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Direct solar light transmission into single-span greenhouses
Agricultural Meteorology, 18(1977) 327--338 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
DIRECT SOLAR LIGHT TRANSMISSION HOUSES
INTO SINGLE-SPAN
GREEN-
T. KOZAI
College of Agriculture, University of Osaka Prefecture, Sakai, Osaka (Japan) (Received August 12, 1976; accepted February 21, 1977)
ABSTRACT Kozai, T., 1977. Direct solar light transmission into single-span greenhouses. Agric. Meteorol., 18: 327--338. A computer model has been developed for calculating the direct solar light transmission into an isolated, single-span greenhouse with non-diffusing covering materials, by which the effects of orientation of the greenhouse, latitude, and season on the spatial distribution of light and its daily variation in the greenhouse can be examined. This paper describes the applications of the model under various conditions. Some of the results obtained for the winter solstice are as follows. (1) In the greenhouse with a height of the side walls equal to one quarter of the width, the difference in transmissivity (the ratio of daily integrated direct solar light on the floor to the one outside) between East--West and North--South greenhouses is 22% in Amsterdam (52°20'N), 12% in Sapporo (43°03'N), and 7% in Tokyo (35°41'N). That is, the difference between the two orientations is larger at higher latitudes. The difference between the transmissivity in Amsterdam and that in Tokyo is more than 10% in a N--S house, but is less than 3% in an E--W house. (2) In the greenhouse with a height of the side walls half of the width, the difference between E--W and N--S greenhouses is less than 5% at any of the three latitudes. The maximum longitudinal spatial variation of the transmissivity over the floor is 40% in Amsterdam and 10% in Tokyo for the N--S house. (3) The reduction in transmissivity of a greenhouse due to the electric fans on the roofs for ventilation is less than 5%.
INTRODUCTION Recently, several workers have developed mathematical models which can predict the light transmission of greenhouses (Manbeck and Aldrich, 1967; Bowman, 1970; Deltour and Nisen, 1970; Smith and Kingham, 1970; Kingh a m a n d S m i t h , 1 9 7 1 ; S t o f f e r s , 1 9 7 1 ; T a k a k u r a e t al., 1 9 7 1 ; B a s i a u x e t al., 1973). While these models have been of great value for the design of greenhouses, the arrangement of structural members, the width and depth of these memb e r s , t h e r e s u l t i n g u n e v e n l i g h t d i s t r i b u t i o n in t h e g r e e n h o u s e h a v e n o t b e e n c o n s i d e r e d in m o s t o f t h e m o d e l s . T h i s is m a i n l y b e c a u s e o f t h e c o m p l e x i t y of the calculation. * Present address: College of Horticulture, Chiba University, Matsudo, Chiba 271, Japan.
328
In a preceding paper (Kozai, 1973), a numerical method was developed for calculating the direct solar light in an isolated, single-span, uncropped greenhouse with flat glass sheets as a function of the arrangement of structural members, the depth and width of structural members, and other factors influencing the transmission of light. Applications of the model to greenhouses having different structural arrangements clearly showed that structural members can account for 60--70% of the total light loss in the greenhouse, and that some relationships exist between the arrangement of structural members and the resulting distribution of transmitted solar light. In this paper, the model is applied to different greenhouse shapes at different latitudes. Furthermore, light transmission of a greenhouse with opaque electric fans for ventilation installed on the roofs or walls were simulated. The computed results have shown that the effect of orientation on the direct solar light transmission into a single-span greenhouse varies with the shape of the house, its structure, and the location (latitude) where the greenhouse is built. Some of the results may provide the basis for the design of greenhouse structure from the view of the light environment. The light transmission into multi-span greenhouses will be described in a later paper.
METHOD OF CALCULATION
The following basic steps are involved in the formulation of a numerical m e t h o d for calculating a distribution pattern of direct solar light reaching the floor level in an uncropped house at time t (sunrise < t < sunset), the distribution of daily totals of solar light on the floor, and the space average of the daily totals. (a) The altitude and azimuth of the sun at time t. (b) Direct solar light intensity JDH(t) on the earth's surface at time t. (c) The altitude and azimuth of the sun relative to a glass sheet k (k = 1, 2, 3 . . . . . n; n is the total number of glass sheets covering greenhouse surfaces). (d) Transmissivity TG(k, t) for the glass sheet ke. (e) Freely transmitting area of the glass sheet, considering structural members being solid. (f) The projection of the sunlit glass area o n t o the floor of a house. (g) The area of the projection intercepted by the floor of the house, RT(k, t). (h) The solar fight intensity at each point on the floor contributed from the glass sheet JID(x, y, k, t) (0 < x < length of the house, 0 < y < width of the house; JID(x, y, k, t) = TG(k, t) • JDH(t), if a point (x, y) on the floor is within the projection. Otherwise, JID(x, y, k, t) = 0 ). (i) By repeating steps (c) through (h) for all the glass sheets, we can o b ~ i n the average transmissivity A T(t) at time t by using the following expression:
329 n
A T ( t ) = ~_~ TG(k, t ) . R T ( k , t ) / F k=l
(1)
where F is the floor area of the house. (j) By repeating steps (a) through (i) for a whole day at certain time intervals, we can obtain the daily total of light relative to the one outside (called "transmissivity" in this paper), ID(x, y), at each point on the floor by the expression: sunset ID(x, y ) =
n
t =su nrise = sunset
(2)
~sun J D H ( t ) " At t = rise (k) Lastly, the space average of the daily integrals of light A D is then: AD =
l e i t h width ~.. ID(x, y ) / F X=O
(3)
y=o
A specification along the lines so far indicated, was developed into a F O R T R A N program for HITAC 8 7 0 0 / 8 8 0 0 machine with the cycle time of 500ns and m e m o r y size of 250 kW. The c o m p u t a t i o n for one aspect of the single-span house we have considered, for one site, for one day, takes about one minute. The instruction manual for the use of the c o m p u t e r program used in the present study is given by Kozai (1975). Further details of the computational procedures described above are shown by Kozai (1973). In order to formulate the computational procedures, the following assumptions were made: (1) internal reflection within a greenhouse is ignored; (2} only the direct solar light transmitted by the glass sheets is computed; (3) A clear glass sheet with parallel surfaces does not diffuse light. A calculation m e t h o d of internal reflection by direct solar light within a greenhouse, the transmissivity of a greenhouse for diffuse light, and the transmissivity of a greenhouse covered with diffusing materials have already been described with some c o m p u t e d results by Kozai and Sugi (1972a, b) and Basiaux et al. (1973). Overall transmissivity of a greenhouse for both direct and diffuse light, TT, is given by the equation: T T = M . D T + (1 -- M) • S T
(4)
where M is the ratio of direct to total solar light, D T the transmissivity of a house for direct light, and S T the transmissivity for diffuse light. S T is practically independent of both orientation and the position of the sun, if a uniformly radiating sky for diffuse light is assumed. The transmissivity may then be considered to be a constant of the greenhouse itself.
