Daylighting design with lightscoop skylights: Towards an optimization of shape under overcast sky conditions

1  Daylighting design with lightscoop skylights: Towards an optimization of shape under overcast sky conditions Authors’ names and affiliations: Ignacio Acosta, University of Seville, Lecturer PhD. Corresponding Author. Jaime Navarro, University of Seville, Professor PhD. Juan José Sendra, University of Seville, Professor PhD. Corresponding Author: Ignacio Acosta, University of Seville, Corresponding Author Tel. number: 0034647550654 Email: [email protected] Permanent address: Institute of Architecture and Building Science, University of Seville, 41012 Seville. Spain Abstract The main aim of this article is to determine a suitable shape for lightscoop skylights, whose main characteristic is a vertical opening oriented in the opposite direction to the solar trajectory, in order to ensure maximum illuminance on the work plane within a room. This type of skylight has a reflector, which is usually rectangular, curved or sawtooth shape, behind the vertical opening. Lightscape 3.2 software was used to carry out the simulations of different rooms with three different shapes of skylight. After trials, it was finally concluded that for this type of skylight, considering a height/width ratio of 4/3, the curved shape produces an increase of average daylight factors close to 3.5% compared with the rectangular shape, while the sawtooth shape produces a decrease of average daylight factors close to 3.5% in a room under overcast sky conditions. Keywords: skylight, lightscoop, daylighting, overcast sky, lighting software. 1. Introduction and objective The use of skylights is frequent in modern architecture since these allow access to daylight in rooms lacking façades, while providing homogeneous lighting over the horizontal plane. Most researchers in this field have based their methodology on classic treatises on daylighting [1] and computer simulation [2]. Lightscoops, with their characteristic vertical opening oriented in opposition to the solar trajectory, are frequently used in museum exhibition rooms, library reading rooms, etc. The term lightscoop should be further clarified, since this type of skylight has been described using a variety of architectural terms. The most widely used definition is provided by Lam [3], who defines this type of skylight as a lightscoop if the opening is oriented towards the open sky, or as a sunscoop if oriented towards the solar trajectory. The shape of the reflector can also be a conditioning factor in the definition of this type of skylight. The CIBSE lighting guide points out [4] that there is a great variety of rooflights depending on the position of the opening and shape of the reflector, most notably the sawtooth and monitor rooflight. This guide also shows the most common advantages and disadvantages of each skylight shape, although it does not quantify the differences between them. Despite the fact that lightscoops are a frequent feature in contemporary architecture, few studies have been carried out on the luminous distribution they generate. Lam is one of the few authors to carry out in-depth studies on their behaviour for daylighting, concluding that lightscoops provide the lowest and steadiest light levels with minimum annual heat gain. In the 2  conclusion to his research with scaled models, Lam suggests different light distributions depending on the shape of the lightscoop reflector. Among recent studies on lightscoops and sunscoops it is worth calling attention to research carried out by García-Hansen et al. [5]. Using 1:20 scale models and different skylight types, the authors used nine photometers to measure luminous distribution within the rooms. One of the latest studies on lightscoops was carried out by Acosta et al. [6,7], and analyzed the correct height/width ratio of the skylight reflector for maximizing lighting inside a room. Using Lightscape 3.2 and Daysim 3.1 simulation programs, the authors concluded that a lightscoop with a rectangular reflector and a 4/3 height/width ratio provided the highest daylight factors under overcast sky conditions. Despite the fact that numerous studies have shown the efficiency of this type of skylight, little attention appears to have been paid to the efficiency of the design in making the most of daylight. The main aim of this article is to determine a suitable shape for lightscoop skylights, in order to obtain higher daylight factors within the spaces they light. 