A statistical study of the thermal performance of a group of 1300 houses on the Canadian Prairies

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A statistical study of the thermal performance of a group of 1300

houses on the Canadian Prairies

NATIONAL RESEARCH COUNCIL OF CANADA

DIVISION OF BUILDING RESEARCH

DBR INTERNAL REPORT NO.

473

A STATISTICAL

STUDY OF THE THERMAL PERFORMANCE OF

A GROUP OF 1300 HOUSES ON THE CANADIAN PRAIRIES

by C.P. H e d l i n and M. B a n t l e

Chsdtsd _{by: Approved by:}

_{L a w *}

_{Gold oats: December, 1982}

Prepared for: Records P u r p o s e s

ABSTRACT

From d a t a on t h e consumption of n a t u r a l g a s and e l e c t r i c i t y i n 1300 h o u s e s i n Regina, l e a s t s q u a r e s a n a l y s i s d e t e r m i n e d t h e s l o p e - i n t e r c e p t r e l a t i o n s h i p between t h e e n e r g y e q u i v a l e n t of t h e n a t u r a l g a s consumed and t h e h e a t i n g degree-days f o r e a c h house, and t h e c o e f f i c i e n t of c o r r e l a t i o n i n e a c h c a s e . Energy r e q u i r e d f o r s p a c e h e a t i n g a s a f u n c t i o n of h o u s e s i z e v a r i e d from 0.4 MJ/m2DD f o r t h e s m a l l e s t h o u s e s t o 0.14 M J / ~ ~ D D f o r t h e l a r g e s t . I n t e n g r o u p s of n o m i n a l l y i d e n t i c a l h o u s e s ( t o t a l 3 5 2 ) , t h e e f f e c t of occupant b e h a v i o u r , c o n s t r u c t i o n v a r i a b i l i t y , changes s i n c e c o n s t r u c t i o n , o r i e n t a t i o n and c o l o r produced d e v i a t i o n s i n t h e s l o p e - i n t e r c e p t r e l a t i o n s h i p of l e s s t h a n 1 0 % i n 213, o r 20% i n 95% of t h e houses. The r e l a t i o n s h i p between n a t u r a l g a s consumption and h e a t i n g degree-days i s n e a r l y l i n e a r i n t h e h e a t i n g p e r i o d , b u t i s d i f f e r e n t i n t h e non-heating p e r i o d and i n t h e p e r i o d of i n t e r m i t t e n t h e a t i n g .

A

STATISTICAL STUDY

OF THE

TlWRHAL

PERFORMANCE OF

A

GROUP OF

1300 HOUSES OM TEE

CAUADIAN PRAIRIES

C.P. H e d l i n and M. B a n t l e

For h o u s e s on t h e Canadian p r a i r i e s , a major p a r t of t h e purchased e n e r g y shows up a s s p a c e h e a t t h a t i s needed t o b a l a n c e h e a t l o s s through w a l l s , windows, roof and f l o o r s d u r i n g t h e h e a t i n g season. Some of t h i s comes a s t h e by-product of l i g h t i n g , cooking, d o m e s t i c w a t e r h e a t i n g , r e f r i g e r a t o r s o r f r e e z e r s . A major p a r t of i t i s provided by t h e f u r n a c e s p e c i f i c a l l y f o r s p a c e h e a t i n g . I n a d d i t i o n t o t h a t o b t a i n e d from

purchased e n e r g y , h e a t a l s o comes from o c c u p a n t s and from t h e sun.

I n any g i v e n h o u s e , such f a c t o r s as occupancy l e v e l s and l i f e s t y l e a f f e c t energy consumption f o r s p a c e h e a t i n g ; however, t h e s i z e of t h e house and i t s h e a t l o s s c h a r a c t e r i s t i c s a r e t h e main f a c t o r s a f f e c t i n g s p a c e h e a t i n g needs. L a b o r a t o r y measurements of t h e t h e r m a l p r o p e r t i e s of components, combined w i t h c a l c u l a t i o n p r o c e d u r e s , a r e s t a n d a r d methods of a r r i v i n g a t h e a t l o s s e s t i m a t e s . These r e q u i r e t h e u s e of a p p r o x i m a t i o n s and c a n n o t t a k e i n t o a c c o u n t t h e e f f e c t s of d i f f e r e n c e s i n c o n s t r u c t i o n and occupancy.

I n some c a s e s , measuring i n s t r u m e n t s c a n be employed t o g a i n i n f o r m a t i o n . However, t h e time and e f f o r t r e q u i r e d l i m i t t h e number of such measurements t h a t c a n be made.

L a b o r a t o r y and f i e l d i n s t r u m e n t a l measurements c a n b e extended a n d , i n some c a s e s , t h e i r v a l i d i t y t e s t e d , by u s i n g t h e t o t a l measured e n e r g y consumptions. l s 2 Where t h e s e v a l u e s a r e measured by u t i l i t y companies,

t h e y may c o v e r a l l of t h e purchased e n e r g y , u n l e s s f i r e p l a c e s o r wood- b u r n i n g s t o v e s a r e used. The i n t e r a c t i o n of many f a c t o r s means t h a t i t i s d i f f i c u l t t o i d e n t i f y some s p e c i f i c e f f e c t s ; t h e l i m i t a t i o n s of such a n a l y s e s must be r e c o g n i z e d and t h e y s h o u l d n o t be e x p e c t e d t o r e v e a l i n f o r m a t i o n a b o u t e f f e c t s t h a t a r e t o o h e a v i l y masked t o b e i d e n t i f i a b l e .

Analyses based on purchased e n e r g y might be d i v i d e d i n t o two

c a t e g o r i e s : t h o s e i n v o l v i n g i n d i v i d u a l h o u s e s and t h o s e i n v o l v i n g g r o u p s of houses. The p r e s e n t s t u d y f a l l s i n t o t h e l a t t e r c a t e g o r y . The

a n a l y s e s a r e s t a t i s t i c a l . A s a r e s u l t , t h e c o n c l u s i o n s a r e drawn f o r p o p u l a t i o n s of h o u s e s and a r e e x p r e s s e d i n terms of p r o b a b i l i t y r a t h e r

t h a n i n t h e p r e c i s e numbers o f t e n a s s o c i a t e d w i t h h e a t b a l a n c e e s t i m a t e s f o r i n d i v i d u a l houses.

