A RATIONAL APPROACH TO GREENHOUSE DESIGN

B J Bailey & G M Richardson AFRC Institute of Engineering Research Silsoe Bedford, U K

Abstract

Greenhouses are required to have high light transmission, adequate structural strength, low cost of construction and low operating costs, which, in northern latitudes, is predominantly the cost of heating. The best design represents the compromise between these conflicting requirements which gives the highest financial return to the grower, and this oan be established using optimisation techniques. These have been applied to a multispan film plastic covered greenhouse. The parameter varied in the optimisation process was the angle of inclination of a symmetric pitched roof. The influence of this angle on the total natural light transmitted into the greenhouse over a season was calculated using a validated prediction model. This was converted to tomato yield assuming yield is proportional to the light integral, and then to crop value. The influence of roof angle on heat loss and the cost of heating was established using simulation models. Finally the influence of roof angle on the material required to build a greenhouse to meet the wind loads required by the national greenhouse building code was determined. The roof angle which gave the biggest margin between crop value and heating cost, i.e. the most profitable greenhouse to operate, was modified by the cost of materials to provide the roof angle for which the greenhouse gave the highest net income over its life. The optimum roof angle is not an absolute value but is influenced by the prices of crop, fuel and construction materials.

1. Introduction

The requirements of a greenhouse are frequently stated to be high light transmission, adequate structural strength and low cost, and low heat consumption may also be included for greenhouses to be used at northern latitudes. In seeking to provide these attributes the greenhouse designer has to make compromises between requirements which are in conflict e.g. designing structural components to reduce light interception can increase costs and increasing the thermal resistance of the greenhouse can reduce light transmission. Making decisions on these compromises is difficult as the designer often has insufficient information to make a reasoned choice and must rely on experience. However, it is possible to make some of the choices in a rational way.

The basic aim of the grower is almost certainly to run his enterprise profitably, consequently the most economic greenhouse is the one which generates the greatest net income. Therefore, if the design options can be expressed in terms of their influences on net income, this can be used as an objective criterion for choosing between options. The aim of the designer is then to select those options

Acta Horticulturae 281, 1990 Greenhouse Construction, Design 111

which maximise net income but still provide a greenhouse of adequate strength. This procedure is an example of constrained optimisation, in which the objective function to be maximised is net income subject to the constraint of appropriate structural strength. This approach to greenhouse design was used by Kurata and Tachibana (1978), who optimised on the basis of maximum winter light transmission and minimum construction cost to provide a structure of adequate strength. In this paper the optimisation analysis is extended to include the influence of light transmission on crop yield and the energy required for heating, and the objective function is evaluated in monetary terms. The analysis is used to determine the optimum roof angle for an even span, multibay, film plastic covered greenhouse which maximises net income subject to the constraint of providing adequate strength.

2. Method

2.1 Greenhouse structure

A greenhouse has to withstand loads generated by wind and snow in addition to the deadloads of the greenhouse itself and possibly the crop. The relative magnitudes of the likely wind and snow loads depend on the geographic location and vary even within a single country. In addition local topography and exposure can have significant influences on the wind loads experienced within a small region. This analysis has been limited to windloads since, for a given site, the variation in wind load distribution with changing roof angle is likely to have the greatest effect on the largest bending moment occurring in the support structure.'

The analysis was carried out for a greenhouse constructed from tubular steel components as shown in figure 1. The span width was 6.4 m and the eaves height was 2.59 m. Each rafter in the duo-pitch roof was considered as an independent, simply supported member under a uniform load. As the height of the ridge is increased greater wind speeds are experienced and consequently the dynamic wind pressure increases. Also the pressure coefficient, which is multiplied by the dynamic wind pressure to give the final" wind load, is influenced by the slope of the roof. The design wind speeds for relatively sheltered greenhouses with this span width and eaves height and with 20 and 45° roof angles can vary between 24 and 26 m/s respectively, (CP3, 1972). The calculated loads were assumed to be uniformly distributed along the length of the rafter. The worst bending moment occurring in either the windward or leeward rafter was used to determine the maximum rafter spacing, (table 1). The tube used for most roof angles was 44.5 mm diameter. However, for the two steepest roofs the increased bending moments required the use of a larger diameter tube where the steel is distributed further from the neutral axis of the tube.

