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Daylighting Computation Methods
From Dot Chart to Digital Simulation
Benjamin Geebelen, ir.-arch.
K.U.Leuven, dept. of Architecture
Introduction
Whatever our surroundings, light is all around us. At all times, every point of every
surface emits, reflects, absorbs and possibly transmits rays of light in an infinite
number of directions. It is not hard to imagine that, in most real-world situations,
light transfer is too complex a matter to be described analytically. This paper gives an
overview of the tools that were devised to find reliable approximations for the
distribution of light in a scene. It will focus on the simulation of skylight.
1 Historical background1
Throughout the ages lighting design, like most aspects of construction, was a question
of craftsmanship and unwritten rules, of precedent and experience. It was the
Industrial Revolution that brought the most rapid change in the applications,
requirements and solutions for daylighting.
Sparked by phenomena of radical sociological change and technological innovation, a
whole range of new building types was invented, such as art galleries, railway
stations, assembly halls, libraries, elementary schools and exhibition halls, building on
advances in the glazing and framing technologies. With gas and oil lighting still
being too expensive, polluting and dangerous, new functional briefs and increased
urban densities entailed new problems and requirements for daylight availability. The
need for daylighting design tools thus originated in an era in which photometry was in
its infancy and luminance had not even been defined.
Early daylighting regulations concentrated on the amount of direct daylight from the
sky and consisted of simple geometric rules, such as the sky-line rule2
or minimal
glazing-area-to-floor-area ratios. By the 1920s the first photometers had been
invented and photometry had evolved sufficiently to allow more precise methods.
These were invented mainly as a means to adjudicate disputes concerning the
obstruction of light by a proposed building. Two of the earliest computation tools are
the Waldram diagram, devised by P.J. and J.M. Waldram, and Pleijels pepper-pot
diagrams. Throughout the 20th
century, until the advent of personal computers, more
graphical methods were conceived, such as the BRS protractor.
Slowly the attention turned towards the internally reflected component. In times
when interiors were often clad in dark natural finishes and covered in the grime ofcontemporary artificial light sources, it had been neglected. However, after the
widespread introduction of electrical lighting, and a confrontation with the massive
solar gains and heat losses of the large glass faades so popular in the 1970s, the
1An interesting historical overview can be found in [2], on which this section was based.
2The sky-line rule states that a room will be well lit if there is a unobstructed view of the sky from the
point of interest.
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significance of reflected light for achieving well-lit rooms with sensible window sizes
became evident. It was recognized as a key feature to help reduce the variation of
illuminance levels across a room. Mathematical prediction techniques were
formulated, striking a balance between the complexity of inter-reflections and the
simplicity of available design data. Some of these formulae are still useful design
tools today.
While the use of these graphical or hand-calculation methods is not fundamentally
challenging, treating large numbers of reference points is likely to become a tedious
and lengthy activity. It is not surprising that some of the first software tools consisted
of digital translations of known hand-calculation methods.
From the early 1980s on, researchers in the field of computer graphics began to
investigate the possibilities of global illumination, the realistic simulation of light
transfer within a scene. First initiatives were aimed at visual appeal without much
care for physical accuracy, but they laid the groundwork for powerful lighting
simulation tools.
During the 1990s research initiatives multiplied with different orientations, ranging
from user-friendly design tools to integrated energy-performance assessment tools.
2 Scale models
Architects have been using scale models for centuries to assess different aspects of
their designs. Many still use scale models today to study the volumetric composition
of their designs or to communicate with clients or consultants.
Unlike thermal, acoustic, structural or hydrodynamic models, models for lighting
studies are not subject to scaling effects. Since the wavelengths of light are so short
with respect to the size of buildings and scale models, its behavior is largely
unaffected. The light distribution in models with carefully duplicated geometry and
material properties will qualitatively and quantitatively match the distribution in the
actual room. This makes the scale model a very useful and intuitive lighting designtool, which every architect is familiar with. Even on a small budget the simplest
model can give an immediate impression of the light distribution in a room or the
dynamics under changing sun positions.
Scale models can also be used for measuring quantitative data. However, for this
purpose the models need to be built with more care. All joints have to be covered
with masking tape and finishes have to match the real building materials as closely as
possible. In order to obtain relevant data, the lighting conditions need to be controlled
or at least monitored. In an outdoor set-up the simultaneous recording of the sky and
the indoor conditions is far from straightforward, and the considerable impact of the
luminance distribution of the sky may complicate an analysis of the results. Under
artificial skies, i.e. hemispherical skies or mirror boxes, the luminance distribution canbe kept constant, which facilitates the measuring procedure.
There are a few limitations to the use of scale models for lighting studies:
It is very difficult to include artificial lighting. Even if the intensity of artificiallight sources can be simulated, the luminance distribution of the luminaires
cannot.
Some finishes, such as fabrics or brickwork, may be difficult to scale. This maycause errors.
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Many artificial skies are only able to simulate overcast sky conditions. Exceptionsare hemispherical skies with individually controlled lamps and the so-called one-
lamp artificial skies [15].
Different studies have indicated that scale models are not the most accurate ofsimulation tools. Reasons for this include poorly represented surface finishes,
light leaks in the model, inexact luminance distributions of the artificial skies,
imprecise placement of measurement instruments Photographs taken under artificial skies cannot be used to judge color in the scene. Hardly any architectural firms own an artificial sky or heliodon. Quantitative
studies can therefore entail high costs. A testing facility and an operator need to
be hired and the model needs to be transported. Due to the restricted time frame,
and because the production of the models requires a great amount of care, so as
not to introduce any light leaks, it may be difficult to make quick alterations to the
model and compare different design alternatives.
3 Graphical, tabular and hand-calculation methods
A whole range of simplified methods has been developed, varying in ease-of-use,
accuracy and applicability. They can be categorized in different ways:
According to treatment of the direct and reflected components: do they produceone or both, or do they produce the total daylight factor in a single step?