T h i s s t u d y i n v o l v e s d a t a from h o u s e s i n which n a t u r a l g a s i s used f o r s p a c e h e a t i n g and, n o r m a l l y , f o r d o m e s t i c w a t e r h e a t i n g , and

e l e c t r i c i t y f o r a l l o t h e r e n e r g y needs. N a t u r a l g a s and e l e c t r i c a l consumption d a t a were p r o v i d e d by t h e Saskatchewan Power C o r p o r a t i o n f o r

about 1340 homes i n t h e c i t y of Regina. Between 20 and 60 r e a d i n g s were a v a i l a b l e f o r e a c h house f o r t h e p e r i o d 1969-77. I n f o r m a t i o n a b o u t t h e s i z e and shape, and some c o n s t r u c t i o n d e t a i l s f o r t h e s e homes was

provided by t h e c i t y of Regina A s s e s s o r ' s O f f i c e .

The y e a r of c o n s t r u c t i o n r a n g e s from 1911 t o 1973; main f l o o r a r e a (MFA) ranged from a b o u t 33 m2 t o 156 m 2 , t o t a l f l o o r a r e a of t h e h e a t e d s p a c e (TFA) from 50 m2 t o 430 m 2 , and h e i g h t from 1 t o 23 s t o r i e s . Most of t h e houses had f u l l basements b u t some had only p a r t i a l basements o r none a t a l l . Those w i t h no basement were b u i l t o v e r c r a w l s p a c e s o r were s lab-on-grade homes.

I n s u l a t i o n l e v e l s v a r i e d . Before 1930 most houses were b u i l t w i t h no i n s u l a t i o n , though i t would have been added t o many of them l a t e r . Those b u i l t between 1945 and 1973 would i n i t i a l l y have had no basement i n s u l a t i o n ; w a l l s would normally have R7

-

R10 i n s u l a t i o n b u i l t i n t o them, and approximately R10 i n s u l a t i o n would have been p l a c e d i n c e i l i n g s .

Heat balance r e l a t i o n s h i ~ s

Fuel consumption v a r i e s w i t h t h e weather. I n t h i s s t u d y , h e a t i n g degree-days a r e used t o r e p r e s e n t t h e weather v a r i a b l e . It i s e x p r e s s e d i n terms of t e m p e r a t u r e T:

where

day

i s t h e average number of h e a t i n g days/day f o r t h e p e r i o d of o b s e r v a t i o n . T i s e q u a l t o t h e o u t s i d e t e m p e r a t u r e (Ta) e x c e p t f o r p e r i o d s t h a t i n c l u d e days having mean t e m p e r a t u r e s g r e a t e r t h a n 18°C. For v a l u e s of T below 15°C t h e d i f f e r e n c e between T and Ta a v e r a g e s l e s s t h a n 0.5 "C ( F i g u r e 1 ) .

The h e a t e q u i v a l e n t of t h e f u e l consumption (EG) c a n b e expressed:

The h e a t e q u i v a l e n t of t h e n a t u r a l g a s i s assumed t o b e 3.73

w/m3

(1000 B T U / ~ ~ ~ ) . IG and SG a r e t h e o r d i n a t e i n t e r c e p t (MJ/day) and s l o p e (MJ/OC) r e s p e c t i v e l y . The s u b s c r i p t G i s used t o d e n o t e n a t u r a l gas. R e s u l t s shown f o r one house i n F i g u r e 2 r e p r e s e n t n a t u r a l g a s and e l e c t r i c i t y consumption o v e r a p e r i o d of about two y e a r s .

I n F i g u r e 3 , h e a t i n p u t s from o t h e r s o u r c e s a r e combined with t h e h e a t e q u i v a l e n t of t h e n a t u r a l g a s and p l o t t e d a g a i n s t T.

ED

r e p r e s e n t s

t h e sum of h e a t i n p u t s from occupants (Eo) e l e c t r i c i t y (EE) and t h e sun (ESR). The g r a p h i s completed by s t a c k i n g EG on t o p of

ED

( t h u s t h e l i n e ETO t = EG

+

ED i n F i g u r e 3a). When t h e u s e f u l p a r t of t h e h e a t from t h e *Throughout t h i s r e p o r t energy q u a n t i t i e s a r e e x p r e s s e d a s d a i l y t o t a l s .

w a t e r h e a t i n g s y s t e m (Ew) i s added t o E t h e t o t a l m i s c e l l a n e o u s h e a t (EM) i s o b t a i n e d . The h e a t e q u i v a l e n t o f ' t h e f u e l s u p p l i e d t o t h e f u r n a c e i s shown (EF) i n F i g u r e 3a.

I n F i g u r e 3b t h e e s t i m a t e d h e a t l o s s [EST = 125

+

19.3 (18

-

T) MJ/day] i s added t o complete t h e h e a t b a l a n c e diagram.

It i s assumed t h a t t h e e n e r g y consumption f o r w a t e r h e a t i n g d o e s n o t v a r y s i g n i f i c a n t l y t h r o u g h o u t t h e y e a r . It i s f u r t h e r assumed t h a t a f i x e d f r a c t i o n of t h a t h e a t i s c o n v e r t e d i n t o s p a c e h e a t and t h a t t h e r e m a i n d e r ( ) i s l o s t . Each of t h e h e a t i n p u t s c a n b e r e p r e s e n t e d i n degree-days u s i n g t h e r e l a t i o n s h i p t h e n f o r t h e m i s c e l l a n e o u s components ( e x c l u d i n g h o t w a t e r ) The t o t a l h e a t i n p u t t o t h e h o u s e a n d From E q u a t i o n 2 , and from E q u a t i o n

5 ,

I n t h i s r e p o r t STot and SG a r e c a l l e d t h e h e a t i n p u t and f u e l

consumption c o e f f i c i e n t s r e s p e c t i v e l y . T h e o r e t i c a l l y a t l e a s t , t h e y a r e i n d e p e n d e n t of t h e i n t e r i o r t e m p e r a t u r e of t h e house. F u r t h e r r e g a r d i n g f u e l c o n s m e d i n t h e f u r n a c e ( E p ) : where SF i s t h e f u r n a c e consumption c o e f f i c i e n t . SG i s a p p r o x i m a t e l y e q u a l t o t h e h e a t i n p u t c o e f f i c i e n t (STot) and t h e f u r n a c e consumption c o e f f i c i e n t (SF). For t h i s r e a s o n , SG i n t h i s r e p o r t i s t a k e n t o be a measure of t h e t h e r m a l b e h a v i o r of h o u s e s and i s u s e d f o r t h a t purpose.

