A SIMPLIFIED METHOD FOR CALCULATING THE EFFECTIVE SOLAR OPTICAL PROPERTIES OF A DRAPERY

Transcription

1 nd Canadian Solar Buildings Conference Calgary, une 4, 7 A SIMPLIFIED METHOD FOR CALCULATING THE EFFECTIVE SOLAR OPTICAL PROPERTIES OF A DRAPERY N. A. Kotey,.L. Wright and M.R. Collins Departent of Mechanical Engineering, University of Waterloo, University Avenue West, Waterloo, ON NL 3G Phone: ext 33885, Fax: , Eail: nakotey@engail.uwaterloo.ca Type of paper: Refereed ABSTRACT The use of draperies to control solar gain through windows is coon in residential and coercial buildings and their potential for reduction of building peak load and annual energy consuption is recognized to be large. Thus, there is a strong need for odels that allow a drapery to be included in glazing syste analysis. As an approxiation, the drapery is odelled as a series of uniforly arranged rectangular pleats with fabric transitting and reflecting diusely any incident radiation. The eective solar optical properties of the drapery are then deterined by considering an enclosure which is representative of the entire series of pleats. The optical properties of the drapery are functions of the pleat geoetry and the optical properties of the fabric. Optical properties are also influenced by the directional nature of the incident radiation. In the case of incident bea radiation, the results are presented as a function of the solar profile angle for a folding ratio corresponding to % fullness. The results for incident diuse radiation on the other hand are presented in ters of fabric properties and the folding ratio of the drapery. INTRODUCTION Draperies provide privacy, reduce glare and iprove aesthetics. They should also reduce solar gain and increase theral resistance. The reduction in solar gain and the increase in theral resistance can noticeably influence building peak load and annual energy consuption. Using coputer siulation, Rudoy and Duran (975), for exaple, reported an annual reduction in the cooling load of an oice space in the range of 5-% when draperies were attached to a window that occupied only 5% of the exterior wall. Their study also showed a reduction of annual heating load of approxiately %. The influence of a drapery on the solar gain through a window is strongly dependent on the solar optical properties of the drapery. Several studies have been carried out to deterine the solar optical properties of draperies as well as the reduction of solar gain when draperies are used. The current study focuses on the reduction of solar gain by characterising the solar optical properties of draperies. By visual inspection, Keyes (967) characterised fabrics by yarn colour (yarn reflectance) as dark (D), ediu (M) and light (L) and by weave as open (I), sei-open (II) and closed (III). Keyes then developed a chart that expressed easured shading coeicient (defined as the ratio of solar gain through a window to the solar gain through a standard clear single-pane glass) as a function of yarn reflectance and weave openness when a drapery was cobined with both regular plate and heating absorbing glass. Whenever the solar optical properties of the fabrics are unknown, Keyes ethod gives an approxiate value of the shading coeicient of glass-drapery cobination. Having acknowledged that fabric colour and weave openness alone were not suicient to deterine accurately the shading coeicient of glass-drapery cobination, Moore and Pennington (967) developed a chart that expressed the shading coeicient as a function of fabric reflectance and transittance. They easured the solar optical properties of fabrics, draperies, and glass-drapery cobinations using various techniques. They also easured the shading coeicient for various glassdrapery cobinations using a solar calorieter. Furtherore, they developed equations to calculate the shading coeicient for glass-drapery cobinations using drapery and glass solar optical properties as inputs. The optical properties of the drapery were estiated by applying a ultiplicative factor to the optical properties of the fabric at noral incidence. The proposed ultiplicative factor accounted for the eect of folding and the variation of the incidence angle of bea radiation. Their calculated shading coeicients agreed quite well with experientally deterined shading coeicients. By careful analysis of fabric transittance and reflectance, yarn reflectance and openness factor, Keyes (967) was able to reconcile the yarn reflectance-openness chart with the fabric reflectance-transittance chart. Keyes (967) universal chart (Figure ) is the basis of the interior attenuation coeicient (IAC) data for glass-drapery cobination found in ASHRAE Handbook- Fundaentals (5). This chart conveniently correlates easured optical properties with eye-

