24852813 lighting handbook day lighting computation methods

8/2/2019 24852813 Lighting Handbook Day Lighting Computation Methods

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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,


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,


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


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



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,



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,



A = the total area of all inner surfaces of the scene,



ground = the reflectance of the ground,

Chv = a correction factor to transform from horizontal to vertical

illuminance and


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).

24852813 lighting handbook day lighting computation methods

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