330
Therefore, in order to know the effects of orientation and latitude on the overall transmissivity of the house, the determination of the transmissivity for direct light is primarily important. DESCRIPTION OF THE GREENHOUSES
Twelve different types of single-span greenhouse were chosen as examples to illustrate the effects of shapes and structure on the light transmission into a greenhouse. Shapes and structures of these greenhouses are shown in Fig.1. All the greenhouses are 4 m wide and are glazed with clear plane glass 3 mm thick. Models AS, AM, and AT are assumed to be composed of glass MODELBS
MODELAS
MODELDS
MODELBM
MODEL AM
MODELDM
MODEL BT
MODEL AT
MODELCMG
MODELCMS
, llllllllllllllllllll/11 ~/
12
It
//'11
IJ
MODEL DT
Fig. 1. Shapes and structures of greenhouses used in the present simulation.
sheets only (i.e., without any structural members). These three houses were chosen to show the reduction of transmitted light due to glass sheets alone. The ridge height of Model AT is 4.5 m and Model AT corresponds to the house four times enlarged vertically from Models AS, or, to the house twice enlarged vertically from Model AM. The roofs of the three houses have slopes of 16 °, 32 °, and 52 °, respectively. The differences of transmitted light among these will indicate the effects of greenhouse shape on light transmission. Model BS, being the same as Model AS in shape, is assumed to be constructed from opaque structural members and glass sheets. The same relation exists between Models BM and AM, and Models BT and AT. The difference of transmitted light between Models BS and AS can then be attributed to the reduction of transmitted light due to the structural members. The length of Models DS, DM, and DT is 20 m, while that of Models AS,
331 AM, and AT is 10 m. Each of Models DS, DM, and DT, however, has the same cross-section as each of Models AS, AM, and AT, respectively. Comparisons of transmitted light of Model AS with Model DS, for example, will show how the average light transmission is affected by the length of a greenhouse. Electric fans for ventilation are assumed to be installed on both sides of the gable ends in Model CMG; on both of the side walls in Model CMS; on both sides of the roofs near the ridge in Model CMR, as shown in Fig.1. The depth of the fans was taken to be 0.5 m. The total area of the fans is 3.0 m 2, the same for the three houses. The structure of the houses is the same as Model BM, except that fans are installed. The effects of the fans and their positions on light transmission can be estimated by analysing these houses. The depth of the structural members was taken to be 3.0 cm and the width of vertical and inclined structural members to be 4.0 cm, but that of horizontal structural members was taken as 2.0 cm for Model BS; 4.0 cm for Models BM, CMG, CMS, and CMR; 8.0 cm for Model BT, giving the same frame ratio (total area of structural members divided by the total surface area) for Models BS, BM, and BT, which is equal to 0.175. The frame ratio (including the fan structures) for Models CMG, CMS, and CMR is equal to 0.200. The fans, therefore, cover only 2.5% of the total surface area in each greenhouse. PARAMETERS AND CONSTANTS To illustrate the influence of the latitude on the relationship between orientation and light transmission, three different places (latitudes) were chosen: Tokyo (35°41'N), Sapporo (43°03'N) in Japan, and Amsterdam ( 52 ° 20' N) in The Netherlands. Simulations have been conducted for the houses in E--W orientation (aspect 0 °) and N--S orientation (aspect 90°), and at 15 ° intervals between the two extreme orientations. The simulations were performed under outdoor lighting conditions of winter solstice (Dec. 22), spring equinox (March 21), and summer solstice (June 22). In this paper mainly the computed results for the winter solstice, the day of the lowest natural lighting, will be discussed. The diurnal course of direct light intensity JDH(t) at the three places, which were used as input data in the present simulation, were calculated by using well known formulas (e.g., Robinson, 1966), assuming the atmospheric transmission coefficients were 0.70 in the winter solstice, 0.64 in the spring equinox, and 0.62 in the summer solstice. The transmissivity of a clear glass sheet for direct light as a function of angle of incidence was calculated using Fresnel's equations (e.g., Takakura et al., 1971). When the angle of incidence changes from 0 ° to 90 ° at 10 ° intervals, the transmissivities of the glass 3 mm thick used in the present analyses are then respectively 0.86, 0.86, 0.86, 0.85, 0.85, 0.82, 0.77, 0.65, 0.40, and 0.00.
332
The floor of a house was conveniently divided into 1,600 grids (40 divisions along the ridge line and 40 divisions across the width, each grid thus being 0.25 (or 0.50) by 0.10 m and the light intensity at each grid point relative to the one outside was computed from sunrise to sunset at 10-min intervals to obtain the distribution of daily light integrals over the floor. A trapezoidal integration method was used to compute the dally integrals of light. The longitudinal sectional distribution of dally light integrals, which will be shown later, was obtained by plotting the average of 39 daily integrals across the floor at each place along the ridge line (the total number of the grid points is ( 4 0 - 1) • (40 -- 1) = 1541}. RESULTS AND DISCUSSION
Dependence of orientation effect on the latitude Fig.2 shows the transmissivity (AD in eq.3) of each of the Models DS, DM, and DT in December as a function of house orientation. In Model DS, the difference in the transmissivity between an E--W house (aspect 0 °) and a 90
m
MODEL DS 80
""~'-
L
70
6O 9
i
0o 0
I
~
30" -
I
L'"
....
60 °
90 °
-
MODEL DM
~ so ¢~ 70
~
60 0°
30 °
60
90 °
~ " 90
~ 80
.
