Towards an analysis of the performance of monitor skylights under overcast sky conditions

1  Towards an analysis of the performance of monitor skylights under overcast sky conditions Authors’ names and affiliations: Ignacio Acosta, Instituto Universitario de Arquitectura y Ciencias de la Construcción, Lecturer PhD. Jaime Navarro, Instituto Universitario de Arquitectura y Ciencias de la Construcción, Professor PhD. Juan José Sendra, Instituto Universitario de Arquitectura y Ciencias de la Construcción, Professor PhD. Corresponding Author: Ignacio Acosta, University of Seville, Corresponding Author Tel. number: 0034647550654 Email: [email protected] Permanent address: Instituto Universitario de Arquitectura y Ciencias de la Construcción, Escuela Técnica Superior de Arquitectura, Universidad de Sevilla, 41012 Sevilla (Spain). Abstract The main aim of this article is to determine a suitable proportion and shape for monitor skylights, which are characterized mainly by two opposite vertical openings fixed by a reflector of variable shape, for ensuring maximum illuminance on the work plane within a room. This type of skylight has a reflector, which is usually rectangular, slanted, sawtooth or curved, behind the vertical openings. Lightscape 3.2 software was used to carry out the simulations of different rooms with four different skylight shapes. All trials are carried out under overcast sky conditions, considered the worst case scenario. Following the trials it is concluded that for this type of skylight, the highest average daylight factors on the work plane are obtained for a height/width ratio close to 1/1, regardless of the reflector shape. In addition, it is concluded that the performance of the rectangular shape is poorer than that of the other shapes; the slanted shape has a better performance when the height/width ratio is lower, the curved shape produces greater daylight when the height/width ratio tends towards 1/1 and the sawtooth shape generates higher daylight factors when the height/width ratio is higher. Keywords: monitor skylight, skylight, monitor, daylighting, overcast sky. 1. Introduction and objective 1.1. State of the art From the beginnings of architecture, skylights have often been used to allow daylight in interior rooms, while providing homogeneous lighting to the horizontal plane. At present, skylight design is widespread in modern architecture, given its aesthetic and energy-efficiency qualities [1]. In consequence, skylight design has been widely studied, from the oldest of treatises [2] to the most modern manuals [3,4]. The monitor skylight is one of the most conventional designs since it provides much greater illuminance than lightscoop or sunscoop models [5]. This type of skylight is defined by two opposite vertical openings fixed by a reflector of variable shape. 2  Both openings permit a greater penetration of daylight, although unlike lightscoop skylights, they do not prevent incident sunlight in the inner space [6]. Therefore it is a skylight model suited to cold or mild climates where solar radiation does not generate high thermal gains [7]. 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 [8] that there is a great variety of skylights depending on the position of the opening and shape of the reflector, most notably the sawtooth and monitor skylights. This guide also shows the most common advantages and disadvantages of each skylight shape, although it does not quantify the differences between them. The most common shape for monitor skylights is rectangular, given their simple construction. Nevertheless, there are other architectural solutions for the design of monitor skylight reflectors which can be slanted, sawtooth or curved. Monitor skylight reflectors redirect the light towards the inner space, so that it is essential to study their shape and proportion in order to establish the maximum daylight performance. In addition, colour in the reflectors causes variations in the tone of daylight, producing an increase in the feeling of brightness, and in turn promoting a reduction of energy consumption in artificial daylighting [9] if combined with lighting controls such as photosensors. Current research on skylight design is based on the results obtained using lighting simulation programs and on the study of illuminance using scale models. Several authors, notably Tsangrassoulis et al. [10], have carried out comparisons on the most frequent simulation techniques, reaching conclusions on the methods most suited to predicting daylight within a space. However, the results obtained using lighting simulation programs are not completely accurate, as established by Kim et al. [11], although they can be of use in establishing design criteria supported on the study of relative results. In addition, other authors base their research on scale models. A notable example is the study by García-Hansen et al. [12], which uses a 1:20 model and introduces 9 light meters to evaluate the distribution of illuminance. Nevertheless, as concluded by Thanachareonkit et al. [13], scale models have a significant margin of error so they should be contrasted using computer simulation or full scale models. As a result, studies on skylights are often based on lighting simulation programs, as deduced from the most recent research [14,15,16]. However, in spite of the extensive research on skylight design there are currently no solid studies on the daylight factors produced by monitor skylights. This research aims to fill this gap, providing a series of trials based on lighting simulation programs. 