World Applied Sciences Journal 10(10): 1247-1254, 2010
ISSN 1818-4952
© IDOSI Publications, 2010
Horizontal Distribution of Daylight Factor with Reference to Window Wall Ratio
in Pendentive Dome Buildings in Tropics, Case of Kuala Lumpur
Mehrdad Mazloomi
School of Housing, Building and Planning,
Universiti Sains Malaysia Minden Campus, 11800 Penang, Malaysia
Abstract: Daylighting design plays important role in architecture of religious buildings such as churches and
mosques where pendentive dome construction is frequently used. In daylighting design, many designers face
difficulty in estimating the interior share of light which is usually expressed by daylight factor due to complexity
of interior form. This study aims to provide designers with a rather high precision rule of thumb for average
daylight factor in pendentive dome building. Thus, it investigates the Daylight Factor [DF] distribution of such
buildings with reference to the tropics. It takes the Window Wall Ratio [WWR] into account and seeks its
influence on daylight factor. By a 12 X 12 points grid, it examines five different ratios including 0.1, 0.2, 0.3, 0.4
and 0.5 on DF of the floor beneath the dome. The results endorse the direct relation of WWR and DF. The least
WWR equal to 0.1 yields an average DF of 0.55% while the greatest WWR of 0.5 yields in average DF of 2.56%.
The intermediate WWR in steps of 0.2, 0.3 and 0.4 correspond to 1.04, 1.56 and 2.07 percent respectively.
As a relatively precise rule of thumb, any increment in consequent steps of WWR with 0.1 intervals results in
0.5% increase in DF. This can be employed by architects and interior designers for lighting design of
pendentive dome buildings in tropical region.
Key word:Daylight Factor Window Wall Ratio
Architecture and Interior design
Pendentive dome
INTRODUCTION
Daylighting in Buildings and Importance of Window
Wall Ratio: The importance of adequate daylight
factor has two folds, one relates to architectural
aspects and the other one deals with energy purposes
[1]. The architectural fold of daylight factor lies in
with indoor visibility and psychological aspects of
daylighting
while
the
energy fold concerns
consumption of energy for the lighting purposes.
Architecturally, an interior space with low daylight
factor could result in gloomy feeling for the occupants
and users of the space. A space with low daylight
availability inversely affects the space’s vividness.
Likewise, inadequate daylight factor may hinder
resident from perceiving the architectural elements that
the architect has designed in order to enrich the spatial
feeling. The least arising issue due to inadequate
daylight availability is the decline of quality of colors
discretion. In worse cases it can be compared to colorblindness that observer fails to distinguish colors
Lighting design
Tropical region
clearly. The other fold of importance of lighting
design regards energy issues. This fold has
daylighting concerns in which the energy consumption
of building rises due to shortage of daylighting. A
building with low daylighting level needs employment
of artificial lighting for compensating the dearth of
lighting. This increases the energy use of building
whereas the adequate of daylight can significantly
reduce the energy bills. To these extents, the daylighting
and its energy related matters are highly considered in
many energy wise buildings because the daylighting is
accounted to reduce the artificial lighting up to 50% [2]. In
many countries, the building codes and regulations
require designers to implement strategies in order to
reduce the energy use by employ a rating system to
evaluate the building performance. This is another reason
that designers must deal with daylight. Daylighting is
amongst the most proper solutions to achieve a more
efficient building in terms of energy use. Both architecture
as well as the energy folds of daylighting impel designers
to pay special attention to the lighting of buildings.
Corresponding Author: Mehrdad Mazloomi, School of Housing, Building and Planning,
Universiti Sains Malaysia Minden Campus, 11800 Penang, Malaysia.
Tel: (006) 04-6533888 Ext. 2184, Fax: (006) 04-6576271, E-mail: [email protected].
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World Appl. Sci. J., 10(10): 1247-1254, 2010
The daylighting importance, however, is not equal
for architectural and energy purposes. The importance of
architectural aspect of daylighting availability is far more
important than its energy purposes in certain type of
buildings. For instance, in religious architecture the
daylight application is tied with the divine concept [3].
The light that penetrates the building through the
windows is perceived to hold a celestial quality. The
pierce of light into the spatial mass of the interior which
is made dark as a result of its closures is assumed to
resemble the blossom of belief into the heart of the
devout. Therefore, daylight is vital to such buildings to
promote the spatial perception and enhance the
integration level of the space with its function. It is where
the daylight is indispensable to the building and its
design and cannot be simply compensated by artificial
lighting [4]. In these buildings, providing daylight
becomes an important issue which architect has to
confront. In spite of existence of devices to be installed
on fenestration, provision for daylight must be dealt in
design stage because when constructing completed there
would not be much feasibility to alter daylight availability.
Taking advantage from daylight is possible with admitting
the natural light into the building through the
fenestrations and apertures. The fenestration as the
passage of light governs the light admittance hence
fenestration design leads to control of admitted light.