According to applicability: can they handle vertical, horizontal or slopingwindows? Can they handle saw-tooth roof lights?
According to daylight conditions: which kinds of sky luminance distributions canthey handle? Typical for simplified methods is that they cannot handle complex
sky luminance distributions. They are only applicable to azimuthally invariant
sky models, mostly uniform or overcast.
According to output: do they produce mean, minimum or maximum values, or canthey handle arbitrary reference points?
According to form: do they consist of tables, equations, protractors,nomograms, dot charts or diagrams? According to underlying light transfer model: are they based on the Flux Transfer
method, the Lumen Method, or do they have another foundation?
The computation of the direct and the reflected components are so different that many
simplified methods merely produce one of both. It is then possible to choose one
method for each component and use them in conjunction, e.g. a protractor for the
direct and an equation for the reflected component. However, it is always wise to
choose methods that make similar allowances for deterioration of decorations, dirt on
the windowpanes, framing and window bars, and transmission losses of the glazing
type.
A detailed discussion of all available methods would go beyond the scope of thissection. Only the most common ones are briefly discussed. A more general overview
can be found in [1].
3.1 The direct component
Because the direct component of the daylight factor depends on relatively few
parameters the shape of the windows, their transmission characteristics and their
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position relative to the reference point its computation has often been captured in
graphical or tabular form.
One of the oldest methods, dating back to 1923, is the Waldram diagram. This kind
of diagram consists of a grid of squares, each of which represents an equal portion of
daylight factor, on which one can draw the projections of windows and obstructions
as seen from the reference point. In order to know the direct component of the
daylight factor, one simply needs to count the squares within the outline of the
projection. The diagram was designed in such a way that vertical edges remain
vertical in the projection. Horizontal edges, however, need to follow the shape of the
so-called droop lines in order to take the cosine law of illumination and the non-
uniform luminance of the sky vault into account. The one shown in Fig. 1 is based on
the luminance distribution of an overcast sky and allows for glazing losses. This
method offers fairly good accuracy.
External obstruction
Angles of azimuth
0102030405060708090 80 9070605040302010
Droop lines of horizontal edgesparallel to plane of window
Droop lines of horizontal edges atright angles to plane of window
90
70
60
50
40
30
20
10
Unobstructed view of sky
30
20
40
50
60
70
80
Anglesofaltitude
Fig. 1 Waldram diagram for CIE Overcast Sky and vertically glazedapertures, including corrections for glazing losses. As an example a large
window and an obstructing tower are indicated. Each square indicated in fine
lines corresponds with a daylight factor of 0.1%.
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Pleijel followed a similar approach for the design of his pepper-pot diagrams. Here
the direct component of the daylight factor can be obtained by counting the dots that
fall within the contours of the projection. The great advantage of this kind of diagram
is that the density of the dots accounts for the non-linearity of the illumination, so that
projections can be made without deformations. The drawback, however, is that
counting the dots can become a very tedious task.
Fig. 2 Pepper-pot diagram or dot chart for the sky component of thedaylight factor on horizontal planes (from [16]). This diagram applies to vertical
windows and the CIE Standard Overcast Sky.
The BRS Daylight Protractors are probably the most widely used graphical tools
[3]. They come in pairs: one primary protractor or daylight scale, and one auxiliary
protractor or correction scale. Protractors are available for different sky types and
various slopes of glazing. The main advantage of protractors is that they can be used
straight onto plans and sections of the proposed room. They are very easy to use.
Fig. 4 and Fig. 4 show an example for vertical glazing. The primary protractor is
placed onto a section drawing. It provides the sky component or the equivalent sky
component of an external obstruction as the difference between the readings of the top
and bottom edge. The secondary protractor is placed onto a plan drawing and deliversthe correction factors for windows of finite length. For the externally reflected
component an additional correction factor of 0.2 is usually used. Protractors are less
practical for irregular compositions. However, it is usually possible to assume an
average simple outline.
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Fig. 3 BRS protractors for the CIE Standard Overcast Sky and verticalwindows.
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Fig. 4 The use of Building Research Station protractors.
During the very early stages of design, when scale drawings are not yet available, one
can use the BRS Simplified Daylight Tables. For very simple geometric
compositions these tables provide the sky component.