1.2. Objective The main aim of this article is to determine a suitable proportion and shape for monitor skylights, in order to ensure maximum illuminance on the work plane within a room. The reflector shapes considered with this type of skylight are rectangular, slanted, sawtooth or curved, and different height/width ratios of the vertical and roof openings are used. The comparison of all the calculation models, with different shapes and different height/width ratios, determines the relative improvement provided by the monitor skylights studied. All trials were carried out under overcast sky conditions representing the worst case scenario. Therefore, the daylight factor is considered the reference measurement when determining the performance of all calculation models. Lightscape 3.2 software was used to carry out the simulations of different rooms with four different shapes of skylight. 3  2. Description of Methodology for Calculation 2.1. Choosing the calculation conditions All trials were conducted under overcast sky conditions, because these represent the worst case scenario. By definition, the calculation of daylight factors is carried out considering an unobstructed sky of assumed or known illuminance distribution, excluding direct sunlight. The overcast sky model used in the methodology is that defined by Moon-Spencer [17], 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 [18], which is known as traditional overcast sky: Sky type 16. 2.2. Choosing the calculation program Lightscape is a lighting and visualization application that uses both radiosity and raytracing algorithms where only the radiosity solution is considered for the quantitative results. The radiosity algorithm applied uses progressive refinement and adaptive meshing methods. Several studies have confirmed the correct behaviour of this calculation program [19,20]. Simulation programs based on the radiosity process can only define surfaces emitting a completely diffuse inter-reflection, unlike the programs which use the raytracing process. However, programs which use the radiosity process are more precise when using high inter-reflection values [19]. The accuracy of calculations using the radiosity process depends basically on the mesh spacing. For the calculation model in this research, mesh spacing is between 10 and 20 cm, sufficient to guarantee that precise results are obtained [20]. In addition, a trial was carried out contrasting parameters to determine the values suited to the calculation model. The calculation parameters used by this program are shown in table 1. LIGHTSCAPE 3.2 Calculation Radiosit y Sk y Conditions Traditional Overcast Sk y Mesh Spacing Min 0.10 m Max 0.20 m Subdivision Contrast Threshol d 0.65 Sk y li g ht Accurac y 0.60 Source Direct Source Min 0.12 Subdivision Accurac y 0.42 Indirect Source Min 0.24 Subdivision Accurac y 0.42 Shadow Grid Size Five Tolerances Len g th 0.0005 Ra y Offset 0.001 Initialization Min Area 0.01 Table 1: Calculation parameters of the lighting program Lightscape 3.2. 4  The results obtained with Lightscape 3.2 are compared with those obtained with DaySim 3.0, which uses the raytracing algorithms provided by the Radiance Engine. Therefore, the conclusions are contrasted with two lighting programs based on different algorithms. DaySim 3.0 also allows the calculation of dynamic metrics, such as daylight autonomy, which determine the energy saving produced by the monitor skylights. 2.3. Choosing the calculation model The model used for the trials was a room 9 m wide by 9 m long by 4.5 m high. A monitor skylight, 6 m long and with variable height “H” and width “W”, was placed in the centre of the roof (fig. 1). This type of skylight has a reflector behind the vertical openings, the shape of which can be rectangular “R”, slanted “D”, sawtooth “S” or curved “C”. 