evaluation of overheating protection with sun-shading systems

EVALUATION OFOVERHEATING PROTECTION WITHSUN-SHADING SYSTEMSTilmann E. Kuhn and Werner J. PlatzerDept. Thermal and Optical Systems, Fraunhofer Institute for Solar Energy Systems ISE, Oltmannsstr. 5, D-79100Freiburg, Germany, Phone: ++49 (0)761/ 4588-297, Fax: ++49 (0)761/4588-132, tilmann.kuhn@ise.fhg.deAbstract – Sun-shading systems have to provide thermal and visual comfort reliably and economically.At the same time, they should prevent unwanted solar gains in summer and permit high solar gains inwinter. This paper describes a method for the assessment of the heat barrier effect of different types ofsun-shading systems together with the associated control strategy.The starting point for the performance assessment is adequate characterization, appropriate to the size andcomplexity of the facade of the assessed building. The thermal characterization consists of the angledependentdetermination of the Total Solar Energy Transmittance g with a calculation method, which isvalidated with calorimetric measurements. The combination with typical irradiance distributions allowsthe evaluation of different control strategies. This paper shows that it is essential for the reliability of thecalculated cooling and heating loads, that this calculation is based on a control strategy, that fits with thepriorities of the building users.1. INTRODUCTIONOptimal use of daylight and solar heat gains in buildingsis made possible by the use of good sun-shading systems.This means that sun-shading systems must be able tocontrol and regulate solar gains through facades. Atpresent, there are no reliable standard methods for theevaluation of the effectiveness of sun-shading systems.This means that architects and building designers have tomake their own decision on the methodology. Frequently,this decision is wrong, as we know from buildings withoverheating problems in summer. In some of these cases,the Fraunhofer ISE made studies in order to detect theerror. The most frequent problem in our experience is thatpeople do not want to use the shading systems in the waythey are planned to be used. One example: In many casesbuilding designers assume that people are willing to closethe slats of venetian blinds in summer, which is not truein most cases. The demands of the future users of thebuilding have to be taken into account in an early stage ofthe planning process! The effectiveness of a sun-shadingsystem has to be assessed with methods that are able totake the various demands into account. This means thatthe planning team of a building has to agree on a controlstrategy that fits with the priorities of the future users.We developed a methodology to assess the effectivenessof a sun-shading system together with the associatedcontrol strategy. The methodology has been validatedwith internal and external venetian blinds supplied by thecompany Hüppe Form, Oldenburg, Germany. The nextsection is a discussion of the requirements of users. Apresentation of the methodology then follows.2. USER REQUIREMENTSrequirementsonsunshadingsystemsFigure 1: User requirements.thermal requirementsdaylighting andoptical requirementslow costshigh reliabilityaesthetic requirementscompliance with technicalboundary conditions(mounting dimensions, dimensionswhen the blind is fully retracted,...)protection againstfire, noise, weatherFigure 1 gives an overview of the requirements for sunshadingsystems. The most important factors for thebehaviour of users are the thermal and daylightingrequirements.Figure 2 specifies thermal and optical requirements indetail. It should be recognized that it is impossible tooptimize all criteria simultaneously. It is alwaysnecessary to find the compromise that best matches the..

