The effect of house length on the light transmissivity of single and multispan greenhouses

J. agric. Engng Res. (1985) 32, 163-172

The Effect of House Length on the Light Transmissivity Single and Multispan Greenhouses

of

D. L. CRITTEN* An investigation into the effect of gable ends on the light transmissivity of finite greenhouses is described. Initially, verification of a three-dimensional computer model of a greenhouse was carried out by comparing predicted results with those from an earlier experimental investigation, this used scaled physical models of single span greenhouses under direct and diffuse light conditions. The effect of increasing greenhouse length under both diffuse and direct sunlight conditions is then predicted for symmetric roofed E-W single and multispan houses, and for different combinations of two wall heights and two roof angles. Under diffuse light conditions, transmissivities near the gable end are shown to be up to 3% higher than those for corresponding infinitely long houses, and fall to within 1% of the asymptotic value at a distance of about 1 span width from the gable end. Under direct light conditions, transmissivities are shown to be different in detail for the two types of houses, for example, the influence of the gable penetrates more deeply into multispans (up to three span widths) than single spans up to two span widths), and functional differences occur along the house length. However, for E-W houses, the broad form of the gable influence on transmissivity is common to both house types, and shows an increasing penetration with increasing wall and roof angle, and a reduction of transmissivity near the gable at midwinter compared with an increase of midsummer. Tables are presented to indicate the house length required to provide at least a two-span length at the house centre over which the transmissivity is within 1% of that for an infinitely long house.

1.

Introduction

Commercial greenhouses are usually very long in comparison with their height and span width. As a result it is usually sufficient when creating greenhouse models to assume an

effectively infinite length, under which conditions at the ends have zero effect on mean house transmissivity. Several authors1,2,3 have adopted the approach for computer modelling, while Bowman’ carried out experimental work on single span roof models which were long in comparison with their width. Smith and Kingham and Thomas6 created computer models for small single span three-dimensional houses, but did not predict the detailed effect of the gable ends. Kozai et al.* however, comment briefly on the effect of house length on its average transmissivity. They note that, during the winter period in Osaka, Japan, the average direct light transmissivity is barely affected by house length for the E-W orientation, but decreases noticeably as the length increases if the orientation is N-S. Edwards and Lake’ qualitatively support these conclusions for a U.K. widespan house. To carry out full-scale experimental work on the transmissivity of commercial greenhouses, it is essential to keep the ground area of the house as small as possible to reduce capital and heating costs. It is, therefore, necessary to predict how far the gable end effects penetrate into the house, so a central zone can be defined over which the light levels may be assumed to be those of an infinite house. In addition, such information will be of value in predicting the variations of plant growth associated with light variations introduced by gable ends. This paper reports an investigation into the gable end effects on light transmissivity for single and multispan greenhouses, using a computer mode1*,s capable of evaluating both infinite and three-dimensional greenhouses. Briefly, at each of a number of surface elements within each transparent greenhouse plane, natural light falling on a greenhouse from either the sky vault, ?? NIAE,

Wrest Park, Silsoe, Bedford MK45 4HS, England

Received.

I5June1984; accepted mrewed

form 8 October 1984

163 OO21-8634/85/060163+

10%03.00/O

0 1985 The British Society for Research in Agncultural Engmrenng

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Fig. I. Average transmissivities from computer computer model beam conditions; 0 -e, experimental model (Schulze); 3% cl --O, house length/span =2.0; (a) 30” roof. N-S house;

and physical models for struciureless single span houses under direct ?? - --•, computer model (two dimensional); (three dimensional); added to results of Schulze to allow for losses. Wall height/span=OZ; (b) 50” roof, N-S house; (c) 30” roof, E-W house; (d) SO” roof, E-W house.

treated as a hemisphere, or the sun, was divided into solid angular elements. The light intensity was then modified, and reflected beams were generated due to the passage of the light through the greenhouse planes. The contributions of each transmitted beam and corresponding reflected beams to the floor irradiance were noted as a function of position within the floor, and summed over all angular and plane elements, thus resulting in a distributed floor irradiance pattern. The ratio of the internal to the external irradiance gives the transmissity. To obtain reasonable program execution times for the three-dimensional model, the greenhouse planes were subdivided into large elements, of the order of 0.1 spans. This has been shown to produce unacceptably large statistical scatter in point to point resultqB but when averaging over house width or length or both was carried out, scatter was found to be satisfactorily reduced. Initially, a check was made on the predictions of the three-dimensional model by comparison with the work of Schulze,‘O who carried out an extensive investigation into the light transmissivities of structureless glass models of short greenhouses. Confirmation of the predictions of Kozai et al.= for direct light was sought for the U.K. latitude, and, in addition, the gable end

