A composite
photograph showing the interior of a model within an image of the inside
of the Artificial Sky.

Daylight Modelling in an Artificial Sky as a Teaching Aid to the understanding of Daylight

Mike Baker


Optimising the use of daylight in a building is essential to minimise the use of energy and production of pollution, and for occupant health. Designing for daylight use can be a significant determinant in the development of architectural form. It is therefore necessary to understand how daylight is distributed within an interior. This paper sets out the techniques for using a simple mirror-box artificial sky as an aid to that understanding through generic testing of daylight models and analysis of specific design proposals, going beyond establishing the basic Daylight Factor. The paper discusses the construction of models and the need for accuracy in both model making and experimental technique. The use of orientation factors is introduced to weight measured values according to the orientation of the sources of light in the modelled building, equivalent to testing in a more realistic sky luminance distribution. Interpretation and presentation of data, together with the causes of divergence between predictions and reality are discussed.

Keywords: artificial sky, mirror-box (artificial) sky, overcast sky, daylight modelling, daylight factor, orientation factor.

This image shows Mike Baker's Artificial
Sky from the inside.

Photo 1: Inside a Mirror-Box Artificial Sky

1 Introduction: The value of physical modelling for teaching and studying daylight performance of buildings

Testing a physical model of a design proposal within an artificial sky can yield much information relating to the daylight performance. The Daylight Factor (DF) for the working plane throughout the space is the basic measurement. By relating the DF to statistical daylight availability data, the periods for which the desired level of illumination is achieved can be determined. With this information, the implications of the design for energy use and cost may be estimated. In addition to the quantitative data, the visual quality of the distribution of light within the modelled space may be assessed, and recorded by conventional or digital photography.

Generic studies of daylight models are arguably yet more valuable as the acquired knowledge will contribute to the design process at the conception stage, introducing criteria that will influence the form of a building.

Computer-based lighting simulation systems such as RADIANCE [1] offer some advantages over physical modelling, share some of the same problems, and uniquely suffer others: testing a model in an artificial sky provides a physically interactive method for quickly assessing different design tactics - by changing position of shading devices, changing facade details and ceiling types, for example - providing a useful teaching environment.

2 Description and development of CIE overcast sky distribution in a Mirror-Box Artificial Sky

The CIE Overcast sky model, having a symmetrical luminance distribution about the zenith and therefore unaffected by orientation, can be quite accurately reproduced using a mirror-box set-up as described by Hopkinson [2] and originally developed at the BRE. The example here is a simplified version developed at the Martin Centre [3], based on a nominal 2.4m square, and illuminated with sixteen 36W colour corrected lamps. This arrangement provides an illuminance of about 2500lux which is quite adequate when used with modern photometers of high sensitivity. The workspace is sufficient for relatively large models, and for demonstration to two or three students.

image shows a model being used for photography within the artificial

Photo 2: Photographing a model inside the Artificial Sky

3 Model construction

Whilst the micro-order of the wavelength of light enables accurate simulation using scale models, there are specific needs for the accuracy of the models themselves. Designers frequently make simplistic models of their proposals, at one time in balsa wood, now more often in foamboard, and invariably without any surface treatment in the belief that this 'purity' reveals the true form of their design. But as form can only be perceived when lit, and the lighting of interiors is dependant on the many interreflections from the surfaces of the interior, then the correct photometric characteristics - reflectance, texture and colour - are essential to accurate analysis and appreciation of the interior.

3.1 Structure

Appropriate scale of the model is the first consideration. 1:20 is suitable for quite detailed examination of a space, but a two-storey model is at the limit of what can be tested with reasonable accuracy in a sky of the size described. 1:50 permits testing of larger spaces, but will make the modelling of some elements - windows, shading devices - more difficult, and the measurement of vertical DFs impracticable. On occasions it may be necessary to use an intermediate scale, say 1:33 (such scales are available, or could be constructed on card). Cardboard, foamboard and medium density fibreboard (MDF) are useful materials for the main enclosure and subdivisions of a modelled space. MDF is excellent for large spans and for machining, though this requires workshop facilities and some skill. Foamboard is relatively easily worked, but is less stable and not opaque, needing surface treatment to make it lightproof. All joints must be made lightproof either by their own integrity or by covering with opaque paper or adhesive tape.

The ability to introduce different elements and surfaces during the test programme may be accommodated by sliding different ceiling or wall panels into a coherent outer shell. A grid should be marked out on the floor surface to locate photocell positions. Specific access to move the photocell around must be provided if the model's window openings are glazed. This access may be made to double with a camera view-point.

