- Repository@Napier

Transcription

- Repository@Napier

Daylighting Performance of Tubular Solar Light Pipes:
Measurement, Modelling and Validation
By
Xiaodong Zhang
A thesis submitted to Napier University for the degree of Doctor of
Philosophy
November 2002
Daylighting Performance of Tubular Solar Light Pipes:
Measurement, Modelling and Validation
a
To my
family
9.1nl,
V9 Cý9
)ý,fQa Iyu
-la M,%Z
and
my
motherland
China
ii
ABSTRACT
The innovation of natural daylighting light pipe took place more than twenty yearsago. Sincethen its
daylighting performancehasbeenreportedin a number of studies.To date,however, no mathematical
bends
light
includes
the
that
within
pipes hasbeen madeavailable.
straight-run
and
effect
of
method
Therefore,a generalmathematicalmodel for light pipes is desirableto assessand predict its daylighting
light
Furthermore,
the
can
enable
assessment
of
pipe system's
a
general
model
such
performance.
efficiency and potential in energy saving.
A modified form of daylight factor, Daylight PenetrationFactor (DPF), hasbeen introducedto build a
sophisticatedmodel that takesaccountof the effect of both internal and external environmentalfactors,
and light pipe configuration. Measurementsand mathematicalmodelling activities aimed at predicting
the daylighting performanceof light pipes with various configurationsunder all weatherconditions in
the UK were undertaken.A generaldaylighting performancemodel, namely DPF model, for light pipes
was developedand validated.The model enablesestimationof daylight provision of the light pipes
with a high degreeof accuracy,i.e. R2values of 0.95 and 0.97 for regressionbetweenpredictedand
measuredilluminance were respectivelyobtainedfor the abovemodel.
The DPF model usesthe most routinely measuredradiation data,i.e. the global illuminance as input.
Consideringthat in real applications,light pipes installed in a particular building may not receivethe
full amount of global illuminance as measuredby local meteorologicaloffice. This may be due to
partial shadingof the light pipe top collector dome.Therefore,to enablethe application of the DPF
model in practical exercisesfundamentalwork on sky diffuse illuminance measurementshave been
undertaken.
An exhaustivevalidation hasbeencarried out to examinethe DPF model in terms of the structureof
the model and its performance.The DPF model was comparedagainststudiesby other independent
researchersin the field. Independentdata setsgatheredfrom a separatesite were used to validate the
performanceof the DPF model. Comprehensivestatisticalmethodshave beenapplied during the course
of validation. Relevant,brief economicand environmentalimpact of the technology under discussion
has also beenundertaken.
One of the main achievementsof this work is the mathematicalmethod developedto evaluatethe
daylighting performanceof light pipes. T'heother main achievementof this work is the development
and validation of the DPF models for predicting light pipes' daylighting performance.
iv
DECLARATION
I hereby declarethat the work presentedin this thesiswas solely carried out by myself
at Napier University, Edinburgh, exceptwhere due acknowledgementis madeand
that it has not beensubmittedfor any other degree.
XIAODONG MANG (CANDIDATE)
DATE
iii
ACKNOWLEDGEMENTS
I must thank my supervisors,ProfessorsTariq Muneer, JorgeKubie and Mr Terry Paynefor their
constantencouragement,support and guidancethroughoutthe period of my research.
This work would not havebeenpossiblewithout the financial support from Napier University, and I
offer my gratitude to all involved in funding this project.
To my friends and colleaguesat Napier University, I warmly acknowledgeyour friendship and support:
Abdulaziz Imtithal, Dr Ana Booth, Dr Baolei Han, Dr Neil Hey, Dr Tom Grassie,Bill Campbell, Bill
Young, FatemaFairooz, GeorgePringle, Ian Campbell,Kevin McCann, MuhammadAsif, Randall
Claywell and Stewart ScotlandHill. I thank ProfessorA Kudish (Israel) and AssociateProfessorJ Lam
(Hong Kong) for providing data for mathematicalmodelling. I thank Dr Gabriel Lopez for his
friendship and advice in the eveningbefore my viva. I must give credit to Miss Amina Muneer for
lending me her room, from time to time, as a laboratory for light pipe performancemeasurements.
Credit is due to David Jenkins(MonodraughtTCS) for developingLux plot basedon DPF model.
I'd like to thank my parents,Shuying Gong and Xinhua Zhang, for supportingme the past twenty-eight
years.Without your love and education,I could not achieveanything.
V
CONTENTS
I
TITLE
IV
ABSTRACT
V
ACKNOWLEDGEMENTS
CONTENTS
VI
LIST OF FIGURES
xi
xvi
LIST OF TABLES
xviii
NOMENCLATURE
1.
I
INTRODUCTION
1.1 THE UTILIZATION OF ELECTRICITY
2
1.2 DAYLIGHTING AND ENERGYCONSERVATION
2
1.3 DAYLIGHTING AND LIFE
3
1.4 DAYLIGHTING IN BUILDINGS
4
1.5 WINDOWS AS TRADITIONAL DAYLIGHTING DEVICES
5
1.6 INNOVATIVE DAYLIGHTING DEVICESAND LIGHT PIPES
6
1.6.1 MIRROR, PRISMATIC GLAZING, LIGHT SHELFAND ATRIA
6
1.6.2 LIGHT PIPE
7
9
1.7 Aims OF THE PRESENTRESEARCH
13
REFERENCES
2.
SOLAR LIGHT PIPE AS AN INNOVATIVE DAYLIGHTING
DEVICE
20
2.1 THE DEVELOPMENTOF SOLAR LIGHT PIPESYSTEM
20
2.2 THE CONCEPTOF LIGHT PIPE
24
2.3 THE STRUCTUREOF PASSIVESOLAR ZENITHAL TUBULAR LIGHT PIPE
25
2.3.1 THE DAYLIGHT COLLECTOR
26
2.3.2 THE LIGHT PIPETUBE
26
2.3.3 THE DIFFUSER
26
2.3.4 SEALING COMPONENTS
27
2.3.5 COMPLETE LIGHT PIPESYSTEM
27
2.4 WORKING MECHANISM OF LIGHT PIPE
27
2.4.1 OPTICALPROCESS
27
2.4.2 EXTERNAL DAYLIGHT ENVIRONMENT
28
2.4.3 THE DESIGNOF LIGHT PIPE
28
vi
3.
2.5 SUMMARY
29
REFERENCES
30
PREVIOUS WORK
44
3.1 APPLICATIONS OF LIGHT PIPES
45
3.1.1 APPLICATIONS OF LIGHT PIPESIN RESIDENTIAL AND OFFICEBUILDINGS
46
3.1.2 LARGE-SCALE COREDAYLIGHTING BY LIGHT PIPE
48
3.1.3 LIGHT PIPECOUPLEDTO LASER-CUT LIGHT-DEFLECTING PANELS
48
3.1.4 LIGHT PIPESYSTEMUSING BOTH NATURAL AND ARTIFICIAL LIGHT
49
3.1.5 INTEGRATION OF LIGHT PIPEDAYLIGHTING AND NATURAL VENTILATION
SYSTEMS
51
3.1.6 THE USE OF LIGHT PIPE SYSTEMS IN DEEP PLAN BUILDINGS
52
3.1.7 A SOLID LIGHT GUIDE SYSTEM: AIR-CLAD OPTICAL ROD
53
3.2 WORKING MECHANISM OF LIGHT PIPES
3.2.1 UNDERSTANDING
OF THE DAYLIGHT TRANSMISSION WITHIN LIGHT PIPES
3.2.2 CRITICAL APPRAISAL
3.3 RESEARCH METHODS FOR EVALUATING THE EFFICIENCY OF LIGHT PIPES
4.
53
54
55
55
3.3.1 THE EFFICIENCIES OF LIGHT PIPE SOLAR COLLECTORS AND DIFFUSERS
56
3.3.2 THE EFFICIENCY OF LIGHT PIPE TUBE
57
3.3.3 THE EFFICIENCY OF LIGHT PIPE 13ENDS
58
59
3.4 THE DESIGN OF LIGHT PIPES
61
3.4.1 CARTER'S DESIGN CHARTS FOR LIGHT PIPES
62
3.4.2 DESIGN METHOD BASED ON COEFFICIENTS OF UTILIZATION
62
63
3.5 SUMMARY
64
REFERENCES
66
RELEVANT THEORIES
70
4.1 DAYLIGHT PENETRATIONFACTOR
71
4.2 TRANSMISSION OF SKY DIFFUSELIGHT AND SUNLIGHT WITHIN LIGHT PIPES
73
4.2.1 TRANSMISSION OF SUNLIGHT WITHIN LIGHT PIPETUBE
73
4.2.2 TRANSMISSION OF SKY DIFFUSELIGHT WITHIN LIGHT PIPETUBE
74
4.3 ZENITH LUMINANCE MODELS
4.3.1 MOON AND SPENCER'SOVERCASTSKY MODEL
75
75
vii
4.3.2 MUNEER'S
4.3.3 PEREZALL-SKY MODEL
77
4.3.4 KiTTLER, DARULA AND PEREZ'S STANDARD SKY MODEL
77
4.4 INTERNAL
4.4.1
4.5
76
MODEL
ILLUMINANCE
SURFACE
LAMBERTIAN
78
DISTRIBUTION
AND LAMBERT'S
COSINE
LAW
78
4.4.2 THE INVERSE SQUARE LAW
79
4.4.3 RADIATIVE
79
STATISTICAL
4.5.1
MEAN
VIEW FACTOR METHOD
METHODS
BIAS ERROR
4.5.2 ROOTMEAN
FOR EVALUATION
OF MODEL
79
PERFORMANCE
80
(MBE)
SQUARE
ERROR
80
(RMSE)
4.5.3 PERCENTAGE AVERAGE DEVIATION (PAD)
4.5.4
SLOPE AND THE VALUE
PREDICTED
OF THE COEFFICIENT
VERSUS MEASURED
81
OF DETERMINATION
OF
ILLUMINANCE
4.5.5 HISTOGRAM OF ERRORS
82
83
REFERENCES
5.
81
MEASUREMENTS AND DATA PROCESSING
88
5.1 NAPIER SOLAR STATION
89
5.2 INTERNAL ILLUMINANCE SENSORS,DATA-LOGGER AND STANDS
90
5.3 DAYLIGHTING PERFORMANCEMONITORING IN REAL BUILDING - CURRIE TEST
92
ROOM
5.4 DAYLIGHTING
PERFORMANCE MONITORING UNDER ALL SKY CONDITIONS -
CRAIGHOUSE TEST ROOM
5.5 DAYLIGHTING
93
PERFORMANCE MONITORING UNDER ALL SKY CONDITIONS -
MERCHISTON TEST ROOM
95
5.6 INTERNAL DAYLIGHT DISTRIBUTION BY LIGHT PIPES - CRAIGHOUSE TEST ROOM 96
6.
5.7 DIFFUSER COMPARISON
CURRIE TEST ROOM
-
97
REFERENCES
98
MATHEMATICAL
MODELLING
103
6.1 LIGHT PIPEDESIGNAND DPF MODELLING
104
6.2 THE DPF OF A STRAIGHT LIGHT PIPE
106
6.2.1 PARAMETER ANALYSIS
106
6.2.2. MODELLING AND VALIDATION
107
6.2.3 SUMMARY
109
viii
6.3 STRAIGHT LIGHT PIPEDPF MODEL (S-DPF)
110
6.4 ELBOWED LIGHT PIPEDPF MODEL (E-DPF)
112
6.5 LIGHT PIPEVIEW FACTOR DPF MODEL (V-DPF)
113
6.6. PARAMETRIC ANALYSIS
114
6.6.1 EFFECT OF OtsAND
114
6.6.2 EFFECT
7.
OF R AND
KT
115
L
6.6.3 EFFECT OF DISTANCE D AND DIFFUSERHEIGHT H
115
6.6.4 EFFECT OF LIGHT PIPEBENDS
115
6.6.5 EFFECT OF INTERNAL REFLECTION
115
6.6.6 EFFECT OF DIFFUSERTYPE
116
6.7 A COMPARISONBETWEENWINDOWSDF AND LIGHT PIPEDPF
118
6.8 COST AND VALUE ANALYSIS OF TUBULAR LIGHT PIPES
119
6.8.1 ENERGY CONSERVATION
120
6.8.2 HEALTH
122
6.8.3 WORK PERFORMANCE AND PRODUCTIVITY
123
6.9 SUMMARY
124
REFERENCES
126
SHADOW
BAND DIFFUSE MEASUREMENTS
CORRECTION
144
7.1 BACKGROUND
7.2 DRUMMOND'S
146
METHOD
146
7.2.1 THEORY
7.2.2 EXAMINATION
OF 'MEASURED'
DIFFUSE CORRECTION FACTOR
7.3 NEW MODEL BASED ON SKY-DIFFUSE DISTRIBUTION INDEX
8.
144
147
149
7.3.1 THEORETICAL ANALYSIS
149
7.3.2 VALIDATION
151
7.4 SUMMARY
154
REFERENCES
156
VALIDATION
166
OF DPF MODELS
8.1 CHECKING THE LINEAR MODEL BY STATISTICAL TECHNIQUE - RESIDUALS PLOT
166
8.2 VALIDATION
OF S-DPF MODEL USING MERCHISTON TEST ROOM DATA
168
8.2.1 CASE-BY-CASE ASSESSMENTOF THE S-DPF MODEL UNDER NON-HEAVYOVERCASTSKY CONDITIONS(KT>0.2)
168
ix
8.2.2 PERFORMANCE ASSESSMENT OF THE S-DPF
MODEL UNDER HEAVY-
OVERCASTSKY CONDITIONS(KT<0.2)
171
8.2.3 PERFORMANCEASSESSMENTOF THE S-DPF MODEL UNDER ALL-SKY
173
CONDITIONS
8.3 COMPARISON OF DPF MODELS AGAINST RESULTS DUE TO INDEPENDENT
RESEARCHES
175
8.4 THE DESIGN TOOLS
177
8.5 LIMITATIONS OF THE DPF MODELS
178
REFERENCES
180
9. CONCLUSIONS
AND FURTHER
WORK
209
APPENDIX 1: THE METHOD FOR CALCULATING THE VIEW FACTORS FROM DIFFERENTIAL AREAS TO
SPHERICAL SEGMENTS BY NARAGHI
215
APPENDIX 11: LIST OF PUBLICATIONS
217
x
LIST OF FIGURES
14
Figure 1.1 World energy supply scenario....................................................................
Figure 1.2 UK Energy Flows 1998,dti, Departmentof Trade and Industry, 2000..... 15
Figure 1.3 ManchesterAirport departurelounge with solar chandeliers.....................16
16
Figure 1.4 Beam sunlight in a side-lit room ................................................................