165

D. L. CRITTEN

8411 0

IO

20

30

40

50

Roof angle Fig. 2. Average transmissivities from computer and physical models for structureless single span houses under uniform radiance overcast sky conditions; ?? ?? , computer model (three dimensional); ?? ----a, computer model (two dimensional) ; 0 0, experimental model (Schulze), 3% added to results of Schulze to allow for loss: wall height/span = 0.2; house length/span = 2.0.

effects at the equinox (21 March) and midsummer were investigated. Consideration of the sun’s path in the sky suggests that the gable ends may contribute a noticeable effect at midsummer in the E-W orientation, but have much less of an effect in the N-S orientation. In the winter period the opposite is true. The gable end length required to approach the infinite house transmissivity, may vary with both greenhouse roof and wall height and this is investigated.

2.

Comparison between three-dimensional computer model transmissivity predictions and the corresponding physical model results of Schulzelo

Using a parallel beam light source mounted on a swivel, Schulze simulated daily transmissivity measurements under direct light conditions at different times of the year, for various single span greenhouses. Due account was taken of the effects of light path length variations with the sun’s altitude. Computer predicted transmissivities for a selection of Schulze’s model greenhouses were obtained from both the two-dimensional infinite greenhouse and three-dimensional greenhouse models, and comparison between these results and those of Schulze are presented in Fig. Z(u)-(d) for direct light over the period December-June, and Fig. 2 for diffuse overcast light, the latter being for a uniform radiance sky, not a standard overcast radiance sky. Direct light transmissivities over the period June-December (not shown) are mirror images of the presented values. An overall 3% compensation for light absorption by the 2 mm glass is added to Schulze’s results. The two-dimensional infinite house transmissivities show marked differences during the winter period for the N-S house (Fig. I(a) and (b), and smaller but still noticeable differences during the summer period for the E-W house (Fig. I(c) and (d) .). To explain these variations, the transmissivity along the length of the 30” roof N-S house at midwinter and midsummer is shown in Fig. 3(a) and (b) . The presence of high reflected energies occupying a significant part of the total ground area increases the transmissivity relative to that for the infinitely long house.

LIGHT

TRANSMISSIVITY

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70

AND

HOUSE

LENGTH

I 2

I Distance

from northern

I

2

edge/span

Fig. 3. Three dimensional model transmissivity variations along the length of a 30” roof greenhouse, with N-S orientation at midwinter and midsummer, compared with infinite house transmissivity; PPP-, infinitely long house; length/ span = 2.0; wall height/span I 0.2; (a) 17 December; (b) 20 June.

The magnitude of the peaks, produced by the roof planes (Fig. 3(a)) and the north wall (Fig. 3(b)) should be viewed as semi-quantitative only because of the large greenhouse plane element sizes used (Section 1). 3.

The effects of gable ends on transmissivity in multispan houses

3.1 Computer model modiJication If it is assumed that the multispan houses under investigation contain a sufficient number of spans for the light transmission over their central spans to correspond to that for an infinite number of spans, then the calculation of transmissivity can be simplified. Since all spans are identical, then the contribution, transmitted or by reflection, of any span (n-m) to any other span n is the same as the contribution of span (n) to span (n+m) (m+ve or -ve). Therefore, if light input to span (n) only is specified, and the contribution to any span (n+m) obtained, the light actually entering span n is obtained by superimposing the contribution in span (n + m) on to span n, and summing over m. To predict the effects of reflections from the roofs, it is however still necessary to include a large number of spans in the model. For this purpose, each multispan was taken to contain 11 spans. For the typical dimensions of the houses investigated, the roof height (total height less wall height) was less than half the span width, so that rays with elevations of 5” or more will generally be correctly intercepted by the roof planes before striking the ground. Lower angle rays will generally be of lower intensity, and highly attenuated after passage through at least 10 planes (5 spans), and so the error due to the omission of further roof planes was assumed negligible. 3.2 Scope of investigation and results Four symmetric roofed E-W multispan houses have been investigated; these had wall heights of zero and 0.4 span, which were combined with roof angles of 26” and 45”. The house lengths

167

D. L. CRITTEN TABLE 1

Multispan greenhouse length required to obtain at least a two-span length within 1% of the infinite house transmissivity over the central region of the house on given date Totalgreenhouse length, spans Source of light House b

House a

IO0

96

House d

House c

0.4 45” 4 8 6 8

+ c

G

92

88 84 (b)