The cost of a 1000 m2 multi-bay film plastic covered greenhouse with a roof angle of 25° was taken to be £8000. The cost for other roof angles was obtained by determining the relative change in the amount of steel required for the rafters and using a steel price of £500/tonne. The variation of greenhouse cost with roof angle is shown in figure 2. In a more exposed site with higher wind speeds at ridge height the cost

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for the 25° reference house will increase and the sensitivity of cost to roof pitch will also increase. The same effect would also occur for a building of higher eaves height on a site with the same degree of shelter.

2.2 Light transmission and crop value

The light transmission of the greenhouse was calculated using the method developed by Critten (1987). This is based on calculations of the light losses for diffuse light and direct beam sunlight, caused by individual components in the greenhouse structure, (with e.g.) gutters, glazing bars, purlins, roof trusses and by the greenhouse cover. The losses for the covering material are calculated from a measured value of the diffuse light transmission. The individual light losses of the components are summed and combined with the cover losses to give values for the total loss under the two light conditions. These are combined using weighting factors for the expected proportions of diffuse and direct solar radiation derived from long term meteorological data, to give the total solar radiation transmitted into the greenhouse during the four seasons. This method was used to calculate the light transmission of the greenhouse described above for the four seasons using the rafter dimensions given in table 1. These values were used with 25 year average total solar radiation data for Kew (ISES 1976) to determine the solar radiation received in the greenhouse, figure 3.

The influence of light on crop value was assessed on the basis of the greenhouse being used to grow one crop of tomatoes per year. Cockshull (1988) reported that, during the production phase, the yield of tomatoes is proportional to the solar radiation integral. In an average year a tomato crop in the United Kingdom is expected to yield 36 kg/m2 with a value of £25/m2. The data depicted in figure 3 was used with this value to determine the yield for greenhouses with other roof angles, (table 2). Crop value was obtained using the average price for tomatoes in the UK.

2.3 Greenhouse heating

The greenhouse cover was taken to be a thermic polyethylene film with a far infra red transmissivity of 0.3. Heat transfer coefficients were determined by calculating the heat transferred to the inner surface by natural convection, thermal radiation and latent heat, and from the outer surface by forced convection and thermal radiation. The thermal resistance of the film plastic was small in comparison with the boundary layer resistances and so was not included, however, the loss of energy by thermal radiation through the cover was taken into account. The coefficient was calculated as a function of windspeed for an internal temperature of 15°C, an external temperature of 5°C and a sky temperature of 0°C. The resulting coefficients were used with average values of air temperature, solar radiation and windspeed recorded at Cardington, Bedfordshire between 1972 and 1977 to calculate the annual energy required to maintain a minimum greenhouse temperature of 16°C. The influence of roof angle on energy consumption is shown in figure 4 and the cost of heating is given in table 2.

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3. Results

The cost of the greenhouse occurs once, when the greenhouse is purchased, but the cost of heating occurs each year. To combine these expenditures the method of discounted cash flow was used. This takes into account the true valué of money in relation to time. A sum of money today is worth more than the same sum at some future date because it can earn interest in the intervening period, and if both capital and interest are invested compound interest is earned. Thus the present value of a sum to be spent, or received, at some future date is the amount which will, with compound interest at some specified rate, equal the sum in the future. In this paper the time period is taken as 10 years which is assumed to be the life of the greenhouse and the interest rate used was 10 %.

The annual costs can be separated into fixed and variable costs depending on whether they are influenced by the angle of the greenhouse roof. The former include the costs of plants, substrate, electricity, chemicals, biological control and the labour to raise and maintain the plants. The latter includes the costs of heating, and labour for harvesting and marketing. Information prepared by the U K Agricultural Development and Advisory Service (Personal communication, 1989) shows that for a greenhouse of 1000 m2 producing a tomato yield of 36 kg/m2, the annual fixed costs are £7.68/m2, the cost of harvesting is £6.29/m2

and marketing costs are 15 t of the market value. These variable costs were calculated for each roof angle using the appropriate crop value given in table 2. The net annual income given in table 2 the difference between the crop value and the sum of the fixed and variable costs of production. This was used with the discount factor of 6.145, appropriate for 10 years at an interest rate of 10 J, to give the present value of the annual income.