2 nd Canadian Solar Buildings Conference Calgary, une 4, 7 observed values to deterine the shading coeicient of glass-drapery cobination thus aking it a practical tool for designers in the field. However, optical properties easureents carried out by Moore and Pennington (967) with a spectrophotoeter revealed that for spectrally selective fabrics, the optical properties in the visible spectru could be uch dierent fro the properties in the near infrared spectru. Consequently, the solar averaged properties dier fro the average in the visible spectru. In such situations, using visual judgeent to predict shading eects could give inaccurate results. Figure. Fabric classification (reproduced fro ASHRAE, 5). The first attept to quantify the cuulative eect of folding (or pleating) and the directional nature of incident radiation on the solar gain through draperies was carried out by Ozisik and Schutru (96). To deterine the eectiveness of % fullness draperies in reducing the solar gain through a sunlit window, Ozisik and Schutru (96) tested draperies of dierent fabrics in cobination with regular and heat absorbing glass using a solar calorieter. They presented their results in ters of the solar heat transfer factor, K, defined as the ratio of the solar gain to the insolation. Note that the K value is identical to the Solar Heat Gain Coeicient (SHGC) defined in ASHRAE (5). Ozisik and Schutru (96) results showed that the K values were independent of incidence angle for incidence angles ranging fro to 5. For incidence angles greater than 5, they suggested a decrease in K values by % for each increase in incidence angle. They also proposed a reduction of % in K values for incident diuse radiation. Furtherore, they presented a variation of K values with respect to solar optical properties of the fabric at noral incidence and observed that the reflectance was the doinant property influencing the solar gain. In addition to the solar gain tests, Ozisik and Schutru (96) perfored a series of tests to investigate the eect of pleating on the solar optical properties of draperies. They easured the angular transittance and reflectance of both fabrics and draperies with a pyrhelioeter. Their results showed that the transittance of the drapery at noral incidence was alost the sae as that of the corresponding fabric. However, at an incidence angle of 45, the transittance of the drapery was % less than that of the fabric. For incident diuse radiation, the transittance of the drapery was also % less than that of the fabric. The reflectance of the drapery, on the other hand, was about % less than that of the fabric at noral incidence and about % less at 45 incidence. Yellot (965) experientally deterined the solar heat gain factor (defined as solar gain through a standard clear glass for a given insolation) and the shading coeicient of draperies in cobination with clear and heat absorbing glass for a wide variety of fabrics using an outdoor solar calorieter. He also easured the solar optical properties of fabrics as well as glass-fabric cobinations at various angles of incidence using a custo-ade instruent. The easureents were taken at varying incidence angles ranging fro 6 to 9. His experients showed that the solar heat gain factor for a typical glass-fabric cobination decreases as the incidence angle increases although the shading coeicient reained fairly constant. To explore the eects of varying wall-solar aziuth on the reflectance of fabrics and draperies, Yellot (965) used a reflectoeter to easure reflectance of a typical light coloured fabric and a drapery in a solar calorieter. His results showed that although the reflectance of both fabric and drapery varied with wall-solar aziuth, there was very little dierence between the reflectance of the fabric