3.2 Openings

Dimensional accuracy and detail of the sources of daylight is essential. Window frames and glazing bars may obscure up to 35% of the structural opening, deep mullions may act as secondary light sources. Omission of these details, or lack of compensation will affect the whole study.

Glazing of the openings must be considered. Correction factors (table 2) are commonly applied to the measurements derived in unglazed models. But these factors may be over simplistic. Transmission of light through glass decreases rapidly once the angle of incidence exceeds 60∞. A space sidelit by vertical facade glazing may, if the view of the sky from the window is obscured by other buildings or topography, derive most light from a higher altitude and at an increased angle of incidence. Spaces sidelit by lightwells or atria are thus affected.

Where it is difficult to fix glazing into the detail of a model opening, it may be easier to fix the glazing bars and facade surfaces to a sheet of glass forming the glazed wall of the model.

The transmission of light through transparent and translucent materials is accurately handled by RADIANCE.

This image shows the atrium of the Housing 21

Photo 3: Housing 21 Headquarters Atrium

3.3 Detail: shading devices

One of the main values of physical modelling is that once the spatial model is made, one can quickly, if at times crudely, test shading and reflecting devices. But to be meaningful, such devices will eventually need to be modelled with some accuracy.

To ease their construction, small elements such as louvres may be modelled at a larger scale than that of the spatial model, providing that the overall geometry is maintained. The degree to which the scale might be increased is limited by where it may be judged that the distinction between the transmissive and non-transmissive part of the element is of a scale which would inaccurately redistribute light into the interior.

The characteristics of translucent materials - where a sample of the 'real' material cannot be used - can be difficult to reproduce accurately: the hemispherical transmission of the real material may differ from layers of tracing paper or drafting film assembled to give the same more easily measured normal transmission values.

3.4 Interior Surfaces

Interior surfaces should have reflectances as near as possible to the likely finishes of the real building. Ceilings and walls, where they are painted, are relatively easy to model, as are larger scale structural elements. Standard emulsion paint is useful as most manufacturers quote diffuse reflectance values. The texture of surfaces may be more difficult to replicate.

The photometric characteristics of floor finishes, particularly if carpeted, may also be difficult to replicate as the material is likely to have a non-uniform reflectance. However, in many office or institutional spaces the floor surface is unlikely to be a significant reflector as it may be obscured by furnishings, and, indeed, it would be more useful to model the furniture itself. But even in these situations there may be critical areas as is demonstrated in photo 3, where the reflectance of the carpet at the base of the atrium is half that of the model tested, consequently much less light than predicted is reflected up on to the ceiling.

Values for the diffuse reflectance of common materials are given in Daylighting Design [4] .

3.5 Internal obstructions: furnishings

Furnishing details are frequently not the responsibility of architects, and probably rarely in mind at the stage when a design proposal is being tested in an artificial sky, but the presence of furniture, the clutter of VDUs, reference books - and occupants - can significantly impede distribution of light. For example, the vertical carrel screens commonly used in open plan offices will reduce the DF to 0.59 of its unobstructed value, 6m from the facade in a sidelit space. It is therefore important to anticipate where a view of the principal light source or sources may be obstructed when the space is occupied, and to introduce model furnishings if the study is to have any accuracy.

Model of office in photograph below. The office at Headquarters 21.

Photo 4: A model of the inside of the Housing 21 Headquarters building
Photo 5: The real interior of the Housing 21 Headquarters building

This image shows a model of an office created to test daylight

Photo 6: Overshadowing - Setting the model in context

Table 1 Effect of furnishings above workplane level in model of cellular office

DF when furnished above workplane as FRACTION of DF in unfurnished Base Case

1 2 3 4 5 6m from facade
1.0 0.9 0.9 0.8 0.7 0.6 furnished above workplane

4 Setting up for collecting data

4.1 Basic measurements

To calculate the Daylight Factor, the ambient or unobstructed illuminance at the centre of the worktable is first measured, without any overshadowing by the model. The illuminance is then measured at the predetermined locations within the model, with the model in the centre of the worktable. The photocell should be placed with receptor at workplane height, the model scale equivalent of 800-900mm. The Daylight Factor, usually expressed as a percentage, is therefore given by:

In / Iamb × 100 = DF%

Where In is the interior illuminance, Iamb is the outdoor horizontal illuminance under an unobstructed overcast sky.