This study comprises two areas of analysis:

I. The nature of the linear fuel consumption

-

heating degree-day

relationship [EG

=

IG

+

SG (18

-

T)] (fuel consumption means all of the

natural gas used).

a. The continuity and linearity of fuel consumption

-

degree-day

plots,

h. The coefficients of correlation of fuel consumption

-

degree-day

relationships for houses,

c. The uncertainty of slope of the fuel consumption

-

degree-day

relationship.

TI. Factors affecting fuel consumption:

a.

Size of house,

b.

Differences in the fuel consumption coefficient (SG) for

nominally identical houses.

FUEL

COUSUHPTIOB

-

HEATIBG DEGREE-DAY RBLATIOBSHIP

The continuity and linearity of fuel consumption

-

degree-day

relationship

The year may be divided into three parts: the heating season, in

which furnace heat is required continuously; the non-heating season, in

which no furnace heat is required; and a transition period in which

furnace heat is required intermittently. These differences in heating

requirements and other seasonal effects would be expected to produce

discontinuity, or at least non-linearity in the fuel consumption

-

degree-day relationship. Such plots usually show a generally linear

distribution, but the data for individual houses are usually too sparse

and too scattered to permit firm conclusions to be drawn about linearity.

However, statistical analysis using data for a group of houses allows the

use of a large number of points and averaging to get a more precise

picture of a general relationship.

For the equation

IG and SG can be found by least squares analysis.

It is necessary to distinguish between measured energy consumption

(EG) and predicted consmption

(Ep). For the first, the relationship

might b e more p r o p e r l y w r i t t e n a s a n approximat ion:

w h i l e E p = IG (18

-

T)

.

E q u a t i o n 2 c a n b e m o d i f i e d t o r e a d

where E is a c o r r e c t i o n t o t h e observed h e a t i n g degree-days needed t o

make t h e o b s e r v e d energy consumption c o i n c i d e w i t h t h e p r e d i c t e d v a l u e .

The n a t u r e of E a s an a v e r a g e f o r a group of h o u s e s was s t u d i e d

u s i n g d a t a f o r 2 3 f u l l basement bungalows b u i l t i n t h e 1960's.

was found f o r e a c h of a p p r o x i m a t e l y 1000 d a t a p o i n t s . These were averaged o v e r 1 ° C i n t e r v a l s f o r 1 8 > T

'

8 and o v e r 2°C i n t e r v a l s f o r 8 > T and were p l o t t e d a g a i n s t 18

-

T =

day day

i n F i g u r e 4. For

T = 17.5

e

i s approximately +0.5"C. I n t h e r e g i o n T

>

10, t h e d i f f e r e n c e between t h e observed and t h e p r e d i c t e d r e l a t i o n s h i p r e a c h e s a maximum a t T

=

l l ° C , where E = - l ° C , a n e r r o r of a b o u t 25% ( d o t t e d l i n e ) . Such

d e v i a t i o n , assuming t h a t i t i s r e a l , would c o r r e s p o n d t o a s p a c e h e a t i n g r e q u i r e m e n t which i s less t h a n t h a t p r e d i c t e d by h e a t i n g d e g r e e d a y s . For T < 9OC t h e r e i s some e v i d e n c e of d e v i a t i o n i n t h e o t h e r d i r e c t i o n . The n e g a t i v e v a l u e of E f o r T >

9

and t h e p o s i t i v e v a l u e of E f o r T < 9 would seem t o c o r r e s p o n d t o a change i n f u e l demand f o r s p a c e h e a t i n g .

I n t h e f o l l o w i n g a n a l y s i s a l l of t h e d a t a p o i n t s were used; no a t t e m p t was made t o e x c l u d e summer v a l u e s .

The p e r i o d s covered were of unequal l e n g t h , r a n g i n g from 30 d a y s t o a s l o n g a s 250 d a y s i n i s o l a t e d c a s e s , and a v e r a g i n g a b o u t 65 days. If t h e l o n g e r t e s t p e r i o d i s d e s i r e d t o produce a more a c c u r a t e d a t a p o i n t , t h e n w e i g h t i n g i n p r o p o r t i o n t o t h e l e n g t h o f p e r i o d would be

a p p r o p r i a t e . T h i s q u e s t i o n was n o t i n v e s t i g a t e d h e r e o t h e r t h a n t o compare i n t e r c e p t s , s l o p e s and c o e f f i c i e n t s of c o r r e l a t i o n , u s i n g d a t a f o r 15 h o u s e s , and a n a l y s i n g b o t h ways ( i . e . d a t a p o i n t s weighted i n d i r e c t p r o p o r t i o n t o t h e time span, and p o i n t s n o t w e i g h t e d ) . The a v e r a g e s of t h e i n t e r c e p t s , s l o p e s and c o e f f i c i e n t s of c o r r e l a t i o n f o r weighted and unweighted r e s u l t s d i f f e r e d by 1.7, 0.1, and 0.3% of t h e mean v a l u e s r e s p e c t i v e l y . However, f o r i n d i v i d u a l c a s e s t h e r e a r e more

s i g n i f i c a n t d i f f e r e n c e s . Maximum d i f f e r e n c e s i n i n t e r c e p t , s l o p e and c o e f f i c i e n t of c o r r e l a t i o n were 20,6 and 3% r e s p e c t i v e l y . Using t h e same sequence, s t a n d a r d d e v i a t i o n s were 12.5, 2.5 and 1.0% of t h e mean v a l u e s .