and the drapery for a given wall-solar aziuth. The results of the preceding studies (Keyes, 967, Moore and Pennington, 967, Ozisik and Schutru, 96 and Yellot, 965) could be very useful in predicting the solar gain through windows with indoor draperies. However, they were liited to single glazed windows. Given that a significant nuber of double glazed windows are installed in practice, an in-depth theoretical analysis was carried out by Farber et al. (963) to ascertain the reduction of solar gain through double glazed windows with indoor-side shading. More specifically, they considered venetian blinds as well as draperies installed at the indoor-side of the double glazed window by theoretically estiating the solar gain. Of particular interest was the deterination of the apparent (eective) solar optical properties of the

3 nd Canadian Solar Buildings Conference Calgary, une 4, 7 drapery using a siplified rectangular configuration that is representative of the drapery. The calculated apparent optical properties were based on the solar optical properties of the fabric and the assued geoetry. Farber et al. (963) assued that the fabric is diusely reflecting and diusely transitting although the reflectance and transittance for bea radiation vary with incidence angle. Their calculation involved a separate treatent of the front and the cavity portions of the drapery with the front portion having the sae optical properties as the fabric. However, the deterination of the apparent optical properties of the cavity portion involved angle factors leading to siultaneous integral-dierential equations with foridable solution techniques. Nonetheless, the solution of the cavity portion was added to the front portion and the results averaged to give the apparent optical property of the drapery. To validate the theoretical analysis carried out by Farber et al. (963), Pennington et al. (964) perfored a series of experients using an outdoor solar calorieter to easure the solar gain of coplex fenestration systes at various angles of incidence (or profile angles). Furtherore, they used the pyrhelioeter installed in the calorieter to easure the solar optical properties of fabrics, draperies and glass-drapery cobinations at various angles of incidence. Within the range of incidence angles considered, the experientally deterined solar optical properties and solar gain copared favourably with the theoretical results. Little research has been conducted on the solar optical characteristics of drapery fabrics in recent ties. To copleent the eort of past researchers on the characterisation of drapery fabrics, Hunn et al. (99) designed an apparatus to easure the bidirectional transittance and reflectance distribution of bea radiation incident on both fabrics and draperies. The easureents revealed the eect of textile properties (openness of weave, fibre cross section and fabric structure) on the distribution of sunlight. Such inforation is particularly useful in the context of daylighting siulation through windows with drapery attachents. However, this experiental ethod is not only tie consuing but also liited in its capabilities. The bidirectional solar optical properties obtained by easureents can be incorporated into a atrix layer calculation ethod like the one developed by Kles (994a and 994b) to predict the solar gain of coplex fenestration systes. In the current study, noral-heispherical solar optical properties of fabrics were easured using a UV/VIS/NIR spectrophotoeter. The spectrophotoeter is a double bea, direct ratio recording, rapid scanning high perforance instruent with a scan rate of n/in for UV- Vis and 8n/in for NIR, a resolution of <.5n for UV-Vis and <.n for NIR, and repeatability characteristics of <.5n for UV-Vis and <.n for NIR. It has an extended spectral range allowing it to scan between and 3.3μ. Having obtained the solar optical properties of a typical fabric, the eective solar optical properties of the drapery were deterined as functions of the optical properties of the fabric and the geoetry of the drapery. More specifically, the fabric is assued to transit and reflect bea radiation diusely. In addition, the fabric optical properties are assued to be independent of the angle of incidence. This siplified approach significantly