priorities of the user. Three examples shall demonstratethis:1 For many systems, good visual contact to theexterior is only possible with reduced heatprotection.2 In many cases, a sufficient supply of daylight isonly possible with reduced heat protection.3 The winter solar gains are reduced, when shadingsystems are used for glare protection.thermalrequirementsdaylightingand opticalrequirementsFigure 2: Daylighting and thermal requirementshigh solar gains in winterlow solar gains in summerand high thermal comfortsufficient supplyof daylighthomogenous illuminationof the roomglare protectionprivacy protectionoptional room darkeningvisual contact to exteriorpleasant color impression3. g-VALUE AS A MEASURE FOR SOLAR GAINS3.1 The meaning of gTo assess the heat barrier effect of shading systems, acharacteristic number is needed which quantifies the solarthermal gains through facades: The total solar energytransmittance g. The g value specifies the total fraction ofincident solar energy which is transmitted through abuilding component. The transmitted energy fractionconsists of two parts: The solar transmittance and thesecondary internal heat transfer factor q i .heat100%reflection00000 11111111110000000000 1111111111 00000roller blind11111 00000glazing0000 11111111 00000000 11111111 00000000 11111111 000010 %absorption20 %heattransmittanceg-value= 0.2 ) (q i( τ e = 0.1 )Figure 3: The meaning of the total solar energy transmittance g(g = 0.3)Figure 3 illustrates the meaning of g for the example ofan internal roller blind. In this case, a g value of 0.3means that 30% of the incident radiation is transmittedinto the building. The following factors influence theeffectiveness of blinds and shutters, the exact value of gdepends on these boundary conditions:.• The position of the blind (internal, integrated orexternal).• g depends on the glazing and the blind. Inparticular the effectiveness of internal blinds ishigher, if they are mounted behind a solar controlglazing, instead of a glazing with the heat mirroron the outer surface of the inner pane (heat mirrorglazing). The reason is that in the first case, thereflected radiation from the blind is mainlyabsorbed in the outer pane. In the second case it ismainly absorbed in the inner pane.• The wind conditions.• The ventilation of the gaps.• The direction of the incident irradiation.Especially the last point is commonly neglected or nottreated correctly during cooling load calculations. It isimportant to note that the g value can be higher foroblique angles of incidence. This is very often the casewith blinds made of slats that can be tilted and controlstrategies with variable tilt angles of the slats. This meansthat the angular dependence of g must be taken intoaccount.3.2 Methods for the determination of gThere are two fundamentally different methods to determineg:• direct calorimetric measurementIn this procedure a segment of the real facade (e.g.1m 2 glazing plus blind without the frame andsurrounding support structure) is measureddirectly. This is done by irradiating the sampleeither with sunlight or a solar simulator. Behindthe facade, the transmitted energy is determinedcalorimetrically.For a detailed discussion see [Platzer et. al. 1997]or [Platzer 2000]• calculation methodsThe starting point of this method is thedetermination of the optical properties of thedifferent layers of the facade (e.g. transmittance,reflectance and absorptance of a venetian blindwith a defined tilt angle of the slats). These fundamentalproperties can be determined by opticalmeasurements or with additional calculations bywhich the overall properties of the layers arecalculated from the material properties.The second step is the calculation of the solardirect-hemispherical transmittance τ e of the wholesystem and the absorptance in each of the layers.The last step is the calculation of q i , the inwardflowing fraction of the overall absorbed energy.The sum of τ e and q i equals g.

Comparative discussion of the two methods:Advantages of the calorimetric measurement:• Direct measurement without model assumptions.This means that it is a reliable method.• No modeling necessary. This means, that thismethod is quicker for complex configurations.• Since real samples are assessed, deviations fromthe ideal properties of the samples are included inthe result (e.g. unequally tilted slats).Disadvantages of the calorimetric measurement:• Many time-consuming measurements are requiredto cover all the required combinations of glazingand blind with the defined operation modes andangles of incidence.• A sample of the facade has to be constructed andsent to the laboratory.Advantages of the calculation methods:• When the model has been prepared, the effect ofmodifications can be assessed quickly and easily.(e.g. different tilt angle or color of the slats)• No samples of the whole facade segment arerequiredDisadvantages of the calculation methods:• Validation with calorimetric measurement is mandatory.• At present there are no standards or draft standardswhich consider the angular dependence of g.3.3 Description of the chosen methodThe Fraunhofer Institute for Solar Energy Systems ISEcompared different calculation methods with calorimetricmeasurements for the company Hüppe Form, Germany.Together with the R+D department of this company, wehave chosen a practical method that is accurate, but nottoo costly. In this calculation method, the characterizationof the optical properties of the venetian blinds is donewith ray-tracing methods. The physical mechanismsconsidered during the ray-tracing process are shown infigure 4.The results of the ray-tracing process are the opticalproperties (reflectance, absorptance and transmittance) ofa venetian blind for variable tilt angles of the slats andvariable directions of the incident irradiation. The basis ofthe method is a geometrical model of the blind, whichdescribes the form of the slats, the distance between theslats and possibly existing perforated