ABSTRACT

The evaluation of shading devices is generally carriedout using a sequence of shadow pattern imagesshowing the progression of solar penetration forparticular times of the day or year. This approach canreveal when solar penetration may occur, say at thesummer solstice, but it cannot give a quantitativemeasure of the degree and likelihood of solarpenetration over a representative period of a full year.This paper describes a new image-based technique toquantify the effectiveness of shading devices. It isfounded on predictions of direct solar irradiation usinghourly meteorological data for a full year. In additionto numerical output, the technique produces synopticimages that reveal the spatial and temporal variation ofsolar irradiation. There are no practical limits on thescene geometry and buildings with thousands ofindividual shading elements can be evaluated. Thetechnique is designed to be both fast and highlyscalable making it suitable for the evaluation of a largenumber of design variants. This is demonstrated in thepaper using a parametrically defined model of acomplex roof shading system based on the ChangiAirport Terminal 3 design. The three thousand sixhundred fins that comprise the roof shading systemwere generated using a parametric scheme where thefin orientation has a random component. A total offorty-two design variants of the roof shading systemwere evaluated using the new technique.

INTRODUCTION

The usual assessment method for solar penetration isbased on one or more ‘snapshot’ images showingviews of the internal surfaces illuminated by direct sunat certain times of the year [BRE, 96]. This can beachieved using scale models with a heliodon or berendering-based. The images in Figure 1 show aninternal view of a ‘Drafting Office’ 3D computermodel (top) and two frames from an animationsequence that was generated to show the progressionof solar penetration from the rooflights and windows.The internal view and the animation were rendered

using the Radiance lighting simulation system [WardLarson et al., 98]. The animation frames comprisepairs of images showing the sun’s view of the building(left) and the internal view from high above (right).The sequence was generated for all daylight times at15 minute intervals for the first day of each monthJanuary to June. For the image on the right of theanimation frames, the roof was eliminated from theview using a feature in Radiance called ‘clippingplanes’. A green ‘wash’ of ambient light was used toprovide a subdued background against which thebright patches of solar penetration are clearly seen.Computer simulation offers many advantages overphysical modelling approaches for the conventional

Figure 1. Traditional approach to modelling solarpenetration: generate progression of shadow patternsfor various times of the day or year.

PRECISION MODELLING OF PARAMETRICALLY DEFINED SOLARSHADING SYSTEMS: PSEUDO-CHANGI

J. Mardaljevic BSc MPhil PhDInstitute of Energy and Sustainable Development (IESD)

De Montfort University, Netherleys BuildingScraptoft, Leicester LE7 9SU, UK

Tel. +44 (0) 116 257 7972, Fax. +44 (0) 116 257 7981Email jm@dmu.ac.uk

Eighth International IBPSA Conference Eindhoven, Netherlands

August 11-14, 2003

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shadow-pattern analysis. For example: detail can beaccurately modelled at any scale; the generation ofmovie sequences can be automated; and, the Radiance‘clipping plane’ technique has no equivalent inphysical (i.e. scale) modelling. These advantagesnotwithstanding, the fundamental limitations of thebasic approach remain unchanged: it is essentiallyqualitative. The conventional assessment method canonly disclose when solar penetration may occur butcannot make any quantitative measure of it.

For complex shading systems comprised of many,possibly thousands, of individual shading elements,the conventional shadow-pattern approach is unlikelyto offer any meaningful basis for design evaluation.Doubly so when there are a number of design variantsthat need to be considered. Consider the concept-rendering of the roof shading system proposed forChangi Airport Terminal 3 in Singapore, Figure 2.This gives a visual impression of a highly complexshading system envisaged for the terminal building byarchitects Skidmore, Owings & Merrill.

The precise details for the Changi roof design were notknown to the author. It is understood however that, forthe concept-rendering, a parametric scheme with arandom component was used to orientate thethousands of shading fins. A critical design factor forthe Changi Terminal 3 roof will have been thepotential for solar gain at floor level, and theassociated cooling load - quantities beyond the graspof the conventional shadow-pattern approach.