The artificial sky lamps should be switched on to warm up for 30 minutes before measurements begin. Despite this, their output is likely to fluctuate throughout their use. If, to account for these fluctuations, the unobstructed illuminance is monitored by replacing the photocell or second photocell on top of the model during the tests, it should be noted that the unobstructed illuminance will increase with height from the workplane. This affect should first be measured and the error - about 10% per 100mm for the size of artificial sky described here - compensated. If two or more photocells are used, they should be compared under identical conditions. Any variation between the cells should be compensated by application of a calibration factor when calculating the DF.

It is important that anyone in the artificial sky is below the workplane whilst the measurement is taken as their presence will otherwise affect the luminance distribution. For this reason, a photometer with remote photocell is essential.

4.2 Overshadowing

The reflection of the model in the mirror at the horizon will itself cause overshadowing. This is rarely a problem as few buildings have a totally unobstructed view of the horizon. However, the reflectance of the outside of the model should be considered.

Frequently, it will be necessary to model obstructions - neighbouring buildings or other parts of the building under test - with the correct geometry and appropriate reflectance for their facades, but otherwise of lower accuracy. Two-dimensional silouhettes are usually adequate for this. Ground reflectance also should be modelled as this can be a significant secondary light source. Values for typical ground reflectances are given in [4].

4.3 Vertical DF

For some environments, the DF on a vertical plane (DFv) such as the wall of a gallery may have more significance than on a notional horizontal workplane. It is important to note that the DFv expressed is a percentage of the unobstructed ambient illuminance on the horizontal plane. As with the DF on the horizontal workplane, the DFv may be used to estimate the number of days when the desired illuminance on the wall is likely to be exceeded.

Locating the photocell accurately on a vertical plane is difficult, particularly in small scale models, and needs planning at the model construction stage. This is an area of study where RADIANCE has a distinct advantage.

4.4 Glazing factors

If the model is unglazed, then the measured DFs should be reduced by a factor appropriate to the type of glazing system (table 2), and by a further factor, sometimes called the maintenance factor, to allow for soiling of the glass (table 3).

Table 2 Transmission factors for glazing systems (clear glass)

single glazing 0.85
double glazing 0.75
triple glazing 0.7

Table 3 Transmission factors for soiled glazing

location inclination type of work in the building
clean dirty
vertical 0.9 0.8
non-industrial sloping 0.8 0.7
horizontal 0.7 0.6
vertical 0.8 0.7
dirty industrial sloping 0.7 0.6
horizontal 0.6 0.5

4.5 Orientation and Orientation Factors

For spaces which are daylit by more than one source, the contribution of each individual source or facade may be analysed by blacking-out the other sources.

The luminance distribution of the CIE overcast sky reproduced by the mirror-box artificial sky is symmetrical about the zenith, and the orientation of the model is not significant. But a real overcast sky is brighter in the south. By application of orientation factors appropriate to the orientation of the building being modelled, more accurate predictions of DF may be made. It can be seen from the values for the UK (table 4) that the difference between North and South is sufficient to have a significant affect on window design.

Table 4 Orientation factors for the UK: diffuse

North 0.77
East 1.04 Factors will vary if sky luminance is averaged for
South 1.20 a shorter period, say a 09.00 - 17.00 working day
West 1.00

4.6 Calculating the Daylight Factor

The equation in 4.1 may now have to be modified if the model is unglazed, and to compensate for soiling of the glazing. If appropriate, correction for calibration of two or more cells, and for elevation of the reference cell - the cell measuring the ambient illuminance (3.1) - should be applied. The equation will be:

(In / Iamb × 100 ) × glazing factor × soiling factor × calibration factor = DF%

The resulting DF may then be multiplied by the orientation factor. If the space is lit by windows on more than one side, then the calculation must be made for each set of illuminance measurements, made by blacking out each facade in turn (4.5), multiplying each set by the appropriate orientation factor, and the resulting DFs added to find the aggregate value. It would be useful to have set up a spreadsheet by this time.

5 Presenting data

The distribution of light throughout a space on the plane on which the illuminance has been measured is well illustrated with isolux on a plan or section of the space. However, it is difficult to superimpose other sets of results in this way. For comparative studies it is preferable to select a critical section or sections through the space and superimpose line charts on these.

When discussing the differences between results, it may be a point of semantics, but perhaps a value should be expressed as a fraction of another - the base case - rather than as a percentage of a percentage.

5.1 Daylight Factor: difference between two means

For sidelit spaces in particular, the difference in illuminance throughout the space is inevitably considerable: Lynes [5] proposes that for visual comfort, the average DF for the front half of the space should not exceed the average for the rear half of the space by more than a factor of 3. That is:

DFave Half nearest light source / DFave Half furthest from light source > 3

It is useful to see if this criterion is met.