2. Description of Methodology for Calculation 2.1. Choosing the calculation conditions By definition, the calculation of daylight factor components is carried out considering an unobstructed sky of assumed or known illuminance distribution, excluding direct sunlight. The definition of traditional overcast sky is used to calculate the sky component. The overcast sky model, used in the methodology, is that defined by Moon-Spencer [8], where the luminance values are distributed according to the following: L = LZ·(1+2sin)/3 where “LZ” is the luminance at the zenith of the sky vault and “” the projection angle. This implies that the lowest luminance value in an overcast sky vault occurs on the horizon, and is equivalent to a third of the maximum luminance at the zenith: L0 = LZ /3 The formulation established by Moon-Spencer corresponds to the definition of overcast sky accepted by the CIE [9], which is known as traditional overcast sky: Sky type 16. 3  2.2. Choosing the calculation program The analysis of the daylight factors was carried out using simulation program Lightscape 3.2, which calculates luminous distribution using a radiosity process. Several studies have confirmed the correct behaviour of this calculation program [10,11]. The calculation parameters used by this program are shown in table 1. Lightscape 3.2 Sky Conditions Overcast Sky Mesh Spacing Min 0.10 m Max 0.20 m Subdivision Contrast Threshold 0.65 Skylight Accuracy 0.60 Source Direct Source Min 0.12 Subdivision Accuracy 0.42 Indirect Source Min 0.24 Subdivision Accuracy 0.42 Shadow Grid Size Five Tolerances Length 0.0005 Ray Offset 0.001 Initialization Min Area 0.01 Table 1: Parameters of the calculation program. 2.3. Choosing the calculation model The model used in the trials to determine the efficiency of different shapes of lightscoop reflectors is a room with variable floor size and a height of 4.5 m, with a skylight in the centre of the ceiling. Three different sizes of floor plan were considered to ensure general conclusions that did not depend on room measurements: 1. Square room, 9 m wide by 9 m long. 2. Rectangular room, 12 m wide by 6 m long. 3. Rectangular room, 6 m wide by 12 m long. Three different shapes of skylight (R, C and S) were studied for each room and defined according to floor measurements (1, 2 and 3): R. Rectangular skylight C. Curved skylight S. Sawtooth skylight Figure 1 represents the different room and skylight shape combinations. 4  Figure 1: Calculation models. The skylight on the roof is 6 m long with variable height (Y) and width (X) (fig. 2). The roof and walls of the skylight are 0.20 m thick. The work plane on which daylight factors are studied is located 1.00 m above the floor. The model represents the typical dimensions of a museum or library room. The low height of the ceiling in relation to the measurements of the space allows a distribution of light that is largely dependent on the Sky Component and is therefore suitable for analyzing the efficiency of the skylight proportions under study. Figure 2: Characteristics of the calculation models. To adapt the results to the skylight proportions the optical properties of surfaces –reflection, inter-reflection and transmission– are considered invariable. The inter-reflection of all the surfaces is completely diffuse under Lambert’s cosine law, and as a result the light falling on a surface is reflected in all directions. Each surface has a different reflection index: the ceiling and skylight have an index of 0.9, the walls 0.7, and the floor 0.5, normal values in the design of interiors. Nine different proportions were analyzed for each shape of