This paper describes a new technique to predict solarpenetration in buildings which is founded on animage-based simulation of the total annual irradiationdue to direct sun incident on internal building surfaces.The new approach has several advantages over thestandard method. For example, all possible sunpositions are accounted for, and, because the analysisis founded on realistic meteorological data (e.g. testreference year time-series), a quantitative measure ofdirect solar penetration is obtained. Thus it is possibleto make reliable quantitative comparison of two or

more design variants. For this paper, the new approachwas used to evaluate 42 design variants of a highlycomplex roof shading system similar to that envisagedfor Changi Airport.

NEW APPROACHSTIMAPThe new approach is called Spatio-TemporalIrradiation Mapping (STIMAP). The spatial mapreveals the quantity and distribution of total annualdirect irradiation incident on a building surface orsurfaces. Whereas the temporal map shows thepropensity for high instantaneous irradiation acrossthose surfaces throughout the year. Example resultsfrom an earlier study on the effectiveness of a brise-soleil are shown in Figure 3 [Mardaljevic, 01].

Figure 2. Rendering showing visual impression ofChangi Terminal 3. Image by J. Seagull, copyrightPixel by Pixel and Skidmore, Owings & Merrill.

Figure 3. Rendering and STIPMAP analysis ofbuilding with brise-soleil.

TAI [Wh/(m2yr)]

0.0E+00

1.0E+04

2.0E+04

3.0E+04

4.0E+04

5.0E+04

With brise soleil

With brise soleil

1 2 3 4 5 6 7 8 9 10 11 12Month

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Ho

ur

******

(a)

(b)

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Spatial Map

(c)

Wh/m2

N

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The spatial map clearly shows high levels of totalannual direct irradiation for some sections of thebuilding perimeter, Figure 3b. The propensity for solarpenetration throughout the year is revealed in thetemporal map, Figure 3c. This shows that the highestlevels of solar penetration will occur between thehours 17h00 to 19h00 for the months April to August,and during early morning for the winter months.

The adoption of an image-based approach impartssignificant advantages over the conventionalassessment methods. In addition to providing precise,quantitative performance data, the images can beeasily understood with the bare minimum ofexplanation. Indeed, those architects that have workedwith the analyses have remarked that it is far easier togain an insight into shading performance fromSTIMAP images than from the usual sequence ofshading pattern images (Private Communication:James Nicholls, SGP Architects, UK). This is becausethe spatial map is, in effect, a (quantitative) cumulationof a ‘movie’ sequence of shading patterns for an entireyear at a short time-step. Furthermore, the STIMAPimages are more readily intelligible than thecommonly used sun-path stereographic-projectioncharts [Energie, 00].

STIMAP - Theoretical basisThe total annual (direct) irradiation, or TAI, iscomputed using physically-based lighting simulation(i.e. rendering) techniques. The standard (UNIX)Radiance lighting simulation system is used as therendering ‘engine’ in STIMAP. The Radiance systemhas been rigorously validated by the Author andproven to be highly accurate for daylight modelling[Mardaljevic, 01]. The key to the new technique arethe algorithms that allow the efficient computation ofimages of the total annual irradiation based on hourly(or sub hourly) meteorological data, e.g. test referenceyear (TRY) (in US, TMY) time-series. Using hourlyvalues, a brute force approach would entail thecomputation of ~4,000 irradiation renderings - one foreach hour of daylight. In STIMAP, the total annualirradiation is accurately synthesised from a muchsmaller number of renderings (~200). This is achievedby transforming the problem from the time-seriesdomain to the sun-position domain.

The transformation involves several stages. First, theabove-horizon sun positions that occur annually at thelocation of the proposed building are computed usingstandard equations [Tregenza et al., 93]. The localeused for the pseudo-Changi example described belowwas the Midlands, UK. Any geographical locationcould be used, the only requirement is a suitable TRYdataset. Although a timestep of 1 hour is usual forTRYs, a 15 minute time-step for sun positions is usedas the default to ensure a smooth distribution. The sun

positions for the Midlands, UK are shown inFigure 4(a). The distribution in altitude and azimuth isdivided into ‘bins’ using a grid of arbitrary resolution.Here a grid size of 8˚ was used for both angles. Thisbin-size is commensurate with a timestep ofapproximately half an hour (because the sun traversesan arc of 15˚ every hour). The number of sun positionsthat occurred in each bin are counted, and the bin-mean sun position evaluated, Figure 4(b). The numbercounted for each bin is indicated by shade (seeadjacent legend), and the bin-mean position is markedby a cross (x). For this combination of locale and binsize, there were 179 bins that contained one or moresun positions. A series of 179 irradiance renderingsshowing the floor plan are then computed - one eachwith a unit radiance sun at the bin-mean sun position.A good position to ‘view’ the floor plan is from highabove its approximate mid-point. This is the positionof the ‘virtual camera’ for the renderings. From thisvantage point it is possible to ‘see through’ the roof ofthe building by applying the forward clipping plane inRadiance. This eliminates all visible surfaces in frontof the vantage point to a set distance withoutinterfering with the simulation of the propagation oflight. The total annual irradiation image due to all thesun conditions in the TRY is synthesised from these179 irradiance renderings.