Figure 1.5Undergrounddaylighting at the SpaceCentrebuilding, University of
17
.............................................................................
17
Figure 1.6 Conceptof light shelves.............................................................................
18
Figure 1.7 Generic forms of atrium buildings .............................................................
18
Figure 1.8 A schematicof light pipe system................................................................
Figure 2.1 Invention by Hanneborgfrom Norway in 1900: apparatusfor transmitting
Minnesota,Minneapolis, USA
31
...................................................
32
Figure 2.2 Sutton patentedtubular skylight in 1994in the USA .................................
(Ref.
3)
into
basements
stores
or
other
sunlight
33
Figure 2.3 Bixby tubular skylight systems..................................................................
Figure 2.4 Comparisonof O'Neil's coneshapedlight tube againstconventional
34
.................................................................................................
35
Figure 2.5 Typical Monodraughtlight pipes
...............................................................
36
Figure 2.6 The family map of light pipe ......................................................................
Figure 2.7 Schematicdiagram of passivesolar zenithal tubular light pipe .................36
column light tube
Figure 2.8 Monodraught (UK) light pipe tubesthat useReflectalite 600 PET film 37
....
Figure 2.9 Appearancesof different types of diffuser
38
.................................................
Figure 2.10 Demonstrationof the different daylighting effects by a clear diffuser and
39
an opal diffuser ....................................................................................................
Figure 2.11 An explodedview of a typical light pipe systemby Monodraught (UK) 40
Figure 2.12 A generalprocessof daylight collection, transmissionand distribution
41
through light pipes ...............................................................................................
42
..........................................
43
Figure 2.14 Sky vault divided into small patcheswith respectiveluminance
.............
Figure 2.13 The pattern sunlight travel through light tube
Figure 3.1 Representationof the sky luminancedistribution under non-overcast
68
conditions............................................................................................................
.
Figure 3.2 Vector presentationof Bahrain sky radiancedistribution: (a) clear sky
kt=0.7, (b) part-overcastsky kt=0.5, (c) thin overcastsky kj=0.35 and (d) heavy
69
kt=0.2
sky
overcast
.
.............................................................................................
xi
Figure 4.1 Sunlight of intensity I and elevation ccdescendinga 2-D straight light pipe
84
..............................................................................................................................
Figure 4.2 A projectedview along the axis of a straight tubular light pipe tube, with
light entering at distancex from the axis followed by its incident on the internal
surfaceat projected angle I and travels distanced betweenreflections...............84
85
Figure 4.3 The uniform overcastsky vault devided into 21 patches
...........................
85
Figure 4.4 Emitted radiation from a surface
................................................................
Figure 4.5 The inversesquarelaw
86
...............................................................................
Figure 4.6 The calculation of view factorsbetweena point and a hemispheresurface
87
..............................................................................................................................
99
Figure 5.1 Napier University CIE First-Classsolar station
.........................................
100
Figure 5.2 Schematicof the Currie test room and light pipe system
.........................
101
Figure 5.3 Light pipe systeminstallation in Currie, Edinburgh
................................
Figure 6.1 The developmentof the proposedDPF model: systemstructureof the
developmentof DPF model (a) and the procedureto validate the model (b) 130
....
Figure 6.2 Variation of daylight penetrationfactor as a function of distance,D
131
......
Figure 6.3 Daylight penetrationfactor variation as a function of solar altitude
(D=155cm)
.........................................................................................................
Figure 6.4 Daylight penetration factor as a function of sky clearness index, kt (D =
131
155cm; solar altitude = 49±0.5")
132
.......................................................................
Figure 6.5 Plot of calculatedinternal illuminance againstmeasuredinternal
illuminance for all distances
132
..............................................................................
Figure 6.6 Plot of calculatedinternal illuminance againstmeasuredinternal
illuminance for D= I 94cm
..................................................................................
133
Figure 6.7 Light entering a light pipe descendsvia a seriesof inter-reflections
133
.......
Figure 6.8 Scatterplot of calculateddue to Eq. 6.9 (Y-axis) againstmeasuredinternal
illuminance (X-axis) for straight light pipes (units = lux)
134
.................................
Figure 6.9 Scatterplot of calculateddue to Eq. 6.11 (Y-axis) againstmeasured
internal illuminance (X-axis) for elbowed light pipes (units ý lux)
134
..................
Figure 6.10 Scatterplot of calculateddue to Eq. 6.9 (Y-axis) againstmeasured
internal illuminance (X-axis) for straight light pipes (units = lux)
135
....................
Figure 6.11 DPF for 420mm-diameterlight pipe as a function of a, and kt, (a) for
straight light pipe and (b) for light pipe with two bends(D=H=1.2m) .............136
xii
Figure 6.12 Effect of aspect ratio on DPF, (a) for straight light pipe and (b) for light
137
bend
(420mm-diameter,
D=H=1.2m)
pipe with one
.........................................
Figure 6.13 Comparison of the predicted DPFs for straight light pipe and elbowed
light pipes with one, two, three and four bends (530mm-diameter, (X,=45',
D=1.2m, H=lm)
.................................................................................................
Figure 6.14 Comparison between external and internal illuminance due to different
138
138
diffusers
..............................................................................................................
Figure 6.15 The comparison of an old opal against a clear diffuser (transparency
property) .............................................................................................................
139
Figure 6.16 The comparison of an old opal against a clear diffuser (reflectivity
140
property) .............................................................................................................
Figure 6.17 Ring pattern and "pools of light" phenomenon seen in Bahrain light pipe
project ................................................................................................................
Figure 7.1 Comparison of the range of diffuse irradiance correction factor given by
141
157
Drummond's method and actual results
.............................................................
Figure 7.2 Scatter plot of true diffuse irradiance versus corrected irradiance using the
proposed (top) and Drummond's model (bottom) -Bracknell data ................... 158
Figure 7.3 Proposed model's error histogram under all-sky (a), heavy overcast (0 < kt
< 0.2) (b), part-overcast (0.2 < kt: 5 0.6) (c) and clear-sky (0.6 < kt <1) (d)
159
data
Bracknell
conditions ................................................................................
Figure 7.4 Drummond model's error histogram under all-sky (a), heavy overcast (0 <
kt: 5 0.2) (b), part-overcast (0.2 < kt: 5 0.6) (c) and clear-sky (0.6 < kt <1) (d)
conditions - Bracknell data................................................................................ 160
Figure 7.5 Scatter plot of true diffuse irradiance versus corrected irradiance using the
data
(top)
(bottom)
Sheva
161
Drummond's
Beer
and
model
proposed
...............
Figure 7.6 Proposed model's error histogram under all-sky (a), heavy overcast (0 < kt
< 0.2) (b), part-overcast (0.2 < kt:!ý 0.6) (c) and clear-sky (0.6 < kt <1) (d)
conditions - Beer Sheva data ............................................................................. 162
Figure 7.7 Drummond model's error histogram under all-sky (a), heavy overcast (0 <
kt:!ý 0.2) (b), part-overcast (0.2 < kt: ý 0.6) (c) and clear-sky (0.6 < kt <1) (d)
conditions - Beer Sheva data ............................................................................. 163
Figure 8.1 A satisfactoryresidualsplot
181
.....................................................................
xiii
Figure 8.2 Examples of characteristics shown by unsatisfactory residuals behaviour
181
......................................................................................................................
Figure 8.3 The residualplot of the differencebetweenpredicted and measuredinternal
illuminances (Y-axis) versuspredictedvalues(X-axis) for S-DPF model, Unit:
lux
182
......................................................................................................................
Figure 8.4 Histogram of absolute error due to S-DPF model, Unit for X-axis: lux.. 182
Figure 8.5 The residual plot of the difference between predicted and measured internal
illuminances (Y-axis, Unit: lux) versus solar altitude (X-axis, Unit: degree) for S183
DPF model
.........................................................................................................
Figure 8.6 The residualplot of the differencebetweenpredictedand measuredinternal
illuminances (Y-axis, Unit: lux) versus sky clearness index (X-axis) for S-DPF
183
model..................................................................................................................
Figure 8.7 Scatter plot of predicted internal illuminance against measured internal
illuminance (light pipe 0.21m in diameter and 0.61m in length), Unit: lux ...... 184
184
illuminance (light pipe 0.2 1rn in diameter and 1.22m in length), Unit: lux
......
185
illuminance (light pipe 0.33m in diameter and 0.61m in length), Unit: lux
......
Figure 8.10 Scatter plot of predicted internal illuminance (Y-axis) against measured
internal illuminance (X-axis), (light pipe 0.33m in diameter and 1.22m in length),
Unit: lux
.............................................................................................................
185
186
......
186
......
187
......
Figure 8.14 Validation: scatter plot of measured (X-axis) internal illuminance versus
data,
heavy-overcast
S-DPF
(Merchiston
(Y-axis)
due
to
model
predicted values
sky), Unit: lux .................................................................................................... 187
Figure 8.15 Validation: scatter plot of measured internal illuminance (X-axis) versus
predicted values (Y-axis) due to S-DPF model (Merchiston data, heavy-overcast
sky, 0.21m in diameter and 0.61m in length), unit: lux ..................................... 188
x1v
heavy-overcast
(Merchiston
data,
(Y-axis)
due
S-DPF
to
model
values
predicted
due
(Merchiston
data,
heavy-overcast
(Y-axis)
S-DPF
to
model
values
predicted
data,
(Y-axis)
due
S-DPF
(Merchiston
heavy-overcast
to
values
model
predicted
predicted values (Y-axis) due to S-DPF model (Merchiston data, hcavy-overcast
predicted values (Y-axis) due to S-DPF model (Merchiston data, all weather),
unit: lux .............................................................................................................. 191
Figure 8.23 Scannedcopy of page 15 of report by Loncour et al [4]
192
........................
Figure 8.24 Scannedcopy of page 16 of report by Loncour et al [4]
193
........................
Figure 8.25 Scannedcopy of Figure 5 of Carter [5]
194
..................................................
Figure 8.26 Scannedcopy of Figure 6 of Carter [5]
194
..................................................
Figure 8.27 Comparativeplots showing close conformancebetweenLiverpool
195
measurementsand Napier's DPF model estimates............................................
Figure 8.28 Plot showing measuredexternaland internal illuminance at Napier
University, unit: lux
196
...........................................................................................
Figure 8.29 Loss of flow energyat entranceto a conduit
196
..........................................
Figure 8.30 Loss of flow energyduring the 'starting-length' within the conduit
197
......
Figure 8.31 An exampleof lux plot [Courtesy:David Jenkins,Monodraught]
197
........
Figure 8.32 An illustration of "vertical" distanceH, and "total" distancesD usedin
DPF model
198
.........................................................................................................
xv
LIST OF TABLES
Table 1.1 World fossil fuel reserves to production ratio, years (BP 1999 statistics)... 19
Table 5.1 Designs of light pipes that were monitored in Craighouse campus, Napier
102
...........................................................................................................
Table 5.2 Designsof light pipes that were monitored in Merchiston Campus,Napier
102
University
...........................................................................................................
Table 5.3 Internal daylight distribution testson light pipes installed in Craighous
University
102
................................................................................
142
Table 6.1Coefficients usedin Eqs. 6.5 & 6.6 ............................................................
Table 6.2 Validation results for the model representedby Eq. 6.5............................142
Table 6.3 Validation results for the model representedby Eq. 6.6............................142
142
Table 6.4 Coefficients usedin Eqs. 6.9 - 6.13
..........................................................
143
Table 6.5 Error statisticsfor Eqs. 6.9 - 6.13..............................................................
Table 6.6 Relationshipbetweena 'conventional' window daylight factor and an
Campus,Napier University
143
..........................................................
Table 7.1 Mean Bias Error (MBE), Root Mean SquareError (RMSE) and Percentage
equivalentdaylight factor for a light pipe
Average Deviation (PAD) comparisonof the proposedmodel versus
164
........................................................................
Table 7.2 Histogram percentageerror analysisresults,Bracknell. Figures given below
164
are the number of data points in eachcategory..................................................
Table 7.3 Statistical comparisonof the two models under discussion- Bracknell data.
Drummond's method,Bracknell
164
............................................................................................................................
Table 7.4 Mean Bias Error (MBE), Root Mean SquareError (RMSE) and Percentage
Average Deviation (PAD) comparisonof the proposedmodel versus
165
Drummond's method,Beer Sheva
.....................................................................
Table 7.5 Histogram percentageerror analysisresults,Beer Sheva.Figures given
165
below are the number of datapoints in eachcategory
.......................................
Table 7.6 Statistical comparisonof the two models under discussion- Beer Sheva
165
data
. ....................................................................................................................
Table 8.1 Statisticalresults for the performanceof S-DPF model under heavy199
overcastsky conditions (kt:ý0.2) ........................................................................
Table 8.2 Internal illuminance distribution (0.33m-diameterlight pipe, 18thDee 2000)
200
............................................................................................................................
xvi
Table 8.3 Summary of the Internal illuminance distribution test results (Craighouse
test room)
201
...........................................................................................................
Table 8.4 Light pipe design guideline for mid-summerfor Kew, UK. (Time = 10am
l't July, Height of diffuser to the working plane = 2m)
202
.....................................
Table 8.5 Light pipe design guideline for winter for Kew, UK. (Time =I OamI"
February,Height of diffuser to the working plane = 2m)
203
..................................
Table 8.6 Light pipe design guideline for spring and autumn for Kew, UK. (Time =
I OarnI stApril, Height of diffuser to the working plane = 2m)
204
.........................
Table 8.7 Light pipe designguideline for mid-summerseasonfor Kew, UK. (Time =
Vt
mid-noon July, Height of diffuser to the working plane = 2m) ....................205
Table 8.8 Light pipe design guideline for winter for Kew, UK. (Time = mid-noon I"
February,Height of diffuser to the working plane = 2m)
206
..................................
Table 8.9 Light pipe design guideline for spring and autumn for Kew, UK. (Time =
mid-noon 1s'April, Height of diffuser to the working plane = 2m) ..................207
Table 8.10 Measurement Settings
..........
Table 8.11 Envelop for DPF models
..............................................................
.............................................................