'
70
MODEL DT
~~" - TOKYO ( 3 5 ° 4 1 ' N ) -----SAPPORO (43003'N)
..... 60
I 0o
E-W
AMSTERDAM I 30 °
,
"-.
(52"20'N) I 60 o
HOUSE ORIENTATION (DEC. 22)
90 o
N-S
Fig.2. Transmissivities o f greenhouses as a f u n c t i o n o f house orientation.
333
N--S house (aspect 90°) is 7% in Tokyo, 12% in Sapporo, and 22% in Amsterdam. This difference is smaller in Model DM and much smaller in Model DT than in Model DS. That is, the difference in transmissivity between an E--W house and a N--S house is larger in a lower ridge greenhouse (as in Model DS) than in a higher ridge one (as in Model DT) and the orientation effect is more pronounced at higher latitudes. Furthermore, the transmissivities of the three houses in E--W orientation are much the same at different latitudes, whereas those in N--S orientation are very different. It is also noticeable that the transmissivity of Model DS in N--S orientation is very low and is about 60%, even though it was assumed to be composed of clear glass sheets only (i.e., without structural members). The transmissivities of Models BS, BM, and BT in December are also presented as a function of house orientation in Fig.3. These houses are assumed 70 MODEL
50
-
-
BS
TOKYO
-----
SAPPORO
.....
AMSTERDAM
40
i
]
0 °
w
MODEL
v
""
[
._
,
60 °
30 o
70
"~.
90 °
BM
6o
50
-
-
TOKYO
AMSTERDAM
.....
~ 4o ~'-
70 MODEL
BT
60
50 -
-
TOKYO
. . . . .
40
AMSTERDAM I
O °
,
30 °
I 60 °
I 90 °
N-S
E-W HOUSE ORIENTATION (DEC.
22)
Fig.3. Transmissivities o f greenhouses as a f u n c t i o n o f h o u s e orientation.
to be composed of glass sheets and structural members, so that the transmissivities will be about 20% lower than those with glass sheets only. The length of the house is half that of Models DS, DM, and DT. Because of the
334
shorter length of the house, the orientation effect and its dependence on the latitude are somewhat ambiguous compared with those in Fig. 2. Kingham and Smith (1971) calculated the effects of orientation in England at aspects intermediate between E--W and N--S. They found that transmission losses in both timber vinery and alloy wide-span houses in winter are negligible up to 15 ° from E--W, and that the losses are still quite small at 30 ° from E--W, but that thereafter the transmission losses increase steeply. Similar results are obtained for Model BS, but n o t for Models BM and BT.
LonNtudinal light gradients along the length of a N--S house To explain why the transmissivity of a N--S house changes so much with the shape of house and latitude, we must consider the distribution of transmissivities over the greenhouse floor (e.g., ID(x, y) in eq.2) as ~/ell as the space averaged transmissivity. Fig.4 gives the longitudinal light gradients in Model AS, AM, and AT in N--S orientation at different latitudes. The transmissivity at each point on
~ODEL AS~-S ~ .OOSED ,~C; ~O!MODE~/A-~I-NO ,-~USE~-DEC 2~ . 90I MODELAT, N-S HOUSE,DEC~ 80
,o,o
v F-
//
~7o ~__SA,,ORO. . . . . .
(/
/ ) : ,o! . . . .
/
-2~ 6 0
i
,'
i
I
5
'°
60~,, /
,,' !
AMSTERDAM
'-~
//-
/' 60 --TOKYO -----SAPPORO ..... AMSTERDAM
~
5Q____l
I
50
lO lO DISTANCEFROMNORTHGABLEEND(meter)
1
I
I
5
10
Fig.4. Longitudinal light gradients in N--S houses at different latitudes at the winter solstice.
the floor along the length of the house is the average across the width. As can be seen from the figure, longitudinal light gradients are very steep in N S houses. Since these houses were assumed to be composed of only glass sheets, the non-uniformities of light are n o t caused b y shadows due to opaque structural members, but caused by differences in transmission of light due to different angles of incidence on the two slopes of the roof, the sides, and the gable ends. In each house, the high transmissivity on a south floor is attributable to the high transmission of g h s s s h e e t s of the south end, because the incidence angle of direct light t o t h e glass is very small in December. The incidence angles at n o o n in winter solstice, for example, are 1 4 ° in Amsterdam, 23 ° in Sapporo, and 3 2 ° in T o k y o . Therefore, since light transmission of glass
335 changes very slightly with an incidence angle less than 30 ° , there is almost no difference in the transmissivity on the southern part of the floor at the three different latitudes. On the other hand, the low transmissivity on a north floor is caused by low light transmission of the roofs. Besides, the transmissivity is strongly affected by the latitudes, because the light transmission of glass decreases more and more rapidly with the increase of incidence angle at angles greater than 40 ° . Incidence angles of direct light to the roofs of Model AS at noon in winter solstice, for instance, are 77 ° in Amsterdam, 68 ° in Sapporo, and 60 ° in Tokyo. In Amsterdam, the floor of Model AS north of the centre receives light transmitted only through the roofs and sides. However, the light transmitted through the south end reaches further and further north with higher latitudes, and with higher ridge greenhouses (such as Models AM and AT). Thus, the space average of the transmissivity should be dependent on the length of a house, even if the cross-sections of houses are the same. In a N--S house with infinite length, the average transmissivity is determined only by the light transmission of the roofs and, to a lesser extent, of the sides. These extreme values for a N--S house with the same cross-section as Model AS are given by the transmissivity of Model AS to the north floor (the left-hand side of each curve in Fig.4). On the contrary, in a N--S house with a relatively short length compared with the dimensions of the cross-section (as in Model AT), the latitude makes almost no difference to the transmissivity.
Daily variation of the space averaged transmissivity Fig. 5 shows calculations of daily variations of the space averaged transmissivities (AT(t) in eq.1) of N--S houses in winter solstice. The transmissivities in the afternoon are n o t shown in the figure, because they are symmetric to those of the morning in respect to noon. As described above, the transmissivity of Model BS in Amsterdam is clearly inferior to those in Tokyo and Sapporo. The transmissivity in Amsterdam was f o u n d to decrease steadily during the morning to a m i n i m u m of 42% around n o o n and then to increase again in the afternoon. The reduction of the transmissivity around noon is due to both the lower transmission of the light passing through the roofs and the extensive roof bar shadows. The effects of shadows due to Solid structural members on the transmissivity were analysed in detail by Kozai (1974). The transmissivity of Model BT in Amsterdam rapidly rises toward noon to a m a x i m u m of 67% when a high proportion of direct light begins to enter through the south end.