Weighting was used i n a l l c a s e s i n t h i s p a p e r e x c e p t f o r t h e d a t a i n F i g u r e 2.

Amount of v a r i a t i o n i n f u e l c o n s u m ~ t i o n a c c o u n t e d f o r bv h e a t i n g degree-days

The r e l i a b i l i t y of t h e s e l e a s t s q u a r e s r e l a t i o n s h i p s i n d e s c r i b i n g t h e f u e l consumption o f h o u s e s depends o n how much of t h e v a r i a t i o n i n e n e r g y consumption i s a c c o u n t e d f o r by t h e h e a t i n g degree-day p a r a m e t e r . Measures of t h i s a r e g i v e n by t h e c o e f f i c i e n t of c o r r e l a t i o n ( r ) and t h e c o e f f i c i e n t of d e t e r m i n a t i o n s ( r 2 ) .

C o e f f i c i e n t s of c o r r e l a t i o n were c a l c u l a t e d f o r a number of h o u s e s . F i g u r e 5 , which i s b a s e d o n results f o r 571 h o u s e s of a l l s t y l e s and a g e s , shows t h a t f o r a p p r o x i m a t e l y 26% of t h e h o u s e s t h e c o e f f i c i e n t of c o r r e l a t i o n was a b o u t 0.99, f o r 75% of them i t exceeded 0.95 and f o r 90% i t exceeded 0.90. The c o e f f i c i e n t o f d e t e r m i n a t i o n i s d e f i n e d a s t h e f r a c t i o n of v a r i a n c e ( v a r i a t i o n ) t h a t i s e x p l a i n e d by t h e r e l a t i o n s h i p . A s c a l e f o r c o e f f i c i e n t of d e t e r m i n a t i o n i s g i v e n a t t h e t o p of F i g u r e 5. T h i s i n d i c a t e s t h a t t h e r e l a t i o n s h i p e x p l a i n e d 80% of t h e v a r i a t i o n i n a b o u t 92% of t h e c a s e s , and 90% of t h e v a r i a t i o n i n 75% of t h e c a s e s ; t h e r e m a i n i n g v a r i a t i o n presumably c o u l d b e d u e t o a l l o t h e r e f f e c t s .

No s p e c i a l e f f o r t was made t o d e t e r m i n e t h e c a u s e of low

c o r r e l a t i o n s . I n a few c a s e s t h e r e a s o n was a p p a r e n t ; swimming p o o l s may r e q u i r e a g r e a t d e a l of h e a t and s o d i s t o r t t h e e n e r g y consumption

-

degree-day r e l a t i o n s h i p t h a t i t becomes u n u s a b l e a s a measure o f h o u s e t h e r m a l performance. U n c e r t a i n t y i n t h e f u e l consumption c o e f f i c i e n t ( S G ) The n a t u r a l g a s

-

degree-day r e l a t i o n s h i p i n F i g u r e 2 h a s a r e g r e s s i o n c o e f f i c i e n t ( s l o p e ) of 23.08 MJ/DD, a n i n t e r c e p t o f 161 MJ/day, and a c o r r e l a t i o n c o e f f i c i e n t of 0.980. F u r t h e r , t h e 99% c o n f i d e n c e i n t e r v a l f o r t h e s l o p e i s g i v e n by 23.08

'

2.19 MJ/DD,

i . e . t h e r e i s a 1% chance t h a t t h e s l o p e would d i f f e r from t h e c a l c u l a t e d v a l u e by a s much a s 2.19 M J / D D . The 90% c o n f i d e n c e i n t e r v a l i s g i v e n by 23.08 2 1.33 M J / D D . ~

Ninety-nine p e r c e n t c o n f i d e n c e i n t e r v a l s f o r s l o p e s were computed by t h e a n a l y s i s of d a t a f o r 400 h o u s e s o f a l l s t y l e s , b u i l t a f t e r 1945. These v a l u e s were used t o c a l c u l a t e t h e h a l f - w i d t h s o f t h e c o n f i d e n c e bands a s a p e r c e n t a g e o f t h e c a l c u l a t e d s l o p e . The f r e q u e n c y c u r v e peaks a t a b o u t 99%, b u t i t i s skewed and t h e mean v a l u e i s a p p r o x i m a t e l y 10%

( F i g u r e 6 ) .

S e v e r a l o t h e r f e a t u r e s of t h i s method of r e l a t i n g e n e r g y consumption t o h e a t i n g degree-days m i g h t b e mentioned. The r e l i a b i l i t y o f i n d i v i d u a l p o i n t s w i l l v a r y w i t h t h e s p a n of t i m e t h a t may n o t b e d i r e c t l y a c c o u n t e d f o r by h e a t i n g degree-days, b u t may b e more a f f e c t e d by s o l a r r a d i a t i o n and wind. However, i t would b e d i f f i c u l t t o a s s i g n a v a l u e t o t h i s a v e r a g i n g e f f e c t .

I n t h i s s t u d y , a r a t h e r l a r g e number of d a t a p o i n t s , c o v e r i n g a number of y e a r s , was a v a i l a b l e f o r e a c h house. When t h e method i s u s e d

t o a s s e s s house performance, i t must be done o v e r a much s h o r t e r t i m e p e r i o d . F u r t h e r a n a l y s i s would b e needed t o b e t t e r e v a l u a t e t h e a c c u r a c y of t h e method, b u t e x p e r i e n c e s u g g e s t s t h a t r e a s o n a b l e i n d i c a t i o n s can be o b t a i n e d even o v e r s h o r t p e r i o d s ( e . g . , h a l f a y e a r o r a y e a r ) a s l o n g a s b o t h warm- and cold-weather r e s u l t s a r e o b t a i n e d .