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 1: Characteristics of the calculation models. In order to adapt the results to the skylight proportions, the optical properties of surfaces –reflectance, reflection and transmittance– are considered invariable. The 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 reflectance index: the ceiling and skylight have an index of 0.9, the walls 0.7, and the floor 0.5, common values in the design of interior spaces. Nine different proportions were analyzed for each reflector shape, considering a length for the variable “W” of 1 to 5 m, as well as a value for variable “H” of 1 to 5 m. As a result, the surface of the horizontal area corresponding to the aperture in the 5  ceiling and the half 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 4 shapes studied, totalling 36 trials (fig. 2). Figure 2: Longitudinal section of the calculation models. Each calculation model is defined by a number determining the height/width ratio for the skylight, as can be seen in figure 2. As shown in figure 1 and developed in figure 2, each monitor skylight is defined by a specific shape:  Rectangular monitor skylights have a double opening and a flat reflector.  Slanted monitor skylights have a double opening and a double chamfer with a fixed angle of 45º.  Sawtooth monitor skylights have a double opening and a double reflector which converge at a vertex at midheight in the skylight.  Curved monitor skylights have a double opening and double cylindrical reflector. The daylight factors and the coefficient of uniformity measured on the work plane are studied for each calculation model. The conclusions have also been compared using the calculation of dynamic measurements [21], which depend on the area’s climate conditions, time of use and the use of shading devices. The study of daylight autonomy allows the assessment of the energy saving produced by each type of skylight. In order to confirm the results obtained, the daylight factors and the coefficient of uniformity are also studied for different room ratios, considering long and wide rooms instead of the initial calculation model. 3. Calculation This is a calculation of the maximum, average and minimum daylight factors measured on the work plane of each calculation model. The daylight factor is considered the reference measurement for determining the performance of all calculation models as it represents the potential of daylight provided by the monitor skylight [22]. In addition, the coefficient of uniformity for each skylight is shown. This is defined as the quotient of the minimum values over the average values for the daylight factors and represents a measurement of the uniformity of the illuminance distribution of daylight. All trials were carried out considering the conditions established in the methodology described above. 6  3.1. Calculation of rectangular monitor skylight The first trial analyzes the variation of daylight factors in the case of a monitor skylight with rectangular shape (R). Figure 3 shows the maximum (R.DF.MAX), average (R.DF.AVE) and minimum (R.DF.MIN) daylight factors measured on the work plane, considering a monitor skylight with rectangular shape and variable height/width ratio. The coefficient of uniformity (DF.MIN/AVE) for each skylight model is also shown. Figure 3: Maximum, average and minimum daylight factors on the work plane in a room with rectangular monitor skylight. 3.2. Calculation of slanted monitor skylight The second trial analyzes the variation of daylight factors in the case of a monitor skylight with slanted shape (D). Figure 4 shows the maximum (D.DF.MAX), average (D.DF.AVE) and minimum (D.DF.MIN) daylight factors measured on the work plane, considering a monitor skylight with slanted shape and variable height/width ratio. The coefficient of uniformity (DF.MIN/AVE), an indicator of illuminance distribution, is also shown. 7  Figure 4: Maximum, average and minimum daylight factors on the work plane in a room with slanted monitor skylight. 3.3. Calculation of sawtooth monitor skylight The third trial analyzes the variation of daylight factors in the case of a monitor skylight with sawtooth shape (S). Figure 5 shows the maximum (S.DF.MAX), average (S.DF.AVE) and minimum (S.DF.MIN) daylight factors measured on the work plane, considering a monitor skylight with sawtooth shape and variable height/width ratio. The coefficient of uniformity (DF.MIN/AVE) for each skylight model is also shown. Figure 5: Maximum, average and minimum daylight factors on the work plane in a room with sawtooth monitor skylight. 8  3.4. Calculation of curved monitor skylight The final test analyzes the variation of daylight factors in the case of a monitor skylight with curved shape (C). Figure 6 shows the maximum (C.DF.MAX), average (C.DF.AVE) and minimum (C.DF.MIN) daylight factors measured on the work plane, considering a monitor skylight with curved shape and variable height/width ratio. The coefficient of uniformity (DF.MIN/AVE) for each skylight model is also shown. Figure 6: Maximum, average and minimum daylight factors on the work plane in a room with curved monitor skylight. 