For any fixed (or almost fixed) configuration of self-radiant entities (i.e. sun) in a scene, an irradiationimage of the scene is equal (or almost equal) to thenormalised irradiation image multiplied by themagnitude of the radiant output of the sourceconfiguration. For example, the irradiation imagefor a scene ‘lit up’ by a sun of radiance is givenby:

Figure 4. Procedure to determine the sun position forthe sun and the anisotropic sky renderings from thedistribution of annually occurring sun positions (15minute timestep).

50 100 150 200 250 300Azimuth [deg]

0

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Alti

tude

[deg

]

Nocc = 179 Ptot =17635

50 100 150 200 250 300Azimuth [deg]

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]

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(1)

Where is the normalised irradiance image for thescene computed using a sun of unit radiance atposition , and is the integration period, i.e. thetime-step used for the distribution shown in Figure 4.The actual sun position needs to be at or near to theposition . Here, the position is the bin-meanposition and or near to applies to all those sunpositions in that bin. Note that the irradiation image issimply the normalised irradiance image (an array)multiplied by the product of two scalars. It is possibleto synthesise an irradiation image for each time-step ofthe TRY using Eqn. 1 and then sum the images to givean image for the total annual irradiation. This totalhowever can be computed far more efficiently by firstevaluating bin-totals on a bin by bin basis as follows.The bin-total irradiation image for bin is:

(2)

where, is the solar radiance for position andis the normalised irradiance image for bin .

Here, is also used to denote the set of positions forthat bin, and is the number of elements (i.e.positions) in the set. Note that the summation is simplythe arithmetic total of the sun radiances for the all thesun positions in bin and so accounts for all thevarying sun conditions for that bin e.g. clear, cloudy,hazy etc. Also, it is a simple matter to synthesise atime-series of the instantaneous direct irradianceaveraged across the floor plan. This quantity will beneeded to determine the peak solar cooling load.

The solar radiance values for this analysis werederived from the direct normal irradiance time-seriesof the Kew TRY, Figure 5. The hourly values of the

TRY were interpolated to a 15 minute time step tomatch that used for the distribution in sun positions(Figure 4). The irradiation image total for theentire year is computed by summing the bin-totals forall the bins in the distribution as follows:

(3)

For the distribution shown in Figure 4, the number ofbins = 179. Annual totals of irradiation are the moststraightforward to derive using this method. However,the summation can easily be modified to produce atotal for any desired fraction of the year, e.g. seasonaltotals, monthly totals, am and pm totals etc.

The computation times for the renderings are veryshort because only direct irradiation is modelled. Theset of 179 renderings for each unique roof design takesonly about 10-15 minutes, and the entire run for 42cases only a few hours (Apple iMac, 800MHz, G4).

PARAMETRICALLY DEFINEDSHADING SYSTEMSThe Pseudo-Changi ModelThe building model used to demonstrate the newapproach was inspired by the concept-rendering ofChangi Terminal 3 (Figure 2). The form of the schemeused to orientate the fins was not known, and the finaldesign may differ from that shown in the concept-rendering. Accordingly, the model devised for thispaper is referred to as “pseudo-Changi”.

A parametrically defined shading system is one wherea key property of the system (e.g. fin orientation) isgoverned by some rule (i.e. equation). The geometryof the shading system is then generated using the rule.It is often a simple matter to change one or moreparameters of the rule which allows the possibility forgenerating any number of variants of the originaldesign. The roof structure of the pseudo-Changi modelcomprised 3,600 shading fins positioned just under adouble-glazed roof. Each fin was 3m square, thoughthe absolute dimensions are not relevant for thepurpose of demonstration. The fins were arranged inrows of opposing pairs, i.e. ones that shared the same‘hinge’, Figure 6.