FACTORS

AFFECTIBG FUEL COHSUMPTIOBJ FOR SPACE

EEATIRJG

S e v e r a l s e t s of v a r i a b l e s may a f f e c t f u e l consumption f o r s p a c e h e a t i n g . One s e t i n c l u d e s s i z e , s h a p e a n d s t y l e , e . g . , s i n g l e s t o r e y ,

two s t o r e y o r s p l i t l e v e l . A second s e t i n c l u d e s f a c t o r s s u c h a s o r i e n t a t i o n , occupancy and c o l o r . The most i m p o r t a n t v a r i a b l e s a r e t h e r m a l i n s u l a t i o n and a i r t i g h t n e s s . I n t h i s s t u d y of s i z e e f f e c t , t h e i r i n f l u e n c e s w i l l b e n u l l i f i e d u n l e s s t h e r e e x i s t s a s i z e - t h e r m a l p r o p e r t y dependence f o r t h e h o u s e s . T h i s c o u l d n o t be d e t e r m i n e d w i t h any c e r t a i n t y .

House s i z e and s t y l e

S e v e r a l d i f f e r e n t measures of house s i z e might be used. These i n c l u d e volume, e x t e r i o r s u r f a c e a r e a a n d f l o o r a r e a . None i s i d e a l . A c t u a l l y t h e y a r e f a i r l y c l o s e l y r e l a t e d t o one a n o t h e r . The r a t i o o f volume t o t o t a l f l o o r a r e a i s a p p r o x i m a t e l y e q u a l t o c e i l i n g h e i g h t o r f l o o r - t o - f l o o r h e i g h t . Apart from c a t h e d r a l c e i l i n g s and a few o t h e r s p e c i a l c a s e s , c e i l i n g h e i g h t s i n t h e k i n d of h o u s e i n t h i s s t u d y would r a n g e from a b o u t 2.3 t o 2.45 m , a d i f f e r e n c e of a b o u t 6%.

It s h o u l d be n o t e d t h a t t h e t e r m ' f l o o r a r e a ' i s u s e d l o o s e l y h e r e . The s i z e s a r e b a s e d o n e x t e r i o r measurements. Thus o c c u p i a b l e f l o o r a r e a i s l e s s t h a n t h e i n d i c a t e d amount by a q u a n t i t y a p p r o x i m a t e l y e q u a l t o t h e p r o d u c t of p e r i m e t e r and w a l l t h i c k n e s s . The e x t e r i o r measurement h a s been used b e c a u s e i t i s t h e normal way of e x p r e s s i n g house s i z e i n

t h i s r e g i o n .

The r e l a t i o n s h i p between e x t e r i o r s u r f a c e a r e a and f l o o r a r e a f o r most h o u s e s c a n b e e x p r e s s e d a p p r o x i m a t e l y a s

Ext. S u r f . a r e a = P x H x of f l o o r s

+

2 MFA ( 1 4 ) where P i s t h e p e r i m e t e r of t h e house (m),

H

i s t h e f l o o r - t o - f l o o r h e i g h t

(m) and MFA i s t h e p l a n area (m2).

I n t h e s e h o u s e s , p e r i m e t e r b e a r s a f a i r l y c l o s e r e l a t i o n s h i p t o p l a n a r e a . An a n a l y s i s w a s done on 106 h o u s e s of d i f f e r e n t f l o o r a r e a a n d / o r p e r i m e t e r , i n c l u d i n g a l l t h e s t y l e s mentioned p r e v i o u s l y ( F i g u r e

7).*

*Because of e r r o r s i t i s p o s s i b l e t h a t some of t h e h o u s e s were of t h e same d e s i g n , even though t h e d a t a s u g g e s t e d t h a t t h e y were d i f f e r e n t .

These came from a g r o u p of 742 post-1945 h o u s e s . The r e l a t i o n s h i p between p e r i m e t e r and p l a n a r e a , o b t a i n e d by l e a s t s q u a r e s f i t t i n g i s

P

= 17.3

+

0.24

MFA

w i t h a s t a n d a r d e r r o r of e s t i m a t e e q u a l t o 1.9 m , o r 4.8% of t h e a v e r a g e p e r i m e t e r . S t a t i s t i c a l l y , E q u a t i o n 8 s h o u l d a p p l y w i t h i n 4.8% f o r 68% of t h e houses and w i t h i n 9.6% f o r 95% of t h e houses. The g r o u p i n F i g u r e 7 i n c l u d e s f o u r h o u s e s t h a t s t a n d a p a r t from t h e o t h e r s . T h e i r p e r i m e t e r s exceed t h e a v e r a g e f o r t h e i r s i z e by 12 t o 25%. Each o f them was t h e o n l y h o u s e of i t s k i n d . I f t h e y a r e e x c l u d e d , t h e s t a n d a r d e r r o r of e s t i m a t e d r o p s t o 2.6%.

P

= 18.0

+

0.23

MFA

_{( 1 6 )} The two terms on t h e r i g h t s i d e of E q u a t i o n 14 a r e a p p r o x i m a t e l y e q u a l f o r bungalows, i . e . t w i c e t h e p l a n a r e a i s a p p r o x i m a t e l y e q u a l t o t h e t o t a l w a l l a r e a . T h e r e f o r e i f E q u a t i o n 15 was used a s a n a p p r o x i m a t e v a l u e of P i n E q u a t i o n 14, t h e r e i s a 68% c h a n c e t h a t t h e e r r o r i n

s u r f a c e a r e a r e s u l t i n g from t h i s a p p r o x i m a t i o n would be l e s s t h a n 2.4%

and a 95% c h a n c e t h a t i t would b e l e s s t h a n 4.8%.