regions of the slats.The optical properties of the individual slats aredetermined in a measurement. The next step is acomputer simulation of an optical measurement, whichmeans that many virtual light particles (photons) areincident on the blind with a defined direction. Theevaluation of this virtual experiment is to count thereflected and the transmitted photons. The ratio of thereflected or transmitted photons to the incident photons isthe reflectance or transmittance respectively.incidentphotonsrollformed slat80 mmabsorptionscatteringglossysurface72 mmFigure 4: Schematic drawing of the mechanisms, considered in the raytracingmethod3.4 Validation of the methodThe accuracy of the method has been assessed for twodifferent internal venetian blinds and one externalvenetian blind. The following systems were provided tous by the manufacturer Hüppe Form, Oldenburg,Germany:• External venetian blind with metallic light grey slats.The width of the slats is 80 mm, the vertical distancebetween the slats 72 mm. The slats are rollformedand convex (edges curved downwards). A schematicdrawing of the slats is shown in figure 4.• Internal venetian blind with white slats. The width ofthe slats is 25 mm, the vertical distance between theslats is 20 mm. The slats are convex and perforated,except for an 8 mm broad area in the middle of eachslat. »Perforated« means that there are many smallholes in the slat. The transmittance of the perforatedarea was 7.7%.• Internal »daylighting« venetian blind. The slats areconcave (edges curved upwards), the upper side iscoated with a mirror foil, the lower side is paintedmatt light gray. The width of the slats is 25 mm, thevertical distance between the slats 20 mm. The slatsare convex and perforated, except for an 8 mm broadarea in the middle of each slat. The transmittance ofthe perforated area was 7.7%.

Table 1: Internal white venetian blind 25 mm (perforated) in combinationwith heat-mirror double glazed unit (DGU) K-Plus S (g DGU = 0.67,U DGU = 1.5 W/(m 2 K)). Tilt angle 0° means that the slats are in ahorizontal position.altitudeangleazimuthangletilt angleof theslatsg valuecalorimetricallymeasuredg Model(calculated)relativedeviation0 0 63° 0.42 0.41 -3%0 45 63° 0.41 0.40 -3%0 60 63° 0.36 0.38 7%0 0 closed(79°)0.34 0.35 1%45 0 0° 0.50 0.47 -5%60 0 0° 0.43 0.42 0%60 0 closed 0.32 0.33 1%Table 2: Internal »daylighting« venetian blind (perforated) incombination with heat-mirror glazing K-Plus S (g DGU = 0.67, U DGU = 1.5W/(m 2 K)).altitudeangleazimuthangletilt angleof theslatsg-valuecalorimetricallymeasuredg Model(calculated)relativedeviation0 0 63° 0.34 0.39 15%0 45 63° 0.38 0.39 3%0 60 63° 0.39 0.37 -5%0 0 closed(77°)0.35 0.29 -17%45 0 0° 0.60 0.62 3%60 0 0° 0.56 0.57 1%60 0 closed 0.30 0.29 -2%Table 3: External venetian blind pearl-silver 80 mm (not perforated) incombination with heat protection glazing K-Plus S (g DGU = 0.67, U DGU =1.5 W/(m 2 K)).altitudeangleazimuthangletilt angleof theslats0 0 closed(73°)g-valuecalorimetricallymeasuredg Model(calculated)0.02 0.050 45 closed 0.03 0.050 60 closed 0.03 0.0545 0 0° 0.09 0.1360 0 0° 0.04 0.0860 0 closed 0.01 0.04For the validation measurements, the blinds werecombined with a heat-mirror glazing manufactured byPilkington. The product name of the glazing is K-Plus S.The comparison between measured and calculated gvalues is shown in table 1-3. For the case of the internalwhite venetian blind, one can see the excellent agreementbetween measured and calculated values (table 1).For the »daylight« venetian blind, we found in principlethe same very good agreement. There are two exceptions:The first and the fourth measurement. In the first case themeasurement is difficult, because of the strong dependenceof g on the tilt angle of the slats.(In this case theslats are closed 8° more than cut-off 1 ). In the fourth casewe assume that the blind was not always closed exactly inthe same way.The calculated results for the external venetian blinds arealways slightly higher than the measured values.Concerning the heat barrier effect, the calculated valuesare on the safe side. The absolute difference (around 0.3)is sufficiently small.The results of this section can be summarized with thefollowing statements: The results of the calculationmethod have been validated with three very differenttypes of blinds and different combinations of altitude andazimuth angle. For these validation measurements, theblinds have been combined with a heat protectionglazing. The agreement between modeled andcalorimetrically measured values is very good.4. MODELING OF THE SKY RADIANCEThe angle-dependent g value is not sufficient for theevaluation of the heat barrier effect of sun-shadingsystems for two reasons: Most of the control strategiesfor venetian blinds use variable tilt angles of the slatswith the tilt angle depending on the actual position of thesun. In addition, the angular distribution of the irradiationhas to be considered. This means, that it is necessary totake into account typical weather and irradiation data forthe location of the building. In our calculations this wasdone on the basis of hourly direct horizontal and diffusehorizontal irradiance data taken from the respective TestReference Year (TRY) [Blümel et. al., 1986]. The skyradiance distribution was calculated using the Perezmodel [Perez et. al., 1990 ], [Perez et. al., 1993]. Thecontinuous radiance distribution of the diffuse sky wasdiscretized by splitting it into 145 circular angularpatches with cone openings of 11.15° according toTregenza [Tregenza, 1987]. The ground was assumed tobe an isotropic diffuse reflector with an albedo of 0.2.The ground surface was divided into 90 discrete patches.Direct irradiation was treated as a parallel beam. Thedirection of the beam was calculated from the geogra-1 The slat position »Cut-Off« depends on the direction of the irradiance.In this position the slats are opend as wide as possible without lettingthe sun shining directly through the blind.