3.5. Daylight factor results As can be deduced from figures 3 to 6, the highest daylight factors are observed in the monitor skylights with a height/width ratio between 2.5/3.5 and 3.0/3.0, so it is concluded that the maximum values are obtained for a height/width ratio close to1/1. On the opposite side, daylight factors decrease noticeably for skylights with height/width ratio 1.0/5.0 and 5.0/1.0. It can be observed that the skylight ratio is a key variable in the efficient use of daylight, as shapes with a height/width ratio near 1/1 show an increase of almost double the daylight factors of shapes with height/width ratio 1.0/5.0 and 5.0/1.0. In addition, there is a noticeable increase in the daylight factors produced by slanted, sawtooth and curved shapes, compared with those generated by the rectangular shape with the same ratios. This is due to the reflectors of these shapes being able to redirect reflected light to the inside of the room, unlike the case of the rectangular shape, which produces a greater scattering of daylight through the opposite openings, the reflector being less efficient. As regards the study of the coefficients of uniformity, it can be observed that the results are similar for almost all proportions of monitor skylights, which suggests that the illuminance distribution does not depend largely on height/width ratio. Specifically, it can be observed that skylights with a height/width ratio near 1/1 produce a coefficient of uniformity that is noticeably higher than other ratios for monitor skylights, especially narrower skylights, with a height/width ratio tending to 5/1. 9  Thus, it is concluded that in the case of a monitor skylight, the height/width ratio which produces the greatest daylight factors and the greatest uniformity has a value close to 1/1, that is to say, the height and width in the skylight are equal. This is true of all the monitor skylight shapes analyzed in this study. 4. Analysis of room ratios In order to confirm the conclusions obtained in the previous trials, each monitor skylight is assessed under different room ratios, considering the methodology established above. The room ratios used in this trial are the following:  Square room, 9 m wide by 9 m long by 4.5 m high.  Wide room, 12 m wide by 6 m long by 4.5 m high.  Long room, 6 m wide by 12 m long by 4.5 m high. The qualities of the inner surfaces of the room are those established previously. Each shape of monitor skylight, as well as the different skylight ratios defined in the methodology, is analyzed for each room ratio, as can be seen in figure 7. Figure 7: Characteristics of the calculation models, according to different room ratios. Therefore, the average daylight factors measured on the work plane are obtained for each calculation model. In addition, the relative difference of the average daylight factors, according to wide and long rooms compared to square rooms, is shown in the figures in order to clarify the difference in results. 4.1. Calculation of rectangular monitor skylight The first trial of this chapter analyzes the variation of daylight factors in the case of a rectangular (R) monitor skylight, according to square (S), wide (W) and long rooms (L). Figure 8 shows the average daylight factors considering a square room (S.R.DF.AVE), a wide room (W.R.DF.AVE) and a long room (L.R.DF.AVE), as well as a rectangular monitor skylight with a 16  6. Analysis of energy saving and contrast of results In order to determine the energy saving of each calculation model, as well as to contrast the results obtained, a new trial was developed with DaySim 3.0. This lighting program allows the calculation of daylight autonomy [21], which defines the independence of artificial lighting of the room and therefore, the energy saving, when considering a proper use of daylighting. As explained above, DaySim 3.0 uses the raytracing algorithms provided by the Radiance Engine. Accordingly, the results obtained in the previous trials were compared with a different metric under a different calculation engine. The accuracy of DaySim 3.0 has been confirmed by several studies [23,24]. The calculation parameters used with this lighting program, as well as the calculation conditions, are shown in table 3. DAYSIM 3.0 Calculation Ra y -tracin g Sk y Conditions All-weather sk y conditions Ambient Bounces 6 Ambient Divisions 1200 Ambient-Su p er Sam p les 20 Ambient Resolution 300 Ambient Accurac y 0.1 Limit Reflection 6 S p ecular Threshol d 0.15 S p ecular Jitte r 1.00 Limit Wei g ht 0.004 Direct Jitte r 0.000 Direct Sam p lin g 0.200 Direct Rela y s 2 Direct Pretest Densit y 512 Location New York, Lt. 40,00º L g . -73,00º, New York.wea Orientation West and East Occu p anc y From 8.00 to 17.00 with intermediate breaks. Illuminance 500 lux Shadin g device No Table 3: Calculation parameters and conditions of the lighting program DaySim 3.0. As can be observed in table 3, the monitor skylight openings