Figure 5. Test reference year time-series for directnormal irradiation. The time-series of 8,760 hourlyvalues is shown as a 365 (day) by 24 (hour) array.

I psun

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Figure 6. Close-up of pseudo-Changi roof.

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‘Hinge’ line Row of opposing pairs

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Parametric schemeThe rest position for each of the shading fins was 0˚ tothe horizontal, i.e. fully ‘closed’. The fin was displacedfrom rest (i.e. ‘opened’) depending on the magnitudeof a (uniform) random number. A probability factorgoverned the likelihood that a fin would be opened forany given random number. The probability factorapplied to the shading fins was one design parameter,the other was the overall orientation of the roof whichwas varied from 0˚ to 180˚ in steps of 30˚. A preferreddesign for shading systems of this type may be to havefins on one side of the hinge that are more open thanthose on the other. This allows the possibility foraspects not prone to solar penetration to be more openfor the provision of daylight, Figure 7.

The parametric scheme for displacing the fins was asfollows. For the rows of fins initially on the north sideof the hinge:

Where is a uniform random number in the range 0 to1, and is a probability factor in the range 0.4 to 0.9.This factor was fixed for each of the design variants.For the rows of fins initially on the south side of thehinge:

With this scheme, there is a probability of 0.3 that thefins on either side of the hinge remain closed. For

= 0.4, there is a probability of 0.1 that the fin will beopened to 4˚ and a probability of 0.6 that it will beopened to 25˚ (for , the fin initially on the north sideof the hinge). The design variant where = 0.4 hasthe highest probability of ‘open’ shading fins, and theone where = 0.9 has the lowest probability.

Renderings showing the view of the roof shadingsystem from above together with the pattern of solar

penetration on the floor for one sun position are givenin Figure 8. Note the clumping pattern visible in the

arrangement of the fins and the shadow pattern on thefloor. Computation of the total annual directirradiation was carried out for all combinations of sixprobability factors (0.4 to 0.9 in steps of 0.1) and sevenorientations (0˚ to 180˚ in steps of 30˚). The results arepresented in the following section.

RESULTS

Spatial and temporal irradiation maps were producedfor each of the 42 variants for the roof shading system.For reasons of brevity however, the temporalcomponent of the analysis is not presented in thispaper. The total annual irradiation averaged across thefloor area was determined from the irradiation images.This single value characterises the overallperformance of the each variant of the shading systemin terms of solar radiation incident on the floor,Table 1.

Figure 7. Fins in rows of opposing pairs.

θsθn

Glazed roof

Shading finsdisplaced from‘closed’ position

if x 0.3<( )then θn 0˚=

if x 0.3≥( )and x V<( )( )then θn 4˚=

if x V≥( )then θn 25˚=

xV

if x 0.3<( )then θs 0˚=

if x 0.3≥( )and x V<( )( )then θs 8˚=

if x V≥( )then θs 50˚=

V

θnV

V

Figure 8. Renderings showing views of the shadingsystem and the pattern of solar penetration on thefloor (one sun position).

TAIProbability factor

0.4 0.5 0.6 0.7 0.8 0.9

Ori

enta

tion

0˚ 62.7 55.7 47.9 40.5 29.9 19.8

30˚ 59.8 53.1 44.8 37.5 29.8 18.2

60˚ 53.3 46.0 43.5 35.1 26.2 16.9

90˚ 47.1 41.9 37.2 30.4 23.9 15.3

120˚ 41.1 36.8 32.7 28.4 20.5 12.5

150˚ 35.7 33.1 29.6 24.9 18.2 10.7

180˚ 34.0 32.2 29.4 24.5 19.2 11.1

Table 1. Total annual solar irradiation averagedacross floor area (kWh/m2) for all 42 design variants.

30˚

N

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The results in Table 1 reveal the precise relationbetween the two design parameters (probability factorand orientation) and the total annual irradiation. Thepeak instantaneous irradiance (PII) averaged acrossthe floor area was also determined, Table 2.

Irradiation images for two of the design variants areshown in Figure 9 together with renderings giving aview from above of the shading fin array (these twovariants are identified in Table 1 and Table 2 withheavy yellow tint).