208
208
xvii
NOMENCLATURE
ao- alo
Ap
Coefficients used in Eqs. 6.9 - 6.13
Ape
b
Light pipe aspectratio for straight light pipes (=light pipe length / diameter)
Light pipe aspectratio for elbowed light pipes
Radiancedistribution index
B,,
Normal beam irradiance (W/m 2)
d
D
DF
The distancebetweenthe projection of the diffuser centreon the working plane and the point
of interest(in)
Distancefrom light pipe diffuser to a given position P(x, y, z) (in)
Daylight factor
DPF
Eed
E,
(x,
for
P
factor
light
daylight
The
y,
z)
position
penetration
pipe
)
y,
Horizontal diffuse irradiance(W/m)
Horizontal global irradiance (W/m 2)
g
Evd
Horizontal diffuse illuminance (lux)
Evg
Horizontal global illuminance (lux)
E,
Estimated internal illuminance (lux)
stimated
Eintemal
Internal illuminance at a given point (lux)
illuminance at the point P(, ) (lux)
Internal
Einternal
(x,y,z)
y,,
Emeasured Measured internal illuminance (lux)
f
Diffuse irradiancethat is obscuredby shadowband: Drummond's method (W/m2)
fD
The diffuser factor
flen
The equivalent-lengthfactor
floss
The energy-lossfactor
Fe
External environmentalfactors
Fg
Fi
Light pipe configuration factors
Internal environmentalfactors
FD
Drummond diffuse irradiancecorrection factor basedon isotropic radiancedistribution
Fp
Proposeddiffuse irradiancecorrection factor basedon anisotropicradiancedistribution
Fv(,., )
y,,
G
H
i
lo
I0
IL
The view factor betweenlight pipe diffuser and a plane elementat P(x,y,z)
Horizontal global irradiance(W/m2)
Height of the diffuser over the working plane
Angle at which light incident on the reflecting surfaceof light pipe tube (degree)
The intensity of radiation in normal direction
Intensity of radiation along a direction that has angle 0 with the normal to a radiation-emitter
horizontal diffuse illuminance (lux)
k,
Sky clearnessindex
L
Length of the straight light pipe (in)
Lb
Length of the light pipe bend (in)
L,
Zenith radiance (W M-2 sr-1)
L,
Zenith luminance(Cd/m2)
L, o
Zenith luminanceof a sky patch of a altitude of 0 (Cd/m2)
Coefficient usedin Eqs. 6.9 - 6.13
in
Xviii
N
P
P (X,
Y,Z)
R
Number of bends
The proportion of the sky area obscured by the shadow band
A given location at which illuminance is to be estimated
t
Radius of light pipe tube (m)
Hour angle (radian)
to
Sunset hour angle (radian)
T
Transmission of daylight within light pipe tube
View angle of the shadow band subtended at the diffuse irradiance sensor
The distance between a bunch of incident light and the axis of light pipe tube (m)
Solar altitude (radian) = cc,
W
X
Cc
P
5
Slope of any given tilted surface (radian)
Sun's declination (radian)
ýD
0
Light pipe diameter (mm)
Angle between the considered point and the position of the sun (radian)
Latitude of the measurement site (degree)
The altitude of a given sky patch (radian)
P
4
Surface reflectance of mirrored light pipe
Zenith angle in Perez model, (radian)
IV
Azimuth of a sky patch (radian)
7
xix
1. INTRODUCTION
Energy is an essentialcomponentfor all activity and is required for the production of all goods and the
provision of all services.For thousandsof yearshumansociety hasbeenusing fossil fuel as a major
form of energyresource.However, becausehuman activity accelerates,fossil fuels are being depleted
at a faster rate than ever before. All forms of fossil fuels have their respectivecycle of domination and
depletion phase(Fig. 1.1). According to the energystatisticspublishedby BP [11, the world's resource
to production ratio is projected to be 62 years,as shown in Table 1.1. Therefore,the current scenarioof
fossil fuels depletion is causingconcernsacrossthe world, especiallyin the developednations.The
solution to abovechallengeconsistsof two aspects,namely, to saveenergyand to exploit renewable
energy.
A topic closely relatedto energyconservationis the issueof environmentprotection. Throughout the
world, the concernon the negativeimpactsof excessiveenergyconsumptionon natural environmentis
arising. In this respect,one major argumenthasbeenon the associatedproblem of thermal pollution
from conventionalpower plants [2]. The InternationalPanelfor Climate Changehas arguedthat the
world is definitely getting warmer. In England,the 1990sexperiencedfour out of the five warmest
yearsin a 340-yearrecord, with 1999being the wan-nestyear ever recorded.Global warming and its
affiliated changesin the world's climate would have enormousconsequencesfor people,economiesand
the environment.Many projections of the world's future climate show more intenserainfalls or
snowstorms,which are likely to lead to large-scaleflooding of many locations.Betweenthe 1960sand
the 1990s,the number of significant natural catastrophessuch as floods and stormsrose three-fold, and
the associatedeconomiclossesroseby a factor of nine. Therefore,the global warming and its
associateddisastrousclimatic impacts on the environmentand economicshave madeit necessaryfor
the whole human society to explore more efficient and environmentally friendly energyresources.
Presentresearchon the innovative daylighting device light pipe that utilizes solar energy is a new effort
towards this end.
1.1 THE UTILIZATION
OF ELECTRICITY
Nowadays,energythat takesthe form of electricity and fuel hasbecomethe backboneof our society.
However, during the causeof converting primary fuels into final use energy,a substantialpart of
energy is lost. Figure 1.2 showsthe energy flows in the UK for the year of 1998 [3]. It is shown that in
the year of 1998,the UK final usersconsumed169.4million tonnesof oil equivalentenergy, out of
which electricity accountsfor 31.7 million tonnes.Within the 31.7 million tonnesof electricity, 25.2
6.5
by
the
tonnes
and
other
million tonneswere
power
station,
were generated nuclear
million
producedby thermal-electricity plant. The conversionefficiency of a typical nuclear station in the UK
is about 37 per cent [4]; while for conventionalsteamstations,the ratio of fuel used for electricity
generationto electricity generatedis about 12 per cent. Therefore,the overall energyefficiency for
electricity generationis poor with the utility ratio lower than 25 per cent.
The use of electricity is not only inefficient but also environmentally detrimental.The combustionof
fossil fuels is responsiblefor the majority of emissionsof carbondioxide C02, sulphur dioxide S02 and
nitrogen oxides N02 [4]. CarbonDioxide is the main greenhousegas,which may contribute to global
warming and climate change.Sulphur dioxide and oxides of nitrogen are the main causeof acid rain.
According to the UK Energy Sector Indicators,in the UK emissionOf C02 from power station is the
largestsingle source,which accountsfor 26.7% of the total emissions.As to S02 and N02,
correspondingfigures are 57.1% and 21.2% respectively.Nuclear power station is also
environmentallyharmful becausethe potential hazardposedby nuclearwasteto the natural
environment.'llierefore, the reduction of electricity production and consumptionnot only savesenergy
resources,but also protectsthe natural environmentthat our human society relies on.
1.2 DAYLIGHTING
AND ENERGY CONSERVATION
In the United Kingdom, electrical lighting accountsfor an estimated5% of the total primary energy
consumedper annum.Office buildings in the UK may consumeup to 60% of their total energy in the
form of electric lighting [5]. The total amountof electricity consumedby domestichousehold
appliancesincreasedby 85% between 1970and 1998 [4]. According to the UK Energy Sector
2
Indicators, for a typical domestichousehold,lighting accountsfor more than 23% of total electricity
consumption.Exploitation of daylight can thus produce significant savings.Researchhas shown that
savingsof 20% to 40% are attainablefor office buildings that utilise daylight effectively. Benefits and
savingsassociatedwith daylight designare manifold. Reductionsin lighting energyhave the knock-on
effect of lowering cooling and heating energyconsumptionin a building [6]. Another significant
benefit of using daylight is it is totally free and clean, which makesit one of the most cost-effective
meansof reducing electricity consumption.Therefore,applying more efficient daylighting designsin
buildings will contribute to energy conservationand environmentalimprovement.
1.3 DAYLIGHTING
AND LIFE
Nowadays,people spendmost of their lives in buildings, e.g. offices, housesfactories, suppermarkets,
stadiumsand so on. Thesebuildings are sheltersfor humansto provide them safety and comforts.
However, in seekingshelter,people also needto be in touch with the external environment.Daylight
enablesa visual contactto the outsideworld. Daylight is also required to enhancethe appearanceof an
interior and its contentsby admitting areasof light and shadethat give shapeand detail for objects.The
inclusion of daylight in the workspaceprovidesworkers with social and physiological benefits.
Sunlight variation affects many activities of being on the earth.Humansare also affected to seasonal
and daily variation of sunlight. Daylight that is brought into interior spacetells people the changeof
external environmentaland thereforereleasesthe feeling of isolation and monotony. Researchhas
shown that daylight has an important bearing on the humanbrain's chemistry. Light entering via eyes
stimulatedthe nerve centreswithin the brain, which controls daily rhythms and moods.Further
researchhas also establisheda link betweenhuman exposureto light and Serotonin,a substance
identified as a neurotransmitter.Lack of Serotoninis known to be a causeof depression.By receiving
enoughamount of daylight, people can positively adjust the production of Serotoninso as to tune their
physical and spiritual condition better. Therefore,daylight affectsmulti-aspectsof human life and has
an important bearing on the whole society.
3
1.4 DAYLIGHTING
IN BUILDINGS
The sourceof daylighting is the sun. The sun is a huge nuclear reactorthat hasbeen continuously
emitting solar radiation for around4.5 billion years.It shouldremain more or lessas it is for another
5.5 billion years [7]. The term solar radiation refers to the energyemanatingfrom the sun. Daylight is
the part of energy containedwithin the visible part of the solar radiation spectrum.Human eye is the
organ by which humanbeing perceive daylight. It receiveslight that is omitted or reflected by objects,
and convertsthe light rays into signalsthat can be recognizedby the brain, which producesthe
perceptionof vision. Daylight itself has a continuousspectrumwith apparentdifference in brightness.
Human eye's sensitivity to spectralcolour varies from violet to red, which is correspondingto the solar
radiation spectrumof 0.39 to 0.78 pm. Although daylight coversonly a narrow band of the whole solar
radiation spectrum,it has a fundamentaland significant bearing on humanbeing's life on the earth.
On the earth, daylight has two components,one is the direct beam (sunlight) from the sun, and the
other is the sky-light. The latter one is a result of the scatteringof sunlight within the ambient
atmosphereof the earth. For a building, the more light it admitted,the better its habitantscan see.
However, the daylight quantity shouldbe controlled to be in a range.Too much daylight can be
troublesomein somesituations,For example,residentsmay feel discomfort by direct sunray in their
field of view. Solar heat gain is anotherkiller of building design.The use of large glazedareain an
attempt to admit more daylight can causesolar overheating.However, comparedto sunlight, sky-light
is cooler, gentler, diffuse and more visible with a significantly smaller infrared component.Thus, in
situationswhere daylight is desiredwith minimal solar heat gain, sky-light can provide the best quality
of daylight.
Comparedto artificial light, daylight is of better quality. The good colour renderingqualities of natural
light helps to reduceeyestrain.Another benefit of using daylight is it improves the health of human
body. Lack of daylight exposurefor a long time hasbeen found to be the causeof mood swings and
depression.Peoplealso react to changingseasonswith alteredmoodsand behaviour. This phenomenon
exacerbatesin somehigh-latitude location where peoplesuffer lack of daylight seasonally.For
example,the common disorder amongpeople who live in Northern Europehas beendiagnosedas
seasonalaffective disorder (SAD). Therefore,to allow sufficient daylight in building designhas a
4
significant bearing on maintaining and improving occupants' health condition. To admit as much as
possible daylight into buildings and meanwhile to minimize the glare and solar gain level is an
important balancethat building designersneedto achieve.
1.5 WINDOWS
AS TRADITIONAL
DAYLIGHTING
DEVICES
Window is the mostly widely used daylighting device in buildings. The main function of a window has
beendescribedas, "to provide an outsideview and to permit light to penetratethe interior of a building
in such quantity and with such distribution that it provides satisfactoryinterior lighting results" (8].
Therefore,the application of windows in buildings design is more than illuminating engineering;it is
also a scienceon living and working environmentalhealthy. It is often stated,that peopleprefer to
work where thereare windows and that the exclusion of daylight leadsto a senseof deprivation and a
lack of well being. However, in practisethe designand application of window is limited by various
reasonsapart from lighting.
One handicapof using window in buildings is that the window's performanceis greatly constrainedby
the external natural and man-madeobstructions.As a solution, larger sized windows are usedto
compromisethe lack of incident daylight due to externalobstruction.However, this can producesome
thermal, visual and acousticdiscomfort relatedproblems.Large windows may be a main reasonfor
extra solar gain or heat loss, discomfort and disability glare, strong noise, and concernsfor safety as
well. During the last decade,window technologyhas seendramaticchanges.The appearanceof multiglazedwindow with low-emissivity coatings,gas cavity fillings and insulating frame has greatly
improved window's thermal, visual and acousticperformances.Nevertheless,the application of these
new techniquesis presently costly.
There are also circumstanceswhere windows cannotbe used as daylighting devices.For examples,for
interior room within large buildings or corridors betweenrooms where daylight cannotreach,windows
are not applicable.However, in someof thesecases,skylight hasbeenused extensivelyand
satisfactorily as daylight provider. A skylight can be consideredas a horizontal or slopedwindow on
the roof of a building. Skylight works effectively in daylighting a perimeterzone of a building.
However, the designof skylight can be a difficult task. When skylight admits sky diffuse light into
5
buildings, it also allows sunlight penetrateinto interior spaces.Sunlight transferredthrough skylight
can causeheatand visual discomfort. Therefore,decisionshave to be made on the size and orientation
of skylight with regard to the balancebetweenthe admissionof sufficient daylight and exclusion of
excessivesunlight.
Both windows and skylights can be classified as conventional passive daylighting devices. A main
feature of passive solar devices is they use the form and fabric of buildings to admit, store and
distribute solar energy for heating and lighting without additional energy input and consumption. A
good "one-off'
design of passive solar device can provide both environmental and economical benefits.
However, a major difficulty in designing windows and skylights is the design of control system or
mechanism that can ensure the maximum use of desirable daylight, and minimize the induction of solar
and vision discomforts. People realise conventional windows have two major drawbacks. First, the
most concentrated form of natural light, namely sunlight, is effectively useless as a working illuminant,
and secondly in a deep building without rooflights daylighting is restricted to areas near the window
[9]. Tberefore, in the last twenty years, effort has been made to develop innovative daylighting systems
that can improve the distribution of daylight in a space, and to control direct sunlight so that it can be
used as an effective working illuminant.
1.6 INNOVATIVE
DAYLIGHTING
DEVICES AND LIGHT PIPES
Generally there are five types of innovative daylighting devicesincluding mirrors, prismatic glazing,
light shelves,atrium and light pipes. There are also various occasionswhere unique daylighting designs
are applied to serveboth lighting and other purpose.For instance,Figure 1.3 showsthe solar
chandeliersusedin ManchesterAirport departurelounge.