The capital cost of the greenhouse can also be considered as fixed and variable depending on whether they are affected by changes in the roof angle. Fixed costs include the environmental control equipment at £6.5/m2, and the cost of erection. The latter could be considered to increase with increasing roof angle but in the absence of firm information it was assumed to be constant at £3.0/m2. The only variable cost is the cost of the greenhouse itself. A recurrent cost is the replacement of the film plastic cover which was assumed to occur after 34 and 6§ years at a cost of £1.2/m2 on each occasion, after discounting these give a present value for the replacement costs of £1.5/m2.

The net present value of the income created by the greenhouse is the present value of the income minus the capital costs and the present value of the recurrent costs. The net present values for the different greenhouse roof angles are shown in figure 5.

4. Discussion

This analysis indicates that the most profitable film plastic covered greenhouse has a roof angle of 30°. This contrasts with current designs which have substantially flatter roofs. The net

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present values follow the variation in light integral closely, figures 3 & 5, and variations in heating and capital costs have only minor infuences. Consequently light transmission is the most important feature of the greenhouse. Most film plastic covered greenhouses have curved roofs and not pitched ones as considered in this paper. However, Critten (1988) showed that the light transmission of a curved roof greenhouse was equal to a pitched roof house in which the roof inclination was equal to the inclination of the chord from gutter to the centre of the curved roof. The results of figure 3 show the light transmitted by the covering material increases with roof angle but at angles of greater than 30° the benefits were offset by increased structural losses as the rafter spacing was reduced. This reduction was necessary in order to provide additional strength to withstand the increased wind loads. This suggests that, instead of using circular rafters, there would be an advantage in using asymmetric members which could better withstand the bending loads and have sections which intercepted less light.

The method outlined in this paper represents a way for the greenhouse designer to take an optimial approach to design. Its implementation does require information on the application of the greenhouse in order that appropriate crop values and heating costs can be used. The analysis can also be used to test the sensitivity of a greenhouse design to possible changes in costs.

References

Kurata, K., Tachibana, K., 1978. Greenhouse design with the optimisation technique. Acta hort. 37: 21-30

Code of Practice CP3, 1972. Code of basic data for the design of buildings, Chapter V : Loading : Part 2. Br. Stand. Inst. London

Critten, D.L., 1987. A design guide for calculating light transmission losses in multispan greenhouses and plastic tunnels. Rep. No. 23,' AFRC Inst. Engng Res, Silsoe

ISES, 1976. Solar Energy, a UK assessment. Rep. of UK Section Intl. Solar Energy Society

Critten, D.L., 1988. Light transmission through structureless multispan greenhouse roofs of "Gothic arch" cross section. J. agric. Engng Res. JU_: 319-325

Cockshull, K.E., 1988. The integration of plant physiology with physical changes in greenhouse climate. Acta hort. .229, 113-123

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Table 1 - Rafter spacing

Roof angle rafter spacing tube dia deg m mm

15 1 . 5 1 4 4 . 5 2 0 2 . 07 n

25 2 . 4 9 ti

3 0 2 . 1 9 H

35 1 . 7 2 n

4 0 1 . 7 1 6 0 . 3 45 1 . 0 0 ti

Table 2 - Influence of greenhouse roof angle on annual income

Angle Light Crop Energy Heating Variable Net received value used cost production

costs income*

deg GJ/m2 £/m2 GJ/m2 £/m2 £/m2 £/m2

15 1.918 22.579 1.853 4.046 5.443 5.346 20 2.016 23.671 1.871 4.101 5.719 6.167 25 2.097 24.621 1.897- 4.158 5.948 6.831 30 2.112 24.798 1.932 4.235 5.991 6.888 35 2.106 24.727 1.975 4.329 5.819 6.895 40 2.055 24.128 2.031 4.452 5.678 6.314 45 1.869 21.944 2.106 4.615 5.302 4.343

• includes fixed production costs of £7.684/m2

Fig. 1. Components of greenhouse

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74

Cost £/m2

44.5mm tube

60.3mm tube

20 40 Roof angle, deg

60

2.5,

2.0.

1.5.

1.0.

0.5

0.0

Annual light integral GJ/m2

^ — ^ ^ V Light received » inside greenhouse

Loss due to structure

20 40 Roof angle, deg

60

Fig. 3. Light transmitted into Fig. 2. Capital cost of greenhouse greenhouse and modes of light loss

Energy consumption GJ/m2

20 40 Roof angle, deg

60

30 -,

25

20.

15-

10

5-I

Net present value £/m2

20 40 Roof angle, deg

60

Fig. 5. Total net income provided Fig. 4. Annual emergy consumption by greenhouse

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