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Energy saving using morning and evening civil twilight in the State of Bahrain
Renewable Energy, Vol.5, Part IL pp. 1547-1552, 1994 Elsevier Science Lid Printed in Great Britain 0960-1481/94. $7.00.1-0.00
Pergamon
E N E R G Y SAVING USING MORNING A N D EVENING CIVIL TWILIGHT IN THE S T A T E OF BAHRAIN W.E. A l n a s e r
University of Bahrain, Department of Physics, P. O. Box 32038, Bahrain ABSTRACT :
Comparison between the total solar irradiation including a n d excluding the civil twilight in B a h r a i n is studied. The solar i n t e n s i t y of the civil twilight (morning a n d evening twilight) in B a h r a i n is calculated. The calculations show t h a t the m a x i m u m civil twilight is on s u m m e r solistice (longest day) lasts for 52.3 min a n d the least on winter solistice (shortest day) for 50.7 min. In spring a n d a u t u m n equinox (day equal to night), the duration of the civil twilight is 46.1 rain. Monteith a n d Unsoworth e q u a t i o n [7] which estimates the daily global insolation for location having unprolonged d u s k a n d d a w n was evaluated for Bahrain. Their equation was found to fit very well with the m e a s u r e d d a t a in B a h r a i n (percentage difference of 6.5%). Discussion on the energy saving by introducing s u m m e r a n d winter time in B a h r a i n is presented INTRODUCTION :
Twilight is the time preceding sunrise and following s u n s e t w h e n the sky is p a r t l y i l l u m i n a t e d . Civil twilight is the interval w h e n the time zenith distance (03 ) referred to the earth's center of the center of the s u n ' s disc is between 90°50 ' a n d 96 °, n a u t i c a l twilight is the interval between 96 ° a n d 102 ° a n d astronomical twilight is t h a t between 102 ° and 108 ° . Twilight i n c r e a s e s the length of the day. Civil twilight e n d s w h e n the altitude of the s u n is 6 ° below the horizon; it is the lightning-up time for road vehicles [1]. The brightness of the sky varies t h r o u g h o u t twilight. It was found t h a t when the s u n is 6 ° below the horizon (i.e. at the end of civil twilight) the s k y b r i g h t n e s s A in log scale is +2.7; w h e n the s u n is 12 ° below the horizon (i.e. w h e n nautical twilight ends) A decreases to 0; when the s u n is 18 ° below the horizon (i.e. after astronomical twilight ends and it is fully night-time) A decreases to -3.1. The d u r a t i o n of the civil twilight in the Spring a n d A u t u m n equinox (solar declination angle 8 = 0) becomes m i n i m u m (day length = night length). The s u m of the morning and evening twilight is larger in s u m m e r solstice t h a n winter solstice [2]. The d u r a t i o n of the twilights (morning and evening) increases as the latitude ~ of the Iocatlon increases. 1547
1548 B a h r a i n is located a t l a t i t u d e 26°N a n d l o n g i t u d e 50 °. D o m e s t i c c o n s u m e r s u s e m o s t of t h e e l e c t r i c i t y p r o d u c e d w h i c h is a r o u n d 56.4%, C o m m e r c i a l 25.8%, I n d u s t r i a l - 17.2% a n d A g r i c u l t u r a l - 0 . 0 0 6 % [3]. G o v e r n m e n t office h o u r s are 7 : 0 0 a m to 2 : 1 5 pm. B a h r a i n is a n Islamic c o u n t r y , M u s l i m s a r e o b l i g a t e d to p r a y five t i m e s a d a y (at F a j e r o r b e f o r e s u n r i s e , n o o n , a f t e r n o o n , d u s k a n d night).