1.6.1 Mirror,
prismatic glazing, light shelf and atria
In daylighting design,mirrors are mainly usedto collect, reflect and redirect direct sunlight. A simple
mirrored louver systemis shown in Fig. 1.4.This systemintendsto make use of direct sunlight in a
controlled way so as to improve the daylight distribution within an interior area.There are also more
complicatedmirror systemsthat can lead sunlight into areasdeepwithin buildings. Figure 1.5 showsa
6
heliostat system that is used in a university building in Minneapolis. The system beams the sunlight
through a lens into an undergroundlaboratory,saving electrical lighting and cooling costs [10].
Prismatic glazing can be usedto alter the direction of incoming daylight. When beamtraversesa prism,
its path is turned through 90" or smaller angle.This refraction phenomenonenablesprismatic glazing
to be usedas a substitutefor mirrored louvres systemshown in Fig. 1.4.There are also sunlightdiffuse
light
higher
in
but
from
that
throughout
the
year,
admit
systems
reject
sunlight
prism
excluding
the sky. The diffuse light is then directedto the ceiling so asto provide a controlled and comfortable
daylit interior.
Light shelveswork on the principle of reflection to redirect sunlight and sky light. The light shelvesare
horizontally or nearly horizontally placedreflective baffle mountedup a window, or betweena view
window and a clerestorywindow. Both interior light shelvesand exterior light shelvescan be used.
Figure 1.6 showsan interior light shelvebeing placedbetweena view window and a clerestory
window. Daylight from the clerestorywindow is reflectedto the ceiling and then further diffused more
evenly into the deepareaof the room. When thereis no direct sunlight, light shelvescan help to
improve the uniformity of light in the space.
Atrium, or called coveredcourtyardhavebeencommonly usedin North America andhasbeenentering
the UK aswell [10]. Atrium is rather an innovative building designconceptmore than an daylighting
technique.They createnew dimensionto large buildings that providesmore useableand pleasantdaylit
spacefor occupants.Figure 1.7 showsgenericforms of atrium buildings.
1.6.2 Light pipe
Light pipe is an innovative design to direct daylight into deep areas within buildings where daylight
cannot reach. The system is crudely analogous to the fibre optic cable, the difference being that the
latter device has much higher transmission efficiency. A schematic of light pipe system is shown in
Fig. 1.8. Daylight is gathered via a polycarbonate dome at roof level and then transmitted downwards
to interior spaces within buildings. The internal surface of the light pipe is coated with a highly
reflective mirror finish material (typically with a reflectance in excess of 0.95) that helps in achieving a
7
reasonable illuminance indoors when daylight is introduced via a light diffuser. The light-reflecting
tube is adaptableto incorporateany bendsaroundbuilding structural components.
Like other innovative daylighting devices,light pipe utilizes sunlight that accountsfor two thirds of
global illuminance in a clear day. Both sky daylight componentsare gatheredby light pipe and then
transmittedand diffused into interior whereneedto be day lit. Becauseof its main structureas a wellsealedtube, light pipe has addedpotential advantagein reducing excessivesolar gain. Sincepiped
daylight emits off only from light pipe diffuser, the output daylight is easierto control than other
innovative daylighting systems.Light pipe's flexibility in its structure,allows designersput diffusers
directly upon where needto be lit, so as to achievea good internal daylight distribution.
The combineduse of windows and light pipes can reduceglare and further improve the balanceof
daylighting within a room. In daylighting, therehas always beena dilemma for designers.It is that on
one hand large exposureof sky through window is not encouragedbecauseit can causevision
discomfort, while on the other hand a high daylight factor is always preferableand important for
building users.Furthermore,many architectsobject to unilateral daylighting, due to the excessive
highlight and shadowit may cause.However, by applying light pipes aboveproblems can be solved.
By introducing redirectedand diffused daylighting into deepareaof a room, glare from windows is
reducedand daylighting is of a better uniformity. For skylight designers,the attemptto admit more sky
diffuse light by enlarging the faqadeareaalways involves dangerof introducing undesirablesunlight
into buildings. As a comparison,light pipes transmit sunlight and sky diffuse light by multi-reflect
mechanism;thereforethe output daylight is much more uniform and diffused than that by a skylight.
Another potential advantagethat light pipe possessesis that it can be used in multi-storey buildings,
while the use of skylight is usually limited to the perimeterzone of a building.
As addressedbefore, the applicationsof light pipes in buildings can bring multi-fold benefit. Compare
to other innovative daylighting devices,light pipe seemsalso have potential advantagesin terms of
visual and thermal performanceand applicability. Moreover, the fact that light pipes have been
commonly used in the USA and Australia implies its further developmentin the United Kingdom and
Europe.However, for most UK and Europeandaylighting designers,light pipe is still a relatively new
8
concept[ 11]. Researchthat focus on the evaluationof light pipe's daylighting performanceis therefore
in needto reveal its perspectiveand to push forward its development.
1.7 Aims OF THE PRESENT RESEARCH
The difficulties in identifying all decisivefactors that affect the performance,and in quantitatively
weighing the contributions of thesedecisive factors are the main barriers to appraisinglight pipe's
efficiency. The complexity in the mechanismby which light pipes transmit daylight makesit difficult
to appraisethe performanceby meansof physical modelling. On the other hand,prior to this research,
the lack of light pipe performancedata that include both sufficient environmentaland geometricaldata
made it impossibleneither to model the performanceusing mathematicalmethods.
The overall objective of this work is to provide a generalmathematicalmodel for the prediction of light
pipe daylighting performance.Although the performanceof light pipe has beeninvestigatedin a
number of studies[12-14], up to the initiation of this researchno mathematicalmethod that includes
the effect of both geometricaland environmentalfactors hasbeenmadeavailable. End goals are to be
achievedfollowing a logical processfrom raw datacollection to evaluationof mathematicalmodels.
The aims of the current researcharepresentedbelow in turn.
(1) To conducta literature review of works in the field in order to provide a basic grounding in the
subjectmatter and familiarise onesself with methodologiesagainstwhich the presentwork may be
compared.By literature research,it is intendedto summarisethe to date developmentin light pipes
daylighting performancemeasurementand simulation. The searchfocusesparticularly on the
prediction of performanceof light pipe systemsof various designsand under different weather
conditions.
(2) To developa logical method of building mathematicalmodel for predicting the daylighting
performanceof light pipes. Although the complexity in the working mechanismof light pipe makesit
difficult to appraiseits performance,to the aid of mathematicalsoftware and the computing ability by
PC, it is possible to developa computermodel so as to describelight pipe's daylight transmission
charactersin a mathematicalmanner.As an instantresult of a project of limited resource,the proposed
9
mathematicalmodel can have a limited applicability. However, more importantly the study aims to
producea valid researchmethod, and a framework under which further developmentin daylighting
performancemodelling can be conductedin a consistentdirection leading to the final solution. This
aim, as a principle guidesthe implement of the presentresearchfrom the day one to the end, and is
therefore embodiedthrough out this report. The work conductedand the conclusionsdrawn to satisfy
this aim can be found in Chapter4.
(3) To form a substantial foundation for mathematical modelling by monitoring daylighting
performance of light pipes both in real application and in test rooms. Extensive and detailed
geometrical and environmental data, namely the light pipe configuration information, internal
illuminance and external weather conditions, sun's position and so on need to be gathered.
Measurements on the performance of light pipes in separate test rooms are to be under-taken so as to
enable the validation of the proposed model using independent data. This work is presented in Chapter
5.
(4) To analyse the working mechanism of light pipes. By analysing the measured data and physical
reasoning, build the analytical framework relating the input and output of the proposed model, and
identify the most decisive factors that affect light pipe's daylighting performance. To determine the
"best" mathematical expression to describe the daylighting transmission pattern of light pipe, choose
suitable solar radiation data as input and, choose the "best" internal daylight distribution model to
describe the output of the proposed model. To validate the proposed model using independent data by
means of statistical evaluation. The work is reported in Chapters 6 and 8.
(5) For solar energyapplicationsdesign,global and diffuse horizontal irradianceand beamnormal
irradianceare the three most important quantities.Global horizontal illuminance (E,, ) can be easily
measuredusing a pyranometer.As to the measurementof diffuse horizontal illuminance (Evd))the most
common approachis to use a shadowband aidedpyranometerto interceptbeam irradiance.The
measurementson E, 9 and Evdare widely available aroundthe world by local Met Offices. In real light
pipe applications,treesand buildings that obscurepart of sky diffuse light and sometimessun beam
reducethe input illuminance to the light pipe systems.Under suchconditions, to apply the proposed
10
model, total available illuminance needto be estimatedbasedon E,, and Evddata available from local
Met Offices.
Napier University CIE first-class solar radiation station is currently using the shadowband device to
provide the horizontal diffuse irradiance data.However, it is well known that the shadowband that is
used to block the sunshinealso shadessomediffuse irradianceas well. Hence it is necessaryto correct
the measureddiffuse irradianceobtainedusing the shadowband instrument.The most commonly used
method to correct the shadowband diffuse data is the Drummond method. However, Drununond
method is purely geometricaland thereforeunderestimatesthe true diffuse value. To obtain a more
accurateestimationof the true diffuse irradiance,new correction methodbasedon anisotropymodel
shall be developed.Work carried out for this aim and conclusiondrawn are reportedin Chapter7.
(6) In recentyears,solar light pipes have firmly set their foot within the UK market place [ 15].
However, till this researchno designtool for light pipe practices,which is basedon sophisticated
mathematicalmodel, hasbeenmadeavailable.The understandingof light pipe's daylighting
performanceby designersin the UK is neither clear nor more valid than limited experience,if there is.
Moreover, becausethe lack of model that can predict the perforinanceof light pipes, the assessment
of
the potential contribution of daylighting using due product to energysaving is rather crude and
empirical. Researchon identifying the potential barriers to exploit daylight in Britain [10] concluded
that, to increasethe exploitation of daylight in the UK it appearsnecessaryto overcome,by education
and demonstration,countervailing tendencieshold by thosedesignerswho are lack of credenceon
daylighting. Therefore,work of producing a convenientdesignguideline for light pipe practices,which
is basedon the proposedmathematicalmodel, is suggested.The proposedmodel also enablesthe
estimationof electricity saving due to light pipe applicationsunder the UK climate, which can provide
useful information basefor national policy decision-makers.This work is reportedin Chapter8.
(7) During the courseof presentresearch,the commercialdevelopmentof light pipe in the UK hasbeen
quite rapid. One main progressin improving light pipe's daylighting performanceis the application of
translucenttype of diffuser. Therefore it would be worth to investigatethe effect of using new type of
diffuser on light pipe's daylighting performance.Thesework are addressedin Chapter6.
11
(8) Daylight factor hasbeenacceptedas an industry standardfor window design,However, for
innovative daylighting devicesand someof the new designs,especiallythosethat utilize not only skylight but also sunlight, to dateno generalmethod is availableto assesstheir daylighting performance.
Basedon the conceptof light pipe daylight penetrationfactor, DPF, introduced in presentstudy along
with other well-establisheddesignmethodssuch as daylight coefficient a referencemethod may be
adoptedfor an agreedstandard.In this respect,it will avail to proposean approachbasedon a Figure of
Merit (FoM) to the purposeof introducing a generalmethod for assessingall daylighting devices.Work
on this is reportedin Chapters6 and 9.
12
REFERENCES
1. bqp: //WWW. bi). com/worldenerg
2. Muneer, T. (1991) Blow for N-plants on global warming TheScotsman3 June
3.The Departmentof Trade and Industry (2000) UK Energy Flows 1998
4.The Departmentof Trade and Industry (1999) UK Energy SectorIndicators, 6
5. Muneer, T. (1997) Solar radiation & daylight modelsfor the energyefficient designofbuildings,
Architectural Press,Oxford
6. Zhang, X and Muneer, T. (2000) A MathematicalModel for the Performanceof Light pipes Lighting
Researchand Technology,32 (3), 141-146
7. htlp://www. hao.ucar.edu/public/education/general/general.
html
8. Hopkinson, R. G., Petherbridge,P., and LongmoreJ. (1963) Daylighting, Heinemann,London
9. Littlefair, P. J. (1989) Innovative daylighting systems,Designingfor Natural and Artificial Lighting,
Building ResearchEstablishment
10. Crisp, V. H. S. and Littlefair, P. J., Cooper,I. and McKennan G. (1988) Daylighting as a Passive
Solar Energy Option: an assessment
of its potential in non-domesticbuildings, Building Research
EstablishmentReport, ISBN 0851252877
11. Muneer, T., Abodahab,N., Weir, G., Kubie, J. (2000) Windowsin Buildings thermal, acoustic
visual and solar performance.Architectural Press,Oxford
12. Shao,L. (1988) Mirror lightpipes: Daylighting performancein real buildings Lighting Research
and Technology,30 (1), 37-44
13. Yohannes,1. (2001) Evaluation of the PetformanceofLight pipes Usedin Offices, PhD Thesis,
Nottingham, Nottingham University
14. Oakley, G., Riffat, S. B. and Shao,L. (1999) Daylight performanceof lightpipes Proceedingsof the
CIBSENational Conference,Harrogate,London, CharteredInstitution of Building ServicesEngineers,
159-174
15. Zhang, X. and Muneer, T. (2002) A Design Guide for PerformanceAssessmentof Solar Light
pipes Lighting Researchand Technology,34(2), 149-169
13
World Energy Supply Scenario
10
CL
(D
C
a)
76
0
Hydrogen
Wood k coal
80
60 -
Non-sustainable
fuel
I
Increasingly
sustainable
fuel
1
40 -
0
20Hydrocarbons
(Gases)
CL
1850
ii0o
1950
2000
2050
2100
Figure 1.1 World energy supply scenario
14
II-
TOTAL FINAL CONSUMPTION
cl---i
BQý)
L
ir
I
irn
>Iii
II
}
Ir
f 118
It
1 fIH
I
4
M,
oil
Xm
"0 1
I
S. LWOdWI
Lý
CNV NOuonCIOWd
snON30IONI
V
R. Y.
r
Cie
'-fl. 9m
R-f
J
d. p. -
k. -Qý
Od.
II
IL
Figure 1.3 Manchester Airport
departure lounge with solar chandeliers
While
Ceiling aCls Me
d&, V d1fl. so,
tle c
111off"
D, ff. se light
M,, m, ed
louv'sa
'Oorn
Direct
sunlight
cannot
strike
occ. va"T
Figure 1.4 Beam sunlight in a side-lit room
16
Figure 1.5 Underground
Minneapolis, USA
The
light-shelf
light.
in direct
from
front
works
It redistributes
to back of a iciorn.
contrast
reducing
solar
concept
and
daylighting
at the Space Centre building, University
of Minnesota,
well
light
also
intercepting
gain
High performancoý concept used at
Lockheed Missile and Space CompanY,
Sunnyvale,
California, USA, with
Oaped
office,
light sholf duhning poornoler
loss of light to inletiol,
wilhout
Clearglass
space.