Transmissivity of a greenhouse with electric fans for ventilation It is becoming popular in Japan to use electric fans for ventilation to lower the air temperature inside a greenhouse when the temperature is too high for the growth of plants. It may then be questioned how much the ventilation fans reduce the light transmission into the greenhouse. Besides, they may
336 70 -
MODEL BS
60
50 x \
I
40
I
(''-,-
i
I
7O
MODEL B M N
v
5o . . r \
x~_
c~ 50 sr
I
~: 40 k-,-
0
MODEL 8T
t j
t
50
--TOKYO
(35°41'N)
-----SAPPORO
.....
4o
(43°03'N)
AMSTERDAH ( 5 2 ° 2 0 ' N )
I 9
I
I
10 11 TRUE SOLAR TIME ( h o u r )
(N-S ORIENTATION,
12
DEC. 22)
Fig. 5. Daily variations of space averaged transmmsivities of N--S houses at the winter so~tice. cause a non-uniform spatial distribution o f light over the floor, because they are usually the largest opaque members among the structure. The reduction of transmissivity due to shadows caused by the fans is presented in Fi~6. The positions of the fans installed are chosen as parameters, as shown in the figure. The transmissivity of a greenhouse without ventilation fans (Model BM) is also given for reference. In December, the transmissivities of Model CMG in N--S orientation and Model CMS in E--W orientation in Tokyo is about 5% lower than that of Model BM in the corresponding orientations. The transmissivity of Model
337
~
DEC. 22
70
o--o
MODEL BM
0 - - 0 MODEL CMG ~ - - X MODEL CMS ~ MODEL CMR
~ Oo
30 °
60 °
90 °
MAR. 21 >. 70
(..9 50 • ~:
,
0 o
I
L
I
L
30 °
60 °
90°
30°
60°
90° N-S
I.-- 701JUNE 22
6°T 50 0 o
E-W
HOUSE ORIENTATION (TOKYO, 35°41 'N)
Fig.6. Transmissivities orientation.
of greenhouses
with ventilation
f a n s , as a f u n c t i o n
of house
:
CMR is, however, almost the same as that of Model BM in any orientation, since most of the shadows of the fans installed on the ridge move outside the greenhouse floor when the sun's altitude is relatively low throughout the day. In June, the transmissivity of Model CMR is about 5% lower than that of Model BM in any orientation and the fans on the roofs may cause an uneven distribution of the transmissivity over the floor. On the other hand, the transmissivities of Models CMG and CMR are almost the same as that of Model BM in any orientation, since the light enters mainly through the roofs into the greenhouse when the sun's altitude is relatively high. Thus, the ventilation fans positioned on the sides and ends do not cause any serious reduction of transmissivity in summer. ACKNOWLEDGEMENTS The author is very much indebted to Professor Dr. K. Yabuki and Professor Dr. Y. Mihara for their critical advice and stimulating interest. Appreciation is also expressed to Dr. T. Alberda, Dr. J. Goudriaan, Dr. G. E. Bowman, and Mrs. Chadwick for critically reading and correcting the English text.
338 REFERENCES Basiaux, P., Deltour, J. and Nisen, A., 1973. Effect of diffusion properties of greenhouse covers on light balance in the greenhouse. Agric. Meteorol., 11: 357--372. Bowman, G. E., 1970. The transmission of diffuse light by a sloping roof. J. Agric. Eng. Res., 15: 100--105. Deltour, D. and Nisen, A., 1970. Les verres diffusants en couverture des serres. Bull. Rech. Agron. Gembloux, NS, V, 1: 232--255. Kingham, H. G. and Smith, C. V., 1971. Calculated glasshouse light transmission: the effect of orientation of single glasshouses. Exp. Horticult., 22: 1--8. Kozai, T., 1970. Studies on the solar irradiation in glasshouses (1). J. Agric. Meteorol., Tokyo, 26 : 123--130 (in Japanese). Kozai, T., 1973. Numerical experiments on light transmission into greenhouses (1). J. Agric. Meteorol., Tokyo, 2 9 : 1 7 9 - - 1 8 7 (in Japanese). Kozai, T., 1974. Numerical experiments on light transmission into greenhouses (2). J. Agric. Meteorol., Tokyo, 2 9 : 2 3 9 - - 2 4 8 (in Japanese). Kozai, T., 1975. A computer program for the calculation of the direct solar irradiation in single-span greenhouses. J. Agric. Meteorol., Tokyo, 31 : 89--94 (in Japanese). Kozai, T. and Sugi, J., 1972a. Studies on the solar irradiation in glasshouses (2). J. Agric. Meteorol., Tokyo, 2 7 : 1 0 5 - - 1 1 5 (in Japanese). Kozai, T. and Sugi, J., I972b. Studies on the solar irradiation in glasshouses (3). J. Agric. Meteorol., Tokyo, 2 8 : 7 9 - - 8 8 (in Japanese). Manbeck, H. B. and Aldrich, R. A., 1967. Analytical determination of direct visible solar energy transmitted by rigid plastic greenhouses. Trans. ASAE, i 0 : 564--567; 572. Robinson, N., 1966. Solar Radiation, Elsevier, Amsterdam, 347 pp. Smith, C. V. and Kingham, H. G., 1970. A contribution to glasshouse design. Agric. Meteorol., 8: 447--468. Society of the Agricultural Meteorology of Japan, 1975. A Guide to Greenhouse Design. Report of a working group on greenhouse design, 99 pp (in Japanese). Stoffers, J. A., 1971. Lichtdurchl~ssigkeit yon Gew~chsh~usern in Blockbauweise. Inst. Tuinbouwtech., Wageningen, Publ. 39. Takakura, T., Jordan, K. A. and Boyd, L. L., 1971. Dynamic simulation of plant growth and environment in the greenhouse. Trans. ASAE, 15: 964--971.