reduces coputational tie. The eective optical property odels developed in this study provide useful input to the ulti-layer glazing/shading layer odels previously developed for building energy siulation (Wright and Kotey, 6). It is therefore anticipated that the siplified odels will be highly valuable in building energy siulation. MODEL DEVELOPMENT Solar optical properties of a drapery are deterined by considering an enclosure which is representative of the drapery. Figure a shows a representative geoetry of the drapery where s is the pleat spacing and w is the pleat width. The optical properties are functions of the drapery geoetry and the fabric optical properties as well as profile angle, Ω. Drapery optical properties are odelled based on the following assuptions and siplifications: The geoetric configuration of the drapery is a series of uniforly arranged rectangular pleats The thickness of the fabric is negligible The surfaces of the pleats are perfectly flat Incident diuse radiation is uniforly distributed The fabric transits and reflects diusely any incident bea radiation. More recent undocuented easureents show that ost fabrics exhibit such optical characteristics The optical property odels for the drapery pertaining to bea radiation require the bea-diuse reflectance of the forward-facing and backwardfacing surfaces of the fabric (, bd and bf, bd ) as well as the bea-diuse transittance of the fabric (τ bd). The superscript is attached to the solar optical properties of fabric to distinguish the fro the eective solar optical properties of the drapery. Furtherore, the optical property odels for the drapery require the diuse-diuse reflectance of the forward-facing and backward-facing surfaces (, dd and bf, dd ) as well as the diuse-diuse transittance of the fabric (τ dd). Fro the assuption that fabric is a perfect diuser, it follows that, bd, bf, bd and τ bd are independent of the angle of incidence and hence, bd =, dd =, bf, bd = bf, dd = bf and τ bd = τ dd = τ. Moreover, 3

4 nd Canadian Solar Buildings Conference Calgary, une 4, 7 c) a) b) Incident bea radiation, I bea Incident bea radiation, I bea Ω g Ω g a a w w G 5 9 w 4 w w 4 w w 9 G G 4 G 9 G 4 G 3 w 3 3 G 8 w 8 8 G 5 G 7 G 6 w 6 6 w 7 7 d f a w 5 5 G 5 w G G 6 w 6 G 6 d G 7 w 7 w w 7 b e w 4 4 G 4 G 3 w 3 3 G G 9 G 8 w 8 w c f c c k k s e Bea-Diuse Solar Optical Properties The calculation is subdivided into two categories depending on whether the horizontal surface of the botto half of the enclosure (as shown in Figures a and b) is fully or partially illuinated. For a fully illuinated horizontal surface, the line segent de w. The corresponding nine-surface odel is shown in Figure a. A partially illuinated horizontal surface gives rise to a ten-surface odel with de < w as shown in Figure b. The following subsections describe the nine- and ten-surface odels. Nine-Surface Model As shown in Figure a, bea radiation incident on surfaces w 6 and w 7 is reflected diusely into the enclosure. A portion of the bea radiation incident on surfaces w 6 and w 7 is diusely transitted. Diuse radiation in the enclosure will also be transitted and reflected diusely by all surfaces. The following definitions apply: i is the radiosity of surface i, G i is the irradiance on surface i, Z i is the diuse source ter due to incident bea radiation on surface i. Fro the definitions of, G and Z, the following equations can be written: = Z + G () = τ G9 + bf bf G () Incident diuse radiation, I di g d w G G 5 8 w 5 G 5 G 6 w w 8 w 6 6 G 3 w 3 3 G 8 G 7 Figure. Enclosure Geoetry for Calculating Drapery Optical Properties a) Incident Bea Radiation (nine-surface odel) b) Incident Bea Radiation (ten-surface odel) c) Incident Diuse Radiation since bea-bea transission and reflection are negligibly sall (perfectly diusing fabric), τ bb =,, bb = and bf, bb =. Consequently, only, bf and τ are required as inputs to the odel. The folding ratio, defined as the total width of the fabric divided by the width of the drapery, gives an indication of the percentage fullness of the drapery. For exaple, a % fullness corresponds to a folding ratio of. Fro Figure a, it can be seen that the folding ratio equals + w/s. w 7 7 f k 4 = Z 4+ τ G6 + G4 (3) bf = Z 6 +τ G4 6 (4) 6 = Z 7 (5) 7 7 = 8 8 G (6) 9 = τ G + G9 (7) Also, the diuse source ters can be calculated as: Z = τ I bea (8) s Z 4 =τ I bea (9) de s Z 6 = I bea () de Z 7 = I bea () where cos( Ω) de = s () sin( Ω) The irradiance on each surface of the top half of the enclosure is given by: 4