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Sky component of the daylight factor [%]
1.30 2.50 3.70 4.90 5.90 6.90 7.70 8.40 9.00 9.60 10.70 11.60 12.20 12.60 13.00 13.70 14.20 14.60 14.90 15.00
5 1.20 2.40 3.70 4.80 5.90 6.80 7.60 8.30 8.80 9.40 10.50 11.10 11.70 12.30 12.70 13.30 13.70 14.00 14.10 14.20
4 1.20 2.40 3.60 4.70 5.80 6.70 7.40 8.20 8.70 9.20 10.30 10.90 11.40 12.00 12.40 12.90 13.30 13.50 13.60 13.70
3.5 1.20 2.40 3.60 4.60 5.70 6.60 7.30 8.00 8.50 9.00 10.10 10.60 11.10 11.80 12.20 12.60 12.90 13.20 13.20 13.30
3 1.20 2.30 3.50 4.50 5.50 6.40 7.10 7.80 8.20 8.70 9.80 10.20 10.70 11.30 11.70 12.00 12.40 12.50 12.60 12.70
2.8 1.10 2.30 3.40 4.50 5.40 6.30 7.00 7.60 8.10 8.60 9.60 10.00 10.50 11.10 11.40 11.70 12.00 12.20 12.30 12.30
2.6 1.10 2.20 3.40 4.40 5.30 6.20 6.80 7.50 7.90 8.40 9.30 9.80 10.20 10.80 11.10 11.40 11.70 11.80 11.90 11.90
2.4 1.10 2.20 3.30 4.30 5.20 6.00 6.60 7.30 7.70 8.10 9.10 9.50 10.00 10.40 10.70 11.00 11.20 11.30 11.40 11.50
2.2 1.10 2.10 3.20 4.10 5.00 5.80 6.40 7.00 7.40 7.90 8.70 9.10 9.60 10.00 10.20 10.50 10.70 10.80 10.90 10.90
2 1.00 2.00 3.10 4.00 4.80 5.60 6.20 6.70 7.10 7.50 8.30 8.70 9.10 9.50 9.70 9.90 10.00 10.10 10.20 10.30
1.9 1.00 2.00 3.00 3.90 4.70 5.40 6.00 6.50 6.90 7.30 8.10 8.50 8.80 9.20 9.40 9.60 9.70 9.80 9.90 9.90
1.8 0.97 1.90 2.90 3.80 4.60 5.30 5.80 6.30 6.70 7.10 7.80 8.20 8.50 8.80 9.00 9.20 9.30 9.40 9.50 9.50
1.7 0.94 1.90 2.80 3.60 4.40 5.10 5.60 6.10 6.50 6.80 7.50 7.80 8.20 8.50 8.60 8.80 8.90 9.00 9.10 9.10
1.6 0.90 1.80 2.70 3.50 4.20 4.90 5.40 5.80 6.20 6.50 7.20 7.50 7.80 8.10 8.20 8.40 8.50 8.60 8.60 8.60
1.5 0.86 1.70 2.60 3.30 4.00 4.60 5.10 5.60 5.90 6.20 6.80 7.10 7.40 7.60 7.80 7.90 8.00 8.00 8.10 8.10
1.4 0.82 1.60 2.40 3.20 3.80 4.40 4.80 5.20 5.60 5.90 6.40 6.70 7.00 7.20 7.30 7.40 7.50 7.50 7.60 7.60
1.3 0.77 1.50 2.30 2.90 3.60 4.10 4.50 4.90 5.20 5.50 5.90 6.20 6.40 6.60 6.70 6.80 6.90 6.90 6.90 7.00
1.2 0.71 1.40 2.10 2.70 3.30 3.80 4.20 4.50 4.80 5.00 5.40 5.70 5.90 6.00 6.10 6.20 6.20 6.30 6.30 6.30
1.1 0.65 1.30 1.90 2.50 3.00 3.40 3.80 4.00 4.30 4.60 4.90 5.10 5.30 5.40 5.40 5.50 5.60 5.60 5.70 5.701 0.57 1.10 1.70 2.20 2.60 3.00 3.30 3.60 3.80 4.00 4.30 4.50 4.60 4.70 4.70 4.80 4.80 4.90 5.00 5.00
0.9 0.50 0.99 1.50 1.90 2.20 2.60 2.80 3.10 3.30 3.40 3.70 3.80 3.90 4.00 4.00 4.00 4.10 4.10 4.20 4.20
0.8 0.42 0.83 1.20 1.60 1.90 2.20 2.40 2.60 2.70 2.90 3.10 3.20 3.30 3.30 3.30 3.30 3.40 3.40 3.40 3.40
0.7 0.33 0.68 0.97 1.30 1.50 1.70 1.90 2.10 2.20 2.30 2.50 2.50 2.60 2.60 2.60 2.60 2.70 2.70 2.80 2.80
0.6 0.24 0.53 0.74 0.98 1.20 1.30 1.50 1.60 1.70 1.80 1.90 1.90 2.00 2.00 2.00 2.10 2.10 2.10 2.10 2.10
0.5 0.16 0.39 0.52 0.70 0.82 0.97 1.00 1.10 1.20 1.30 1.40 1.40 1.40 1.40 1.50 1.50 1.50 1.50 1.50 1.50
0.4 0.10 0.25 0.34 0.45 0.54 0.62 0.70 0.75 0.82 0.89 0.92 0.95 0.95 0.96 0.96 0.96 0.97 0.97 0.98 0.98
0.3 0.06 0.14 0.18 0.26 0.30 0.34 0.38 0.42 0.44 0.47 0.49 0.50 0.50 0.51 0.51 0.52 0.52 0.52 0.53 0.53
0.2 0.03 0.06 0.09 0.11 0.12 0.14 0.16 0.20 0.21 0.21 0.22 0.22 0.22 0.22 0.23 0.23 0.23 0.23 0.24 0.24
Ratioheightofwind
owaboveworkingplane:distancefromw
indow
[-]
0.1 0.01 0.02 0.02 0.03 0.03 0.04 0.04 0.05 0.05 0.05 0.06 0.06 0.06 0.06 0.07 0.07 0.07 0.07 0.08 0.08
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.2 1.4 1.6 1.8 2 2.5 3 4 6
Ratio width of window to one side of normal : distance from window [-]
Table 1 BRS Simplified Daylight Table for vertical glazed rectangularwindows.
3.2 The internally reflected component (IRC)
It is far more difficult to obtain a good estimate of the reflected component, since it
depends on scene geometry and material properties of all surface finishes in the scene.
Because of the endless possibilities it is hard to parameterize both and translate them
into graphical form. Most simplified methods for the internally reflected component
therefore consist of equations and nomograms.
A number of sources prescribe different formulae for the internally reflected
component, with different parameters and allowances. However, most of them can betraced back to only a few basic ways of abstracting the scene.
The Split-Flux Method regards the scene as consisting of only two surfaces: the floor
with the part of the vertical walls below the center of the window and the ceiling and
the part of the vertical walls above the center of the window. It is then assumed that
the light from the sky is distributed over the lower part, and the externally reflected
light over the upper part. For clear glazing the average direct illuminance of the lower
part can then be expressed as:
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l
gskyg
gldA
AEE
..
,
, = (1)
where
ldE , = the average direct illuminance of the lower part,
g = the specular transmittance of the glazing,
Eg,sky = the illuminance of the window due to the sky,
Ag = the area of the window and
Al = the area of the lower part of the scene.