F a j e r p r a y e r s t a r t s w h e n t h e s u n is u n d e r t h e
h o r i z o n b y 17.5 ° (nearly d u r i n g t h e b e g i n n i n g of t h e m o r n i n g a s t r o n o m i c a l twilight). T h i s m e a n s t h a t t h e p e o p l e offer FaJer p r a y e r s in t h e v e r y e a r l y s u m m e r m o r n i n g s (eg. a t 3 : 0 5 w i n t e r (on 2 0 t h J a n u a r y , p r a y e r h o u r s a f t e r t h e F a j e r p r a y e r (eg. a t 6 : 2 7 am). T h i s s u g g e s t s t h a t
am on 15th starts at 5:00 o n J u n e 15th advancing the
J u n e a n d a t a l a t e r t i m e in am). T h e s u n rises n e a r l y 1.5 at 4:45 am and on June 20th s t a n d a r d to m a k e time, u s e of
t h e twilight will b e v e r y u s e f u l a n d will s a v e electricity. T h i s p a p e r d e a l s w i t h t h e c a l c u l a t i o n of t h e d u r a t i o n of t h e m o r n i n g a n d e v e n i n g twilight f r o m w h i c h we will s h o w t h a t a c o n s i d e r a b l e s a v i n g of e n e r g y will r e s u l t f r o m m a k i n g u s e of t h e s e twilight. METHODS OF CALCULATIONS :
To c a l c u l a t e t h e s u m of t h e d u r a t i o n of m o r n i n g a n d e v e n i n g civil twilight (T) we u s e t h e following e q u a t i o n s : T = 1-~[tog°-to96]
(1)
w h e r e to98 a n d to9o are t h e h o u r a n g l e s a t 9 6 ° (civil twilight) a n d 9 0 ° ( s u n s e t or s u n r i s e ) r e s p e c t i v e l y . to a t a n y z e n i t h d i s t a n c e c a n be c a l c u l a t e d u s i n g t h e following e q u a t i o n [4] :
to
cos_ 1 i c o s e z - sin ¢ sin 81
w h e r e 8 is t h e s o l a r d e c l i n a t i o n angle [5] 8 = 2 3 . 4 5 sin I1360
284 + n 1 365 ]
(3)
n is t h e d a y of t h e y e a r s t a r t i n g o n I s t J a n u a r y ( F e b r u a r y is t a k e n a s 2 8 days). R e c o m m e n d e d v a l u e s of t h e a v e r a g e d a y s for m o n t h s a n d v a l u e s of n b y m o n t h are t a k e n f r o m Klein [6] (table i) as follows :
1549 T a b l e 1 : R e c o m m e n d e d A v e r a g e D a y s for M o n t h s a n d V a l u e s of n b y M o n t h s F o r t h e A v e r a g e D a y of t h e M o n t h
n for ith Month
D a y of M o n t h
Date
i
17
17
-20.9 -13.0
January
n, D a y of Year
8, D e c l i n a t i o n
February
31+i
16
47
March
59+
i
16
75
-2.4
April
90+
i
15
105
9.4
May
120 + i
15
135
18.8
June
151 + i
11
162
23.1
July
181 + i
17
198
21.2
August
212 + i
16
228
13.5
September
243 + i
15
258
2.2
October
273 + i
15
288
-9.6
November
304 + i
14
318
-18.9
December
334 + i
10
344
-23.0
is t h e l a t i t u d e of t h e l o c a t i o n in B a h r a i n (¢ = 26°N). To k n o w t h e t i m e a t w h i c h e i t h e r t h e m o r n i n g or e v e n i n g twilight s t a r t s or e n d s in B a h r a i n , we h a v e to c o n v e r t t h e h o u r a n g l e s into local t i m e TLW b y u s i n g t h e following e q u a t i o n : co TLW = 12 h r s . + - ~ - ~ - h r s . - 4 ( L s T - LLoc)min - E m i n (4)
LST is t h e s t a n d a r d m e r i d i a n for t h e local t i m e zone (LsT for B a h r a i n - 4 5 °) W a n d LLoc is t h e l o n g i t u d e of t h e l o c a t i o n in q u e s t i o n in d e g r e e s (LLoc for B a h r a i n -50°).
T h e "+" m e a n s "+" for e v e n i n g twilight a n d for s u n s e t a n d "-"
for m o r n i n g twilight a n d for s u n r i s e .