5 nd Canadian Solar Buildings Conference Calgary, une 4, 7 = 4 j = G i F ij j i =, 4 (3) while the irradiance on each surface of the botto half of the enclosure is given by: = 9 j = 5 G i F ij j i =5, 9 (4) The view factor, F ij, is the fraction of diuse radiation leaving surface i that is intercepted by surface j. The view factors can be deterined by Hottel s crossed string rule (e.g., Hollands 4). Since there is no incident diuse radiation on surfaces w 3 and w 5, 3 = 5 =. Equations ()-(7) are linear and can be solved by atrix reduction with I bea set to unity. The front bea-diuse transittance and reflectance are: s G3 + τ ( w8 G8 + w7 G7 + w7) τ f, bd = (5) s + τ G 5 f, bd = (6) where sin( Ω) w 8 = w (7) cos( Ω) and w7 = s w8 (8) Ten-Surface Model The following equations are written (see Figure b): = Z + G (9) bf = τ G () bf = τ G8 () 4 4 bf = Z 5 +τ G7 5 () 5 bf = Z 7 +τ G5 (3) 7 7 = τ G4 (4) 8 8 = G (5) 9 9 = τ G + G (6) The diuse source ters Z, Z 5 and Z 7 are calculated fro equations (8), (9) and () respectively. The irradiance on each surface of the top half of the enclosure is: = 5 j = Gi F ij j i =, 5 (7) Siilarly, the irradiance on each surface of the botto half of the enclosure is: = j = 6 Gi F ij j i =6, (8) Since there is no incident diuse radiation on surfaces w 3 and w 6, 3 = 6 =. Equations (9)-(6) are solved with I bea set to unity and the front beadiuse transittance and reflectance are: G3 + τ G9 τ f, bd = (9) + τ G 6 f, bd = (3) Diuse-Diuse Solar Optical Properties The diuse-diuse transittance and reflectance of the drapery are calculated using the eight-surface odel shown in Figure c. For a uniforly distributed diuse radiation incident on the front surface of the enclosure, I di, the following equations are written: = τ I di + G (3) bf = τ G8 (3) bf = τ G6 (33) 4 4 bf = τ G4 (34) 6 6 = G (35) = τ G + G (36) 8 The irradiance on each surface of the top half of the representative enclosure is given equation (3) while the irradiance on each surface of the botto half of the enclosure is: = 8 j = 5 G i F ij j i =5, 8 (37) To solve equations (3)-(36), I di is set to unity and the front diuse-diuse transittance and reflectance are: G3 + τ G7 τ dd = (38) + τ G 5 f, dd = (39) The back eective solar optical properties of the drapery can easily be calculated with the sae set of equations described above by interchanging the reflectances of the forward-facing and the backwardfacing surfaces of the fabric. Ideally, the optical property calculations for the drapery ust be perfored for every wavelength required by the corresponding optical properties of the fabric. However, for the sake of siplicity, the solar 5

6 nd Canadian Solar Buildings Conference Calgary, une 4, 7 (spectrally-averaged) optical properties of the fabric are used. RESULTS AND DISCUSSION The solar optical properties of a wide variety of fabrics were easured using a UV/VIS/NIR spectrophotoeter. More specifically, the spectral optical properties of each fabric ( (λ), bf (λ) and τ (λ)) were obtained at direct-noral incidence and the solar (spectrally-averaged) optical properties were calculated using the 5-point selected ordinate ethod as described in ASTM E93-96 (996). Nine fabric saples that fall into each classification shown in Figure were selected for analysis. The fabric transittance and reflectance of the selected saples are given in Table. All the saples have their reflectances on both sides to be the sae and hence only one reflectance value is shown in Table. Table. Solar Optical Properties and Classification of Fabrics Fabric Transittance Fabric Reflectance ASHRAE Classification Sybol.3.5 Open weave, dark-coloured I D.3. Sei-open weave, dark-coloured II D.7 Closed weave, dark-coloured III D 4.3 Open weave, ediu-coloured I M.3 Sei-open weave, ediu-coloured II M.36 Closed weave, ediu-coloured III M.54.4 Open weave, light-coloured I L.5.48 Sei-open weave, light-coloured II L 7 Closed weave, light-coloured III L Given the solar transittance and reflectance of each fabric, the eective solar optical properties of