The average direct illuminance of the upper part can be expressed in a similar way:
u
ggroundg
gudA
AEE
..
,
, = (2)
where
udE , = the average direct illuminance of the upper part,
g = the specular transmittance of the glazing,
Eg,ground = the illuminance of the window due to the ground,Ag = the area of the window and
Au = the area of the upper part of the scene.
Both Eg,sky and Eg,ground are estimated based on the horizontal illuminance under an
unobstructed sky. The illuminance due to the sky for a vertical surface can fairly
easily be computed as follows:
obstrvhhskyg CCEE .., = (3)
where
Eg,sky = the illuminance of the window due to the sky,
Eh = the horizontal illuminance in the open field,
Chv = a correction factor to transform from horizontal to verticalilluminance (0.5 for a uniform sky, roughly 0.4 for a CIE Overcast
Sky) and
Cobstr = a correction factor for exterior obstructions.
For an overcast sky BRE lists values for the product of both correction factors
depending on the angle of obstruction measured from the center of the window [4].
These can be found in Table 2. Alternatively Cobstrcan be approximated as
=
901 obstrobstrC
(4)
where
obstr = the angle of obstruction [].
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Angle of obstruction [] Ch v.Cobstrn [%]
No obstruction 39
10 3520 31
30 25
40 2050 14
60 10
70 7
80 5
Table 2 Correction factors for the illuminance of the windows due to the skyaccording to BRE.
For the illuminance of the window due to the ground, the ground is regarded as a
perfectly diffuse surface with constant luminance
hgroundground
EL .= (5)
where
Lground = the luminance of the ground,
ground
= the reflectance of the ground, usually taken as a minimum of 0.1
and
Eh = the horizontal illuminance under an unobstructed sky.
The illuminance of the window can then be approximated according to
2..
2,
hgroundgroundgroundg
ELE
== . (6)
If we regard both parts of the scene as two parallel infinite planes, we can compute the
average illuminance and luminance of the upper part of the scene as follows:
ul
ldlud
u
EEE
.1
. ,,
+
= (7)
and
ul
ldluuduuuu
EEEL
.1
....
1.
,,
+
== (8)
where
uE = the average illuminance of the upper part of the scene,
udE , = the average direct illuminance of the upper part of the scene,
ldE , = the average direct illuminance of the lower part of the scene,
uL = the average luminance of the upper part of the scene,
u = the average reflectance of the upper part of the scene and
l = the average reflectance of the lower part of the scene.
The average internally reflected component of the daylight factor can then be
computed as:
+
=
l
obstrvhlu
u
groundu
lu
ggIRC
A
CC
A
ADF
...
2
..
.1
.
(9)
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whereIRC
DF = the internally reflected component of the daylight factor,
g = the specular transmittance of the glazing,
Ag = the area of the window,
Au = the area of the upper part of the scene,
Al = the area of the lower part of the scene,
u = the average reflectance of the upper part of the scene,
l = the average reflectance of the lower part of the scene,
ground = the reflectance of the ground,
Chv = a correction factor to transform from horizontal to vertical
illuminance and
Cobstr = a correction factor for exterior obstructions.
This only applies to clear glazing. For diffuse glazing the average direct illuminance
values should be computed differently:
l
ggroundgskyg
gld
A
AEEE .
2
.,,
,
+= (10)
and
u
ggroundgskyg
gudA
AEEE .
2.
,,
,
+= . (11)
The average internally reflected component of the daylight factor can then be
computed as follows:
+
+
= obstrvh
ground
l
l
u
u
lu
ggIRC
CCAA
ADF .
2.
1.
2.
.1
.
. (12)
A slightly simpler variation of the Split-Flux principle is theIntegrated-Sphere
Approximation, in which the entire scene is regarded as a closed sphere with
constant luminance. For this situation the average luminance can be estimated
according to
=
1
dL
L (13)
where
L = the average luminance of the inner surfaces of the scene,
dL = the average luminance of the inner surfaces of the scene due to
direct illumination and
= the average reflectance of the inner surfaces of the scene.
Using equations (1) and (2) we can estimated
L as follows:
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( )skyglgroundgu
gg
l
l
gskyg
glu
u
ggroundg
gu
l
ld
lu
ud
u
d
EEA
A
AA
AEA
A
AE
A
A
AE
AE
L
,,
,,
,,
....
.
..
....
....
1
....
+=
+=
+=
(14)
where
u = the average reflectance of the upper part of the scene,
l = the average reflectance of the lower part of the scene,
Au = the total surface area of the upper part of the scene,
Al = the total surface area of the lower part of the scene,
A = the total area of all inner surfaces of the scene,
udE , = the average direct illuminance of the upper part of the scene,
ld
E,
= the average direct illuminance of the lower part of the scene,
g = the specular transmittance of the glazing,
Ag = the area of the window,
Eg,ground = the illuminance of the window due to the ground and
Eg,sky = the illuminance of the window due to the sky.
If we substitute Eg,ground and Eg,sky using equations (3) and (6), we can compute the
average internally reflected component of the daylight factor as follows:
( )
+
= obstrvhl
ground
u
ggIRC
CCA
ADF ..
2..
1.
.
(15)
where
IRCDF = the average internally reflected component of the daylight factor,
g = the specular transmittance of the glazing,
Ag = the area of the window,
A = the total area of all inner surfaces of the scene,
u = the average reflectance of the upper part of the scene,
l = the average reflectance of the lower part of the scene,
ground = the reflectance of the ground,
Chv = a correction factor to transform from horizontal to vertical
illuminance and
Cobstr = a correction factor for exterior obstructions.
This is the method prescribed by BRE [4]. A value of 0.1 is assumed for ground andTable 2 lists values for the correction factors.