DIRECT SOLAR LIGHT TRANSMISSION HOUSES
INTO SINGLE-SPAN
GREEN-
T. KOZAI
College of Agriculture, University of Osaka Prefecture, Sakai, Osaka (Japan) (Received August 12, 1976; accepted February 21, 1977)
ABSTRACT Kozai, T., 1977. Direct solar light transmission into single-span greenhouses. Agric. Meteorol., 18: 327--338. A computer model has been developed for calculating the direct solar light transmission into an isolated, single-span greenhouse with non-diffusing covering materials, by which the effects of orientation of the greenhouse, latitude, and season on the spatial distribution of light and its daily variation in the greenhouse can be examined. This paper describes the applications of the model under various conditions. Some of the results obtained for the winter solstice are as follows. (1) In the greenhouse with a height of the side walls equal to one quarter of the width, the difference in transmissivity (the ratio of daily integrated direct solar light on the floor to the one outside) between East--West and North--South greenhouses is 22% in Amsterdam (52°20'N), 12% in Sapporo (43°03'N), and 7% in Tokyo (35°41'N). That is, the difference between the two orientations is larger at higher latitudes. The difference between the transmissivity in Amsterdam and that in Tokyo is more than 10% in a N--S house, but is less than 3% in an E--W house. (2) In the greenhouse with a height of the side walls half of the width, the difference between E--W and N--S greenhouses is less than 5% at any of the three latitudes. The maximum longitudinal spatial variation of the transmissivity over the floor is 40% in Amsterdam and 10% in Tokyo for the N--S house. (3) The reduction in transmissivity of a greenhouse due to the electric fans on the roofs for ventilation is less than 5%.
INTRODUCTION Recently, several workers have developed mathematical models which can predict the light transmission of greenhouses (Manbeck and Aldrich, 1967; Bowman, 1970; Deltour and Nisen, 1970; Smith and Kingham, 1970; Kingh a m a n d S m i t h , 1 9 7 1 ; S t o f f e r s , 1 9 7 1 ; T a k a k u r a e t al., 1 9 7 1 ; B a s i a u x e t al., 1973). While these models have been of great value for the design of greenhouses, the arrangement of structural members, the width and depth of these memb e r s , t h e r e s u l t i n g u n e v e n l i g h t d i s t r i b u t i o n in t h e g r e e n h o u s e h a v e n o t b e e n c o n s i d e r e d in m o s t o f t h e m o d e l s . T h i s is m a i n l y b e c a u s e o f t h e c o m p l e x i t y of the calculation. * Present address: College of Horticulture, Chiba University, Matsudo, Chiba 271, Japan.
328
In a preceding paper (Kozai, 1973), a numerical method was developed for calculating the direct solar light in an isolated, single-span, uncropped greenhouse with flat glass sheets as a function of the arrangement of structural members, the depth and width of structural members, and other factors influencing the transmission of light. Applications of the model to greenhouses having different structural arrangements clearly showed that structural members can account for 60--70% of the total light loss in the greenhouse, and that some relationships exist between the arrangement of structural members and the resulting distribution of transmitted solar light. In this paper, the model is applied to different greenhouse shapes at different latitudes. Furthermore, light transmission of a greenhouse with opaque electric fans for ventilation installed on the roofs or walls were simulated. The computed results have shown that the effect of orientation on the direct solar light transmission into a single-span greenhouse varies with the shape of the house, its structure, and the location (latitude) where the greenhouse is built. Some of the results may provide the basis for the design of greenhouse structure from the view of the light environment. The light transmission into multi-span greenhouses will be described in a later paper.
METHOD OF CALCULATION
The following basic steps are involved in the formulation of a numerical m e t h o d for calculating a distribution pattern of direct solar light reaching the floor level in an uncropped house at time t (sunrise < t < sunset), the distribution of daily totals of solar light on the floor, and the space average of the daily totals. (a) The altitude and azimuth of the sun at time t. (b) Direct solar light intensity JDH(t) on the earth's surface at time t. (c) The altitude and azimuth of the sun relative to a glass sheet k (k = 1, 2, 3 . . . . . n; n is the total number of glass sheets covering greenhouse surfaces). (d) Transmissivity TG(k, t) for the glass sheet ke. (e) Freely transmitting area of the glass sheet, considering structural members being solid. (f) The projection of the sunlit glass area o n t o the floor of a house. (g) The area of the projection intercepted by the floor of the house, RT(k, t). (h) The solar fight intensity at each point on the floor contributed from the glass sheet JID(x, y, k, t) (0 < x < length of the house, 0 < y < width of the house; JID(x, y, k, t) = TG(k, t) • JDH(t), if a point (x, y) on the floor is within the projection. Otherwise, JID(x, y, k, t) = 0 ). (i) By repeating steps (c) through (h) for all the glass sheets, we can o b ~ i n the average transmissivity A T(t) at time t by using the following expression:
329 n
A T ( t ) = ~_~ TG(k, t ) . R T ( k , t ) / F k=l
(1)
where F is the floor area of the house. (j) By repeating steps (a) through (i) for a whole day at certain time intervals, we can obtain the daily total of light relative to the one outside (called "transmissivity" in this paper), ID(x, y), at each point on the floor by the expression: sunset ID(x, y ) =
n
t =su nrise = sunset
(2)
~sun J D H ( t ) " At t = rise (k) Lastly, the space average of the daily integrals of light A D is then: AD =
l e i t h width ~.. ID(x, y ) / F X=O
(3)
y=o
A specification along the lines so far indicated, was developed into a F O R T R A N program for HITAC 8 7 0 0 / 8 8 0 0 machine with the cycle time of 500ns and m e m o r y size of 250 kW. The c o m p u t a t i o n for one aspect of the single-span house we have considered, for one site, for one day, takes about one minute. The instruction manual for the use of the c o m p u t e r program used in the present study is given by Kozai (1975). Further details of the computational procedures described above are shown by Kozai (1973). In order to formulate the computational procedures, the following assumptions were made: (1) internal reflection within a greenhouse is ignored; (2} only the direct solar light transmitted by the glass sheets is computed; (3) A clear glass sheet with parallel surfaces does not diffuse light. A calculation m e t h o d of internal reflection by direct solar light within a greenhouse, the transmissivity of a greenhouse for diffuse light, and the transmissivity of a greenhouse covered with diffusing materials have already been described with some c o m p u t e d results by Kozai and Sugi (1972a, b) and Basiaux et al. (1973). Overall transmissivity of a greenhouse for both direct and diffuse light, TT, is given by the equation: T T = M . D T + (1 -- M) • S T
(4)
where M is the ratio of direct to total solar light, D T the transmissivity of a house for direct light, and S T the transmissivity for diffuse light. S T is practically independent of both orientation and the position of the sun, if a uniformly radiating sky for diffuse light is assumed. The transmissivity may then be considered to be a constant of the greenhouse itself.