It needs the designers to give a special attention to the
fenestration. In fenestration design, the designer must
deal with two majors namely the window material
properties and fenestration geometry. The fenestration
material properties are mostly related to transmittance
value of the translucent material of window, its reflection
and absorption, all provided by the manufacturer. In this
aspect, role of designer is limited to selecting the
appropriate material whereas in other aspect pertaining
to fenestration geometry the designer has a critical role
For the fenestration geometry, it is the architects’
responsibility to take care of it since it is solely design
that identifies the total area of apertures. Therefore
designer’s role is optimization of the opening as
acknowledged in many building regulation. The other
concern during the design stage is the daylighting
distribution which is unevenly distributed in building.
Although in many cases the average daylight factor of
space is taken into account for lighting design but the
maximum, minimum and the range in which the daylight
factor varies are amongst other crucial factors for a higher
resolution design. Therefore designers must tackle two
concerns in the same time, meaning that they have to
simultaneously consider the fenestration area and its
relation to the distribution of daylight. This requires
determining the fenestration area with regards to the
availability of daylight. It urges architects to involve in
rather complicated and time taking calculation process.
In this context, a rule of thumb would be of great help to
architects as well as interior designers.
The daylighting availability in buildings is assessed
by the daylight factor. The daylight factor is the ratio of
daylight illumination level of a point at the interior to that
of an outdoor point on a horizontal plane which receives
the whole sky illumination [5]. According to definition of
CIE luminance, the daylight factor is usually examined and
assessed under overcast skies [6]. It is expressed in
percentages by the following formula:
DF = Ep/Ee x 100
Where DF is Daylight Factor, Ep is the interior
illuminance of point P and E e is the exterior illuminance [7].
This accentuates the importance of the size of
fenestration which is expressed as a ratio of total area of
window to the total area of its wall so called Window Wall
Ratio. The ratio cannot excess 1 which is a façade that is
ultimately opened up by a translucent material and has a
function akin to a window. Many studies take the steps of
WWR into account that usually vary between 0.1 and 1
with 0.1 intervals depending upon their objectives [8-11].
The larger the windows area the more lighting can enter
the interior [12]. Yet, the extent to which the WWR
elevates the DF has to be studied.
Pendentive Dome Buildings: The Pendentive dome
denotes surmounting a dome over another dome. In the
other words, it is constructing a dome on a dome while the
former one is regarded as the pendentive dome and the
latter is called the base. The head of the base dome is cut
to enlarge and unify the interior space in order to integrate
the inner space of both domes. The four sides of the basis
are cut to make a quadrangle form in plan (Fig. 1). The
building which uses this method of construction is
regarded as pendentive dome building in which has a
main square hall in plan with a surmounted dome above it
as the roofing method. This sort of method of
construction by pendentive dome dates back to Sassanid
dynasty in old Persia [13] and has been employed in
well-known building with religious function like Hagia
Sophia in modern Istanbul [14]. Although many churches
follow the same method after Hagia Sophia, but the
method has been used to construct mosques by Muslims
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World Appl. Sci. J., 10(10): 1247-1254, 2010
Fig. 1: The base dome with its side and head cuts retrieved from Bruins [16]
as well. After conquer of Istanbul, Ottomans employed
and developed the method for constructing new mosques.
The influence of the application of pendentive dome by
mosque has been such utmost to the architectural
historians that they deem it as an essential part of
Ottoman style [15]. Even after centuries, several countries
like Malaysia foster the same concept and follow the
method of building mosque by pendentive structures.
MATERIALS AND METHODS
This study quantifies the daylight factor of a
pendentive dome building. It assesses the horizontal
distribution of daylight factor on a working plane inside
the building. The plane is a set grid composing of 12 X 12
nodes each of which is to show the daylight factor value
for that particular point. The plane is 0.1 meter above the
floor of the hall to serve for the religious function of the
building. The magnitude of the points is shown in sets of
counter lines with 0.1 intervals starting from 0% to 5.5%
as the extreme values. The range of bands remains the
same for all examining models for the ease of comparison.
The modeling (Fig. 2) is carried out by Ecotect V5.60 as
the computational program which has been utilized for
many studies [17-19] and its reliability has tested against
the physically surveyed studies [20].
The model is configuration of a 12 X 12 meters square
base dome with a 6 meter radius pendentive dome. The
fenestration area is divided into three windows in line with
Ottomans style with the same height of 4.10 meters from
the 0.2 sill height and the equal distance between
windows. Due to the limitation of the façade which is semi
circular form, the larger windows height is not possible
because it would be off the façade boundaries otherwise.
Fig. 2: The general view of model
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Fig. 3: The direct and diffuse solar radiation in Kuala Lumpur
The WWR is set into 0.1 intervals with five steps
including 0.1, 0.2, 0.3, 0.4 and 0.5. Due to the similar
reason of the façade limitation, the WWR=0.6 and/or
higher is not possible. For modeling, a high precision of
4096 spherical ray tracing has been applied with CIE
overcast sky condition. The details of window’s
properties are shown in Table 1. The interior is white
washed with the plaster for walls and dome and the floor
is carpeted.