DiscussionThe analysis has demonstrated the relative ease andspeed with which a large number of design variants ofa complex shading system can be evaluated in terms ofdirect solar penetration. As noted, the pseudo-Changiroof example was used solely to showcase the newtechnique. The design parameters and performancespecification for the actual Changi roof were notknown, so no attempt was made to guess what theymight be. The clumpy patterns in total annualirradiation that result from the parametric schemepresent some interesting design possibilities

(Figure 9). The areas of high total annual irradiationcould be used to locate the trees and planting that thearchitects envisage for this building (Figure 2).

PIIProbability factor

0.4 0.5 0.6 0.7 0.8 0.9

Ori

enta

tion

0˚ 124 107 88 73 52 35

30˚ 122 110 87 72 56 33

60˚ 126 102 94 73 52 32

90˚ 122 100 92 66 50 32

120˚ 116 100 87 68 47 30

150˚ 96 85 69 55 39 24

180˚ 70 65 56 45 35 20

Table 2. Peak instantaneous solar gain averagedacross floor area (W/m2) for all 42 design variants.

Figure 9. Rendering of shading fin configuration and image of total annual irradiation for two variants.

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V = 0.5, orientation = 60˚ V = 0.8, orientation = 60˚

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Protection from direct solar penetration is one part ofthe design specification for a shading system. Theprovision of adequate daylight is another key function.The author has demonstrated the accurate predictionof time-varying internal illuminances based on thesame meteorological data used here to predict totalannual irradiation [Mardaljevic, 00]. In a full-blownperformance analysis, the design of the roof shadingsystem could be tailored with some precision tobalance the competing requirements of solarprotection and daylighting.

The new technique can of course be used to image anybuilding surface including the shading devicesthemselves. This could be used to optimize the designof complex shading structures by identifying thoseparts of the structure that experience low levels ofirradiation, i.e. possibly redundant structure that addslittle to the overall shading of the building. If required,views showing the floor and walls together could berendered using ‘fish-eye’ view parameters from avantage point just below the ceiling. Total annualirradiation images for these views would be computedas before.

When detailed comparisons are required to fine-tune adesign, a technique called difference mapping can beapplied to pairs of both the spatial and the temporalmaps. A difference map is simply one spatial (ortemporal map) subtracted from another. Thedifference maps disclose precisely how one designperforms relative to another in terms of where (spatialdifference) and when (temporal difference) solarpenetration occurs.

In terms of the precision and scope of the analysis, andthe swiftness of the computation, it is hard to see howa physical (i.e. scale) model approach could rival theevaluation presented here.

CONCLUSION

The shading analysis described here offers a markedadvance over traditional, largely qualitative, methods.The new technique can be applied to very complexshading systems, working either directly with 3DCAD models, or, as shown here, using parametricallydefined geometries. The images showing total annualirradiation are easy to interpret and disclose muchgreater information on overall shading performancethan the more numerous, but qualitative, shadow-pattern images of the conventional method. Thenormalised irradiance images can be processed toproduce irradiation images and/or numerical data onvirtually any spatio-temporal aspect of direct solarpenetration. The reduction of data to summary metricsallows for the reliable comparison of any number ofdesign variants.

ACKNOWLEDGEMENT

Rob Shakespeare (Indiana University, USA) createdthe 3D model used in Figure 1. The author wishes tothank Architects Stephen George & Partners(Leicester, UK) for permission to use the buildingmodel shown in Figure 3. The movie sequence used inFigure 3 can be down-loaded from:

http://www.iesd.dmu.ac.uk/~jm/sg98jm.mov

REFERENCESBRE Designing with Innovative Daylighting Building

Research Establishment Report BR302 (1996)Energie Solar shading for the European climates

Energy Research Group, University CollegeDublin, European Commission Report, 2000http://erg.ucd.ie/mb_shading_systems.pdf

Mardaljevic, J. The Simulation of Annual DaylightingProfiles for Internal Illuminance Lighting Res.Technol. 32(3) (2000)

Mardaljevic, J. The BRE-IDMP dataset: A newbenchmark for the validation of illuminanceprediction techniques Lighting Res. Technol. 33(2)(2001)

Mardaljevic, J. A new image-based technique topredict solar penetration CIBSE NationalConference, July 2001

Tregenza, P. and Sharples, S. Daylighting AlgorithmsETSU S/1350 (1993)

Ward Larson, G. and Shakespeare, R. Rendering withRadiance: The Art and Science of LightingVisualization San Francisco: Morgan Kaufmann.(1998)

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