Hrs. m e a n s t h a t t h i s v a l u e is in h o u r s
a n d m i n m e a n s t h a t t h e v a l u e is in m i n u t e s . F o r B a h r a i n , e q u a t i o n {4} c a n b e r e - w r i t t e n a s follows : co TLW= 12 hrs. + _--:-- 2 0 m i n - E m i n 15
(5}
E is t h e e q u a t i o n of t i m e in m i n u t e s a n d c a n b e c a l c u l a t e d u s i n g S p e n c e r ' s e q u a t i o n [7]:
E = 229.2 /
0 . 0 0 0 0 7 5 + 0 . 0 0 1 8 6 8 c o s B - 0 . 0 3 2 0 7 7 sin B ) - 0 . 0 1 4 6 1 5 c o s 2B - 0 . 0 4 0 8 9 s i n 2B
(6)
1550
w h e r e B = { n - I) 3 6 0 365
I
RESULTS AND DISCUSSIONS
:
Fig. I s h o w s t he s u m of t he m o r n i n g and evening civil twilight t h r o u g h o u t the year. M a x i m u m twilight is on 2 1 s t J u n e (and lasts for 52.4 min) and on 2 1 s t D e c e m b e r (which lasts for 50.7 min). The s h o r t e s t twilight is on 18th M a r c h a n d 2 6 t h S e p t e m b e r a n d lasts 46.1 min. Since t h e s e figures are close to a n h o u r t h e n a d v a n c i n g t h e time on 18th M a r c h (for e x a m p l e c h a n g i n g the clock from 5:00 a m to 6:00 am) would m a k e people go to their d u ties (which s t a r t at 7:00 am) on 21st J u n e 1 h o u r a n d 14 min (new time) after t he s u n r i s e i n s t e a d of 2 h o u r s and 14 m i n (old time). This will tak e a d v a n t a g e of the s u n l i g h t a n d t he twilight.
Also t he people will be
coming h o m e earlier from work t h a n before and t herefore have m ore time to enjoy th e s ky lights a nd the twilight after dusk. This p r o c e s s would help th e c o u n t r y save large a m o u n t s of money. If we a s s u m e t h a t t h e r e are I million lamps, r a t e d 100 watts, t h a t would be switched off as people leave h o u s e s earlier by one hour , t h e n the a m o u n t of m o n e y t h a t c a n be saved is calculated as follows : a m o u n t saved in I ~ =
P o w e r of t h e l am p (W) x No. of l am ps x 32 {files} 1O0000O
i.e. a m o u n t saved in IK) =
(7)
(100W)(I000000){32) = 3200 I000000
This m e a n s t h a t the saving will be BD 3200 per h o u r i.e. n e a r l y 0.6 million B a h r a i n i Di na r s every six m o n t h s (since the time will be p u t b a c k to n o r m a l on 2 6 t h September). Also since the n u m b e r of h o u s e s in B a h r a i n are nearly 8 0 0 0 0 an d a h o u s e probably h a s 4 air conditioners on the average, t h e n if as a r e s u l t of a d v a n c i n g t he time (on 18th March and p u t t i n g it to n o r m a l on 2 8 t h September), people will switch off half of their air c o n d i t i o n e r s d u r i n g this h o u r .
The a m o u n t of m o n e y saved will be BD 5180 per d a y i.e. nearl y
1.0 million a y e a r (This is a s s u m i n g t h a t each air conditioner has a n electric power of 2 0 0 0 W) Monteich [8] r e p o r t e d t h a t the daily solar radiation can be found u s i n g the following relation : H=
2S o
Imax
(8)
1551
Gmax is the m a x i m u m solar irradiation recorded d u r i n g the y e a r (In B a h r a i n Imax -- 9 9 1 .5 Wm "2) and S O is the m a x i m u m s u n s h i n e d u r a t i o n [3].
2 c o s -I {-tan So = y-g
tan
8)
{9)
This m e a n s t h a t on 2 1 s t J u n e (So = 13.6 hrs.), t he daily average sol ar irradiation will be 8 5 8 8 . 8 Whm "2 (30.92 M j m 2 ) .