phical position, date and time. For the calculation of thisradiance distribution a modified version of the programgendaylit has been used [Reinhart et al. 2000].5. ASSESSMENT OF THE HEAT BARRIERFUNCTIONALITY OF BLINDS TOGETHER WITHTHE ASSOCIATED CONTROL STRATEGY5.1 Control strategiesIn the following, we demonstrate the new methodologyfor the case of an external venetian blind with white slatsin combination with heat protection glazing (Interpaneiplus neutral R, U DGU = 1.2 W/(m 2 K), g DGU = 0.60). Theslat width and slat geometry of the venetian blind isshown in figure 4. The starting point of the performanceassessment is the decision about the control strategy. Asstated above, this decision should be made together withthe client and – if possible - the future user. This meansthat we are not able to define a general control strategy asa basis of the assessment. Instead of trying to do this, wewant to assess the performance of the system for two verydifferent control strategies.1 Strategy »closed«With this strategy, the slats are always closed totally,when the facade is irradiated directly by the sun. Theblind is fully retracted, when the facade is in theshade or when there is no direct illumination. For agiven combination of blind and glazing, this controlstrategy maximizes the overheating protection andglare protection 2 when the sun hits the facadedirectly. This control strategy ignores the need forvisual contact to the exterior. The dimensions of theroom and the windows will determine whether thesupply of daylight is sufficient or not.2 Strategy »cut-off«As for the first strategy, the blind is fully retracted,when the facade is in the shade or when there is nodirect illumination. When the sun is shining directlyon the facade, the slats are tilted into the cut-offposition.The slat position »cut-off« depends on theactual position of the sun. In this position, the slatsare opened as far as possible without letting the sunshine directly through the blind.This control strategy eliminates glare caused bydirect irradiation from the sun 2 and it ensures somekind of minimum overheating protection. AnAdvantage is the visible contact to the exteriorbecause of the opened slats, at least for higherpositions of the sun. Because of the protection of theroom from direct irradiation, the strategy ensures,that there are no directly lit stripes on desks orworkbenches. This means, that it elmininates veryuneven illumination of the room. The dimensions ofthe room and the windows will determine whetherthe supply of daylight is sufficient or not. Accordingto our experience, this strategy can be used veryoften as a worst case for the planning process. Thisdoes not imply at all that an automatic adjustment ofthe slats is necessary. The user is free to close theslats more than cut-off, but overheating protection isnot guaranteed, if the slats are opened further thancut-off. For the cut-off strategy, the tilt angle ofvenetian blinds is determined by the profile angle ofthe sun. The profile angle is the projection of thesolar altitude angle on a vertical plane perpendicularto the surface of the facade.5.2 Angle-dependent g valuesThe following figures 6-8 show the angle dependent gvalue for the example under consideration. The g value isshown in local coordinates, which means that thecoordinate system is fixed with respect to the surface ofthe facade. When the facade is vertical and southoriented, the local and global coordinate systems areequal. In this case local and solar azimuth angles andlocal and solar altitude angles are identical. The localcoordinate system was chosen because it is independentof the orientation of the facade.altitude angle706050403020100-75 -50 -25 0 25 50 75azimuth anglegWert00.06Figure 6: g-value for the external white venetian blind in combinationwith the heat-mirror glazing. Closed slats2 There is no guarantee that this control strategy actually ensuressufficient glare or overheating protection!