Uplightcr
orw dawmier
pMentlal riall. ii(111
Figure 1.6 Concept of light shelves
17
Two-sided
Sm(liv
stilod
atrium
Itwo
open sides)
Three
or conservatorv
Lln eat
"I
ii
afrium
n, (cipen
endsi
s, deo
alfjum
FOLIF sidt-dainum
laiie
(no
open
si(jel
npen
sideýl
Figure 1.7 Generic forms of atrium buildings
Figure 1.8 A schematic of light pipe system
18
Table 1.1 World fossil fuel reserves to production
North America
S& Central America
Europe
Africa
Asia Pacific
World
ratio, years (BP 1999 statistics)
11
65
18
100
42
62
19
2. SOLAR LIGHT
PIPE AS AN INNOVATIVE
DAYLIGHTING
DEVICE
The idea of piping light from a remote sourceto an interior spacefor illumination purposeappeared
about 120 yearsago. Originally designedto distribute central electronic light into buildings, light pipe
is now being adoptedand applied world-widely for both artificial and natural daylighting purposes.
Commercially available light pipe systemsthat employ daylight as lighting sourcehave beenusedin
Australia, America, and Canada.Within Britain alone there are now a number of companiesthat are
profitably trading daylighting light pipe, or called "solar light pipe" productsand with an enviable
is
being
light
increasing
With
the
attention
paid to their
pipes,
more
use
of
solar
rate.
growth
development,especiallyto the daylighting performanceevaluationof the device. Presentstudy is the
further
light
development
the
time
the
aims
a
at
same
at
pushing
of
pipe,
and
prior
production of
developmentof this innovative device. It is thereforenecessaryand desirableto give a full context of
the historical developmentof light pipe systems,so asto presentthe position and significanceof
presentstudy.
2.1 THE DEVELOPMENT
OF SOLAR LIGHT PIPE SYSTEM
The earliestformal record that can be found on light pipe innovation may be the patentthat was
registeredin the United Statesby William Wheeler from the MassachusettsStatein September188 1.
This registeredpatent initially reffied the idea of light pipe as an apparatusfor lighting dwellings and
other structures.This patentedinvention, relatesto a systemof lighting and to a specialapparatus
whereby any desiredamount of the light-producing energyemployedis convertedinto light-vibrations
at a central or single place, from which the light generatedis transmittedand distributed to and
dispersedat any number of placeswhich it is desiredto illuminate by optical conduction,division, and
dispersionof light [I]. It was indicatedby the inventor that before this invention, therehad been
designsof transmitting beams,or said parallel rays, through enclosedpassagesand clear spaceto
produce secondarylights from one luminary sourcefor lighting purposes.Although the inventor
outlined that light pipe is adaptableto any light sources,his designseemednot being able to utilize
natural daylight as lighting source.
20
Nowadays,becausethe long distancesover which light pipe can operate,it hasbeenregardedas
"perhapsthe most technologically exciting innovative daylighting systems"[2]. Light pipe's advantage
of being able to bring light into core areaswithin buildings hasbeennoticed long time ago. Figure 2.1
showsan invention by Hanneborgfrom Norway in 1900 [3]. Sunlight is collectedby a so-called"lightcollector" placed on top of the roof and beamedthrough a vertical "light-conveyer" to the cellar, where
a light distributor is placed for lighting the room. Another near exampleof the samesort is the light
is
by
heliostat
in
Fig.
1.5.
Sunlight
in
Minnesota,
University
the
collected
a
on
as
shown
of
system
pipe
the roof and beamedthrough lensesto a working place 110 ft below the ground.Above two light pipe
light
light
Heliostats
be
"Heliostats
pipe systemmainly relies on
systems.
called
as
pipe"
systemscan
optical devices,namely mirrors and lensesto collect and transmit sunlight. The common featureof
Heliostatslight pipe systemsis the use of device that can track the sun at times. Due to the costly
has
device,
light
by
this
the
system
not
sort
of
pipe
sun-track
expenseand complex control required
beenwidely used.
Having realized the drawbackof "Heliostats light pipe" system,during the last five or six decades,
researchersmademost efforts to developmore cost-effectivelight pipe system.Researchhasbeen
focusedon improving the transmittanceof the "tube" part of light pipe systems,to avoid the
dependenceupon sun-trackingdevices,mirrors and lenses.The most basic form of light pipe tube is
simply an empty shaft with ordinary mirrors on the walls, along which a collimated beam of light can
travel [4]. Reflective metal tubeswas proposedbut any off-axis light has to undergomultiple
reflections, with the result that only closely collimated beamsdo not becomeattenuatedafter a few
metreswithin the tube [2]. Fibre optic bundlescan have very good transmissioncharacteristics[5], but
tend to be prohibitively expensive[6].
In 1980s,new developmentof highly reflective materialsemerged.Whiteheadet al [4,7,8] proposeda
hollow acrylic prismatic light tube that has a transmittanceof between0.95 and 0.97. At the sametime,
different approacheshavebeentaken to improve the light transmittanceof light tube. One exampleis
the application of metallic coating and finishing techniqueto the inner surfaceof light tube. Another
notable progressin this respectis the useof PET (Polyethyleneterephthalate)film. The appearanceof
abovetechniqueshas acceleratedthe developmentof light pipe systems.
21
In 1990s, innovations of light pipes by different inventors emerged in endlessly. Sutton patented a
"tubular skylight" in 1994 in the USA [9], as shown in Fig. 2.2. According to Sutton, the system
comprises a tubular body, a first transparent cover and a second transparent cover. The material of the
tubular body is either metal, fibre or plastics, and has a finish which is a highly reflective polish or
coating, as found on "l 150 alloy aluminium", electroplating, anodising or metalized plastic film. As a
device to enhance the performance of the said system, a reflector is located within light-pen-neable
into
incident
the system.
to
the
collect
more
sunlight
and
extending
above
roof,
chamber
In 1996however, Bixby pointed out that aboveSutton's invention "requires the use of a reflector
locatedwithin the light-permeablechamberand mountedabovethe roof line. Even when strategically
positioned along the path of the sun, the use of an aboveroof reflector blocks a significant portion of
the sunlight which would otherwiseenter the systemand illuminate the building if the reflector was not
present".Bixby registeredhis invention of tubular skylight for natural light illumination of residential
and commercialbuildings in 1996 [10]. Figure 2.3 showsthe Bixby tubular skylight system.Bixby's
systemcomprisesa highly reflective tubular body positioned in the spacebetweena building's roof and
ceiling with a first end with a semi-sphericaltransparentglobe attachedto a roof assembly,and a
secondend attachedto a ceiling assembly.The ceiling assemblycomprisesa semi-spherical,light
diffusing cap and a molded ceiling mount with a straight sleeve.
The developmentof solar light pipe hasbeenan on-going process.The latest developmenton
improving the collimation of internal daylight deliveredby light pipes hasbeenreportedby O'Neil
[II]. Comparedto previous arts of light pipe system,O'Neil's tubular skylight useslight tube of cone
shapeinsteadof straight column shape.Figure 2.4 showsthe comparison.The coneshapedreflective
tube is constructedwith a larger crosssectionalareanearthe radiant energy-deliveringaperturethan
near the radiant energy-collectingaperture.By this new design,the collecteddaylight can be collimated
and delivered to the desiredareaof the room directly beneaththe luminaire. According to O'Neil, "as
proven by experimentalresults,the new passivecollimating tubular skylight provides significant
advantagesover the prior art, including better solar energycollection, higher throughput optical
efficiency, improved radiant energycollimation, enhancedinterior illumination levels, and more
22
precise positional control of the interior illumination".
However, O'Neil did not give sufficient and
detailed information on the type and material of the luminaire being used in his design. As an integral
part of light pipe system, the design and property of the energy-delivering aperture, or called luminaire,
or diffuser by some literature, has been found having important effect on the daylighting performance
of the system [12,13]. Therefore, in practical applications, the design of light pipe systems needs to
take account of the design of luminaire.
An English company, Monodraught, have been manufacturing and trading light pipe systems
successfully within Europe. By the year of 2000, more than 3000 Monodraught light pipe systems have
been installed throughout the UK in comparison with the figure of about 50 for the year 1997.
Monodraught light pipe systems adopt diffusers of various property and design according to different
is
is
in
Fig.
2.5.
Daylight
light
in
A
Monodraught
typical
system
shown
pipe
real
practices.
needs
interior
downwards
level
dome
to
then
transmitted
spaces
at
roof
and
via
a
polycarbonate
gathered
within buildings. The light-reflecting tube is adaptable to incorporate any bends around building
structural components. The internal surface of the light tube is laminated with Reflectalite 600, a
silverised PET film [14]. The reflective silver layer is sandwiched between the PET film and the
aluminiurn base, which helps in achieving a reasonable illuminance indoors when daylight is
introduced via a light diffuser.
There are various kinds of diffusers that can be employedin Monodraughtlight pipe system,including
dome opal, dome clear,recessedopal and recessedclear diffusers. The recesseddiffusers are more
effective in keepingout dust and preventingheat loss.Opal diffusers are of better diffusive property,
and henceenablean even spreadof daylight within the interior, while clear diffusers possessa better
transparencyand thereforecan maximum the penetrationof daylight. In occasionswhere soft and
uniform daylighting is required,the former kind of diffuser hasbeenwidely used.For application like
open spacein deep-planbuildings and corridors where the brightnessbecomespriority, the latter kind
of diffuser is more suitable.The developmentof light pipe diffuser is an on-going process.News from
Monodraughtreports that a new type of diffuser of diamond shapeis being developedand will be
introduced into the market place soon.
23
As a conclusion, the development of solar light pipe system has been continuing ever since 100 years
ago. Although historically there have been light pipe system of various designs, they generally have
three main components, namely the daylight collecting device, daylight transmitting device and
daylight emitting device. Accordingly, the development of light pipe art has been focusing on these
three components. It has been realized that the improvements on each part of light pipe system will
upgrade the total daylighting performance of the system. However, to date no general method has been
made available to evaluate and compare the performance of various light pipe systems. One major aim
of present study is to establish a generalized standard by which light pipe systems can be compared
against each other, or even against other daylighting devices like windows. With the aid of such a
proposed generalized standard, it is hoped that the development of light pipe family can be more
systematic and clearer.
2.2 THE CONCEPT OF LIGHT PIPE
The term of light pipe hasbeenlong usedto namethe family of non-imagedevicesthat can transmit
light from either artificial or natural light sourceto building interiors for lighting purpose.Becausethe
developmentand application of light pipes to modem buildings havebeennew and fast, so far no
international standardizedcategorizingand / or naming systemhas beenmadeavailableto define and
describethe contentof the family. It is possiblehowever, as a first step,to divide the huge light pipe
family into threegroups.The threegroupsare first, light pipes using artificial lighting as light source;
second,light pipes using externaldaylight as light sourceand the third, light pipes using both artificial
light and externaldaylight as light sources.The light pipe group that usesexternal daylight as light
sourceis also widely called solar light pipe since the ultimate sourceof daylight is the sun. As
addressedin Introduction, becausethe presentstudy emphasizesthe significanceof utilizing and
exploiting renewableenergy,solar light pipe is the main concernof presentresearch.
Within the group of solar light pipe, further classificationcan be defined. The CIE hasset up a
committee TC 3-38 to establishan international standardas a framework for guiding and regulating the
developmentof solar light pipe systems.One major issueon the standardizationidentified by the TC 338 is what constitutesa solar light pipe system.The answerto this questionhas beengiven as,there are
three major types defined by their collecting methods- active zenithal (e.g. Heliostat systems),passive
24
zenithal (e.g. commercially available Solatube,Sunscope,Sunpipeetc systems)and horizontal (e.g.
anidolic ceilings). Among abovethree types, the passivezenithal tubular light pipe has becomethe
most widely usedsolar light pipe system.The family map of light pipe systemis now shown in
Fig. 2.6. Presentresearchfocuseson the daylighting performanceof passivesolar zenithal tubular light
pipe systems.In the following body of this thesis,if not specified,the name of "light pipe" refers to
passivesolar zenithal tubular light pipe.
A passivesolar zenithal tubular light pipe systemcan be defined as a tubular vertical light guidance
systemthat passivelycollects and transmitsexternalnatural daylight to building interiors for lighting
purpose.A schemeof two typical passivesolar zenithal tubular light pipe systemsis shown in Fig. 2.7.
Typical passivesolar zenithal tubular light pipe systemhas three components,namely fixed daylight
collection device, tubular light guide that employsinternal reflection mechanismfor daylight
transmission,and light-demitting apparatusfor dispersingdaylight into designatedareas.
2.3 THE STRUCTURE OF PASSIVE SOLAR ZENITHAL
TUBULAR LIGHT PIPE
Passivesolar zenithal tubular light pipe is the most commercially available light pipe systemin the UK
market place. Light pipes provided by different tradersor manufacturersare to various extent slightly
different from eachother. For example,a light pipe companymay have their own-patentedtechniquein
fixing the light tube on or within a roof structure,or in preventing leakageof rain. However, in terms of
their basic structure,light pipes by different makersare generally the same.
The majority of commercially available light pipes consistof threemain componentsassociatedwith
sealing components.The threemain componentsare daylight collector, light pipe tube and diffuser.
Daylight collector is fitted at the top end of the light tube,usually on the roof, which actsas a semi-lens
to collect daylight and as a cap to prevent the ingressof water and dust. At the bottom end of the pipe
fitted the diffuser, usually to the ceiling to allow the distribution of the daylight into the interior room
space.Propertiesof main componentsof light pipe are describedbelow.
25
2.3.1 The daylight collector
Daylight collector is a clear dome that is mountedon the outsideof the roof 'Me dome is manufactured
from cleanpolycarbonatethat removesundesirableultra violet (UV) light and sealsthe light pipe
againstingressof dust and rain. The domeusually meet the requirementsof fire resistanceand due to
its shapeis self-cleaning.
2.3.2 The light pipe tube
The pipe is constructedfrom a metal tube, typically of alloy aluminiurn material. The inner surfaceof
the tube is laminatedby applying metalizePET (PolyethyleneTerephthalate)film or TIR (Total
Internal Reflective) prismatic optic film. Figure 2.8, for instanceshowsa Monodraught(UK) light tube
that usesReflectalite 600, a silverised PET film as its internal reflective coat. The reflective silver layer
is sandwichedbetweenthe PET file and the aluminiurn basesubstrate.The presenceof an UV inhibitor
in the Reflectalite provides outstandingQUV durability with no delarninationand with no decreasein
total reflectancewhen subjectedto the extremeconditions of UV light.