E q u a t i o n (8) was modified
for h ig h er latitude s w he r e in s u m m e r the dawn and the d u s k are prolonged. A full sine wave was us e d i.e. N
'
H = Imax
fo
2lnt~
sin I~-~o] d t = Imax -So ~, (10)
w h e r e t is t h e time a f t er s u n r i s e . This m e a n H' will be 6 7 4 2 . 2 Whm -2 (24.27 M J m "2) instead of 8588.8 W hm "2. Since the s u m of the civil twilight (morning a n d evening) in B a h r a i n is from 46 to 52 m i n u t e s , e q u a t i o n (8) r e p r e s e n t s B a h r a i n m or e a c c u r a t e l y t h a n e q u a t i o n (10). For example, t he daily a v e r a g e s ol a r i r r a d i a t i o n r e c o r d e d on 2 1 s t J u n e 1993 at B a h r a i n U n i v e r s i t y w a s 8 0 6 4 . 7 W h m -2 (29.03 MJm-2), t h i s is less t h a n t h e calculated H from e q u a t i o n (8) by 6.5% only. REFERENCES
1.
Acker A a n d J a s c h e k C, 1986, "Astronomical Method of Calculation, J o h n Wiley & Sons, Chichester, U.S.A.
.
A l n a s e r W E a n d Awadalla N S, 1991, Astronomical Cal cul at i ons for p r a y e r time a nd twilight, AI-Obykan Press, Saudi Arabia (in Arabic)
.
Central Statistics Organisation Statistical Abstract 1992, p. 401.
.
Duffle J A a n d B e c k m a n W A, 1992, Solar E n g i n e e r i n g of T h e r m a l
(1993), D i r e c t o r a t e of S t a t i s t i c s ,
Processes, 2nd Edition,, A Wiley Interscience Publication, J o h n Wiley & Sons, New York, U.S.A. .
C o o p e r P I, 1969, T he A bs or pt i on of solar r a d i a t i o n in sol ar stills, Solar Energy, Vol. 12, P. 3
.
Klein S A, 1977, C a l c u l a t i o n of the m o n t h l y average i n s o l a t i o n on tilted surface, Solar Energy, Vol. 24, P. 325.
1552
7.
S p e n c e r J W, 1971, Fourier Series R e p r e s e n a t i o n of the position of the sun, Search, Vol. 2 (No. 5), P. 172. Moneith J L and U n s o w o r t h M H, 1990, Principles of Environmental Physics, 2nd Edition, Edward Arnold, London, P. 45,
.
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Figure 1 :
T h e d a i l y v a r i a t i o n o f t h e s u m o f t h e m o r n i n g a n d e v e n i n g civil t w i l i g h t in B a h r a i n ( l a t i t u d e = 2 6 N, l o n g i t u d e = 5 0 ° E).
Pergamon
E N E R G Y SAVING USING MORNING A N D EVENING CIVIL TWILIGHT IN THE S T A T E OF BAHRAIN W.E. A l n a s e r
University of Bahrain, Department of Physics, P. O. Box 32038, Bahrain ABSTRACT :
Comparison between the total solar irradiation including a n d excluding the civil twilight in B a h r a i n is studied. The solar i n t e n s i t y of the civil twilight (morning a n d evening twilight) in B a h r a i n is calculated. The calculations show t h a t the m a x i m u m civil twilight is on s u m m e r solistice (longest day) lasts for 52.3 min a n d the least on winter solistice (shortest day) for 50.7 min. In spring a n d a u t u m n equinox (day equal to night), the duration of the civil twilight is 46.1 rain. Monteith a n d Unsoworth e q u a t i o n [7] which estimates the daily global insolation for location having unprolonged d u s k a n d d a w n was evaluated for Bahrain. Their equation was found to fit very well with the m e a s u r e d d a t a in B a h r a i n (percentage difference of 6.5%). Discussion on the energy saving by introducing s u m m e r a n d winter time in B a h r a i n is presented INTRODUCTION :