are oriented to the west and east and the room is located in New York City. The analysis of daylight autonomy requires the setting of several variables, such as the location, the occupancy time and the control of shading devices. In order to obtain suitable results of daylight autonomy, the monitor skylight has been scaled to half the size. The variation of the scale of the skylight, considering the same room dimensions, also serves to extend the conclusions obtained regardless of the room/skylight ratio. In all cases, the height/width ratio of each skylight is the same as in the previous trials. The qualities of the inner surfaces, as well as the room dimensions, are the same as those obtained in the methodology. As in the above trials, the daylight autonomy is measured on the work plane. The results obtained are shown in figure 14. 17  Figure 14: Average daylight autonomy on the work plane. Rectangular, slanted, sawtooth and curved monitor skylight. As can be deduced from figure 14, the highest daylight autonomy is observed in the monitor skylights with a height/width ratio near 1.5/1.5, regardless of the shape of the reflector. It can therefore be concluded that the maximum values of daylight autonomy, as well as daylight factors, can be observed for a height/width ratio close to 1/1. It should also be noted that the monitor skylights with a height/width ratio near 1/1 reach a value of daylight autonomy close to 80%, considering a surface opening of approximately 10% of the ceiling. 7. Analysis of spacing The distribution of the light within a room makes it possible to determine the spacing between skylights to ensure homogeneous illuminance on the work plane. Accordingly, a new study was carried out, analyzing different layouts for monitor skylights in the same room, in order to establish the correct distance at which they should be placed. For this trial a room that was 27 m long, 9 m wide and 4.5 m high was considered, equivalent to a triple room with three monitor skylights. The monitor skylights were 3 m long and 3 m high, which corresponds to the height/width ratio that allows the best daylight factor performance. The monitor skylights were 6 m wide with variable shape according to the methodology described below. The qualities of the surfaces –reflectance, reflection and transmittance– coincide with those defined in the previous calculation model. Four simulations were carried out for each reflector shape, considering different spacings between the monitor skylights. The spacing considered is proportional to the height of the room, as can be observed in figure 15. 18  Figure 15: Model for the study of spacing between monitor skylights, according to the coefficient of uniformity. The proper spacing between skylights is determined by the coefficient of uniformity. As stated above, the coefficient of uniformity is defined as the coefficient of the minimum values over the average values of daylight factors (DF.MIN/AVE) and represents a measure of the uniformity of the illuminance distribution of the daylight. The higher the coefficient of uniformity, the better the uniformity of light. Consequently, the coefficient of uniformity is calculated for the rectangular monitor skylight (R.DF.MIN/AVE), for the slanted monitor skylight (D.DF.MIN/AVE), for the sawtooth monitor skylight (S.DF.MIN/AVE) and for the curved monitor skylight (C.DF.MIN/AVE), assuming a variable spacing between skylights. The average daylight factor according to the skylight spacing is also calculated. Figure 16 shows the results obtained. Figure 16: Coefficient of uniformity and average daylight factor according to skylight spacing/room height ratio. Rectangular, slanted, sawtooth and curved monitor skylights. As can be deduced from figure 16, the highest coefficient of uniformity is observed for a skylight spacing/room height ratio of 3.0/3.0, which means that for the ratio of the monitor skylight mentioned earlier, the illuminance distribution is optimal when 19  the distance between skylights is the same as the height of the room. This applies to all the shapes analyzed in this study. In any case, it is also observed that all values of the coefficient of uniformity are higher than the recommended values [25]. As can also be observed, considering the range of skylight spacing/room height ratio, the measurement of the average daylight factors is almost inversely proportional to the spacing between skylights. This conclusion can be extended to all shapes of monitor skylights, as can be deduced from Figure 16. It is therefore concluded that the less spacing between skylights, the greater the daylight. The above conclusion is based on a monitor skylight with a height/width ratio of 1/1, the same ratio as that of a skylight spacing/room height ratio considered optimal. Consequently, it is deduced that the appropriate distance between monitor skylights is directly proportional to their height/width ratio. As a specific case, it should be noted that the slanted and sawtooth shape coincide fully when the height/width ratio is 1/1. Therefore, it seems consistent that the coefficient of uniformity should be identical for both shapes. 