altitude angle706050403020100-75 -50 -25 0 25 50 75gWert00.23Figure 7: g-value for the external white venetian blind in combinationwith the heat-mirror glazing. Slats tilted 45°altitude angle706050403020100azimuth angle-75 -50 -25 0 25 50 75azimuth anglegWert00.57Figure 8: g-value for the external white venetian blind in combinationwith the heat-mirror glazing. Slats in horizontal positionFigure 6-8 showed the g value for fixed positions of theslats. For the control strategy »cut-off«, the tilt angle ofthe slats is adjusted according to the actual position of thesun. Figure 9 shows the tilt angle for this strategy and theexample under consideration.5.3 Solar gains and effective g-valuesKnowing the angle-dependent g value and the radiancedistribution of the incident irradiation, we calculated forevery hour of the year the incident solar energy and theenergy transmitted into the building. We did this forsouth, east and north oriented facades. The ratio of themonthly sum of the transmitted to the incident solarmonth,orientationenergy is the effective g value g efffor thismonth.month, orientation monthly sum of solar gainsgeff=monthly sum of incident irradianceIn this effective g-value are all different operation modesof the sun shading system included. In particular, the timeis included, when the system is retracted because of beingin the shade or because of purely diffuse irradiation. Forthe evaluation of the performance it is important to knowthe behavior of the system, when it is not retracted.Because of this, a second effective g value was definedthat takes into account only the time when the system isactive:month, orientationgeff, sunshading active =monthly sum of solar gains, ifmonthly sum of incident irradiance, ifThe following figures show the solar thermal behavior ofthe example under consideration. First we evaluate thecontrol strategy »cut-off«, then we asses the controlstrategy »closed«.In the following figures, the effective g values are plottedwith lines. Figures 10 and 12 show the effective g valuesand the associated solar gains for the whole months,including the time when the venetian blind is retracted.The only difference between figure 10 and 12 is thatfigure 10 is valid for the control strategy »cut-off« andfigure 12 for the strategy »closed«.Figures 11 and 13 show the effective monthly g valuesfor the time, when the sun-shading system is active. Thismeans that all ours with purely diffuse irradiation or withthe facade being in the shade are not considered ing month, orientationeff, sunshading active. The only difference between figure 11and 13 is the control strategy for the blind.system activesystem activetilt angle60504030201020 40 60 80profileangleFigure 9: Tilt angle of the external white venetian blind depending onthe profile angle. The control strategy is cut-off.

TRY5 (Würzburg), External white venetian blind + heat-mirror glazing35300.700.60solar gains [kWh/m^2]2520151050.500.400.300.200.10effektive g values01 2 3 4 5 6 7 8 9 10 11 12monthsolar gains north solar gains east solar gains southg_eff north g_eff east g_eff southFigure 10: Solar gains and effective g values for a vertical facade in Würzburg, Germany (TRY5). The facade consists of the external white venetianblind in combination with the heat-mirror glazing. The control strategy is »cut-off«.0.00External venetian blind + heat-mirror glazing. TRY50.30g_effektiv system active0.250.200.150.100.050.000 1 2 3 4 5 6 7 8 9 10 11 12g_eff shading active northmonthg_eff shading active eastg_eff shading active southFigure 11: Evaluation of the time, when the blind is active. Solar gains and effective g values for a vertical facade in Würzburg, Germany (TRY5).The facade consists of the external white venetian blind in combination with the heat-mirror glazing. The control strategy is »cut-off«.The average annual gfor all orientations and the control strategy »cut-off« is 0.19 for TRY5 (Würzburg,Germany). For TRY3 (Berlin/ Essen, Germany) we found an average value ofeff, sunshading active0.20.