2.3.3 The diffuser
The diffuser takesthe form of a white polycarbonatedomemountedon the ceiling inside the room to
be illuminated. 'Me material of diffuser vary in its property of transparency,so as to meet different
needsfor light distribution within the room. For exampleopal diffusers, which are madeof semitranslucentpolycarbonatematerial, are usually applied in placeswhere uniform daylighting is required.
While clear diffusers, which are madeof transparentpolycarbonatematerialsare preferredin
applicationssuch as corridors in deep-planbuildings where the quantity of light becomespriority.
The shapeof a diffuser can be flat, convex, and concave.Monodraught(UK) has recently developeda
new range of diffusers that are manufacturedfrom clear polycarbonatewith a crystal effect finish. The
developmentof a new type of diffuser of diamond shapeis also underway.Figure 2.9 showsthe
appearancesof different types of difftiser, and Fig. 2.10 demonstratesthe different daylighting effects
achievedby a clear diffuser and an opal diffuser respectively.
26
2.3.4 Sealing components
The application of light pipe systemsrequiresthe installation of sealing componentsto the purposeof
achieving high heat resistanceand preventing solar gain. The sealof the light tube is also important to
keep dust, noise, insects,rain and snow out of the building interiors. A brushednylon gasketat the top
of the pipe preventscondensation,dust and rain from entering the systembut still allows the airs to
expandand contract when subjectto solar gain. The closedcell gasketat ceiling level sealsthe daylight
collector and all the vertical joints are sealedwith silicon and alurninium tape.
2.3.5 Complete light pipe system
An explodedview of a typical light pipe system,by Monodraught(UK) is shown in Fig. 2.11, all the
main componentsand associatedsealingcomponentsare shown.
2.4 WORKING MECHANISM OF LIGHT PIPE
Passivesolar tubular light pipes are designedto collect light from both the sky and the sun. The two
componentsof daylight illuminance are collectedby the hemisphereshapeddome, followed by
multiple reflection of sunlight and skylight through the reflecting tube. Daylight then reachesthe inner
surfaceof the light pipe diffuser wherein a refraction followed by a light-scatteringtakesplace before it
is introducedwithin buildings. Figure 2.12 showsthe generalprocessof daylight collection,
transmissionand distribution within buildings. Ile complexity of light pipe's working mechanism
consiststhree aspects,namely the optical process,the externaldaylight environmentand the designof
light pipe. The three aspectsare analysedas follows.
2.4.1 Optical process
The first aspectis the complicatedoptical processthat takesplace within light tubesand diffusers.
Initially daylight collectedby dome enterslight pipe, then a mixed multi-reflection of sunlight and sky
diffuse illuminances occurswhen daylight is transmittedthrough and diffused within the light tube.
27
After that, a refraction phenomenonhappensin light pipe diffuser when diffused sunlight and sky
diffuse illuminances are further diffused and finally scatteredinto the interior space.
2.4.2 External daylight environment
The secondaspectis the complexity of externaldaylight as the input to the light pipe system.
Throughout the year, the quantity and proportion of sunlight and sky diffuse radiation are not constant.
When sunlight is available, the changeof sun's position causesthe variation of the incident angle at
which the sunrayenterslight tube. This implicatesthat the pattern sunlight travel through light tube is
continuously changingwhen sunlight is available(Fig. 2.13). When the sky is overcastor when clouds
block the sun, skylight becomesthe major externaldaylight source.However, it is well known that the
luminancedistribution of the sky is not unifon-n.The sky vault can be divided into small patchesas
shown in Fig. 2.14. Each sky patch has its own position and brightness;so the transmissionof the sky
illuminance from eachpatchesvarious. Furthermore,the sky illuminance distribution is affectedby the
position of sun, the clarity of the sky, the position of random clouds and so on. Therefore,the process
of sky-light entering light tube and travelling within the tube is a highly dynamic process.Figure 2.14
showsthe sky illuminance emitted from one sky patch entersand travels within the light tube.
2.4.3 The design of light pipe
The third aspectis the designof light pipes. Light pipes vary in their geometric configurations,
including the length, the width and the numberof bendsincorporatedin a light pipe system.Light tubes
applying different internal coating have different internal reflectance.For a given externalenvironment
and at a given point of time, light pipes of different configurationsand having different internal coating
materialsproduce different daylighting performance.For any given weathercondition and sun's
position, the crossareaof a light pipe, affectsthe light pipe's external illuminance admittance.Since the
daylight illuminance is transmittedby meansof internal reflection within the light tube, and the
reflectancealthoughusually high is lessthan 1, a light pipe's overall transmittanceis affectedby the
number of reflections required for a ray of light to descendthe light tube and the tube's reflectance.
The higher the internal reflectanceof the light tube, the higher is the systern'sdaylight transmittance.
28
The lessthe number of reflection required to descentthe entire light tube, the better would be the
system'sperformance.
2.5 SUMMARY
The idea of piping light from a central artificial light sourceto building interiors for lighting purpose
emergedmore than one century ago. However, the developmentof guiding daylight into buildings for
daylighting purposeis new. In the last two decades,the breakthroughin terms of new reflective
materialsand processingtechniqueacceleratedthe developmentof light pipes. The most commercially
available light pipe is the passivesolar zenithal tubular light pipe. Presentstudy focuseson the
daylighting performancemeasurement,modelling and prediction of this kind of light pipe.
The working mechanismof passivesolar tubular light pipe is complicated.The difficulties in
identifying all decisive factors that affect the performance,and in quantitatively weighing the
contributions of thesedecisive factorshavebeenthe main barrier to appraisinglight pipe's efficiency.
Presentstudy aims to conquerthis barrier so as to push further the developmentof light pipe systems.
29
REFERENCES
1. Wheeler,W. (1881) U.S. PatentNo. 247229,United StatesPatentand TrademarkOfffice,
hq: //www. uspto.gov
2. Littlefair, P. J. (1990) Innovative daylighting: Review of systemsand evaluationmethodsLighting
Researchand Technology,22(l), 1-17
3.Hanneborg,0. B. H (1901) U.S. PatentNo. 668404,United StatesPatentand TrademarkOfffice,
hq: //www. uspto.gov
4. Whitehead,L. A., Brown, D. N. and Nodwell, R A. (1984) A new device for distributing
concentratedsunlight in building interiors Energy and Buildings, 6(2), 119-125
5. Fraas,L. M., Pyle, W. R. and Ryason,P. R. (1983) Concentratedand piped sunlight for indoor
illumination, Applied Optics, 22(4), 578-582
6. Smart,M. and Ballinger, J. (1976) Tracking mirror beamsunlighting for interior spaces,Solar
Energy, 12(5), 12-19
7. Whitehead,L. A., Nodwell, R. A. and Curzon, L. (1982) New efficient light guide for interior
illumination, Applied Optics 21(15), 2755-2757
8. Whitehead,L. A., Scott, J. E., Lee, B. and York, B. (1986) Large-scalecore daylighting by meansof
a light pipe, Proceedingsof the 2ndInternatinal Daylighting Conference,Long Beach,Mclean, VA:
Cable Associates,416-419
9. Steven,M. and Sutton (1992) U. S PatentNo. 5,099,622,United StatesPatentand Trademark
Offfice, htip://www. uspto.gov
10. Joseph,A. and Bixby (1996) U.S. PatentNo. 5,546,712,United StatesPatentand Trademark
Offfice, h!ip://www. uspto.gov
I 1.0'Neil, M. (2002) U. S. PatentNo. 6,363,667,United StatesPatentand TrademarkOfffice,
htlp://www. uspto.gov
12. Edmonds,1.R., Moore G. I., Smith G. B. and Swift P. D. (1995) Daylighting enhancementwith
light pipes coupledto laser-cutlight-deflecting panelsLighting Researchand Technology,27(l), 27-35
13. Carter,D. J. (2002) The measuredand predictedperformanceof passivesolar light pipe systems
Lighting researchand Technology,34(l), 39-52
14. ht!p://www. solarsaver.co.uk/Monodraught/sunpipe/inf-com.
htm
30
No. 6.68,404.
0. B. H, HANNEBORG.
Patented.Feb. 19,1901.
APPARATUS FOR TRANSMITTING SUNLIGHT TO BASEMENTSDR.OTHERSTORIES.
)
(No Model.
_____________________________________
I
-.
K
J17WtJZtäP.
,I
for
transmitting
1900:
sunlight
in
Norway
from
Hanneborg
apparatus
by
Invention
Figure 2.1
into basementsor other stores (Ref.3)
31
U. S. Patent
Mar. 31,1992
5,099,622
Sheet 10 of 13
F""
/*
Af
Z7
co
e
/Z-5
A9
FIC 18
Figure 2.2 Sutton patented tubular skylight in 1994 in the USA
32
U. S. Patent
Aug. 20,1996
5,546,712
Sheet I of 3
21
20
18
FIG. 1
12
42
11
26
25
14
19
71
42
13
41
-ý10
15
19
50
ý5
46
47
26
43
100
51
45
48
49
35
44
3
28
28
30
---
34
32
Figure 2.3 Bixby tubular skylight systems
33
U. S. Patent
US
Sheet 2 of 6
Apr. 2,2002
Fig. 2A
Fig. 2B
Prior Art
Improved
10
10
12
11
6,363,667B2
12
R-T
g
15
16
,
J-M.
- 'V,
-800 :
0. )
--\
0
w
14
13
Figure 2.4 Comparison of O'Neil's cone shaped light tube against conventional column light tube
34
Figure 2.5Typical
Monodraught
light pipes
Light Pipe
Daylight source light pipe
Artificial light
source light pipe
active zenithal
passive zenithal
Light pipe using both
daylight and artificial
horizontal
Figure 2.6 The family map of light pipe
(a) Straight
light pipe
(b) Light pipe with bends
Figure 2.7 Schematic diagram of passive solar zenithal tubular light pipe
36
--- --,- . -Icclaille
()0()IE-1, tilm
F '1
Figure 2.9 Appearances of different types of diffuser
38
r,
*4*N)
%
MPOM,
Figure 2.10 Demonstration
diffuser
of the different daylighting
effects by a clear diffuser and an opal
39
Components For Flat Roof Applicafton
Mycarbonate, UV treated top do"ic.
Brushed tiylm
trap
Brushed
tiylm cmdensation
cmdensation trap
breathable gaskeL
gaskcL
and breadiable
and
f
fixingIlugs.
Hig,
impact
Hig,iiiri
ABSc(Alar
with fixing
ipactABS
(;cA[ar widi
ugs.
ABSflat roof flashingplatefor flat roofapplication.
flasilingwill bit,
(Note:Altt,,Mathc Salvanised
rpcltjirMfor asphaltroof ir"Wilatifon.
Standard 61 Omm suctivi5 uf Reflectalite 600
Mite compressible
ceilingsf-al.
Polycarbonate ceiling dome.
(Flat diffusers also available)
Wl screwsandkings pruvided).
for Pitched
Components
Roof Applications
- state tmf -
P, Jy,., b-t..
:n N
UV treAtd
dý
0-j ,j .0.......
and breathaUcgasket.
I'al,
piýP ARS fla,.hing plate.
ifcjf t. W r(., f, 5
I'J. -t-re
Incorporated into the flashing plate
to the top and sides and Mis%'C'5eal
Ow
A C. h- 4 kid 4in 6 pr-irliA
fla4ling to tiles.
300'I'm ýMljvi uf Sunplýw
or lengths to wit ronf cn"nicli(supplied in 2ft NlUnino longwxt"is.
f(w
)
Two p6-cp. aditistable rlfýw
to suit rLx4 up tv 3U* pitd,
(3 plecv adjustable (4bow
fix r(x,(.s up to 45' pimho
Standird 61 Omm SeChons of RAxIalito
(1 m lenol
F.00
also available)
WhIte compressiblecedRigwAl,
Pdycad)mito ceiling don*.
Mat diRusemalw
AMscrem Ald 6-4,p p, ovkkd.
Figure 2.11 An exploded view of a typical light pipe system by Monodraught
(UK)
40
Total extemal illuminance = sky diffuse + sun illuminance
--A
Figure 2.12 A general process of daylight collection, transmission and distribution
pipes
through light
Sun's position I
0
0
Sun's position 2
\\
Liý
Lighttube
Di
Figure 2.13 The pattern sunlight travel through light tube
ýr
Sky diffuse light
A sky patc
(a)
klý
(b)
Figure 2.14 Sky vault divided into small patches with respective luminance
43
3. PREVIOUS WORK
The literature review focused on the following topics and region of work that directly relevant to the
presentstudy:
"
Light pipe applications
"
Working mechanismof light pipes
"
Researchmethodsfor evaluatingthe efficiency of light pipe
"
Design methodsfor light pipes
The daylighting performanceof passivesolar tubular light pipes as natural daylighting device has been
reportedin a number of studies.Thesestudiesare mainly on the following four aspects:daylighting
perfon-nanceof light pipe applications,working mechanismof light pipes, characterizingthe
transmittanceof light pipe's main componentsincluding solar collector, tube and diffuser and
developing designtool for light pipes under "design sky" conditions.
Experimental studies carried out by Shao [I] and Yohannes [2], reported the performance of light pipes
of various designs under changing weather conditions: sunny, overcast, heavily overcast, and overcast
with rain. Abundant illuminance of up to 450lux was reported in test rooms, and intemal/extemal
illuminance ratio variance ftom 0.1% to 1% was reported. Oakley's study [3] on 330-mm diameter light
pipes of differing lengths showed that the illuminance could be as high as 15381ux. An average
illuminance of 366lux and a mean intemal-to-extemal ratio of 0.48% were obtainable.
Mathematicalequationshad beendevelopedto describethe perfon-nanceof mirror light tubes.These
work have focusedon the estimationof the light pipe tube'stransmittanceunder laboratory conditions.
Zastrow et al did theoreticalwork on the transmissionof mirrored light pipe tube [4]. Swift et al [5]
gave an integral equationinvolving light pipe tube's parameters,reflectivity, aspectratio and the angle
of incidenceof the incident radiation. Edmondset al [6] expressedthe transmissionof light pipe tube as
a function of light pipe tube parameters,reflectivity and aspectratio and solar altitude.
44
Studiesundertakenat the University of Technology, Sydney [6] investigatedthe enhanceddaylighting
performanceof light pipes coupledto laser-cutlight-deflecting panels.It was reportedthat the
illumination that can be achievedwith a vertical light pipe decreasesrapidly as the elevation of the
incident light decreases.Ile outputsof light pipes dependstrongly on sun's position and diffuser
design.It was concludedthat the daylighting of small rooms via light pipe may be enhancedby
deflecting low-elevation light more directly through the light pipe using laser-cutlight deflecting
panels.