I n t h e p r e s e n t c a s e t o t a l f l o o r a r e a i s used a s t h e measure of house s i z e . It i s a widely recognized measure and, a s shown above, b e a r s a f a i r l y c l o s e r e l a t i o n s h i p t o e n v e l o p e area. The l a t t e r i s i m p o r t a n t s i n c e h e a t l o s s e s and g a i n s o c c u r t h r o u g h i t . It i s n o t t h e purpose o f t h i s s t u d y t o d e a l w i t h t h e d e t a i l e d s u r f a c e a r e a

-

t h e r m a l r e s i s t a n c e v a l u e s u s e d i n h e a t b a l a n c e s t u d i e s . I n t h i s s t u d y o n l y a v e r y l i m i t e d amount of i n f o r m a t i o n a b o u t t h e t h e r m a l p r o p e r t i e s of t h e e n v e l o p e was a v a i l a b l e ; i t s p u r p o s e i s t o i n v e s t i g a t e o t h e r q u e s t i o n s . For t h e s t u d y of t h e e f f e c t of s i z e t h e houses w e r e d i v i d e d i n t o f i v e d i f f e r e n t g r o u p s b a s e d o n s t y l e . Among h o u s e s b u i l t i n 1945 o r l a t e r , 975 were i n c l u d e d i n t h i s p a r t of t h e s t u d y : 1. 640 s i n g l e s t o r e y houses w i t h f u l l b a s e m e n t s ,

2. 81 houses w i t h more t h a n one b u t l e s s t h a n two s t o r e y s and w i t h f u l l basements,

3. _{79 h o u s e s o f two o r more s t o r e y s w i t h f u l l b a s e m e n t s ,}

4. 96 s p l i t l e v e l h o u s e s ,

5. 79 _{s i n g l e s t o r e y houses w i t h no basements.}

Fuel consumption c o e f f i c i e n t s

(SG) f o r two s t o r e y , f u l l basement

houses a r e p l o t t e d a g a i n s t t o t a l f l o o r a r e a ( F i g u r e 8 ) . V a l u e s f o r h o u s e s of t h e same model were averaged t o produce a s i n g l e p o i n t . 'Lttus e a c h p o i n t r e p r e s e n t s one o r more h o u s e s of a g i v e n model. I n s p i t e of t h e s c a t t e r , t h e p l o t d e m o n s t r a t e s a n upward t r e n d w i t h i n c r e a s i n g s i z e .

To r e d u c e t h e s c a t t e r , f i v e o r more p o i n t s were a v e r a g e d t o produce a s i n g l e v a l u e . n e s e a v e r a g e v a l u e s a r e a l s o shown i n F i g u r e 8.

T h i s a v e r a g i n g was a l s o done f o r t h e o t h e r s t y l e s of h o u s e s l i s t e d above. The combined r e s u l t s a r e shown i n F i g u r e 9. T h i s g i v e s a

c u r v i l i n e a r p l o t w i t h s l o p e s t h a t v a r y from a b o u t 21 W / D D f o r h o u s e s w i t h a t o t a l f l o o r a r e a of 50 m2 t o 50 M J / D D a t 350 m2.

Data were a v a i l a b l e f o r o t h e r g r o u p s of houses which w e r e n o t used i n p r e p a r i n g F i g u r e 9

but

a r e superimposed o n i t . These i n c l u d e h o u s e s b u i l t b e f o r e 1945 and d u p l e x e s . A l l had f u l l basements. It a p p e a r s t h a t o n a v e r a g e t h e h o u s e s of a l l t y p e s , b u i l t between 1911 and 1932, had s l o p e v a l u e s r o u g h l y 25% g r e a t e r t h a n t h o s e on t h e main c u r v e .

C o n s m p t i o n s / d e g r e e d a y f o r d u p l e x e s were s u b s t a n t i a l l y l e s s t h a n t h e a v e r a g e f o r o t h e r h o u s e s of c o r r e s p o n d i n g s i z e .

The c u r v e t h r o u g h t h e p o i n t s i n F i g u r e 9 was used t o p r e p a r e a second c u r v e (SG/A, s c a l e o n r i g h t s i d e of f i g u r e ) . T h i s g i v e s t h e f u e l c o n s m p t i o n c o e f f i c i e n t / u n i t a r e a , d e g r e e d a y v e r s u s a r e a . This shows v a l u e s f a l l i n g s h a r p l y from about 0.42 M J / ~ ~ D D f o r 50 m2 t o 0.15 M J / m 2 D ~ f o r h o u s e s 200 m2 o r l a r g e r .

V a r i a t i o n i n f u e l consumption f o r n o m i n a l l y i d e n t i c a l h o u s e s

The d a t a i n c l u d e v a l u e s f o r a number of g r o u p s o f h o u s e s of t h e same model. These were c o n s t r u c t e d a c c o r d i n g t o t h e same p l a n s , n e v e r t h e l e s s would have somewhat d i f f e r e n t t h e r m a l performances due t o d i f f e r e n c e s i n e x p o s u r e , o r i e n t a t i o n , c o l o r , q u a l i t y of c o n s t r u c t i o n , owner management and changes made by t h e owners a f t e r p u r c h a s e , s u c h a s basement f i n i s h i n g and a d d i t i o n a l i n s u l a t i n g . 4 It i s t o b e e x p e c t e d t h a t f u r n a c e e f f i c i e n c y would a l s o v a r y from house t o house. A s i n d i c a t e d e a r l i e r , s t a t i s t i c a l u n c e r t a i n t y a b o u t t h e s l o p e i n t r o d u c e s a n o t h e r v a r i a b l e . For e l e v e n s u c h g r o u p s , of 12 t o 49 h o u s e s , t h e s l o p e s were found f o r e a c h house. The means a n d s t a n d a r d d e v i a t i o n s of t h e s l o p e s were computed f o r e a c h g r o u p

(Table 1 )

.

F i n a l l y t h e d a t a f o r s e v e r a l of t h e above g r o u p s , comprising 141 h o u s e s , were a n a l y s e d . The s l o p e f o r e a c h h o u s e was found a s a f r a c t i o n of t h e mean f o r i t s group. These f r a c t i o n s were used t o p r e p a r e t h e

f r e q u e n c y d i s t r i b u t i o n p l o t i n F i g u r e 10.