8. Conclusion The analysis carried out on different shapes and ratios of monitor skylights makes it possible to establish architectural design conditions that enable the best performance in daylight to be reached. This performance was based mainly on the study of the daylight factors, which represent the daylight potential for the interior of a room. All the trials used an overcast sky, considered the worst case scenario, as the sky luminance is lower than in other sky models. The shape of the room and the qualities of the surfaces, described in the methodology, are based on the conventional measurements and values of architectural design. The first conclusion obtained from this study is that the highest daylight factors can be seen in rooms with monitor skylights with a height/width ratio close to 1/1. It can be concluded that this statement is true for all monitor skylights models, regardless of the reflector shape and the room ratio. As was deduced in the performance analysis, the rectangular monitor skylight produces daylight factors lower than the rest of reflector shapes considered in this study. This difference is highlighted when the height/width ratio of the skylight is close to 1/1. In addition, it is observed that the slanted shape produces a better performance than the other shapes as the height/width ratio decreases. Specifically, performance increases up to 4.00% when the height/width ratio is equal to 1/5. As is concluded in the analysis of skylight shapes, this statement is based on the effect of the double chamfer of the slanted shape. In short, the slanted monitor skylight is optimal when the height/width ratio is low. It is concluded that the shape of the curved monitor skylight generates daylight factors higher than those obtained from the other shapes when the height/width ratio is close to 1/1. Specifically, daylight increases by 8.00% when the height/width ratio is close to 2.5/3.5. It can thus be deduced that the curved shape results in better performance than the other reflectors when the height/width ratio is close to 1/1. In the opposite situation, the sawtooth monitor skylight generates greater daylight than that observed in the other cases where the height/width ratio is higher. In fact, it is possible to observe an increase of 2.50% in daylight factors when the height/width ratio is equal to 5/1. In short, it can be deduced that the sawtooth shape is ideal when the height/width ratio is low, since the reflector redirects the light towards the interior more efficiently than the other shapes. As regards the relationship between the monitor and lightscoop skylights, several conclusions were reached. Firstly, monitor skylights produce approximately double the daylight of lightscoop skylights providing their height/width ratio is very low, regardless of the reflector shape. In the case of a height/width ratio of 1/5, the increase produced by a monitor skylight is 20  almost 100%. This deduction is based on the fact that the monitor skylight has a double opening and therefore lets in almost twice the amount of daylight that a lightscoop skylight does, despite the fact that a fraction of the daylight which enters through the opening is scattered through the opposite window. In the case with the best performance of the monitor skylight, with a height/width ratio close to 1/1, the scattering of daylight between openings becomes noticeable, since there is only an increase in daylight factors of between 60% and 80% with respect to a lightscoop skylight with the same ratio. The effect of scattering of daylight is highlighted when the openings are very close together, that is to say, when the height/width ratio of the monitor skylight is high. In fact, in the specific case of a height/width ratio equal to 5/1, the increase produced by the monitor skylight is barely 33% over the performance of a lightscoop skylight. As can be concluded from previous studies [16], the behaviour of monitor skylights is quite different to that of other skylight shapes, such as lightwell skylights. As can be observed in the above results, in the case of lightwell skylights the daylight factors decrease in direct proportion to the height/width ratio, while the lightscoop and monitor skylights obtain the maximum values of daylight factors when the height/width ratio reaches a certain value. Monitor skylights have great potential in the use of daylighting, as can be deduced from the analysis of daylight autonomy. A monitor skylight with a height/width ratio near 1/1 reaches a value of daylight autonomy close to 80%, considering