A common and easy-to-use alternative for equations are nomograms. These can be
obtained for different cases. The example shown in Fig. 5 allows the fast computation
of the average internally reflected component for side-lit rooms. Find the point on
scale A indicating the appropriate window-area-to-total-surface-area ratio. Find the
point of scale B indicating the average reflection factor of the interior surfaces.
Connect both points with a line. The point in which this line intersects with scale C
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indicates the average internally reflected component of the daylight factor
disregarding external obstructions. If there are obstructions, find the point on scale D
that indicates the angle of obstruction and connect it with the point you just found on
scale C. The intersection point of this line with scale E indicates the average
internally reflected component with obstructions. The great advantage of nomograms
is their ease-of-use. However, for complex geometries they may offer insufficient
accuracy. Moreover, each nomogram is based on an assumption of the distribution ofreflectance values. One cannot differentiate between the upper and lower part of the
scene, which can cause discrepancies with the values that are computed using an
equation.
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Fig. 5 Nomogram for the average internally reflected component of thedaylight factor (from [10]).
3.3 Combining methods
It is now possible to combine a method for the direct component and one for the
internally reflected component to compute the total daylight factor:
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( ) IRCERCSCIRCDC
DFDFDF
DFDFDF
++=
+= (16)
where
DF = the daylight factor in a reference point,
DFDC
= the direct component of the daylight factor,
DFIRC = the internally reflected component of the daylight factor,DF
SC= the sky component of the daylight factor and
DFERC
= the externally reflected component of the daylight factor.
The direct component is generally regarded as consisting of the sky component, due
to the unobstructed portion of the sky, and the externally reflected component, due to
obstructions. The latter is usually computed in the same way as the former and then
corrected with a reflectance. For a uniform sky BRE prescribes a reflectance of 0.1,
for a CIE Standard Overcast Sky 0.2.
When combining methods, especially from different sources, special attention should
go to:
the transmission of the glazing: is it included in both methods? Is it includedimplicitly or explicitly? Do both methods employ the same value?
additional allowances: does either method include a correction for dirt on theglazing?
the output of the methods: do they provide point values, or average, maximum orminimum values?
3.4 Single-step methods
A few methods approximate the daylight factor without differentiating between a
direct and a reflected component. Most of them use regression to express the daylight
factor as a linear combination of the illuminance of the window due to the sky and the
illuminance due to the reflection off the ground. By measurements in scale models
appropriate coefficients have been established for a number of room geometries,material properties, glazing transmittances, etc.
The best-known method of this type is the Lumen Method, where the daylight factor
can be found as:
uggvKAEDF ...= (17)
or
gggroundugroundgskyuskyg AKEKEDF .... ,,,, += (18)
where
Ev = the vertical illuminance under an unobstructed sky,
Eg,sky = the illuminance of the glazing due to the sky,Eg,ground = the illuminance of the glazing due to the ground,
Ag = the glazing area,
g = the transmittance of the glazing and
Ku, Ku,sky, Ku,ground= coefficients of utilization.
Coefficients of utilization have been published by different sources for a variety of
geometries, glazing systems, sky types, etc.
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3.5 Estimating annual daylight availability
Once the daylight factor in a reference point or on the working plane is known, the
annual daylight availability can be estimated. Based on the function of a space, the
required internal illuminance level can be determined. If we divide this by the
daylight factor, we obtain the required external illuminance level. Based on
meteorological data we can find the percentage of the working year during which thisexternal illuminance level is attained (Fig. 6).
50%55%60%
65%70%75%80%85%90%95%
100%
0 2000 4000 6000 8000 10000 12000 140006AM-6PM 7AM-5PM 8AM-6PM7AM-3PM 8AM-4PM 9AM-5PM
Minimal illuminance in open field[lux]
Percentage ofworking yearduring which
indicatedilluminance is
attained
Daylight availability
Fig. 6 Daylight availability in the Belgium based on meteorological data fromBrussels.
4 Digital simulation
Since the advent of personal computers numerous attempts have been made to
develop software tools that predict the lighting in a proposed room. This sectiondiscusses the theories behind different approaches. Of each approach examples are
given. However, since most software evolves rather rapidly, there is a distinct risk
that the information presented here will quickly be outdated. Discussions of
individual programs are therefore deliberately kept concise.
4.1 Simplified algorithms
A number of programs simply offer a digital translation of the simplified hand
calculation methods discussed above. The main benefit of this approach is an
increased ease-of-use. The input is usually simple and efficient, and results are
delivered instantaneously. The user no longer needs to compute azimuth or altitude
angles, sky components, average reflectance values, total surface areas or internally
reflected components. The drawback, however, is that there is very little
improvement in the accuracy of the results.
This type of software is excellently suited for the initial stages of architectural design,
when important decisions have to be made, based on little information. They allow
the designer to easily and quickly compare different design alternatives. That the
accuracy of the output is so low can be justified by the fact that there are too many
unknowns to allow a precise result. At an early stage the designer is more interested
in qualitative rather than quantitative results.
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A good example of this kind of software is Leso-DIAL, which was developed at
EPFL [14]. It computes the sky component analytically, which implies a slight
improvement of accuracy as compared to manual methods, and estimates the average
internally reflected component using the BRE Split-Flux Formula. The emphasis in
the development of this program was on applicability in early design stages. It cannot
handle complex geometry, but input is extremely straightforward and intuitive.
Reflectance values are entered qualitatively, with values ranging from very dark tovery light, and besides numerical output, it offers a diagnostics module, which
suggests alterations to the design that would improve daylight availability.
Another, much earlier, example is DAYLIT [1]. The goals were similar, but besides
daylighting computations, the program includes electric lighting and thermal
calculations. For its daylighting predictions it uses the Lumen Method as prescribed
by the IES.
Fig. 7 Examples of the Leso-DIAL user interface.