,

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from

centrelspan

Fig. 4. The effect of length on the transmissivity of an E-W multispan greenhouse under direct beam conditions, 21 December, transmissivity averaged over any central span, no structural members; ----, infinitely long house; 1, edge of house. House type ;:;

Wall htlspan 0 0.4 0 0.4

Roof angle 26” 26” 45” 45”

were increased in steps of one span width, until the transmissivity over a central region of two spans length was within 1% of the infinitely long house value. The latter was evaluated using the same greenhouse plan subdivision as that used for the finite length houses. With direct light, large elements have been found to produce errors of a few per cent in the absolute value of transmissivity. These were caused by errors in the amount of light reflected by the roof planes, particularly at grazing incidence,s which occurs, for example, during midwinter over a significant

168

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Fig. 5. The efSect of length on the transmissivity of an E-W multispan greenhouse under diffuse overcast conditions; Transmissivity averaged over central span, no structural members; ----, infinitely long house; I. edge of house; wall height/span = 0.4; roof angle = 45”.

(b)

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4

100

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3 centre/span

Fig. 6. The effect of length on the transmissivity of an E-W multispan greenhouse under direct beam conditions (a) 21 December, (b) 21 March, (c) 21 June; transmissivity over any central span, no structural members; ----, infinitely long house; I, edge of house; wall height/span = 0.4; roof angle = 45”.

part of the sun’s path about midday, so that the averaging out of errors is incomplete. By this technique, however, the approach to the asymptotic transmissivity is more correctly predicted, as the errors tend to remain constant in both cases. The four houses were evaluated under diffuse overcast conditions, and direct beam conditions on 21 December, 21 March and 21 June.

169

D. L. CRITTEN TABLE 2

Single span greenhouselength requiredto obtain at least a two-span length within 1% of the infinite house transmissivity over the central region of the house on given date Total greenhouse length spans Source of light

r

--mm---------_

64

60

c I

I

I

I

2

3

Distance from centre/span

Fig. 7. The efect on the transmissivity of an E-W single span house under diffuse overcast conditions; transmissivity averaged over span, no structural members; -P-p, infinitely long house; 1, edge of house; wall height/span = 0.4; roqf angle = 45”.

The results are summarized in Table 1 which, for the four houses, shows the total house length required to produce at least a two-span length at the centre of the house with the asymptotic transmissivity. Detailed results for direct light on 21 December are shown in Fig. 4, and an example of the diffuse overcast result is shown in Fig. 5 for the 0.4 wall height, 45” roof angle house. In addition, the results for this house on the three dates are compared in Fig. 6. For direct light, the form of the transmissivity variation along the house axis is quite complex. For example, on 21 December, a sharp maximum in transmissivity occurs near the gable end, which then falls away steadily towards the house centre. On 21 June, however, a broad minimum is produced, and, in addition, as the length increases, the transmissivity at intermediate lengths falls and then rises again, to approach the infinite house value.

170

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Fig. 8. The effect of length on the transmissivity of an E-W single span greenhouse under direct beam conditions, (a) 21 December, (6) 21 March. (c) 21 June; transmissivity averaged over span, no struciural members; -- - -, infinitely long house; 4 edge of house; wall height/span = 0.4; roof angle = 45”.

4.

The effects of gable ends on transmissivity in single span houses

Four symmetric roofed houses have been evaluated using the same roof angle and wall height: span ratio as used in the multispan investigation. The scope of the investigation was also exactly as described for the multispan, and the results are summarized in Table 2. The transmissivity of the single span house is less dependent on the gable end, and only the house with the high roof and walls requires more than four span lengths to give a two span asymptotic central region. Further, the functional variation of the transmissivity along the house is more regular than that of the multispan. Results for the 0.4 wall height/span, 45” roof angle house are shown in Fig. 7 for diffuse overcast light and in Fig. 8 for direct light on 21 December, 21 March and 21 June. On 21 December, the direct light transmissivity rises sharply, but monotonically, towards a steady value at a distance of about one span width from the gable end, while on 21 June, it falls more steadily to a level value at up to two spans from the gable end. For the other house dimensions, the form of the transmissivities are similar to those of Figs 7 and 8, but show smaller deviations from the asymptotic value. 5.