Twilight is the time preceding sunrise and following s u n s e t w h e n the sky is p a r t l y i l l u m i n a t e d . Civil twilight is the interval w h e n the time zenith distance (03 ) referred to the earth's center of the center of the s u n ' s disc is between 90°50 ' a n d 96 °, n a u t i c a l twilight is the interval between 96 ° a n d 102 ° a n d astronomical twilight is t h a t between 102 ° and 108 ° . Twilight i n c r e a s e s the length of the day. Civil twilight e n d s w h e n the altitude of the s u n is 6 ° below the horizon; it is the lightning-up time for road vehicles [1]. The brightness of the sky varies t h r o u g h o u t twilight. It was found t h a t when the s u n is 6 ° below the horizon (i.e. at the end of civil twilight) the s k y b r i g h t n e s s A in log scale is +2.7; w h e n the s u n is 12 ° below the horizon (i.e. w h e n nautical twilight ends) A decreases to 0; when the s u n is 18 ° below the horizon (i.e. after astronomical twilight ends and it is fully night-time) A decreases to -3.1. The d u r a t i o n of the civil twilight in the Spring a n d A u t u m n equinox (solar declination angle 8 = 0) becomes m i n i m u m (day length = night length). The s u m of the morning and evening twilight is larger in s u m m e r solstice t h a n winter solstice [2]. The d u r a t i o n of the twilights (morning and evening) increases as the latitude ~ of the Iocatlon increases. 1547
1548 B a h r a i n is located a t l a t i t u d e 26°N a n d l o n g i t u d e 50 °. D o m e s t i c c o n s u m e r s u s e m o s t of t h e e l e c t r i c i t y p r o d u c e d w h i c h is a r o u n d 56.4%, C o m m e r c i a l 25.8%, I n d u s t r i a l - 17.2% a n d A g r i c u l t u r a l - 0 . 0 0 6 % [3]. G o v e r n m e n t office h o u r s are 7 : 0 0 a m to 2 : 1 5 pm. B a h r a i n is a n Islamic c o u n t r y , M u s l i m s a r e o b l i g a t e d to p r a y five t i m e s a d a y (at F a j e r o r b e f o r e s u n r i s e , n o o n , a f t e r n o o n , d u s k a n d night).
F a j e r p r a y e r s t a r t s w h e n t h e s u n is u n d e r t h e
h o r i z o n b y 17.5 ° (nearly d u r i n g t h e b e g i n n i n g of t h e m o r n i n g a s t r o n o m i c a l twilight). T h i s m e a n s t h a t t h e p e o p l e offer FaJer p r a y e r s in t h e v e r y e a r l y s u m m e r m o r n i n g s (eg. a t 3 : 0 5 w i n t e r (on 2 0 t h J a n u a r y , p r a y e r h o u r s a f t e r t h e F a j e r p r a y e r (eg. a t 6 : 2 7 am). T h i s s u g g e s t s t h a t
am on 15th starts at 5:00 o n J u n e 15th advancing the
J u n e a n d a t a l a t e r t i m e in am). T h e s u n rises n e a r l y 1.5 at 4:45 am and on June 20th s t a n d a r d to m a k e time, u s e of
t h e twilight will b e v e r y u s e f u l a n d will s a v e electricity. T h i s p a p e r d e a l s w i t h t h e c a l c u l a t i o n of t h e d u r a t i o n of t h e m o r n i n g a n d e v e n i n g twilight f r o m w h i c h we will s h o w t h a t a c o n s i d e r a b l e s a v i n g of e n e r g y will r e s u l t f r o m m a k i n g u s e of t h e s e twilight. METHODS OF CALCULATIONS :
To c a l c u l a t e t h e s u m of t h e d u r a t i o n of m o r n i n g a n d e v e n i n g civil twilight (T) we u s e t h e following e q u a t i o n s : T = 1-~[tog°-to96]
(1)
w h e r e to98 a n d to9o are t h e h o u r a n g l e s a t 9 6 ° (civil twilight) a n d 9 0 ° ( s u n s e t or s u n r i s e ) r e s p e c t i v e l y . to a t a n y z e n i t h d i s t a n c e c a n be c a l c u l a t e d u s i n g t h e following e q u a t i o n [4] :
to
cos_ 1 i c o s e z - sin ¢ sin 81
w h e r e 8 is t h e s o l a r d e c l i n a t i o n angle [5] 8 = 2 3 . 4 5 sin I1360
284 + n 1 365 ]
(3)
n is t h e d a y of t h e y e a r s t a r t i n g o n I s t J a n u a r y ( F e b r u a r y is t a k e n a s 2 8 days). R e c o m m e n d e d v a l u e s of t h e a v e r a g e d a y s for m o n t h s a n d v a l u e s of n b y m o n t h are t a k e n f r o m Klein [6] (table i) as follows :
1549 T a b l e 1 : R e c o m m e n d e d A v e r a g e D a y s for M o n t h s a n d V a l u e s of n b y M o n t h s F o r t h e A v e r a g e D a y of t h e M o n t h
n for ith Month
D a y of M o n t h
Date
i
17
17
-20.9 -13.0