4.2 Light transfer simulation3
The ambition to simulate the light transfer between the surfaces of scene first emerged
in the field of computer graphics. In the pursuit of more realism of digitally
synthesized images, researchers sought ways of simulating the interaction of light and
objects, of mimicking light being reflected, transmitted and refracted, of computing
shadows and highlights.
The resulting algorithms, generally referred to as global illumination models, all
define approximating solutions for what is known as the rendering equation [11].In its outgoing form this equation expresses the amount of light leaving a surface at a
certain point in a certain direction as the sum of the surfaces own emittance and the
light reflected and transmitted by the surface:
3Algorithms are discussed only briefly in this section. More information can be found in [6] and [7].
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( ) ( ) ( ) ( ) ( )
+= &&&&&&
drLpfpLpLooeo
cos,,,, (19)
where
( )opL &
, = the luminance of the surface at pointp in direction o&
,
( )oe
pL &
, = the luminance of the surface at pointp in direction o&
due to its
own emittance,( )opf
&&
, = the function that describes how light arriving from direction&
is reflected or transmitted to direction o&
at pointp,
r = the point from which the light arriving from direction &
originated,
= the angle between direction &
and the surface normal and
= the total sphere around pointp.
This is clearly a recursive formula: in order to compute the luminance at a point p we
need to compute the luminance values at all points rsurrounding it. It is already a
simplification of reality, since it does not account for an interaction with the medium
or spectral effects.In order to fully simulate the light distribution in a scene we need to solve this
equation for all points in that scene. Except for a limited number of ideal cases, this is
an impossible task:
the equation needs to be solved for an infinite number of points; around each point an infinite number of directions needs to be considered; the functionfis hard to determine for most real-life materials.
The following section discusses the main techniques to find an approximate solution
for the rendering equation.
Historically ray tracing was the first technique to be developed [19]. It overcomes
the problems in solving the rendering equation by limiting the number of investigated
directions and thus tracing individual light rays through the scene. There are two
variants to this scheme. Inforward ray tracing or ray casting light rays are followed
in the direction of light propagation, i.e. from the light source towards the scene.
More common, however, is backward ray tracing, which tracks the light back from
the viewer to the light source.
This recursive algorithm is the literal translation of the rendering equation. The
original goal was to produce realistic images of a geometric scene. Such an image
can be interpreted as a projection of the scene onto a rectangular screen between the
scene and the viewer. This screen consists of an orthogonal grid of picture elements
or pixels, each of which portrays a particular part of the scene with a uniformly
colored square. The color and intensity of a pixel is generally determined by the point
in the scene that is visible in the pixels center or by a grid of points, all visible withinthe pixels boundaries. These points are found by tracing eye rays from the
viewpoint, through the pixel, towards the scene until they hit one of the scenes
surfaces. An estimate for the rendering equation is then found for each of these
points. In theory all directions around a point need to be considered. However, ray
tracing limits this number to only the most important ones, i.e. the directions of the
light sources in the scene, the direction of reflection for reflective surfaces, and the
direction of transmission for transparent surfaces. For each of these directions an
additional ray is traced. Rays that sample a light source will check whether the light
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source is visible to the investigated point. Reflection and transmission rays will look
for the nearest intersection with objects in the scene. For each of these intersections
the process is repeated, thus resulting in a recursive tree of rays (Fig. 8 and Fig. 9).
ImageEye
Pixel
Object 1
Object 2
Object 3
Object 4
Source 1
Source 2
E1
S11
S12
R1
T1
S21
S22
R2
S31
S32
R3
Fig. 8 Backward ray tracing.
Eye
Pixel 1 Pixel 2
E1 E2
Object 1
Source 1
Source 2
S11
S12
T1
R1
T2R2 T3
R3
Object 2
Source 1
Source 2
S21
S22Object 3
Source 1
Source 2
S31
S32
Fig. 9 The recursive ray tree. Eye rays are indicated with E, light-sourcerays with S, reflection rays with R, and transmission rays with T. The Xs
indicate light-source rays that are blocked by other objects or transmission rays
that are not investigated because the material is not translucent.
This technique performs best with scenes that contain ideally specular materials andpoint light sources (Fig. 10). Diffuse material behavior can be reproduced by tracing
additional random rays. Large light sources can be handled by super sampling, i.e.
testing visibility at multiple points across their surfaces. However, since the ray tree
grows exponentially with the number of rays per intersection, these measures have a
considerable impact on computation time.
In its classic form, ray tracing is a view-dependent algorithm: only those points of the
scene are investigated that influence the colors of the pixels in the final image (Fig.
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11). Moving the viewpoint therefore entails a complete new simulation. Moreover,
the result does not really represent the light distribution in the scene, but merely a
limited number of light transfers between an equally limited number of points in the
scene.
Fig. 10 A typical image rendered with classical ray tracing: smoothly curvedsurfaces, sharp reflections, sharp shadows from a point light source, etc.
Fig. 11 In ray tracing only those points are investigated that are important forthe rendered image.
The main counterpart of ray tracing is generally called radiosity and was first
introduced during the mid 1980s [8][13]. This technique adopts a finite-element
approach to overcome the difficulties in solving the rendering equation. By
subdividing the scene into a limited number of patches and nodes, and by specifying
that all light exchange needs to happen between those nodes, the number of possible
light fluxes will also be limited (Fig. 12). The rendering equation is now computed
for n nodes instead of an infinite number of points, and for each node only the n-1
directions of the other nodes are investigated instead of an infinite number of
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directions. The result of this simplification is a system ofn equations expressing the
luminance in each node as a linear combination of the luminance values in the other
nodes. If we can solve the system, the luminance of any point in the scene can be
approximated by interpolation between its surrounding nodes. The nn coefficientsof the system of equations are called form factors. Each form factor describes the
light transfer between a pair of nodes: it is proportional to the fraction of light
transported from one node to the other.
Fig. 12 The number of light fluxes in a radiosity approach is limited.