the drapery were calculated. For the purpose of discussion, three fabric saples, i.e., open weave, ediu-coloured fabric (I M ), closed weave, ediucoloured fabric (III M ) and closed weave, lightcoloured fabric (III L ) are chosen. Figure 3 shows the eective diuse-diuse optical properties plotted against the folding ratio for the three selected fabrics. As seen in Figures 3a and 3b, the eective diusediuse transittance of the drapery decreases with increasing folding ratio for fabrics classified as I M and III M. In contrast, the transittance of the drapery for fabric classification III L increases slightly, reains essentially constant before decreasing as the folding ratio increases (see Figure 3c). The eective diuse-diuse reflectance of the drapery in each fabric classification shows a rather interesting trend. While the reflectance increases sharply to a axiu value before reaining essentially constant with increasing folding ratio for fabric classification I M (see Figure 3a), there exists a general decrease in the reflectance with an increase in folding ratio for fabric classification III M and III L (see Figures 3b and 3c). Note that for w =, when there are no folds at all, the eective optical properties of the drapery corresponds to the solar optical properties of the fabric. Consideration will now turn to the eect of profile angle of incident bea radiation on the solar optical properties of a drapery. A folding ratio of (% fullness) is chosen in this study. Clearly, the eective bea-diuse transittance of the drapery always decreases with increasing profile angle as seen in Figure 4 for all three fabric classifications. For fabrics classified as III M and III L, the eective beadiuse reflectance of the drapery reains approxiately constant as the profile angle increases fro to 4 ; a further increase in the profile angle results in a weak increase in the reflectance of the drapery (see Figures 4b and 4c). Fabrics classified as I M on the other hand show a arked increase in the eective bea-diuse reflectance of the drapery as the profile angle increases fro to 9. Note that the profile angle for a drapery configuration is equal to the wall-solar aziuth angle. On a ore general note, Pennington and Moore (967) acknowledged the diiculty in easuring the solar optical properties of draperies. Given the solar optical properties of the fabric at noral incidence, they proposed ultiplicative constants that could be used to scale down the optical properties of fabric in order to obtain the corresponding optical properties of the drapery. Their deduced scaling constants were based on experients perfored on several fabrics. The present results however show that the solar optical properties of a drapery do not always decrease by a constant factor with respect to folding and/or incidence angle. In fact, the optical properties of a drapery can actually increase with folding ratio as seen in Figure 3. CONCLUSIONS The iportance of odelling solar optical properties of shading devices lies in the need to predict their energy savings potential. In the current study, siplified odels were used to calculate the eective solar optical properties of a drapery for both incident bea and diuse radiation. The drapery was odelled as a series of uniforly arranged rectangular pleats with optical properties dependent on the geoetry, the optical properties of the fabric and the profile angle of incident radiation. The fabric is assued to transit and reflect diusely any incident bea radiation. Given the solar optical properties of the fabric, the drapery odels enable us to explore the eect of folding as well as the variation of the profile angle on the eective optical properties. The results show that the solar optical properties of a drapery do not always decrease by a constant factor with respect to folding and/or incidence angle as proclaied by previous researchers. The siplified solar optical odels can therefore produce results that can serve as useful 6