Discussion

Agreement between the functional form of the transmissivities from the physical model of Schulze and the three-dimensional computer model under direct and diffuse light conditions is satisfactory. For the finite models, the computer predictions for both diffuse and direct light conditions are always a few per cent higher than the physical model results, but this can be accounted for by, for example, inadequate allowance for the effects of absorption by the glass. The deviations from the infinite model over the winter period for direct light are particularly interesting, and the results predicted for the U.K. concur with the predictions of Kozai et al.= for E-W and

171

D. L. CRITTEN

N-S houses over the winter period in Japan. The variations in transmissivity along the length of the two-span length N-S house show the effects of reflection in the middle of the house at midwinter which accounts for the 20% higher average transmissivity compared with the infinitely long house. A similar E-W house during the summer period showed a 5% higher transmissivity than the infinite house, showing that length has some effect on transmissivity even for this orientation. The effects of the gable end on transmissivity show the multispan to behave differently in detail to the single span. For the former, light entering the gable generally penetrates deeper into the house, particularly with higher walls and roofs. For the 0.4 wall height/span, 45” roof multispan house under direct light conditions on 21 June, the transmissivity at the centre of a short house is less than that for an infinite house. This is not observed with the single span. These effects in the multispan may be due to losses by reflection from the roof planes, producing shallow reflected rays during the early and late parts of the day, but a detailed investigation of transmissivity as a function of time of day would be required to confirm this. More generally, there are similarities between the multispan and single span houses. For example, the effect of the gable ends penetrate further into the house with increasing wall and roof height, though the effect is minor under diffuse conditions. Also, under direct beam conditions, there is a reduction in transmissivity at the gable end at midwinter, compared with at increase of midsummer, while at the equinoxes the transmissivity is nearly constant (slightly increasing) towards the gable end. 6.

Conclusions

Predictions from the three-dimensional computer model have been successfully compared with results from physical models for single span houses. The prediction by Kozai et ~1.’that, under direct light conditions in midwinter, gable ends have little effect on transmissivity for E-W houses, but a marked effect for N-S houses has been verified for the latitude of the U.K. Under diffuse conditions there is little difference in gable end transmissivity between multispans and single spans. Near the gable end, transmissivities are up to 3% higher than the asymptote value, and approach to within 1% of the asymptotic after about one span penetration. For E-W houses under direct light conditions, the penetration of the effect of the gable end on transmissivity depends on the type of house, with larger penetration occurring for multispan than for single span houses, and also on wall height and roof angles with the penetration increasing with both. At midwinter, transmissivities generally rise as distance from the gable end increases, but at midsummer they fall. The approach to the asymptotic transmissivity with distance from the gable ends is more complex in multispans than in single spans. For the former, the transmissivity exhibits maxima (winter) or minima (summer), whereas for the latter it approaches the asymptotic transmissivity monotonically towards the greenhouse centre. For single span houses of wall height less than 0.4 span and roof angle less than 45”, a house length of six spans width will always provide a two span width asymptotic transmission at the centre of the house. For corresponding multispan houses, a length of eight spans width is required. Acknowledgement This paper is published

by permission

of the Director

of the NIAE.

REFERENCES

Stoffers, J. A. Lochtdoorlatendheid van met vlakka materialen bedeckte warenhuizen. Instituut voor Tuinbouwtechnik, Wageningen, June 1967 ’ Kozai, T.; Godriaan, J.; Kimura, M. Light Transmission and Photosynthesis in Greenhouses. Wageningen Centre for Agricultural Publishing and Documentation, 1978 ’

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LIGHT

’ Turkewitsch; Brundrett.

77(2)

TRANSMISSIVITY

Light levels in insulated greenhouses.

AND

HOUSE

LENGTH

Joint Meeting ASAE and CSAE, 1971

4 Bowman, G. E. The transmission of dzjiise light by a sloping roof. J. agric. Engng Res., 1970 15(2) lo&150 5 Smith, C. V.; Kingham, H. G. A contribution to glasshouse design. Agric. Meteorol. 1971 8 447468 6 Thomas, R. B. The use of specularly rejecting back walls in greenhouses. J. agric. Engng Res., 1978 23 85-97 ’ Edwards, R. I.; Lake, J. V. Transmission of solar radiation in a large span east-west glasshouse. J. agric. Engng Res., 1964 9(3) 245-249 *Critten, D. L. A computer model to calculate the daily light integral and transmissivity of a greenhouse. J. agric. Engng Res., 1983 28 62-76 s Critten, D. L. The evaluation of a computer model to calculate the daily light integral and transmissivity of a greenhouse. J. agric. Engng Res. (in press) lo Schulze, L. Lichteinstrahlung un glasgededete Gewiichshiiuser, (Solar radiation in glasshouses). Inst. Tech. Garrenb. Landw. tech. Hochsch, Hannover 1955 ‘I’ Critten, D. L. The e#ect of geometric conjiguration on the light transmission of greenhouses. J. agric. Engng Res., 1984 29