Radiosity introduces two major challenges: computing the form factors and solving
the system of equations. Not only is it a difficult task to compute a single form factor,
an average scene can easily contain several thousands of nodes, resulting in millions
of form factors. In addition, it would take exceptional computing times to solve a
system of several thousands of equations. Generally these problems are overcome by
a combination of measures:
form factors are approximated in an efficient way, e.g. by means of ray casting;
the number of form factors is reduced by grouping nodes in a hierarchical way; form factors are only computed on demand; the system is solved iteratively, e.g. by using Jacobi, Gauss-Seidel or Southwell
iteration.
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Fig. 13 A typical image rendered with classical radiosity: diffuse materials,soft shadows, large light sources (image by D. Marini, Universit degli Studi di
Milano).
In many ways radiosity is the opposite of ray tracing. It performs best with scenes
that consist of ideally diffuse opaque surfaces and large diffuse light sources; in its
classical form it is view-independent, and it is an efficient way of estimating the light
distribution in a scene. Both techniques have their pros and cons, which often seem
complementary (Table 3).
Ray tracing Radiosity
View-dependent View-independent
Handles specular behavior best Handles diffuse behavior best
Handles any geometry Performs best with facetted shapes
Can handle transparency Performs best with opaque surfaces
Does not compute the overall light distribution in the scene Does compute the overall light distribution in the scene
Has difficulties with indirect lighting Indirect lighting is treated correctly
Table 3 Comparison between classical ray tracing and classical radiosity.
Not surprisingly many of the best lighting simulation programs use hybrid algorithms,
combining both a radiosity and a ray-tracing step.
For any digital simulation to be appropriate for daylighting, it needs to be able to aptlysimulate the sky, which is a vast light source of non-uniform luminance. Different
algorithms will employ different sky models:
the sky as a large hemisphere with a superimposed luminance distribution: thisapproach may perform well if sky luminance can be expressed mathematically. Aray tracer will then sample the hemisphere at a great number of random points,
each with the appropriate luminance. For more accuracy the hemisphere can be
virtual, as if of infinite size. Luminance is now determined based on the sample
rays altitude and azimuth;
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the sky as a collection of light sources: this approach may be chosen when skyluminance is known at a collection of azimuth / altitude pairs. Ray tracers may
prefer point light sources, whereas radiosity programs may think of the light
sources as disks of constant luminance. Again, for more accuracy these light
sources should be treated as if at an infinite distance from the scene.
An additional difficulty arises when we want to assess annual daylight availability.
The number of individual daylighting conditions for a single assessment can range
from several thousands to several hundreds of thousands, depending on the chosen
time step. For Brussels, a time step of one hour will result in about 4 700 instances.
A time step of one minute4
raises that number to 280 000! Considering that a single
simulation of reasonable accuracy can easily require a few minutes of computation
time, it is obvious that it is unrealistic to run a full simulation for each individual
daylighting condition. This would require two weeks for a time step of one hour, and
two years for a time step of one minute.
Different approaches have been examined:
the daylight-factor method: a single luminance distribution is assumed for all timesteps, usually the CIE Standard Overcast Sky. The scene needs to be simulated
only once, after which the result can be scaled for each time step using the open-field diffuse horizontal illuminance. This is comparable to the approach suggested
for simplified methods and delivers the quickest result. The great disadvantage is
that all directionality of the skys luminance distribution is lost. Since the CIE
Standard Overcast Sky represents a distribution in which the highest luminance
values are concentrated in the area of the zenith, which does not apply to partly
cloudy or clear skies, this method will underestimate the daylight availability for
side-lit room and overestimate the daylight availability for top-lit rooms;
interpolation between extremes [20]: the scene is simulated once for an overcast-sky luminance distribution, and once for a clear-sky distribution. For each time
step the result is then obtained by interpolating between these two. The weight
factor can be based on the cloud ratio or the effective sunshine probability. This
approach is also very efficient, but still neglects the azimuthal dependence of
luminance distributions. Moreover, an interpolation between two extreme
conditions is not necessarily a good representation of an intermediate condition.
interpolation between extremes with monthly sun positions [5]: to include theazimuthal dependence, the previous approach can be extended to include a
circumsolar region. Typically a clear sky with sun is simulated for each hour of
the 15th
of every month, resulting in 150 additional simulations. This still leaves
the problem of intermediate skies unsolved.
classified weather data: Herkel and Pasquay have tried to group time steps into aset of some 450 categories of similar sun position, direct and diffuse illuminance
[9]. This solution performs reasonably well, but results in a stepped cumulative
daylight distribution. daylight coefficients: instead of simulating the entire sky, the sky vault is thoughtof as consisting of a set of discrete elements of constant luminance. The
contribution of each element to the indoor light distribution is simulated to
produce the daylight coefficients. For each time step the indoor light distribution
4It has been argued that such short time steps are necessary to accurately model the behavior of
lighting control systems [17].
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can then be obtained as a linear combination of the daylight coefficients, using the
sky elements luminance values as coefficients. Typically a set of 145 sky
elements is used. This approach strikes a good balance between accuracy and
computation time.
4.3 Examples of simulation software
By far the most well-known and popular package is Radiance [18]. Development
began during the 1980s as a study of how rendering techniques such as ray tracing
could be applied to lighting simulation. Previously the aim had merely been to
produce good-looking images without much care for the physical correctness. Over
the years Radiance has evolved into a set of some 50 different programs, constituting
one of the most powerful and most accurate simulation suites currently available. It
has often been used as the backbone of other simulation programs.
The core algorithm behind Radiance is ray tracing. However, to account for the
contribution of diffuse indirect light, a mesh of nodes is introduced into the scene in
which irradiance is cached. These are used for indirect light source sampling.
The program has seemingly endless possibilities. The user can define complex shapesand material behavior, add luminance patterns, define sky luminance distributions,
etc. In addition, its accuracy has been extensively validated and documented [12].