reflector, considering a length for the variable “X” of 1 to 5 m, as well as a value for variable “Y” of 1 to 5 m. As a result, the surface of the horizontal area corresponding to the hole in the 5  ceiling, and that of the vertical area corresponding to the opening of the skylight always add up to the same surface area for all models. This is to say, 9 skylight measurements were analyzed for each of the 3 shapes studied, taking into consideration 3 different room models, totalling 81 trials (fig. 3). Figure 3: Longitudinal section of trial models. The maximum, average, and minimum values of the daylight factors observed on the work plane were simulated using the calculation model. These values were the result both of the Sky Component and the Internally Reflected Component. All the definitions used in this article are included in the CIE glossary [12]. 6  3. Calculation 3.1. Calculation of the skylight shapes for a square room, 9 m wide by 9 m long 3.1.1. Daylight factors calculation The first trial analyzed a square room with a lightscoop skylight in the centre of the ceiling and a variable reflector shape (models 1R, 1C and 1S as represented in fig. 1). The maximum, average, and minimum daylight factors on the work plane were calculated following the methodology described and considering 9 ratios for each skylight shape (fig. 3). Table 2 shows the results obtained. Grey-shaded cells represent the highest daylight factors for each skylight shape. SQUARE ROOM 9 x 9 RECTANGULAR SKYLIGHT (1R) HEIGHT/WIDTH RATIO DAYLIGHT FACTOR MAX AVE MIN 1x5 2.38% 1.51% 0.47% 1.5x4.5 3.49% 2.22% 0.71% 2x4 4.50% 2.84% 0.94% 2.5x3.5 5.27% 3.31% 1.14% 3x3 5.69% 3.58% 1.28% 3.5x2.5 5.80% 3.62% 1.30% 4x2 5.48% 3.36% 1.17% 4.5x1.5 4.79% 2.79% 0.95% 5x1 3.65% 1.97% 0.70% CURVED SKYLIGHT (1C) HEIGHT/WIDTH RATIO DAYLIGHT FACTOR MAX AVE MIN 1x5 2.38% 1.53% 0.48% 1.5x4.5 3.55% 2.25% 0.73% 2x4 4.62% 2.89% 0.93% 2.5x3.5 5.48% 3.42% 1.17% 3x3 6.02% 3.73% 1.29% 3.5x2.5 6.08% 3.75% 1.32% 4x2 5.70% 3.44% 1.19% 4.5x1.5 4.86% 2.84% 0.94% 5x1 3.66% 1.99% 0.68% SAWTOOTH SKYLIGHT (1S) HEIGHT/WIDTH RATIO DAYLIGHT FACTOR MAX AVE MIN 1x5 2.34% 1.51% 0.48% 1.5x4.5 3.45% 2.21% 0.70% 2x4 4.45% 2.82% 0.89% 2.5x3.5 5.18% 3.25% 1.00% 3x3 5.61% 3.47% 1.09% 3.5x2.5 5.76% 3.49% 1.09% 4x2 5.47% 3.22% 1.03% 4.5x1.5 4.75% 2.67% 0.83% 5x1 3.65% 1.90% 0.59% Table 2: Maximum, average and minimum daylight factors on the work plane. Room of 9 x 9 x 4.5 m. Rectangular, curved and sawtooth skylights 6 m long with a variable height and width. 7  3.1.2. Relative difference calculation Figure 4 shows the relative difference of the average daylight factors on the work plane produced by the different skylight shapes. The relative difference is calculated by comparing the different skylight shapes with the same height/width ratio, taking the average daylight factors obtained from the skylight with a rectangular reflector as reference value. Figure 4: Relative difference of the average daylight factors on the work plane. Room of 9 x 9 x 4.5 m. Rectangular, curved and sawtooth skylights 6 m long with variable height and width. 3.1.3. Analysis of results From table 2 it can be deduced that regardless of the shape of the reflector, the highest average daylight factors are found for a skylight measuring 3.5 x 2.5 m with a height/width ratio of approximately 4/3. As observed in figure 4, the curved reflector produces an increase in the average daylight factors over those obtained with the rectangular reflector. This difference increases in the case of the room with a 3 x 3 m skylight and a reflector height/width ratio of 1/1, reaching a maximum relative difference of 4.27%. In contrast, the sawtooth reflector brings about a decrease when compared with the average daylight factors obtained with the rectangular reflector. This difference is greater for the room with a 4.5 x 1.5 m skylight, with a reflector height/width ratio of 3/1, where a maximum relative difference of 4.17% is reached. Finally, it was observed that in the case of a 3.5 x 2.5 m skylight with a height/width ratio of approximately 4/3, the curved reflector produces a 3.55% increase of the average daylight factors over those found for rectangular shapes, while the sawtooth reflector causes a decrease of 3.55%. These assessments were carried out on the work plane of a square room using the method described under overcast sky conditions. 