Table 1 shows t h a t t h e s t a n d a r d d e v i a t i o n i n s l o p e s r a n g e s from a low of 6.9% t o a h i g h of 22.9% and a v e r a g e s approximately 11% (10% i f t h e 22.9% group i s e x c l u d e d ) . T h i s would s u g g e s t t h a t d e v i a t i o n s i n SG (from t h e mean f o r t h e group) due t o t h e f a c t o r s l i s t e d above ( d i f f e r e n c e s i n e x p o s u r e , q u a l i t y of c o n s t r u c t i o n e t c . ) were l e s s t h a n

+

10 o r 11% i n a b o u t 213 of t h e h o u s e s and less t h a n a b o u t '20% f o r 95% of t h e houses. S i m i l a r l y i n - F i g u r e 10, a p p r o x i m a t e l y 213 of t h e h o u s e s would f a l l i n t h e

s~

r a n g e 0.9 <

,

< 1.1. X

S t u d i e s u s i n g r e c o r d s of consumption f o r n a t u r a l g a s and e l e c t r i c i t y were c a r r i e d o u t o n a p p r o x i m a t e l y 1400 h o u s e s of a l l s t y l e s , r a n g i n g i n s i z e from about 45 t o 400 m2 t o t a l f l o o r a r e a . Slope i n t e r c e p t

r e l a t i o n s h i p s between e l e c t r i c i t y and n a t u r a l g a s consumption and h e a t i n g degree-days were found f o r e a c h house. From a n a l y s i s of t h e s e d a t a t h e f o l l o w i n g c o n c l u s i o n s were reached.

1. The r e l a t i o n s h i p between t h e e n e r g y e q u i v a l e n t of n a t u r a l g a s consumption and h e a t i n g degree-days i s e x p r e s s e d h e r e a s

E~ = I G

+

SG ( ~ D D / d a y ) . It i s n e a r l y l i n e a r f o r many houses. 2. The s l o p e of t h i s r e l a t i o n s h i p , (SG, t h e f u e l consumption

c o e f f i c i e n t ) i s a p p r o x i m a t e l y e q u a l t o t h e c o e f f i c i e n t g i v e n by t h e s l o p e o f t o t a l h e a t i n p u t v e r s u s degree-days (STot) and a l s o t o t h e s l o p e of t h e r e l a t i o n s h i p between f u e l i n p u t t o t h e f u r n a c e and h e a t i n g d e g r e e - d a y s

(%).

T h e r e f o r e SG i s a u s e f u l measure of t h e r m a l performance of t h e house. 3. The r e l i a b i l i t y of SG depends i n p a r t on i t s s t a t i s t i c a l u n c e r t a i n t y . For 400 h o u s e s , t h i s u n c e r t a i n t y a t t h e 99% l e v e l of c o n f i d e n c e averaged a b o u t 10%. 4. The c o e f f i c i e n t s of c o r r e l a t i o n f o r t h e n a t u r a l g a s consumption

-

h e a t i n g degree-day d a t a f o r i n d i v i d u a l h o u s e s v a r i e d

widely. For a p p r o x i m a t e l y 90% of t h e houses i t exceeded 0.90; f o r 50% i t exceeded 0.975.

5. SG i n c r e a s e s w i t h i n c r e a s i n g house s i z e i n a c u r v i l i n e a r

f a s h i o n , r a n g i n g from a b o u t 21 W / D D f o r h o u s e s w i t h a t o t a l f l o o r a r e a of 50 rn2, t o 50 W / D D _{f o r houses w i t h a t o t a l f l o o r a r e a of 350 m2.}

6. For groups of nominally i d e n t i c a l h o u s e s , t h e s t a n d a r d d e v i a t i o n s f o r SG (and a v e r a g e d a i l y consumption of n a t u r a l g a s p l u s e l e c t r i c i t y ) were a p p r o x i m a t e l y 10% of t h e mean v a l u e s f o r t h e groups. These would a p p e a r t o p r o v i d e a measure of t h e combined e f f e c t s of such f a c t o r s a s e x p o s u r e , o c c u p a n t management, f u r n a c e e f f i c i e n c y , c o l o r and o r i e n t a t i o n , a s w e l l a s v a r i a t i o n s i n q u a l i t y of house c o n s t r u c t i o n and changes made a f t e r c o n s t r u c t i o n , o n t h e t h e r m a l performance of t h e house.

1. Lawrence S. Mayer and J e f f r e y A. Robinson. A S t a t i s t i c a l A n a l y s i s of t h e Monthly Consumption of Gas and E l e c t r i c i t y i n t h e Home, C e n t e r f o r Environmental S t u d i e s Report No. 18. P r i n c e t o n U n i v e r s i t y , 1975. 2. C.P. Hedlin and H.W. O r r . A Study o f t h e Use of N a t u r a l Gas and

E l e c t r i c i t y i n Saskatchewan Homes, SHELTER, P r o c e e d i n g s of t h e T e c h n i c a l Program of t h e 9 1 s t Annual E I C Meeting, J a s p e r , A l b e r t a , NRCC 16898, May 1977, pp. 123-131.

3. Edwin L. Crow, F r a n c e s A. Davis and Margaret W. Maxfield. S t a t i s t i c s , C o l e s P u b l i s h i n g Co. L t d . , T o r o n t o , 1978.

4. G.P. M i t a l a s . N e t a n n u a l h e a t l o s s f a c t o r method f o r e s t i m a t i n g h e a t r e q u i r e m e n t s i n b u i l d i n g s , D i v i s i o n o f B u i l d i n g R e s e a r c h , N a t i o n a l Research C o u n c i l of Canada, B u i l d i n g Research Note 117, Ottawa, November 197

6.

Acknowledgement

The a u t h o r s w i s h t o e x p r e s s t h e i r a p p r e c i a t i o n t o t h e Saskatchewan Power C o r p o r a t i o n f o r p r o v i d i n g t h e e n e r g y consumption d a t a and t o t h e Regina C i t y A s s e s s o r ' s o f f i c e f o r p r o v i d i n g s i z e and o t h e r i n f o r m a t i o n a b o u t t h e s e h o u s e s . Without t h e i r a s s i s t a n c e and c o o p e r a t i o n t h e s t u d y c o u l d n o t have been c a r r i e d o u t . We a l s o wish t o t h a n k H.W. O r r and S.S. Tao f o r t h e i r a d v i c e and a s s i s t a n c e and T.B. Remple f o r h i s work i n c a r r y i n g o u t t h e a n a l y s e s .