In its original form, which can be obtained free of charge, the program has no
graphical user interface, which makes it rather daunting for beginners. However, a
recent AutoCAD interface, called Desktop Radiance, makes it far more user friendly.
Many experts will prefer to produce initial scene descriptions with Desktop Radiance
and then manually adapt the resulting files and use the command-line version for
meticulous manipulation.
Like Radiance, SuperLite was also developed at LBL. This program uses radiosity
for the reflected component in combination with Monte-Carlo techniques for the
direct component. Its modeling and visualization capabilities are rather limited, but itcan be useful for early design stages.
Genelux uses a variant of forward ray tracing, which its developers call photons
generation. Particularly interesting is that it is a web-based tool. Users can upload
their models onto a server and order the simulations of their choice. Results can be
downloaded after completion.
One of the programs that were derived from Radiance is ADELINE. It was first
released in 1994 and combines Radiance and SuperLite to produce illuminance levels,
daylight factors, comfort levels and photo-realistic images. In addition, it delivers
lighting data that can be used for thermal simulation. It has a graphical user interface
and a built-in geometrical modeler, but ease-of-use could be improved considerably.
For predictions on an annual basis it interpolates between three luminancedistributions for every hour of the 15
thof every month, i.e. an overcast sky, a clear sky
without sun and a clear sky with sun.
Lumen Micro, which for some years was the American industry standard for
electrical lighting, was enhanced with a daylighting module by the late 1980s. It uses
radiosity to produce numerical results fairly quickly but takes slightly more time to
produce rendered images. Its modeling capabilities may prove too limited for
advanced simulations.
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LightScape also uses radiosity, but offers an additional ray-tracing step to add
specular effects. It can produce illuminance and luminance values for any point or
surface in the scene, as well as highly realistic images. The software has recently
been purchased by AutoDesk and has been incorporated in Autodesk VIZ 4.
In recent years more attention has gone to the accurate and efficient estimation of
annual daylight availability. Interesting in this respect is Passport-Light, developed
in the framework of the EC project Daylight Europe. It uses backward ray tracing
to compute daylight coefficients and can be used as a pre-processing step for time-
step prediction. A similar effort was made by the developers of DAYSIM. This
adapted version of Radiance produces daylight coefficients in a parallel manner.
References
[1] Ander, G.D., Milne, M. and Schiler, M., Fenestration Design Tool: AMicrocomputer Program for Designers, in: Proceedings of the 2
ndInternational
Daylighting Conference, Long Beach, CA, 187-193 (1986).
[2] Baker, N., Fanchiotti, A. and Steemers, K. (eds.), Daylighting in Architecture
A European Reference Book, James & James, London (1993).
[3] BRE,Digest 309 Estimating daylight in buildings: Part 1, Building ResearchEstablishment, Garston (1986).
[4] BRE,Digest 310 Estimating daylight in buildings: Part 2, Building ResearchEstablishment, Garston (1986).
[5] Erhorn, H., de Boer, J. and Dirksmller, M., ADELINE An IntegratedApproach to Lighting Simulation, in: Proceedings of Daylighting 98, Ottawa,
Natural Resources Canada, 21-28 (1998).
[6] Foley, J., van Dam, A., Feiner, S. and Hughes, J., Computer Graphics:Principles and Practice, Addison-Wesley, Reading (1990).
[7] Glassner, A.S., Principles of Digital Image Synthesis, Morgan Kaufmann, SanFrancisco (1995).
[8] Goral, C.M., Torrance, K.E., Greenberg, D.P. and Battaile, B., Modeling theInteraction of Light between Diffuse Surfaces, in: Computer Graphics18(3),
213-222 (1984).
[9] Herkel, S. and Pasquay, T., Dynamic link of light and thermal simulation: onthe way to integrated planning tools, in: Proceedings of the 5th International
IBPSA Conference, Prague, IBPSA, 307-312 (1997).
[10] Hopkinson, R.G., Architectural Physics Lighting, Her Majestys StationeryOffice, London (1963).
[11] Kajiya, J.T., The Rendering Equation, in: Computer Graphics20(4), 143-150(1986).
[12] Mardaljevic, J., Validation of a lighting simulation program under real skyconditions, in:Lighting Research & Technology27(4), 181-188 (1995).
[13] Nishita, T. and Nakamae, E., Continuous-Tone Representation of Three-Dimensional Objects Taking Account of Shadows and Interreflection, in:
Computer Graphics19(3), 23-30 (1985).
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[14] Paule, B., Bodart, M., Citherlet, S. and Scartezzini, J.-L., Leso-DIALDaylighting Design Software, in: Proceedings of Daylighting 98, Ottawa,
Natural Resources Canada, 29-36 (1998).
[15] Schouwenaars, S. and Wouters, P., One-lamp artificial sky and solar simulatorfor daylight measurements on scale models, in: Proceedings of International
Building Physics Conference, Eindhoven, FAGO, TU/e, 283-290 (2000).
[16] van Santen, C. and Hansen, A.J., Licht in de architectuur, J.H.De Bussy,Amsterdam (1985).
[17] Walkenhorst, O., Luther, J., Reinhart, C. and Timmer, J., Dynamic annualdaylight simulations based on one-hour and one-minute means of irradiance
data, in: Solar Energy72(5), 385-395 (2002).
[18] Ward Larson, G. and Shakespeare, R.,Rendering with Radiance The Art andScience of Lighting Visualization, Morgan Kaufmann, San Francisco (1998).
[19] Whitted, T., An Improved Illumination Model for Shaded Display, in:Communications ACM23(6), 343-349 (1980).
[20] Winkelmann, F. and Selkowitz, S., Daylighting simulation in DOE-2: theory,validation and applications, in: Proceedings of the Building Energy
Conference, Seattle, WA, 326-336 (1985).