m u n i t s have t h e same thermal mass a s Unit 1. Each u n i t h a s a 2.6 m2 window f a c i n g one of t h e c a r d i n a l d i r e c t i o n s .
The two-room u n i t s were operated i n two modes t h a t were a l t e r n a t e d every two weeks. I n t h e f i r s t mode, each u n i t was monitored a s two s e p a r a t e rooms; i n t h e second, a i r was c i r c u l a t e d between t h e south and n o r t h rooms, and t h e whole u n i t was treated a s a s i n g l e space. A l l t h e rooms were operated w i t h a n allowable indoor a i r temperature swing of 7OC. Solar g a i n values were obtained by measuring the s o l a r r a d i a t i o n on t h e v e r t i c a l s u r f a c e s . The load v a l u e s were determined by m u l t i p l y i n g t h e h e a t - l o s s c o e f f i c i e n t by t h e sum of t h e d i f f e r e n c e s between t h e h e a t i n g s e t point and t h e measured outdoor temperature.
Comparison of measured and c a l c u l a t e d energy consumptions i s presented i n Tab. 2 f o r both modes of operation. The corresponding s e a s o n a l s o l a r u t i l i z a t i o n f a c t o r s were obtained from Fig. 3 by i n t e r p o l a t i n g between t h e curves f o r t h e a p p r o p r i a t e v a l u e of t h e MGR. The
c a l c u l a t e d values show c l o s e agreement with measured r e s u l t s ; maximum d i f f e r e n c e between the c a l c u l a t e d and measured s p a c e h e a t i n g energy i s l e s s t h a n 5%.
USE AND LIMITATIONS
The use of s o l a r u t i l i z a t i o n f a c t o r c u r v e s t o e s t i m a t e t h e h e a t i n g energy requirement of houses can be summarized i n t h e f o l l o w i n g s t e p s :
-
C a l c u l a t e each of t h e l o s s and g a i n components of Eq 2.-
C a l c u l a t e t h e GLR from Eq 3.-
C a l c u l a t e t h e MGR from Eq 4 ( o r assume 1 f o r s t a n d a r d l i g h t w e i g h t c o n s t r u c t i o n ) .-
Obtain t h e u t i l i z a t i o n f a c t o r corresponding t o t h e GLR and MGR by i n t e r p o l a t i o n fromFig. 1, 2, o r 3 (depending on t h e d e s i r e d a l l o w a b l e temperature r i s e ) .
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S u b s t i t u t e t h i s u t i l i z a t i o n f a c t o r i n Eq 2 t o o b t a i n t h e h e a t i n g energy requirement.The u t i l i z a t i o n f a c t o r s a r e based upon a number of assumptions, some of which impose l i m i t a t i o n s o n t h e u s e of t h e f a c t o r s . They apply o n l y t o s i m p l e d i r e c t - g a i n b u i l d i n g s t h a t do n o t use n i g h t i n s u l a t i o n systems on t h e windows. They should n o t be used f o r mass-walls, a t t a c h e d sun s p a c e s , o r systems u t i l i z i n g a c t i v e thermal s t o r a g e .
I The c a l c u l a t i o n method assumes t h a t a l l o f t h e l o s s components can be o f f s e t by s o l a r
g a i n s whenever and wherever t h e l a t t e r occur. T h i s i s a v a l i d assumption f o r s m a l l open spaces o r where f o r c e d - a i r c i r c u l a t i o n i s provided; i f an a r e a (such a s a basement o r a north- f a c i n g room) i s remote from o r t h e r m a l l y s e p a r a t e d from t h e windows p r o v i d i n g t h e s o l a r g a i n s , however, t h e l o s s from such an a r e a should n o t be i n c l u d e d i n t h e "load" used t o c a l c u l a t e
t h e gain-load r a t i o . Furthermore, t h e mass i n t h i s a r e a should n o t be included i n t h e c a l c u l a t i o n s of t h e MGR. These c o n s i d e r a t i o n s a r e e s p e c i a l l y important when e s t i m a t i n g t h e energy requirements of houses w i t h zone-controlled h e a t e r s .
The accuracy of t h e h e a t i n g energy e s t i m a t e i s more dependent on t h e c a l c u l a t i o n of h e a t l o s s e s and g a i n s t h a n i t i s on t h e l i m i t a t i o n s of t h e s o l a r u t i l i z a t i o n c u r v e s themselves. Heat l o s s and g a i n c a l c u l a t i o n s must a l l o w f o r such f a c t o r s a s t h e lowering of t h e t h e r m o s t a t s e t t i n g a t n i g h t ; e x t e r i o r shading of windows by t r e e s , b u i l d i n g s , overhangs, e t c . ; u s e of b l i n d s and d r a p e s by t h e occupant; and c o r r e c t e s t i m a t i o n of a s e a s o n a l average air-change r a t e .
One should a l s o keep i n mind t h a t t h e u t i l i z a t i o n f a c t o r s permit c a l c u l a t i o n of h e a t i n g energy o n t h e assumption t h a t t h e d e s i g n e r h a s provided some means of l i m i t i n g r i s e i n room temperature. A t h i g h gain-load r a t i o s i t i s q u i t e p o s s i b l e t h a t problems w i t h i n t e r i o r comfort c o u l d a r i s e a s a r e s u l t of o v e r h e a t i n g and g l a r e .