January
n, D a y of Year
8, D e c l i n a t i o n
February
31+i
16
47
March
59+
i
16
75
-2.4
April
90+
i
15
105
9.4
May
120 + i
15
135
18.8
June
151 + i
11
162
23.1
July
181 + i
17
198
21.2
August
212 + i
16
228
13.5
September
243 + i
15
258
2.2
October
273 + i
15
288
-9.6
November
304 + i
14
318
-18.9
December
334 + i
10
344
-23.0
is t h e l a t i t u d e of t h e l o c a t i o n in B a h r a i n (¢ = 26°N). To k n o w t h e t i m e a t w h i c h e i t h e r t h e m o r n i n g or e v e n i n g twilight s t a r t s or e n d s in B a h r a i n , we h a v e to c o n v e r t t h e h o u r a n g l e s into local t i m e TLW b y u s i n g t h e following e q u a t i o n : co TLW = 12 h r s . + - ~ - ~ - h r s . - 4 ( L s T - LLoc)min - E m i n (4)
LST is t h e s t a n d a r d m e r i d i a n for t h e local t i m e zone (LsT for B a h r a i n - 4 5 °) W a n d LLoc is t h e l o n g i t u d e of t h e l o c a t i o n in q u e s t i o n in d e g r e e s (LLoc for B a h r a i n -50°).
T h e "+" m e a n s "+" for e v e n i n g twilight a n d for s u n s e t a n d "-"
for m o r n i n g twilight a n d for s u n r i s e .
Hrs. m e a n s t h a t t h i s v a l u e is in h o u r s
a n d m i n m e a n s t h a t t h e v a l u e is in m i n u t e s . F o r B a h r a i n , e q u a t i o n {4} c a n b e r e - w r i t t e n a s follows : co TLW= 12 hrs. + _--:-- 2 0 m i n - E m i n 15
(5}
E is t h e e q u a t i o n of t i m e in m i n u t e s a n d c a n b e c a l c u l a t e d u s i n g S p e n c e r ' s e q u a t i o n [7]:
E = 229.2 /
0 . 0 0 0 0 7 5 + 0 . 0 0 1 8 6 8 c o s B - 0 . 0 3 2 0 7 7 sin B ) - 0 . 0 1 4 6 1 5 c o s 2B - 0 . 0 4 0 8 9 s i n 2B
(6)
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w h e r e B = { n - I) 3 6 0 365
I
RESULTS AND DISCUSSIONS
:
Fig. I s h o w s t he s u m of t he m o r n i n g and evening civil twilight t h r o u g h o u t the year. M a x i m u m twilight is on 2 1 s t J u n e (and lasts for 52.4 min) and on 2 1 s t D e c e m b e r (which lasts for 50.7 min). The s h o r t e s t twilight is on 18th M a r c h a n d 2 6 t h S e p t e m b e r a n d lasts 46.1 min. Since t h e s e figures are close to a n h o u r t h e n a d v a n c i n g t h e time on 18th M a r c h (for e x a m p l e c h a n g i n g the clock from 5:00 a m to 6:00 am) would m a k e people go to their d u ties (which s t a r t at 7:00 am) on 21st J u n e 1 h o u r a n d 14 min (new time) after t he s u n r i s e i n s t e a d of 2 h o u r s and 14 m i n (old time). This will tak e a d v a n t a g e of the s u n l i g h t a n d t he twilight.
Also t he people will be
coming h o m e earlier from work t h a n before and t herefore have m ore time to enjoy th e s ky lights a nd the twilight after dusk. This p r o c e s s would help th e c o u n t r y save large a m o u n t s of money. If we a s s u m e t h a t t h e r e are I million lamps, r a t e d 100 watts, t h a t would be switched off as people leave h o u s e s earlier by one hour , t h e n the a m o u n t of m o n e y t h a t c a n be saved is calculated as follows : a m o u n t saved in I ~ =
P o w e r of t h e l am p (W) x No. of l am ps x 32 {files} 1O0000O
i.e. a m o u n t saved in IK) =
(7)
(100W)(I000000){32) = 3200 I000000
This m e a n s t h a t the saving will be BD 3200 per h o u r i.e. n e a r l y 0.6 million B a h r a i n i Di na r s every six m o n t h s (since the time will be p u t b a c k to n o r m a l on 2 6 t h September). Also since the n u m b e r of h o u s e s in B a h r a i n are nearly 8 0 0 0 0 an d a h o u s e probably h a s 4 air conditioners on the average, t h e n if as a r e s u l t of a d v a n c i n g t he time (on 18th March and p u t t i n g it to n o r m a l on 2 8 t h September), people will switch off half of their air c o n d i t i o n e r s d u r i n g this h o u r .