Table 1: The details of window’s properties
Case Study: Kuala Lumpur, where the model was
originally developed, is located in southern part of
Malaysia with just 3.1° higher than equator in
Northern Hemisphere. It results in a tropical climate
with year-round variation and rain fall that excesses
than 2000 mm per year. Therefore, most of days have
cloud cover which cuts off a substantial amount of
sunshine thus solar radiation resulting in about 6 hours
sun shine per day in average [21]. The solar radiation
for Kuala Lumpur separated in months [22] is shown in
Figure 3.
The outdoor illuminance which is not a standard
parameter measuring in Malaysian meteorological
stations, can be estimated from the available solar
radiation [23]. The sky design illuminance in modeling is
assumed as 10170 lux according to the Tregenza’s
formula [24].
Characteristics
Quantity
Sky design illuminance
10170 lux
Window clearness
Average (x 0.9)
Window type
Single frame
Visible Transmittance
0.737
Refractive index of glass
1.74
Width
0.6 cm
Density
2300 kgm
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World Appl. Sci. J., 10(10): 1247-1254, 2010
Fig. 4: The range of bands and the frequency of nodes within bands
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RESULTS AND DISCUSSION
Results: Figure 4 shows the horizontal distribution of
daylight factor for different WWR values. In case of
WWR=0.1, the daylight factor varies between 0.3% and
1.1%. The 0.4-0.5 band has the largest share of nodes with
daylight factors which fall into this band. It is followed
by the 0.5-0.6 and 0.6-0.7 bands with 22% and 10%
respectively. Other bands have a share of lower than 5%.
For WWR=0.2, the daylight factor varies between 0.7 and
2.5%. The largest frequency of nodes within a certain
band belongs to the 0.7-0.8 band with 42% of the whole
nodes. After that, the very consequent bands namely
0.8-0.9 and 0.9-1 have the largest share of daylight factor
with 21% and 10% respectively. The bands range for
WWR=0.3 is from 0.7% to 3.7% with the largest value for
1.1-1.2 with 35% share of whole nodes. This is followed
by the bands ranging 1.2-1.3 with 19% and 1.3-1.4 with
12%. For the WWR=0.4 the daylight factor range is
between 1.3 and 4.7, the largest share is the band range of
1.7-1.8 with 22% whereas the next rank is slightly lower
with 21% for the band ranging 1.6-1.7. The third band with
highest frequency is 1.8-1.9 with 13% of the whole nodes.
For WWR=0.5 which ranges between 1.9 and 5.5, the first
rank band is 2.1-2.2 comprising of 20% of nodes with the
daylight factor in this range. The second and third ranks
are the bands ranging 2.0-2.1and 2.2-2.3 corresponding to
frequency value of 18% and 12%. The 2.3-2.4 band has a
considerable value of 10%.
DISCUSSION
WWR increase influences the daylight factor of
the plane. Increase in WWR is associated with increase
in daylight factor as well as the range variation (Fig. 5).
The maximum and minimum of daylight factor increases
with the higher WWR values. It leads to expanding the
range variation from 1.1 to 5.5 for maximum and from
0.3 to 1.9 for minimum for window wall ratios of 0.1 and
0.5 respectively. However, the frequency of nodes within
the most populated band plunges from 53% for WWR=0.1
to 20% for WWR=0.5.
The average daylight factor for each window wall
ratio is calculated based on the all 144 nodes of the grid
(Fig. 6). Figure 7 illustrates the corresponding average
DF for different WWR values. The highest daylight
Fig. 5: Horizontal distribution of daylight factor due to variation of window wall ratio
Fig. 6: The effect on the daylight factor of the plane due window wall ratio from 0.1(the far left) to 0.5 (the far right)
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Fig. 7: The average daylight factor versus window wall ratio
factor average is for WWR equal to 0.5 as high
as 2.56% whereas the lowest is 0.55% corresponding
to WWR=0.1.
The average
DF value for
intermediate WWR steps including 0.2, 0.3 and 0.4 is
1.04, 1.56 and 2.07 percent respectively. This
connotes a relatively precise rule of thumb for
daylight design of a pendentive dome building in tropics.
Any consequent increment in window wall ratio with
0.1 intervals yields 0.5% increase in average daylight
factor. To calculate the average daylight factor for the
WWR values other than these steps the equation
y = 5.05x + 0.041 can be used where ‘x’ is the WWR value
and ‘y’ denotes the average DF. The error of this rule in
prediction of DF due to variation of WWR is less than
0.02%.
CONCLUSION
This study investigated the horizontal distribution
of daylight factor due to variation of window wall ratio in
tropics with reference to the city of Kuala Lumpur in
Malaysia. It showed that:
Increase in WWR is associated with increase in
daylight factor and, expansion in range of bands
accordingly.
The frequency of nodes within the most populated
bands plunges with WWR increase.
Any consequent increment in window wall ratio
with 0.1 intervals yields 0.5% increase in average
daylight factor provided that WWR varies between
0.1 and 0.5.
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