D e s p i t e a l l t h e i n d i c a t e d l i m i t a t i o n s , t h e s o l a r u t i l i z a t i o n f a c t o r does p r o v i d e a simple method of c a l c u l a t i n g t h e c o n t r i b u t i o n of s o l a r h e a t g a i n s f o r d i r e c t - g a i n p a s s i v e s o l a r d e s i g n s a s w e l l a s f o r houses of c o n v e n t i o n a l and s u p e r i n s u l a t e d c o n s t r u c t i o n .
1
REFERENCES1. S.A. Barakat, " S o l a r Reat Gains through Windows i n Canada" (NRCC 18674, N a t i o n a l Research Council of Canada).
2. W.O. Wray, "Design and Analysis of D i r e c t Gain S o l a r Heated Buildings" (LA-8885-MS, Los Alamos S c i e n t i f i c Laboratory).
3. E.L. Cuplinskas, " R e s i d e n t i a l P a s s i v e S o l a r Heating
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Review of Development of Design Aids" ( r e p o r t t o M i n i s t r y of Energy, Province of O n t a r i o , Feb. 1980).4. W.A. Monsen, S.A. K l e i n , and W.A. Beckman, " P r e d i c t i n g of D i r e c t Gain S o l a r Heating System Performance," S o l a r Energy 27: 2 (19811, pp. 143-147.
I
I
5. J. Hay, "A Study of Shortwave R a d i a t i o n of Nonhorizontal Surfaces" (Canadian Climate C e n t r e Report 79-12, Atmospheric Enviroument S e r v i c e , 1979).6. ASERAE Handbook 1977, Fundamentals Volume, Chapter 26 (New York: American S o c i e t y of Heating, R e f r i g e r a t i n g and A i r C o n d i t i o n i n g Engineers, 1977).
7. Ibid., Chapter 22.
8. S.A. Barakat and D.M. Sander, " U t i l i z a t i o n of S o l a r Gain through Windows f o r Heating Houses" (BRN 184, D i v i s i o n of Building Research, N a t i o n a l Research Council of Canada, Ottawa).
9. S.A. Barakat, "A Canadian F a c i l i t y f o r I n v e s t i g a t i n g P a s s i v e S o l a r Heating" ( p r e s e n t e d a t I n t e r n a t i o n a l Symposim o n Experimental Research w i t h P a s s i v e S o l a r Houses, Nice, France, Dec. 1980).
TABLE 1
House Weights f o r Computer Simulation
Thermal Capacity M . J / K = ~ ~ F l o o r Area
D e s c r i p t i o n
Light 0.060 Standard frame c o n s t r u c t i o n , 12.7 mm gyproc w a l l s and c e i l i n g s , c a r p e t o v e r wooden f l o o r .
Medium 0.153 A s above, but 50.8 mm gyproc w a l l s and 25.4 mm gyproc c e i l i n g .
Heavy 0.415 I n t e r i o r w a l l f i n i s h of 101.6 mm b r i c k , 12.7 mm, gyproc c e i l i n g , c a r p e t over wooden f l o o r .
Very Very heavy commercial o f f i c e b u i l d i n g , heavy 0.810 304.8 mm c o n c r e t e f l o o r .
1.0 0.9 0.8 0.7 0.6 F- 0.5 0.4 0.3 0.2
0 HALIFAX, OTTAWA. EDMONTON 0 HAL I FAX. OTTAWA, EDMONTON
SUMMERLAND, B.C.
A SUMMERLAND, B.C. 0.1 VANCOUVER, B.C.
0
G L R G L R
Figure 1. Seasonal solar utilization curves Figure 2. Seasonal solar utilization curves and actual data points for five and actual data points for five loca tions (constant room temperature) locations (room temperature swing =
2.75'~) 1.0 0.9 0.8 0.7 0.6 F" 0.5 F* 0.5
-
0.4 0.4-
0.3 0.3-
0.2 0.20 HAL1 FAX, OTTAWA, EDMONTON
0.1 SUMMERLAND, B.C. 0.1 VANCOUVER B.C. 0 0
-
-
-
-
l , , l # t l n ~ l ~ h . 0 0.3 0.6 0.9 1.2 1.5 0 0.3 0.6 0.9 1.2 1.5 G L R G L RFigure 3. Seasonal solar utilization curves Figure 4. Seasonal solar utilization factor and actual data points for five (constant room temperature) locations (room temperature swing =
5. sOc)
G L R
Figure 5. Seasonal solar utilization factor Figure 6 .
0
(room temperature swing = 2.75 C)
0.3 0.6 0.9 1 . 2 1 . 5 G L R
Seasonal solar utilization factor
(room temperature swing = 5.5'~)
I
G L R G L RFigure 7. Seasonal purchased heating fraction Figure 8. Seasonal purchased heating fraction
G L R
DISCUSSION
S.J. Treado, National Bureau of Standards, Washington, DC: Could the authors please comment on the sensitivity of the solar utilization factor calculation to the assumptions which must be made regarding heat loss due to envelope transmission, air exchange, and below-grade transmission?
D.M.
Sander: The sensitivity of the solar utilization factor to the heat loss is as shown inthe graphs of rl versus
GLR.
This is not affected by assumptions made in calculating losses.Any errors in tze calculation of losses due to simplifying assumptions will, of course, affect the accuracy of the energy estimate using the utilization factors.
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