The a m o u n t of m o n e y saved will be BD 5180 per d a y i.e. nearl y
1.0 million a y e a r (This is a s s u m i n g t h a t each air conditioner has a n electric power of 2 0 0 0 W) Monteich [8] r e p o r t e d t h a t the daily solar radiation can be found u s i n g the following relation : H=
2S o
Imax
(8)
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Gmax is the m a x i m u m solar irradiation recorded d u r i n g the y e a r (In B a h r a i n Imax -- 9 9 1 .5 Wm "2) and S O is the m a x i m u m s u n s h i n e d u r a t i o n [3].
2 c o s -I {-tan So = y-g
tan
8)
{9)
This m e a n s t h a t on 2 1 s t J u n e (So = 13.6 hrs.), t he daily average sol ar irradiation will be 8 5 8 8 . 8 Whm "2 (30.92 M j m 2 ) .
E q u a t i o n (8) was modified
for h ig h er latitude s w he r e in s u m m e r the dawn and the d u s k are prolonged. A full sine wave was us e d i.e. N
'
H = Imax
fo
2lnt~
sin I~-~o] d t = Imax -So ~, (10)
w h e r e t is t h e time a f t er s u n r i s e . This m e a n H' will be 6 7 4 2 . 2 Whm -2 (24.27 M J m "2) instead of 8588.8 W hm "2. Since the s u m of the civil twilight (morning a n d evening) in B a h r a i n is from 46 to 52 m i n u t e s , e q u a t i o n (8) r e p r e s e n t s B a h r a i n m or e a c c u r a t e l y t h a n e q u a t i o n (10). For example, t he daily a v e r a g e s ol a r i r r a d i a t i o n r e c o r d e d on 2 1 s t J u n e 1993 at B a h r a i n U n i v e r s i t y w a s 8 0 6 4 . 7 W h m -2 (29.03 MJm-2), t h i s is less t h a n t h e calculated H from e q u a t i o n (8) by 6.5% only. REFERENCES
1.
Acker A a n d J a s c h e k C, 1986, "Astronomical Method of Calculation, J o h n Wiley & Sons, Chichester, U.S.A.
.
A l n a s e r W E a n d Awadalla N S, 1991, Astronomical Cal cul at i ons for p r a y e r time a nd twilight, AI-Obykan Press, Saudi Arabia (in Arabic)
.
Central Statistics Organisation Statistical Abstract 1992, p. 401.
.
Duffle J A a n d B e c k m a n W A, 1992, Solar E n g i n e e r i n g of T h e r m a l
(1993), D i r e c t o r a t e of S t a t i s t i c s ,
Processes, 2nd Edition,, A Wiley Interscience Publication, J o h n Wiley & Sons, New York, U.S.A. .
C o o p e r P I, 1969, T he A bs or pt i on of solar r a d i a t i o n in sol ar stills, Solar Energy, Vol. 12, P. 3
.
Klein S A, 1977, C a l c u l a t i o n of the m o n t h l y average i n s o l a t i o n on tilted surface, Solar Energy, Vol. 24, P. 325.
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7.
S p e n c e r J W, 1971, Fourier Series R e p r e s e n a t i o n of the position of the sun, Search, Vol. 2 (No. 5), P. 172. Moneith J L and U n s o w o r t h M H, 1990, Principles of Environmental Physics, 2nd Edition, Edward Arnold, London, P. 45,
.
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Figure 1 :
T h e d a i l y v a r i a t i o n o f t h e s u m o f t h e m o r n i n g a n d e v e n i n g civil t w i l i g h t in B a h r a i n ( l a t i t u d e = 2 6 N, l o n g i t u d e = 5 0 ° E).