a surface opening of approximately 10% of the ceiling. That is to say, the consumption of artificial lighting is reduced to 20% throughout the year, considering the calculation conditions. Finally, a complementary study is carried out on the suitable spacing between monitor skylights, to guarantee a high coefficient of uniformity. After carrying out the trial with three square skylights and a variable distance between them, it can be deduced that the skylight spacing/room height ratio is directly proportional to the height/width ratio of the monitor skylight. Specifically, it can be observed that the appropriate distance between monitor skylights with a height/width ratio of 1/1 is the same as a skylight spacing/room height ratio that is also 1/1. It can also be observed that the shape of the reflector is not a determining factor in the distance between skylights. All these conclusions are aimed at establishing the most appropriate design of monitor skylights to guarantee the highest daylight factors under overcast sky conditions. 9. References  [1] K.M. Al-Obaidi, M. Ismail, A.M.A. Rahman, A study of the impact of environmental loads that penetrate a passive skylight roofing system in Malaysian buildings, Frontiers of Architectural Research (2014) 3, 178-191. [2] R.G. Hopkinson, P. Petherbridge, J. Longmore, Daylighting, London: Heinemann, (1966). [3] R. Kittler, M. Kocifaj, S. Darula, Daylight Science and Daylighting Technology, Springer (2012). [4] L. Radetsky, J. Brons, Light Scoops, A Design Guide, Troy, New York: Rensselaer Polytechnic Institute (2013). [5] W.M.C. Lam, Sunlighting as formgiver for architecture, New York: Van Nostrand Reinhold Company Inc., (1986) 148. [6] I. Acosta, J. Navarro, J.J. Sendra, P. Esquivias, Daylighting design with lightscoop skylights: Towards an optimization of proportion and spacing under overcast sky conditions, Energy and Buildings 49 (2012) 394-401. [7] A. Laouadi, M.R. Atif, A. Galasiu, Towards developing skylight design tools for thermal and energy performance of atriums in cold climates, Building and Environment 37 (2002) 1289-1316. 21   [8] CIBSE, Daylighting and Window Design. London: Chartered Institution of Building Services Engineers, 1999. 2.2.3. [9] J. López-Besora, A. Isalgué, H. Coch, I. Crespo, C. Alonso, Yellow is green: An opportunity for energy savings through colour in architectural spaces, Energy and Buildings 78 (2014) 105-112. [10] A. Tsangrassoulis, V. Bourdakis, Comparison of radiosity and ray-tracing techniques with a practical design procedure for the prediction of daylight levels in atria, Renewable Energy 28 (2003) 2157-2162. [11] C.-S. Kim, S.-J. Chung, Daylighting simulation as an architectural design process in museums installed with toplights, Building and Environment 46 (2011) 210-222. [12] V. Garcia-Hansen, A. Esteves, A. Pattini, Passive solar systems for heating, daylighting and ventilation for rooms without an equator-facing façade, Renewable Energy 26 (2002) 91-111. [13] A. Thanachareonkit, J.L. Scartezzini, M. Andersen, Comparing daylighting performance assessment of buildings in scale models and test modules, Solar Energy 79(2) (2005) 168-182. [14] A. Laouadi, A. Galasiu, M.R. Atif, A new software tool for predicting skylight performance. International Daylighting, (2003), 5, 15-18. [15] I. Acosta, J. Navarro, J.J. Sendra, Daylighting design with lightscoop skylights: Towards an optimization of shape under overcast sky conditions, Energy and Buildings 60 (2013) 232-238. [16] I. Acosta, J. Navarro, J.J. Sendra, Towards an analysis of the performance of lightwell skylights under overcast sky conditions, Energy and Buildings 64 (2013) 10-16. [17] P. Moon, D.E. Spencer, Illumination from a Non-Uniform Sky. Illuminating Engineering 37 (1942) 707-726. [18] CIE, Spatial Distribution of Daylight - CIE Standard General Sky, Commission Internationale de l’Éclairage (2003). CIE S 011/E :2003. [19] I. Acosta, J. Navarro, J.J. Sendra, Towards an Analysis of Daylighting Simulation Software, Energies. 4(7) (2011) 1010- 1024. [20] F. Maamari, M. Fontoynont, N. Adra, Application of the CIE test cases to assess the accuracy of lighting computer programs, Energy and Buildings 38 (2006) 869-877. [21] C.F. Reinhart, J. Mardaljevic, Z. Rogers, Dynamic Daylight Performance Metrics for Sustainable Building Design, Leukos 3(1) (2006) 7-31. [22] CIE: International lighting vocabulary. Commission Internationale de l’Éclairage (2011). CIE S 017:2011. [23] C.F. Reinhart, J. Wienold, The Daylighting Dashboard - A Simulation-Based Design Analysis for Daylit Spaces, Building and Environment 46 (2011) 386-396. [24] C.F. Reinhart, M. Andersen, Development and validation of a Radiance model for a translucent panel, Energy and Buildings 38 (2006) 890-904. [25] IESNA: Lighting Handbook 10th Edition, New York: Illuminating Engineering Society of North America, (2012).