7 nd Canadian Solar Buildings Conference Calgary, une 4, 7 input to building load and annual energy calculation tools. Furtherore, siplified odels have advantages especially in the design stages when one wishes to copare the perforance of various draperies that could be installed on windows. a) Eective diuse-diuse solar optical properties b) Eective diuse-diuse solar optical properties c) Eective diuse-diuse solar optical properties f,dd τ f,dd =.3 bf =.3 τ = Folding ratio f,dd τ f,dd =.36 bf =.36 τ = Folding ratio f,dd τ f,dd = 7 bf = 7 τ = Folding ratio a) Eective bea-diuse solar optical properties b) Eective bea-diuse solar optical properties c) Eective bea-diuse solar optical properties f,bd τ f,bd =.3 bf =.3 τ = Profile angle (degrees) f,bd τ f,bd =.36 bf =.36 τ = Profile angle (degrees) f,bd τ f,bd = 7 bf = 7 τ = Profile angle (degrees) Figure 3. Eective solar optical properties of a drapery versus folding ratio for incident diuse radiation a) I M b) III M c) III L. Figure 4. Eective solar optical properties of a drapery (% fullness) versus profile angle of incident bea radiation a) I M b) III M c) III L. 7

8 nd Canadian Solar Buildings Conference Calgary, une 4, 7 ACKNOWLEDGEMENTS Financial support in ters of a Natural Sciences and Engineering Research Council of Canada (NSERC) Graduate Scholarship to N.A. Kotey and ASHRAE 3-TRP funds to.l. Wright are gratefully acknowledged. NOMENCLATURE Sybols de length of illuinated surface () F view factor (diensionless) G irradiance (W/ ) I incident flux (W/ ) radiosity (W/ ) K solar heat transfer factor (diensionless) s pleat spacing () w pleat width () Z diuse source ter due to incident bea radiation (W/ ) Greek Letters λ wavelength () reflectance (diensionless) τ transittance (diensionless) Ω profile angle Subscripts b related to back surface of drapery bb related to bea-bea optical property bea related to bea flux bd related to bea-diuse optical property bf related to backward facing surface of fabric dd related to diuse-diuse optical property di related to diuse flux f related to front surface of drapery related to forward facing surface of fabric i related to i th surface of the enclosure j related to j th surface of the enclosure Superscripts related to fabric solar optical property Abbreviations ASHRAE Aerican Society of Heating, Refrigerating and Air Conditioning Engineers ASTM Aerican Society for Testing and Materials IAC Interior Attenuation Coeicient (diensionless) NIR Near infrared SHGC Solar Heat Gain Coeicient (diensionless) UV Ultraviolet VIS Visible REFERENCES ASHRAE, 5. Handbook of Fundaentals. Aerican Society of Heating Refrigeration and Air Conditioning Engineers, Inc. ASTM E93-96, 996. Standard Test Method for Solar Absorptance, Reflectance, and Transittance of Materials Using Integrating Spheres. Aerican Society for Testing and Materials. Farber, E.A., Sith, W.A., Pennington, C.W., and Reed,.C., 963. Theoretical Analysis of Solar Heat Gain Through Insulating Glass with Inside Shading. ASHRAE ournal, pp. 79. Hollands, K.G.T, 4. Theral Radiation Fundaentals. Begell House, Inc, New York. Hunn, B.D., Grasso, M.M., Beaudry, M.A., and House, P.., 99. Measureent of Bidirectional Solar Optical Properties of Shading Fabrics. ASHRAE Transactions, vol. 97, pp Keyes, M.W., 967. Analysis and Rating of Drapery Materials used for Indoor Shading. ASHRAE Transactions, vol. 73, Part, pp Kles,.H., 994a. A New Method for Predicting the Solar Heat Gain of Coplex Fenestration Syste. Overview and Derivation of the Matrix Layer Calculation. ASHRAE Transactions, vol., Part, pp Kles,.H., 994b. A New Method for Predicting the Solar Heat Gain of Coplex Fenestration Syste. Detailed Description of the Matrix Layer Calculation. ASHRAE Transactions, vol., Part, pp Moore, G.L., and Pennington, C.W., 967. Measureent and Application of Solar Properties of Drapery Shading Materials. ASHRAE Transactions, vol. 73, Part, pp Ozisik, N., and Schutru, L.F., 96. Solar Heat Gain Factors for Windows with Drapes. ASHRAE Transactions, vol. 66, pp. 8. Pennington, C.W., Sith, W.A., Farber, E.A., and Reed,.C., 964. Experiental Analysis of Solar Heat Gain Through Insulating Glass with Indoor Shading. ASHRAE ournal, vol., pp. 7. Rudoy, W., and Duran, F., 975. Eect of Building Envelop Paraeters on Annual Heating/Cooling Load. ASHRAE ournal, vol. 7, pp. 9. Wright,.L., and Kotey, N.A., 6. Solar Absorption by Each Eleent in a Glazing/Shading Layer Array. ASHRAE Transactions, vol., Part, pp. 3-. Yellot,.I., 965. Drapery Fabrics and Their Eectiveness in Solar Heat Control. ASHRAE Transactions, vol. 7, Part, pp