330
Therefore, in order to know the effects of orientation and latitude on the overall transmissivity of the house, the determination of the transmissivity for direct light is primarily important. DESCRIPTION OF THE GREENHOUSES
Twelve different types of single-span greenhouse were chosen as examples to illustrate the effects of shapes and structure on the light transmission into a greenhouse. Shapes and structures of these greenhouses are shown in Fig.1. All the greenhouses are 4 m wide and are glazed with clear plane glass 3 mm thick. Models AS, AM, and AT are assumed to be composed of glass MODELBS
MODELAS
MODELDS
MODELBM
MODEL AM
MODELDM
MODEL BT
MODEL AT
MODELCMG
MODELCMS
, llllllllllllllllllll/11 ~/
12
It
//'11
IJ
MODEL DT
Fig. 1. Shapes and structures of greenhouses used in the present simulation.
sheets only (i.e., without any structural members). These three houses were chosen to show the reduction of transmitted light due to glass sheets alone. The ridge height of Model AT is 4.5 m and Model AT corresponds to the house four times enlarged vertically from Models AS, or, to the house twice enlarged vertically from Model AM. The roofs of the three houses have slopes of 16 °, 32 °, and 52 °, respectively. The differences of transmitted light among these will indicate the effects of greenhouse shape on light transmission. Model BS, being the same as Model AS in shape, is assumed to be constructed from opaque structural members and glass sheets. The same relation exists between Models BM and AM, and Models BT and AT. The difference of transmitted light between Models BS and AS can then be attributed to the reduction of transmitted light due to the structural members. The length of Models DS, DM, and DT is 20 m, while that of Models AS,
331 AM, and AT is 10 m. Each of Models DS, DM, and DT, however, has the same cross-section as each of Models AS, AM, and AT, respectively. Comparisons of transmitted light of Model AS with Model DS, for example, will show how the average light transmission is affected by the length of a greenhouse. Electric fans for ventilation are assumed to be installed on both sides of the gable ends in Model CMG; on both of the side walls in Model CMS; on both sides of the roofs near the ridge in Model CMR, as shown in Fig.1. The depth of the fans was taken to be 0.5 m. The total area of the fans is 3.0 m 2, the same for the three houses. The structure of the houses is the same as Model BM, except that fans are installed. The effects of the fans and their positions on light transmission can be estimated by analysing these houses. The depth of the structural members was taken to be 3.0 cm and the width of vertical and inclined structural members to be 4.0 cm, but that of horizontal structural members was taken as 2.0 cm for Model BS; 4.0 cm for Models BM, CMG, CMS, and CMR; 8.0 cm for Model BT, giving the same frame ratio (total area of structural members divided by the total surface area) for Models BS, BM, and BT, which is equal to 0.175. The frame ratio (including the fan structures) for Models CMG, CMS, and CMR is equal to 0.200. The fans, therefore, cover only 2.5% of the total surface area in each greenhouse. PARAMETERS AND CONSTANTS To illustrate the influence of the latitude on the relationship between orientation and light transmission, three different places (latitudes) were chosen: Tokyo (35°41'N), Sapporo (43°03'N) in Japan, and Amsterdam ( 52 ° 20' N) in The Netherlands. Simulations have been conducted for the houses in E--W orientation (aspect 0 °) and N--S orientation (aspect 90°), and at 15 ° intervals between the two extreme orientations. The simulations were performed under outdoor lighting conditions of winter solstice (Dec. 22), spring equinox (March 21), and summer solstice (June 22). In this paper mainly the computed results for the winter solstice, the day of the lowest natural lighting, will be discussed. The diurnal course of direct light intensity JDH(t) at the three places, which were used as input data in the present simulation, were calculated by using well known formulas (e.g., Robinson, 1966), assuming the atmospheric transmission coefficients were 0.70 in the winter solstice, 0.64 in the spring equinox, and 0.62 in the summer solstice. The transmissivity of a clear glass sheet for direct light as a function of angle of incidence was calculated using Fresnel's equations (e.g., Takakura et al., 1971). When the angle of incidence changes from 0 ° to 90 ° at 10 ° intervals, the transmissivities of the glass 3 mm thick used in the present analyses are then respectively 0.86, 0.86, 0.86, 0.85, 0.85, 0.82, 0.77, 0.65, 0.40, and 0.00.
332
The floor of a house was conveniently divided into 1,600 grids (40 divisions along the ridge line and 40 divisions across the width, each grid thus being 0.25 (or 0.50) by 0.10 m and the light intensity at each grid point relative to the one outside was computed from sunrise to sunset at 10-min intervals to obtain the distribution of daily light integrals over the floor. A trapezoidal integration method was used to compute the dally integrals of light. The longitudinal sectional distribution of dally light integrals, which will be shown later, was obtained by plotting the average of 39 daily integrals across the floor at each place along the ridge line (the total number of the grid points is ( 4 0 - 1) • (40 -- 1) = 1541}. RESULTS AND DISCUSSION
Dependence of orientation effect on the latitude Fig.2 shows the transmissivity (AD in eq.3) of each of the Models DS, DM, and DT in December as a function of house orientation. In Model DS, the difference in the transmissivity between an E--W house (aspect 0 °) and a 90
m
MODEL DS 80
""~'-
L
70
6O 9
i
0o 0
I
~
30" -
I
L'"
....
60 °
90 °
-
MODEL DM
~ so ¢~ 70
~
60 0°
30 °
60
90 °
~ " 90
~ 80
.