5.2 Photography

The qualitative assessment of daylighting in a model space is a valuable element of analysis in artificial sky conditions, so it is desirable to keep a visual record. Camera positions need to be planned at the building stage to accommodate the lens. For conventional photography, the choice of film and filters is never straightforward, though film corrected for artificial light usually gives acceptable results. But even with colour corrected lamps there is still a distinct peak in the green zone of the spectrum, added to the affect of the green iron-oxide of the glass mirrors. The colour balance can be restored with digital post-processing.

When subsequently viewing photographs, whether prints, transparencies (the best) or on video, the brightness range reproduced will be much less than in reality, so analysis of photographs for the risk of glare, for example, is unreliable. Viewing of any media can be improved by viewing on a black background in a blacked-out space and with only the image illuminated.

6 Conclusion

6.1 Numbers in relation to occupancy behaviour

Having made an accurate model, glazed, furnished, maintenance and orientation factors duly applied, how relevant are the predictions? There is a predisposition to assume that it is erroneous predictive modelling which is the cause of any variation between prediction and reality. However, a survey of the Housing 21 Headquarters building, the subject of analysis at the design stage, revealed other causes contributing to divergence. The causes of divergence are categorised as:

  1. Inconsistency of the completed building with model specification
  2. Accuracy of DF measurements for both the model and of the completed building
  3. Differences between the test environment and the real environment when DF measurements were made
  4. Effect of occupants in completed building

The daylighting consultant can, in reality, exercise control only over model accuracy.

6.1.1 Inconsistency

This is not accuracy: This is the problem of reconciling the test model with all of the dimensional (spatial) and component changes which occur during the design and, perhaps, building stages of the project. For example, the Housing 21 Headquarters building model was tested with a shading device, which was subsequently omitted from the final building. The effect of this omission went beyond the doubling of the daylight factor near the facade: in reality, the occupants found it necessary to use the venetian blinds, thereby further changing the daylight distribution in the space. Divergence is not necessarily a deficiency of the modelling and it is not possible to quantify the effect of inconsistency in a general way.

6.1.2 Accuracy

The need for model accuracy has already been expounded. But there are inherent limitations; the difficulty in definition and replication to scale of surface characteristics, where a sample of the final material cannot be included in the model.

Experimental accuracy, both in the model and in real building surveys is critical if comparisons are to be meaningful: the findings of building surveys are vulnerable to several sources of error. The effect of scale on the photometer sensor size is more likely to give rise to error in the survey of real buildings as the sensor will be measuring illuminance over proportionally a smaller area -perhaps 25x or 50x smaller than the scale model - though this may be compensated by averaging an increased number of measurements for comparison with each measurement within the model. It is also frequently difficult to obtain simultaneous unobstructed ambient values for illuminance with which to compare the internal values for calculation of DF.

6.1.3 Environment

The difference between the artificial sky conditions and the inevitably less stable real sky conditions leads to inconsistencies between prediction and reality. The inconsistencies are more likely to occur in buildings where a significant source of daylight is from openings exposed to unobstructed sky and direct sunlight. In this case a stable and 'fully overcast' sky is essential if the comparison with predicted results is to be meaningful.

6.1.4 Occupancy

The interior environment of real occupied buildings - not only the arrangement of furnishings already mentioned, but the perhaps transitory positioning of occupantsí equipment and personal clutter - has a considerable local effect on illuminance values. Building types such as offices and schools will be more vulnerable to the effects of occupancy than, say, galleries.

6.2 Value of daylight modelling

With some care in its execution, daylight modelling is a valuable, interactive way of understanding the distribution of light in an interior, and enables the designer to quickly visualise and assess the affect of different design strategies. Such knowledge can only help to make buildings more enjoyable to their occupants.


N Baker, The Martin Centre for Architectural and Urban Studies. Cambridge University. CB2 2EB UK

Cambridge Architectural Research Limited. Cambridge CB1 1DP UK

Housing 21 Head Office, The Triangle, Baring Road, Beaconsfield, Bucks, HP9 2NA

Jestico + Whiles, 1 Cobourg Street, London, NW1 2HP


  1. Ward, G: RADIANCE 2.4 Synthetic imaging system. Lawrence Berkeley Laboratory, University of California
  2. Hopkinson, R G; Petheridge, P; Longmore, J: Daylighting. Heinmann, 1966
  3. Baker, N; Steemers, K, et al: Daylighting Design. James and James, 2000
  4. Lynes, J A: A sequence for daylighting design, Lighting Research and Technology, Vol 175, pp102-106, 1979

The above is based on a paper given at TIA: 3rd International Conference for Teachers of Architecture, Oxford, UK 9-12 July 2000