8  3.2. Calculation of the skylight shapes for a rectangular room, 12 m wide by 6 m long 3.2.1. Daylight factor calculation The second trial analyzed a rectangular floor plan room measuring 12 m wide by 6 m long. The room has a lightscoop skylight in the centre of the ceiling, and variable reflector shapes (models 2R, 2C and 2S as represented in fig. 1). The maximum, average and minimum daylight factors on the work plane were calculated considering 9 measurements for each skylight shape and following the method described (fig. 3). The results obtained are shown in table 3. Grey-shaded cells represent the highest daylight factors for each skylight shape. RECTANGULAR ROOM 12 x 6 RECTANGULAR SKYLIGHT (2R) HEIGHT/WIDTH RATIO DAYLIGHT FACTOR MAX AVE MIN 1x5 2.49% 1.51% 0.42% 1.5x4.5 3.69% 2.23% 0.64% 2x4 4.77% 2.87% 0.84% 2.5x3.5 5.61% 3.36% 1.03% 3x3 6.08% 3.63% 1.11% 3.5x2.5 6.21% 3.66% 1.14% 4x2 5.87% 3.38% 1.06% 4.5x1.5 5.06% 2.79% 0.84% 5x1 3.90% 1.99% 0.59% CURVED SKYLIGHT (2C) HEIGHT/WIDTH RATIO DAYLIGHT FACTOR MAX AVE MIN 1x5 2.51% 1.51% 0.42% 1.5x4.5 3.75% 2.25% 0.63% 2x4 4.87% 2.91% 0.82% 2.5x3.5 5.81% 3.45% 1.03% 3x3 6.42% 3.77% 1.13% 3.5x2.5 6.50% 3.78% 1.16% 4x2 6.09% 3.46% 1.08% 4.5x1.5 5.20% 2.84% 0.90% 5x1 3.91% 2.01% 0.57% SAWTOOTH SKYLIGHT (2S) HEIGHT/WIDTH RATIO DAYLIGHT FACTOR MAX AVE MIN 1x5 2.51% 1.51% 0.43% 1.5x4.5 3.66% 2.22% 0.59% 2x4 4.70% 2.82% 0.75% 2.5x3.5 5.53% 3.29% 0.86% 3x3 6.03% 3.52% 0.95% 3.5x2.5 6.14% 3.52% 0.96% 4x2 5.83% 3.23% 0.90% 4.5x1.5 5.07% 2.67% 0.78% 5x1 3.89% 1.91% 0.56% Table 3: Maximum, average and minimum daylight factors on the work plane. Room of 12 x 6 x 4.5 m. Rectangular, curved and sawtooth skylights 6 m long with variable height and width. 9  3.2.2. Relative difference calculation Figure 5 shows the relative difference of the average daylight factors on the work plane produced by the different skylight shapes. The relative difference between different skylight shapes with the same height/width ratio is calculated, taking the average daylight factors obtained with the skylight with a rectangular reflector as a reference value. Figure 5: Relative difference of the average daylight factors on the work plane. Room of 12 x 6 x 4.5 m. Rectangular, curved and sawtooth skylight 6 m long with variable height and width. 3.2.3. Analysis of results As was observed in the previous trial and described in table 3, the highest average daylight factors for the rectangular floor plan of the calculation model, regardless of the shape of reflector, were observed for a 3.5 x 2.5 m skylight with a height/width ratio of close to 4/3. In addition, the curved reflector produced an increase of the average daylight factors over those observed in the room with a rectangular reflector. This is greater in the room with a 3 x 3 m skylight and a height/width ratio of 1/1. The maximum relative difference for the rectangular room is 3.34%, substantially less than that observed between both skylights in the square room. In contrast, the sawtooth reflector causes a decrease of the average daylight factors over those obtained with the rectangular reflector. As in the previous trial, this difference is greater for the room with a 4.5 x 1.5 m skylight and a height/width ratio of 3/1. The maximum relative difference in the model under study is 4.38%, similar to that observed in a room with a square floor plan. Finally, it was observed that, with a 3.5 x 2.5 m skylight with a height/width ratio of close to 4/3, the curved reflector produced a 3.34% increase of average daylight factors over the rectangular reflector, while the sawtooth reflector generated a decrease of 3.85%. As expressed in previous trials, these assessments were carried out on the work plane of a rectangular room under overcast sky conditions.