'
70
MODEL DT
~~" - TOKYO ( 3 5 ° 4 1 ' N ) -----SAPPORO (43003'N)
..... 60
I 0o
E-W
AMSTERDAM I 30 °
,
"-.
(52"20'N) I 60 o
HOUSE ORIENTATION (DEC. 22)
90 o
N-S
Fig.2. Transmissivities o f greenhouses as a f u n c t i o n o f house orientation.
333
N--S house (aspect 90°) is 7% in Tokyo, 12% in Sapporo, and 22% in Amsterdam. This difference is smaller in Model DM and much smaller in Model DT than in Model DS. That is, the difference in transmissivity between an E--W house and a N--S house is larger in a lower ridge greenhouse (as in Model DS) than in a higher ridge one (as in Model DT) and the orientation effect is more pronounced at higher latitudes. Furthermore, the transmissivities of the three houses in E--W orientation are much the same at different latitudes, whereas those in N--S orientation are very different. It is also noticeable that the transmissivity of Model DS in N--S orientation is very low and is about 60%, even though it was assumed to be composed of clear glass sheets only (i.e., without structural members). The transmissivities of Models BS, BM, and BT in December are also presented as a function of house orientation in Fig.3. These houses are assumed 70 MODEL
50
-
-
BS
TOKYO
-----
SAPPORO
.....
AMSTERDAM
40
i
]
0 °
w
MODEL
v
""
[
._
,
60 °
30 o
70
"~.
90 °
BM
6o
50
-
-
TOKYO
AMSTERDAM
.....
~ 4o ~'-
70 MODEL
BT
60
50 -
-
TOKYO
. . . . .
40
AMSTERDAM I
O °
,
30 °
I 60 °
I 90 °
N-S
E-W HOUSE ORIENTATION (DEC.
22)
Fig.3. Transmissivities o f greenhouses as a f u n c t i o n o f h o u s e orientation.
to be composed of glass sheets and structural members, so that the transmissivities will be about 20% lower than those with glass sheets only. The length of the house is half that of Models DS, DM, and DT. Because of the
334
shorter length of the house, the orientation effect and its dependence on the latitude are somewhat ambiguous compared with those in Fig. 2. Kingham and Smith (1971) calculated the effects of orientation in England at aspects intermediate between E--W and N--S. They found that transmission losses in both timber vinery and alloy wide-span houses in winter are negligible up to 15 ° from E--W, and that the losses are still quite small at 30 ° from E--W, but that thereafter the transmission losses increase steeply. Similar results are obtained for Model BS, but n o t for Models BM and BT.
LonNtudinal light gradients along the length of a N--S house To explain why the transmissivity of a N--S house changes so much with the shape of house and latitude, we must consider the distribution of transmissivities over the greenhouse floor (e.g., ID(x, y) in eq.2) as ~/ell as the space averaged transmissivity. Fig.4 gives the longitudinal light gradients in Model AS, AM, and AT in N--S orientation at different latitudes. The transmissivity at each point on
~ODEL AS~-S ~ .OOSED ,~C; ~O!MODE~/A-~I-NO ,-~USE~-DEC 2~ . 90I MODELAT, N-S HOUSE,DEC~ 80
,o,o
v F-
//
~7o ~__SA,,ORO. . . . . .
(/
/ ) : ,o! . . . .
/
-2~ 6 0
i
,'
i
I
5
'°
60~,, /
,,' !
AMSTERDAM
'-~
//-
/' 60 --TOKYO -----SAPPORO ..... AMSTERDAM
~
5Q____l
I
50
lO lO DISTANCEFROMNORTHGABLEEND(meter)
1
I
I
5
10
Fig.4. Longitudinal light gradients in N--S houses at different latitudes at the winter solstice.
the floor along the length of the house is the average across the width. As can be seen from the figure, longitudinal light gradients are very steep in N S houses. Since these houses were assumed to be composed of only glass sheets, the non-uniformities of light are n o t caused b y shadows due to opaque structural members, but caused by differences in transmission of light due to different angles of incidence on the two slopes of the roof, the sides, and the gable ends. In each house, the high transmissivity on a south floor is attributable to the high transmission of g h s s s h e e t s of the south end, because the incidence angle of direct light t o t h e glass is very small in December. The incidence angles at n o o n in winter solstice, for example, are 1 4 ° in Amsterdam, 23 ° in Sapporo, and 3 2 ° in T o k y o . Therefore, since light transmission of glass
335 changes very slightly with an incidence angle less than 30 ° , there is almost no difference in the transmissivity on the southern part of the floor at the three different latitudes. On the other hand, the low transmissivity on a north floor is caused by low light transmission of the roofs. Besides, the transmissivity is strongly affected by the latitudes, because the light transmission of glass decreases more and more rapidly with the increase of incidence angle at angles greater than 40 ° . Incidence angles of direct light to the roofs of Model AS at noon in winter solstice, for instance, are 77 ° in Amsterdam, 68 ° in Sapporo, and 60 ° in Tokyo. In Amsterdam, the floor of Model AS north of the centre receives light transmitted only through the roofs and sides. However, the light transmitted through the south end reaches further and further north with higher latitudes, and with higher ridge greenhouses (such as Models AM and AT). Thus, the space average of the transmissivity should be dependent on the length of a house, even if the cross-sections of houses are the same. In a N--S house with infinite length, the average transmissivity is determined only by the light transmission of the roofs and, to a lesser extent, of the sides. These extreme values for a N--S house with the same cross-section as Model AS are given by the transmissivity of Model AS to the north floor (the left-hand side of each curve in Fig.4). On the contrary, in a N--S house with a relatively short length compared with the dimensions of the cross-section (as in Model AT), the latitude makes almost no difference to the transmissivity.
Daily variation of the space averaged transmissivity Fig. 5 shows calculations of daily variations of the space averaged transmissivities (AT(t) in eq.1) of N--S houses in winter solstice. The transmissivities in the afternoon are n o t shown in the figure, because they are symmetric to those of the morning in respect to noon. As described above, the transmissivity of Model BS in Amsterdam is clearly inferior to those in Tokyo and Sapporo. The transmissivity in Amsterdam was f o u n d to decrease steadily during the morning to a m i n i m u m of 42% around n o o n and then to increase again in the afternoon. The reduction of the transmissivity around noon is due to both the lower transmission of the light passing through the roofs and the extensive roof bar shadows. The effects of shadows due to Solid structural members on the transmissivity were analysed in detail by Kozai (1974). The transmissivity of Model BT in Amsterdam rapidly rises toward noon to a m a x i m u m of 67% when a high proportion of direct light begins to enter through the south end.