TABLE 1 MEANS AND STANDARD DEVIATIONS OF FURNACE EFFICIENCY SLOPES

Main T o t a l S t a n d a r d

No. i n C o n s t r u c t i o n f l o o r a r e a f l o o r a r e a Mean S l o p e D e v i a t i o n

Group* Date m2 m2 W/DD % of Mean

- S i n g l e s t o r e y , no basement

17

1946

5

8

12

1957-60

83

2

1

1960-61

8

9

S i n g l e s t o r e y , f u l l basement

47

1952

89

178

28.9

9.3

3

8

1965-67

9

6

191

27.3

7.6

49

1957-64

9

7

193

29.4

10.0

4

4

1965-67

106

193

29.9

10.3

Four l e v e l s p l i t

3

4

1963-71

130

263

36.9

10.6

*9

h o u s e s were r e j e c t e d from t h e o r i g i n a l

347

h o u s e s i n t h e s e g r o u p s , t h r e e b e c a u s e t h e y had h e a t e d swimming p o o l s and s i x b e c a u s e t h e i r s l o p e s d e v i a t e d w i d e l y from t h e o t h e r s of t h e i r group.

F I G U R E 1 O U T D O O R T E M P E R A T U R E T a V S T , T I S B A S E D O N M O N T H L Y A V E R A G E S O F H D D l d a y F O R M A Y T O S E P T E P B E R 1 9 7 5 - 8 0 , S A S K A T O O N F I G U R E 2 N A T U R A L G A S l E G l A N D E L E C T R I C I T Y ( E E l - C O N S U M P T I O N D A T A F O R O N E H O U S E P L O T T E D A G A I N S T T - 1 8

-

H D D l d a y

WASTED HOT WATER EF (ENERGY SUPPLIED T O F U R N A C E ) U S E F U L SPACE HEAT F R O M D O M E S T I C H O T WATER -9- - - 9 - - -

SPACE H E A T FROM OCCUPANTS, SOLAR A N D E L E C T R I C I T Y ( E D ) 1 F I G U R E 3 SPACE HEAT FROM FURNACE STRUCTURAL H E A T L O S S ( E s t v

---

1 ( a ) E N E R G Y I N P U T S F R O M O C C U P A N T S , S O L A R G A I N , E L E C T R I C I T Y F O R N O N - H E A T I N G P U R P O S E S , D O M E S T I C H O T W A T E R S Y S T E M S A N D F U R N A C E F U E L ( b ) S T R U C T U R A L H E A T L O S S S U P E R I M P O S E D O V E R 3 ( a )

I I I

. . . .

.

. .

.o.

...

. . .. _{C A L C U L A T E D V A L U E S O F} E~ -IG G

-

L I N E R E P R E S E N T I N G A P E R F E C T F I T

P

/-

@

-

/ 6

-

0"

...

..a. -

_-

-

-

-

-

-

-

-

-

C

5)'"

1 I I I F I G U R E 4 P L O T O F E G

-

I G I S G ( c ) V S T F O R 23 H O U S E S . T H I S S H O W S A R E L A T I O N S H I P B E T W E E N F L l E L C O N S U M P T I O N ( E G ) A N D H E A T I N G D E G R E E - D A Y S I D A Y

COEFFICIENT OF DETERMINATION

P L O T O F F R E Q U E N C Y

V S

T H E C O E F F I C I E N T O F

C O R R E L A T I O N ( B O T T O M ) A N D C O E F F I C I E N T O F

D E T E R M I N A ' T I O N ( T O P ) F O R N A T U R A L G A S

C O N S U M P T I O N

-

D E G R E E - D A Y D A T A . C L I R V E

B A S E D OIV R E S U L T S F O R

5 7 1

H O U S E S

100

0.9

0.8

1

0.7

I

0.6

0.5

I I

+

I I I I I I I I I I I 1

-

-

-

-

40

20

-

-

1

I

I

I 1

.O

0.9

0.8

0.7

COEFFICIENT OF CORRELATION

UNCERTAINTY % AT 99% CONFIDENCE LEVEL

F I G U R E 6

99% C O N F I D E N C E L I M I T S FOR S G A S P E R C E N T A G E S OF THE S L O P E S

0

0 FULL BASEMENT

-

I STOREY 0

-

FULL BASEMENT

-

2 STOREIS 0

-

D FULL BASEMENT

-

1-2 STOREYS FOUR LEVEL SPLIT

-

-

-

-

-

-

I I I I I I I I

I

> 5 0 6 0 7 0 8 0 9 0 100 110 120 130 M F A ( M A I N F L O O R A R E A ) , m2 F I G U R E 7 E X T E R I O R G R O U N D L E V E L P E R I M E T E R V S N O M I N A L M A I N F L O O R A R E A ( E X T E R I O R M E A S U R E M E N T S I F O R 1 0 6 D I F F E R E N T H O U S E P L A N S

TOTAL FLOOR AREA, m2 ( N O M I N A L )

F I G U R E 8

N A T U R A L G A S C O I V S U M P T I O N

-

D E G R E E - D A Y

S L O P E S ( S G ) V S T O T A L N O M I N A L F L O O R

TOTAL F L O O R A R E A , m 2 ( N O M I N A L )

F I G U R E 9

I

0 FULL BASEMENT

-

I

STOREY

FULL BASEMENT

-

2 STOREYS

0 FULL BASEMENT

-

1-2

STOREYS

A NO BASEMENT

-

I STOREY

FOUR LEVEL SPLIT ₀

-

Q HOUSES BUILT 191 1 - 3 2 (ALL TYPES)

8 _DUPLEXES R013 0. @ 0 O

\

_{* /}

0

N A T U R A L G A S C O N S U M P T I O N

-

D E G R E E - D A Y S L O P E S ( S G )

( D A T A P O I N T S A N D D O T T E D C U R V E ) F O R H O U S E S O F D I F F E R E N T

S I Z E S A N D T Y P E S . S G I A M J / ~ *

D D ( S O L I D C U R V E )

dP

0

0

0

/

0

,/

0

/

/ / 0 0 f 3 1

F I G U R E

10

F R E Q U E N C Y V S S G l % W H E R E S G

=

S L O P E

A N D

=

M E A N F O R G R O U P S O F N O M I N A L L Y

I D E N T I C A L H O U S E S . C U R V E B A S E D O N

D A T A F O R

1 4 1 H O U S E S