Work undertakenby Carter [7] put forward a designmethodintendedfor use either freestandingor in
conjunction with existing daylight analysismethods.Consideringthat the magnitudeof luminous flux
entering the systemis a function of unknown sky conditions,Carter's basedhis work [7] on the
assumptionof a "design sky", which restrictedthe applicability of this method in real practises.
Detailed description,analysisand appraisalof aboveprevious work are presentedseparatelybelow.
3.1 APPLICATIONS
OF LIGHT PIPES
'ne daylighting performanceof passivesolar tubular light pipes hasbeenmonitored in both real and
laboratorial environments.In the UK, literatureson the researchin this respecthave mainly been
reportedby the researchteambasedNottingham University and Liverpool University. Researchcarried
out by L Shaoet al [1] in Nottingham University demonstratedthe daylighting performanceof light
pipes in real applications.Field measurementscarried out at four siteshave beenreported.The four
sitesare the Pearl Centrein Peterborough,the Gurney Surgeryin Norwich, the RivermeadCourt in
Marlow and the Guildford College in London. G. Oakley et al [3] reportedthe performanceof six light
pipes in three different applications,namely a workshop, a residentiallanding and a small office. The
locations of the applicationsare the BeaconEnergy Ltd, the West BeaconFarm and the BeaconEnergy
Centre,which are all locatedsouthwestof Shepshedin Leicestershire.
45
3.1.1 Applications of light pipes in residential and office buildings
Measurementson light pipe's daylighting performancein real buildings by Shao[I], Yohannes[2] and
Oakley'sstudy [3] have presentedgeneraland broad pictures of applicationsof the device.Positive and
qualitative conclusionshave beendrawn on the overall efficiency of the device and the benefitsof
employing it in real applications.Importantly it hasbeenmadeclear that the designtechniqueof light
pipes plays an important role in the application of the device, Shaoet al concludedthat light pipes "can
be effective devicesfor introducing natural daylight into buildings, provided they are designedwith
care". Oakley et al concludedthat light pipes "are proficient devicesfor introducing daylight into
buildings", and "the most effective light pipes are straight, short oneswith low aspectratios and
consequentlylarger diameterlight pipes would probably be more effective". Theseimplicated that the
light pipe itself was a complex systemand required extensiveresearchto provide detailedand
quantitative evaluationsof it.
It was found that the performanceof light pipe systemwas not only dependenton the geometrical
configurationsof the system.External meteorologicaland geographicalconditions havebeenfound to
have effect on the performanceof light pipes. Shaoet al and Oakley et al measuredthe daylighting
performancesof light pipes under different weatherconditions and usedthe ratio of internal total
illuminance to external total illuminance as an indicator of the performance.It was found that the ratio
seemedto vary with different weatherconditions and solar altitudes.Shaoet al found that when the sky
was overcast,the ratio of internal to external illuminance increased.This interestingphenomenonwas
explainedas "probably due to most of light ftom an overcastsky originating from aroundthe zenith
and undergoingfewer reflections/absorptionsas it travels down the light pipe". However,both weather
condition and solar altitude are not independent.Thereforeno certain conclusionson the effect of
weathercondition, and the effect of solar altitude on the daylighting performancecan be given based
on the measurements.It was thereforerealized that to reveal the relationshipbetweenweather
conditions and solar altitude, and the performanceof light pipes, vast databasethat can provide
necessaryinformation on both light pipe itself and its ambient external environmentis needed.
46
Furthermore,by examining the study by Shaoet al and Oakley et al, it was found that the internal
illuminance distribution plays an indispensablerole in the evaluationof the performanceof the device.
Shaofound "the conceptof daylight factor is not appropriatehere asthe sky was clear and dosenot
meet the overcastcondition upon which the daylight factor is based".Therefore,insteadof
conventionaldaylight factor, the ratio betweeninternal illuminance and externalilluminance was used
to indicatethe performanceof light pipes. However, it must be pointed out the ratio is dependanton the
points of interest.For a given light pipe systemunder a given externaland internal environmental
conditions, the ratio for different points within the room, which havevarious vertical and horizontal
distancesfrom the centreof light pipe diffusers have different values for the ratio. Therefore,as an
indicator of light pipe daylighting performance,the ratio shall be defined as a dimensionalvariety that
can describethe internal illuminance distribution due to the light pipes.
Useful information on light pipe designhasbeengiven by Shaoet al and Oakley et al. Qualitative
relationshipsbetweenthe aspectratio and the performance,the use of bendsand the performance,the
weathercondition and the performancehave beenpresented.Basic instructional principals such as to
"avoid excessiveaspectratios and numbersof bends"have beensuggested.However, the attemptto
designlight pipe systemsin real applicationsusing only basic principals and qualitative relationships
might not be successful.Designersneedto know the output of a certain light pipe under certain
externaland internal conditions with certain confidence.Most of the measurementson light pipes in
real buildings carried out by Shaoet al and Oakley et al monitored the total output of a group of light
pipes, where eachindividual light pipe had its own configuration and waspositioned in different
places.It shall also be bom.in mind that the output of light pipes measuredin real applicationscould be
affectedby the shadingof interior layout, for examplesthe shadeof furniture and reflection from walls.
Thesefacts increasethe difficulty in producing exact evaluationand comparisonof the daylighting
performanceof light pipes. In considerationof the presentwork, it was thought that the mathematical
modelling should be basedon measurementsundertakenin laboratories.
47
3.1.2 Large-scale core daylighting
by light pipe
In 1987,Whitehead[8] reportedan application of large-scalecore daylighting by meansof light pipe
system.The light pipe systemwas applied to a five-story conventionaloffice building in Toronto,
Canada.The illuminated areaconsistedof an 186m2core region of the top floor of the building. The
systemincluded five main components,namely, sun tracking device, focusing mirrors, roof apertures
and prism light guide input elbows,prism light guidesand electrical lights. According to the schemeof
the application given by the authors,therewere eight identical sun-trackingand light distribution
systems,installed every 1.22metersin a row. It was reportedthat eachlight guide of approximately
1.22metersin diametercould illuminate 23m2 of office spacewell in excessof 1280lux.It was also
concludedby Whiteheadthat a core daylighting systemsuch as this would be cost effective.
In 1990,McCluney studiedthe application of using water-filled light pipes to transportconcentrated
beam solar radiation from a solar collection systemto a utilization system.According to McCluney, a
systemof suchcan be for the daylighting of the core interior spacesof buildings, spacesthat are far
removed from outsidewalls or the roof and are thereforenot amenableto conventionaldaylighting
with sidelight or toplights. McCluney studiedthe effect of absorptionby water on the color of light and
the colorimetry of water-filtered light. McCluney reportedthat the distancewhich daylight can be
transmittedbefore its color becomesobjectionablein comparisonwith warm white fluorescentlight
appearedto be 6-8m. The distancefor a significant drop in the color-renderingindex of the daylight
transmittedby the systemwas reportedas about I Om.It was found that the visible transmittanceof 5
and 10m long pipes was about 28% and 19%. It was concludedthat water-filled light pipes could be
usedto bring cool, filtered sunlight indoors in a controlled manner [9].
3.1.3 Light pipe coupled to laser-cut light-deflecting panels
Edmonds[61 studiedthe enhancedperformanceof light pipes coupled to laser-cutlight-deflecting
panels(LCP). Edmondspointed out "although light pipes are effective sourcesor natural illumination
for deepareaswithin buildings, the daylighting performanceof the device decreasesrapidly as the
elevationof the incident light decreases".It was found that the combination of laser-cutlight deflecting
48
for
below
illumination
light
the
about
all
angles
of
elevation
performance
panelswith
pipes enhanced
60'. Laser-cutlight-deflecting panelsare of a material that combineslight deflecting propertieswith
is
is
The
to
thickness
transparency.
conventional
glazing,
and
of
similar
glass
material
good viewing
found
large
between
[101.
It
laser
by
laminating
the
that
sheets
of
glass
was
acrylic
sheet
cut
produced
enhancementwas obtainedin winter months, when sunlight is incident at low elevation all day. For a
light pipe 0.3m in diameterand 7.2m in length but without LCP, the transmittanceof it falls below 0.1
for sun elevationbelow about45'. While as a comparison,when such a light pipe is coupledwith a
LCP device, the transmittanceabove0.1 extendsto sun elevation as low as 10". It was therefore
concludedthat the enhancementat low elevationsextendsthe time during which light pipes were
useful [6].
Edmondset at [ 11] also gave the theory of using extractorsand emitters in light pipe systemwithin
large commercialbuildings. 'I'lie author discussedthe application of hollow light pipe for the
distribution of sunlight from the roof or fagadeinto the deepinterior of a building. It was found this
application was suited to climateswith a high direct sun component.However, to use sunlight in
buildings more effectively, a device at the faqadeto direct sunlight into a light pipe and devicesto
extract light from the light pipe and distribute the light into interior shall be included in the system.
Devices for the extraction of light are given the nameof "extractors" and devicesfor light distribution
as "emitters". Edmondset at studiedthe application of using laser-cutlight-deflect panel asextractors
and emitters for light distribution from hollow light pipes. It was concludedthat it was feasibleto
produceextraction and emissiondevicesfor light pipes from simple assembliesof laser-cutpanels.The
extractorsand emittersmay be usedwith rectangularlight pipes to provide light distributions similar in
most respectsto thoseobtainedfrom conventionalluminaries.According to the author, this technology
is also applicableto remote-sourcelighting systemswhere the sourcesmay be either sunlight or
artificial light.
3.1.4 Light pipe system using both natural and artificial light
Aizenberg et al [ 12] reported the application of slit light pipes in the Chkalovskaya Moscow subway
(60m
by
long) structure suspended
hall
illuminated
The
the
a
rectilinear
of
station
was
central
station.
under the oval dome of the main hall. The structure consisted of cylindrical multi-slot light pipes
49
alternating with 12 cubes.According to the above-mentionedauthor, the use of hollow light pipes to
illuminate the subway stationnot only permitted new architecturalsolutions,but also yielded good
economicindices of the system.The number of lighting points in the all was reducedby a factor of 30
and the extent of the electrical grid was reducedby a factor of three.Aizenberg et al statedthat an
important advantageof lighting systemsbasedon light pipe "might be further reduction in maintenance
costsas the light sourcesmay be easily accessedto maintenancepersonnelwithout the needfor tall
laddersor cherry pickers". The operationalexperienceof over 12 years confirmed the high reliability of
the system.The authorsconcludedthat the afore mentionedstation,namely Moscow subway station
was the first station where the problem of light-system operationhad beencompletely solved, since
"accessto the input units for lamp replacementand modification of the electrical systempresentsnot
difficulties, requiresno specialequipment,and may be accomplishedby a single electrician at any
time". According to Aizenberg et al [12] the application of similar artificial lighting systemthat used
light guide was also found in Moscow ring high way. This showsthe wide applicability of artificial
light sourcelight guide system.
Aizenberg et al [13] proposedand studieda solar and artificial light pipe systemcalled "Heliobus" used
in a school building in SanktGallen,Switzerland.It is a four-story building, within which thereare
recreationhalls at the centreof eachfloor. The Heliobus systemwas built to light theserecreation
areas.The systemcomprisedthe following basic elements:a solar light collector, an intermediate
element,a unit containing electric light sources,a vertical hollow light pipe and a diffuser. According
to the above-mentionedauthors,the working mechanismof the systemis: solar light rays capturedby
the light collector are directedthrough the intermediatedevice (by its reflecting surfaces)into the light
pipe and then diffused into areasto be lit. In caseof lack of daylight, a luminous flux of electric light
sourceis directedby an optical systemlocatedin the intermediatedevice. Aizenberg et al statedthat
the performanceof the systemwas highly appreciatedby teachers,administratorsand school pupils.
Testsconducedby Aizenberg showedthat the systemprovided good daylighting even under a cloudy
sky when the sun was absent.It was concludedby afore mentionedauthorsthat the systemtotally met
the requirementsfor lighting under all weatherconditions,with energyconsumptionreduced
significantly due to shorteningof electric lighting operation.
50
3.1.5 Integration of light pipe daylighting and natural ventilation systems
Shaoand Riffat [14] investigatedthe techniqueof integrating light pipe natural daylighting and natural
ventilation using passivestack system.The systemhas a bi-layer structure.In the middle of the
structure is the light pipe, lined with a highly reflective material. The light pipe is surroundedby an
annular spacethat actsas a stack for the exhaustair. The systemcan be further combinedwith a heat
pipe basedsolar heating systemthat can enhancethe natural ventilation. By experimentalmethods,the
authorsstudiedthe daylighting and ventilation performanceof the integratedsystem.The daylighting
performanceenhancementof light pipe due to LCP (Laser-cutPanel) was also examined.It was found
light transmittedthrough the light pipe was higher on clear/sunnydays than on overcastdays,but the
uniformity of the illuminance in the test chamberwas greateron overcast/cloudydays. Solar infrared
transmissionwas found to be 1.5%on a cloudy day comparedwith 1.4%on a sunny day. Light pipe
transmittedmarginally less infrared radiation than visible light. It was shown that by fitting a LCP to a
light pipe, higher level of daylight transmittancecould be achievedfor certainperiods of the day,
dependingon the orientation of the LCP. It was found that an eight air changesper hour were achieved
with the natural stack effect. The authorsconcludedthat the most suitablebuilding types for the
application of the integratedsystemwere educational,office and retail buildings.
Oakely [ 15] also studiedthe integratedsystemof light pipe and ventilation stack. The systemhas two
channels.The central channelis a light pipe that guidesdaylight into occupiedspace;while the outer
channel,also called ventilation stack,enablespassivestackventilation. The study monitored the
performanceof two light pipes with diameterof 2.15m and 2.20m in length in outdoor environmental
chambers.Using tracer-gasmethod,above-mentionedresearchesmeasuredthe low velocity airflow
ratesand natural stack ventilation. Resultsgiven by the author suggesteda good correlationbetween
solar altitude, internal illuminance valuesand the external illuminance values.It was shown that by
fitting a LCP panel to a light pipe, much higher levels of daylight could be achieved.It was found that
the typical air changerate through the passivestack was about eight air changesper hour in winter, and
the temperatureinside the test chamberwas controlled stableat approximately20'C. The authors
concludedthat light pipes were proficient devicesfor introducing daylight into buildings and reducing
costs.