Transmissivity of a greenhouse with electric fans for ventilation It is becoming popular in Japan to use electric fans for ventilation to lower the air temperature inside a greenhouse when the temperature is too high for the growth of plants. It may then be questioned how much the ventilation fans reduce the light transmission into the greenhouse. Besides, they may
336 70 -
MODEL BS
60
50 x \
I
40
I
(''-,-
i
I
7O
MODEL B M N
v
5o . . r \
x~_
c~ 50 sr
I
~: 40 k-,-
0
MODEL 8T
t j
t
50
--TOKYO
(35°41'N)
-----SAPPORO
.....
4o
(43°03'N)
AMSTERDAH ( 5 2 ° 2 0 ' N )
I 9
I
I
10 11 TRUE SOLAR TIME ( h o u r )
(N-S ORIENTATION,
12
DEC. 22)
Fig. 5. Daily variations of space averaged transmmsivities of N--S houses at the winter so~tice. cause a non-uniform spatial distribution o f light over the floor, because they are usually the largest opaque members among the structure. The reduction of transmissivity due to shadows caused by the fans is presented in Fi~6. The positions of the fans installed are chosen as parameters, as shown in the figure. The transmissivity of a greenhouse without ventilation fans (Model BM) is also given for reference. In December, the transmissivities of Model CMG in N--S orientation and Model CMS in E--W orientation in Tokyo is about 5% lower than that of Model BM in the corresponding orientations. The transmissivity of Model
337
~
DEC. 22
70
o--o
MODEL BM
0 - - 0 MODEL CMG ~ - - X MODEL CMS ~ MODEL CMR
~ Oo
30 °
60 °
90 °
MAR. 21 >. 70
(..9 50 • ~:
,
0 o
I
L
I
L
30 °
60 °
90°
30°
60°
90° N-S
I.-- 701JUNE 22
6°T 50 0 o
E-W
HOUSE ORIENTATION (TOKYO, 35°41 'N)
Fig.6. Transmissivities orientation.
of greenhouses
with ventilation
f a n s , as a f u n c t i o n
of house
:
CMR is, however, almost the same as that of Model BM in any orientation, since most of the shadows of the fans installed on the ridge move outside the greenhouse floor when the sun's altitude is relatively low throughout the day. In June, the transmissivity of Model CMR is about 5% lower than that of Model BM in any orientation and the fans on the roofs may cause an uneven distribution of the transmissivity over the floor. On the other hand, the transmissivities of Models CMG and CMR are almost the same as that of Model BM in any orientation, since the light enters mainly through the roofs into the greenhouse when the sun's altitude is relatively high. Thus, the ventilation fans positioned on the sides and ends do not cause any serious reduction of transmissivity in summer. ACKNOWLEDGEMENTS The author is very much indebted to Professor Dr. K. Yabuki and Professor Dr. Y. Mihara for their critical advice and stimulating interest. Appreciation is also expressed to Dr. T. Alberda, Dr. J. Goudriaan, Dr. G. E. Bowman, and Mrs. Chadwick for critically reading and correcting the English text.
338 REFERENCES Basiaux, P., Deltour, J. and Nisen, A., 1973. Effect of diffusion properties of greenhouse covers on light balance in the greenhouse. Agric. Meteorol., 11: 357--372. Bowman, G. E., 1970. The transmission of diffuse light by a sloping roof. J. Agric. Eng. Res., 15: 100--105. Deltour, D. and Nisen, A., 1970. Les verres diffusants en couverture des serres. Bull. Rech. Agron. Gembloux, NS, V, 1: 232--255. Kingham, H. G. and Smith, C. V., 1971. Calculated glasshouse light transmission: the effect of orientation of single glasshouses. Exp. Horticult., 22: 1--8. Kozai, T., 1970. Studies on the solar irradiation in glasshouses (1). J. Agric. Meteorol., Tokyo, 26 : 123--130 (in Japanese). Kozai, T., 1973. Numerical experiments on light transmission into greenhouses (1). J. Agric. Meteorol., Tokyo, 2 9 : 1 7 9 - - 1 8 7 (in Japanese). Kozai, T., 1974. Numerical experiments on light transmission into greenhouses (2). J. Agric. Meteorol., Tokyo, 2 9 : 2 3 9 - - 2 4 8 (in Japanese). Kozai, T., 1975. A computer program for the calculation of the direct solar irradiation in single-span greenhouses. J. Agric. Meteorol., Tokyo, 31 : 89--94 (in Japanese). Kozai, T. and Sugi, J., 1972a. Studies on the solar irradiation in glasshouses (2). J. Agric. Meteorol., Tokyo, 2 7 : 1 0 5 - - 1 1 5 (in Japanese). Kozai, T. and Sugi, J., I972b. Studies on the solar irradiation in glasshouses (3). J. Agric. Meteorol., Tokyo, 2 8 : 7 9 - - 8 8 (in Japanese). Manbeck, H. B. and Aldrich, R. A., 1967. Analytical determination of direct visible solar energy transmitted by rigid plastic greenhouses. Trans. ASAE, i 0 : 564--567; 572. Robinson, N., 1966. Solar Radiation, Elsevier, Amsterdam, 347 pp. Smith, C. V. and Kingham, H. G., 1970. A contribution to glasshouse design. Agric. Meteorol., 8: 447--468. Society of the Agricultural Meteorology of Japan, 1975. A Guide to Greenhouse Design. Report of a working group on greenhouse design, 99 pp (in Japanese). Stoffers, J. A., 1971. Lichtdurchl~ssigkeit yon Gew~chsh~usern in Blockbauweise. Inst. Tuinbouwtech., Wageningen, Publ. 39. Takakura, T., Jordan, K. A. and Boyd, L. L., 1971. Dynamic simulation of plant growth and environment in the greenhouse. Trans. ASAE, 15: 964--971.