TRY5 (Würzburg), External white venetian blind + heat-mirror glazing350.70300.60solar gains [kWh/m^2]252015100.500.400.300.20effektive g values50.1001 2 3 4 5 6 7 8 9 10 11 12monthsolar gains north solar gains east solar gains southg_eff Nord g_eff Ost g_eff SüdFigure 12: Evaluation of the time, when the blind is active. Solar gains and effective g values for a vertical facade in Würzburg, Germany (TRY5).The facade consists of the external white venetian blind in combination with the heat-mirror glazing. The control strategy is »closed«.0.00External venetian blind + heat-mirror glazing. TRY50.05g_effektiv system active0.040.030.020.010.000 1 2 3 4 5 6 7 8 9 10 11 12g_eff shading active northmonthg_eff shading active eastg_eff shading active southFigure 13: Solar gains and effective g values for a vertical facade in Würzburg, Germany (TRY5). The facade consists of the external white venetianblind in combination with the heat-mirror glazing. The control strategy is »closed«.gfor all orientations and the control strategy »cut-off« is 0.04 for TRY5 (Würz-eff, sunshading activeThe average annualburg, Germany).

The difference between the results for both controlstrategies shows, that the control strategy (or the behaviorof the user) has a big influence on the solar gains. Whenthe system is active, the gains differ by a factor of 5,depending on the control strategy!Comparing the solar gains for north and south facades, itis found out that the summer solar gains per m 2 are higherfor north oriented facades than for south oriented facadesfor the external blind and control strategies underconsideration. The effect is caused by the hours withpurely diffuse illumination. It proves the statement, thatthe diffuse irradiation must be taken into account.6. CONCLUSIONSWith the presented methodology it is possible to make acomparative evaluation of sun-shading systems togetherwith the associated control strategies. Whether a sunshadingsystem provides sufficient overheating protectionor not depends on the building (window area, internalloads, ...) and has to be determined for each buildingindividually. The results of the paper can be summarizedin the following statements:• The demands of the future user have to be taken intoaccount in an early stage of the planning process.This means, that the planning team has to agree on acontrol strategy that fits with the priorities of thefuture users. The control strategy can be different fordifferent sun-shading systems.• For a realistic and reliable evaluation of theoverheating protection it is necessary to take intoaccount the angular distribution of the incidentradiation. For this, the determination of the angledependentg value is necessary.• The methodology developed at Fraunhofer-ISE hasbeen validated for different sun-shading systems ofthe company Hüppe Form, Oldenburg, Germany. Itallows a realistic and reliable evaluation of overheatingprotection with sun-shading devices.7 ACKNOWLEDGEMENTSThe validation of the method presented here was fundedby Hüppe Form, Oldenburg. We are grateful to the R&Ddepartment for their willingness to cooperate and theirinterest in exact evaluation of their products. We alsothank them for allowing us to publish the results, so thatwe could present them to a wider audience in this paper.REFERENCES[Blümel et.al., 1986][Perez et.al., 1990][Perez et.al., 1993][Platzer et.al. 1997][Platzer2000][Reinhartet. al.2000][Tregenza,1987]Blümel, K.; Hollan, E.; Jahn, A.; Kähler,M.; Peter, R. Juli 1986.Entwicklung von Testreferenzjahren (TRY)für die Klimaregionen der BundesrepublikDeutschland. Scientific report of theInstitute for Geophysical SciencesTechnical University Berlin.BMFT-FB-T- 86-051Perez, R.; Ineichen, P.; Seals, R.;Michalsky, J.; Stewart, R. Modeling ofdaylight availability and iradiancecomponents from direct and globalirradiance, Solar Energy 44 (5) (1990) 271-289Perez, R.; Seals, R.;, Michalsky, J. Allweathermodel for sky luminancedistribution – preliminary configuration andvalidation, Solar Energy 50 (3) (1993) 235-245.Platzer, W.; Apian-Bennewitz, P.; Kuhn,T.; Dill, F.-U.; Wirth, H.; Wittwer, V.November1997.Studies on the elements of optical andthermal energy transport through largecomponents with transparent thermalinsulation and shading (in german)ETDE- Energy Databse-production no.:DE98G6016Platzer W. J.; May 2000. The ALTSETProject. Angular properties of complexglazings through solar calorimetryto be submitted to EUROSUN 2000Reinhart, C.; Walkenhorst, O.; DynamicRADINACE-based Daylight Simulationsfor a full-scale Test Office with outerVenetian Blinds. Working paper (April 18,2000) to be submitted to Energy andBuildingsTregenza, P. Subdivision of the Skyhemisphere for luminance measurements,Light. Res. Technol. 19 (1987) 13-14.