51
Smith et al [ 16] reportedthe evaluationof dichroic material for enhancinglight pipe daylighting and
natural ventilation in an integratedsystem.It was statedby the authorsthat, "the integration of natural
daylighting and ventilation systemreducessystemcostsand paybackperiod as well as make both
techniquemore attractive to users". It was found that by constructinglight pipe using dichroic
materials,the infrared part of the solar radiation was allowed to be transmittedto the ventilation stack,
while the visible light was guided by the light pipe into interior space.The heatgain to the interior can.
thereforebe reducedand the thermal stack effect strengthened.The transmittanceof a dichroic light
pipe was found to be similar to that of a light pipe with a 95% specularreflectance.The infrared
radiation transmittedthrough the dichroic material into a passivestackwas found to enhancethe
natural ventilation flow by up to 14%. It was concludedby the authorsthat the dichroic material
removedapproximatelyhalf of the solar heat in daylight, and thus provided natural daylight without
overheating.
3.1.6 The use of light pipe systems in deep plan buildings
Daylighting possessesgood potential for applications in area such as tropics where the sky is luminous.
However, because the depth of penetration of daylight through windows into deep plan buildings is
limited, the full utilization of daylight is restricted. It was realized that the limitation of windows could
be complemented by purpose designed light pipe systems. Surapong et al [17) developed a technique
for the use of sunlight through light pipe system in multi-storey buildings. Measurements on the
internal illuminance and temperature were undertaken and the results were compared against calculated
values. Surapong et al used elementary ray-tracing method in modelling internal daylight illuminance
and employed analogous model for calculating heat transfer. According to the computed and measured
internal illuminance data given by the authors, Mean Bias Error (MBE), Root Mean Square Error
(RMSE) and Percentage Averaged Deviation (PAD) were derived. It was noted that the averaged
measured internal illuminance value was as high as 1400lux. The MBE was found to be 308lux, which
was about 22% of the averaged measured internal illuminance. Corresponding figures for RMSE were
found as 808lux and 57%. The PAD was found to be 35%. Based on the comparison between
measured
and computed data, the afore-mentioned authors also pointed out that there might be a higher level of
uniform reflection than assumed. The authors concluded that the analysis method developed by them
was suitable and sufficiently accurate.
52
A casestudy on the use of light pipes for deepplan office buildings was carried out in Malaysia by
Hansenet al [ 18]. The casestudy examineddevelopmentwork on the application of light pipe system
for a high rise building in Kuala Lumpur, Malaysia. Light pipes were used in the high-rise building. For
eachfloor, four light pipes coupledwith LCP (Laser-cutPanel)were used to improve the daylighting
daylighting
light
The
to
the
of
performance
used
simulate
method
of
scale
modelling
was
performance.
pipe. In predicting the daylighting performanceof light pipe, elementarytheory was used.The
found
for
It
that
elevations.
was
various
solar
were
compared
with
measured
values
results
calculated
light pipes coupled with LCP had a good performancefor deepplan buildings. The authorsconcluded
that the use of light pipes "will increasethe passivezone in the building and hencereduceenergy
consumptionby the use of daylight". It was suggested,however, that further study neededto be done in
order to obtain a better distribution of the out coming light from the light pipe system.
3.1.7 A solid light guide system: air-clad optical rod
Researchersin Nottingham University [ 19] proposeda novel "light rods" systemthat can be usedto
transportlight ftom the exterior of a building into its interior spaces.Theserods were designed
sufficiently small so that it canbe fitted into most existing buildings without structural modification.
The light rod systemcombineshigh transmittanceefficiency with small cross-sectionalarea.The
systemrelies on the principal of total internal reflection and makesuse of the transmittanceproperties
of industrial grade extrudedPolymethyl methacrylate.Comparisonwas madebetweenlight rod and
light pipe in terms of daylight transmittance.It was found that when external illuminance was greater
than 35000lux light pipe (aspectratio = 4) performedbetter than light rod (aspectratio = 24), while
when external illuminance was lower than 35000lux, the latter device performedbetter than the former
one. It was concludedthat light rod "transmit at a similar efficiency to a standardlight pipe that has an
aspectratio 6 times smaller", and "the small diameterof the device gives it the potential to provide
daylighting where light pipes cannotbe installed" [ 19].
3.2 WORKING
MECHANISM
OF LIGHT PIPES
The working mechanism of passive solar light pipes is most widely described and understood as
"daylight is gather by the light pipe dome, and then transmitted through the reflective light pipe tube by
53
into
internal
light
diffuser
by
distributed
by
being
followed
spacewithin
pipe
multi-reflection,
buildings". Above descriptionalthough rough and simple, is correct, giving a generalpicture of how
daylight is transmittedthrough light pipes. However, since daylight has two important components,
in
difference
their property, with the quantity and
the
which
are
of
great
sky-light
sunlight
and
namely
light
dynamically,
the
pipe systemschanges
of
performance
proportion of eachcomponentschanging
from time to time.
3.2.1 Understanding of the daylight transmission within light pipes
The understandingof the complex processthat sunlight and sky-light travels through light pipes forms
the basis on which a sophisticatedperformancemodel can be constructed.Previousworks on this
subjecthave beenseen.However, emphasiswas only put on the explanationof the transmissionof
diffuse
light
is
[1,4,5,6].
Sky
light
(or
the secondmost
light
tubes
pipe
sunlight) within
parallel
important componentof daylight, but the contribution of this componentto the daylighting
performanceof light pipes has rarely beenstudied.
The quantity and proportion of the two componentsof daylight vary with the changingof sky
conditions. When the sky is clear, horizontal diffuse illuminance can be ashigh as 1/3 or more of
horizontal global illuminance; while when the sky is overcasthorizontal diffuse illuminance can be
equalto the global illumiance; and when the sky is part-overcast,the proportion of diffuse illumiarince
to global illuminance varies dymatically but can reachas high as 50%. The transmissionof sky difftise
illuminance can have important influence on the overall efficiency of light pipe systems.
Study on the transmissionof sky diffuse light within light pipes was carried out by BBRI (Belgian
Building ResearchInstitute) [20]. Measurementon the diffuse illuminance decreasein a 330 mm light
pipe tube along the length of it was undertakenunder overcastsky conditions. It was reportedthat
diffuse illuminance transmittedby a light pipe had two components,namely the direct view part and
the reflected part. It was shown that the direct view of sky decreasedvery quickly from 100%to I%
after I meter, while the reflectedpart decreased29% per meter.Theseimplied that the physical
processesof the transmissionsof the two daylight componentswithin light pipes were different.
54
3.2.2 Critical appraisal
On light pipe system'stransmittanceof daylight, most efforts have beenput on the theoretical
calculation of light pipe tube's transmittanceof parallel artificial or sunlight [1,4,5,6). Zastrow et al
[4] related the transmittanceof a mirror light pipe to its surfacereflectance,the angle betweenthe
incident light and the light pipe's axis, the length of the light pipe tube, and the diameterof the light
pipe tube. Swift et al [5] and Edmondset al [6] establishedmore complicatedrelationshipbetweenthe
transmittanceof light pipe tube, and the configurationsand the incident angle of parallel light.
However, the application of abovemethodsto the designof light pipes in real practisemay not be
successful.This is becausethesemethodscannotdescribethe transmittanceof sky diffuse illuminance
within light pipe systems.As an example,when the sky is completeovercast,the calculationsbasedon
abovemethodsare not applicable,since the input into the light pipe is only diffuse illuminance and
there is no sunlight component.
BBRI's work [20] on the evaluationof the loss of diffuse illuminance along light pipe tube revealed
that the transmissionof this daylight componentis complex and different from that of the sunlight
component.However, BBRP work is only conductedunder overcastsky conditions.Thereforethe
conclusiondrew by BBRI is not necessarilyapplicableto other weatherconditions.'Me reasonfor this
is that the sky illuminance distribution is not uniform. Figure 3.1 graphically presentsthe radianceor
luminancedistributions that have beenwidely reportedin literatures [2 1]. Figure 3.2 showsthe
different sky illuminance distribution under different weatherconditions.Thus, the transmittanceof sky
diffuse illuminance may vary under different weatherconditions,which implies that the 29% per
efficiency drop can only be applied to real light pipe designwith limited confidence.It is therefore
realized that, to produce a mathematicalmodel that can describethe transmissionof sky diffuse
illuminance within light pipes, measurementson light pipes of various configurationsunder all weather
conditions needto be undertaken.
3.3 RESEARCH METHODS FOR EVALUATING
THE EFFICIENCY
OF LIGHT PIPES
Pervious work on the efficiency of light pipes focused on the evaluation of transmittance of the three
main components of light pipes namely the solar collector (or called dome), the light pipe tube and the
55
diffuser. Different researchershave taken different approachestowards the purposeof assessingthe
efficiency of the components.The proceduresthat were taken and the resultsthat were given by these
previous studiesarepresentedbelow followed by critical appraisal.
3.3.1 The efficiencies of light pipe solar collectors and diffusers
Light pipe solar collector is the first part of the light pipe system that daylight passes through. The
efficiency of solar collector influences the performance of the whole light pipe system. The most
widely used and commercially available light pipe solar collectors are the clear acrylic dome and the
clear polycarbonate dome. The evaluations of solar collectors have been focusing on this particular
type of dome. Pervious works done on this subject have been reported by BBRI (Belgian Building
Research Institute) [20] and Carter [7].
BBRI carried out measurements to test the solar energetic properties of solar collectors (by
Monodraught (UK) Ltd) of various materials. The theoretical values for normal light transmittance of
clear acrylic and polycarbonate domes were reported as 84.3% and 81.3% respectively. Experiment
aimed to determinate the hemispherical transmittance of solar collectors (by Monodraught Ltd) was
also undertaken. Two luxmeters, one put under a solar collector, and the other outside of it serving as a
reference meter were employed. Readings from the former luxmeter was compared to the latter one to
obtain the efficiency ratio. The value of the ratio amounted to 80% for solar collectors. It was therefore
found that, "the use of the normal values instead of the hemisphere values does not lead to a different
result".
The theoretical values for normal light transmittanceof light pipe diffusers of various diameterswere
also measuredby BBRI. The testeddiffusers were Monodraughtopal dome diffusers of diameters330
mm, 450 mm and 530 mm, and the transmittancesfor the diffusers were reportedas 53%, 50% and
54% respectively.Although Monodraught opal dome diffusers were of convex shape,no experiments
were undertakenby BBRI to determinethe hemisphericaltransmittanceof the diffusers.
56
Above values obtainedby BBRI were then comparedagainstthe valuesgiven by manufacturersof
light pipes. It was remarkedin BBRI's report that "thesemanufacturerspecified valuesseemto be
quite idealistic and lead to a performancethat is almost twice as good as the real performance".
Carter [7] studiedthe relationship betweenthe aspectratio of light pipe (with solar collector and
diffuser) and the transmittanceof light pipe. In his work, Carter used dataprovided by Love et al [22]
on above-mentionedrelationship. Love et al producedthe relationshipbetweenpipe efficiency and
aspectratio for light pipes without solar collector or diffuser under overcastsky conditions. To employ
the databy Love et al, Carterusedthe values of 88% as the hemisphericaltransmittanceof solar
collector, and 60% for diffusers to correct the valuesgiven by Love et al.
3.3.2 The efficiency of light pipe tube
The earliestwork on the transmissionof miff ored light pipe tube seemsto be the theoreticalcalculation
given by Zastrow et al [4]. Zastrow et al gave a simple formulation to relate the transmittanceof a
mirror light pipe tube to its surfacereflectance(p), the anglebetweenthe incident light and the tube's
axis (0), the length of the tube (L), and the effective diameterof the tube (d,ff). It is
T=p
/ deff
L* tanO
(3.1)
where T is the transmittance,i. e. the ratio of the amountof light transmittedby light pipe tube to the
incident light.
Swift et al [5] gave an equationto describethe transmissionof collimating light within mirrored light
pipe tube. The equationis
T= (4
1,7r)
f=o
[S2 /o
)1/2 ]Rint(p
S2
-
tanO/s)
X
fl
Ols
int(p
Ols)]Ids
R)[p
tan
tan
(3.2)
-(1 -
where T is the transmittance of the light pipe tube, i. e. the ratio of the amount of transmitted light to
that of incident light, R is the reflectance of the interior surface of the light pipe tube, p is the aspect
57
ratio of the light pipe tube, 0 is the anglebetweenthe incident light and the light pipe tube axis, int is
the integer function, that is int(a) is the integer lessthan or equalto a.
Swift et al comparedthe theoretical transmissiongiven by Eq. 3.2 againstthe measureddata.The
TM)
filmed
diameter
(internal
by
Silverlux
25
3M
tubes
transmissionsof
plastic
surface
with a
nun
rangeof aspectratio were measured.The light sourcewas a HeNe laser whosebeamwas expandedto
be collimated with a diameterof 50 mm. The transmissionof light pipe tubesof the aspectratio of 2,4,
6,8 and 10 was measuredas a function of the angle of incidenceof the collimated beam.The anglesof
incidencewere 0 to 85 degreesin step of 5 degrees.The experimentalresults were found in a good
agreementwith the calculatedvalues.
The light transmissionperformanceof light pipe tube was also given by Edmondset al [6],
P= 410T,,,,,sin Of
[(R
2
="
2-x
2)1/2
IR
], oL/2Rcositan0dX
(3.3)
where P is the power transmissionof light through light pipe tube, 1()is the extraterrestrialintensity
(1353 W/M2) T,,. is the transmissionof the atmosphere,0 is the elevation of sunlight, R is the radius
,
of light pipe tube, p is the reflectanceof the tube, L is the length of the tube, and i is the angle on which
a bunch of sunlight reflects on the internal surfaceof light pipe tube.
3.3.3 The efficiency of light pipe bends
The efficiency of light pipe bendswas studiedmainly by meansof experiments.Oakley et al [3]
comparedthe ratio of internal to external illuminance, which were due to two light pipes, one straight
and the other elbowed with threebends.It was reportedthat, the internal to externalratio for the
elbowed light pipe ("light pipe A") averagedat approximately0.3%, and 0.5% for the straight light
pipe ("light pipe E"). Oakley et al henceconcludedthat becausethe averageratio of position E to A
was found as 1.78,light pipe E was on average43% better than light pipe A and thereforeA losed 14%
light output per bend. It was pointed out that the figure of 14% contradictedMonodraught's figure of
8% loss per bend.
58
The effect of light pipe tube bendson the efficiency of light pipes was also testedby Love et al [22].
Bends of test anglesof 30,60 and 90 degreeswere tested.Internal illuminances were measuredwith
and without light pipe systems(SunScope)that used different numbersof bends.Measurementswere
collected for eachof the tests,and the datawere usedto calculateaveragetransmittanceof the elbow
joint at eachof the test angles.It was reportedthat the transmittancevalues for 30 degreeslight pipe
bendsrangedfrom 70% to 90% with majority of measurementsconcentratedabout 80%.
Efficienciesof lightpipesolar collectors and diffusers
BBRI [20] carried out extensive measurements on the efficiency of light pipe solar collectors of various
materials and shapes. Measurements were also undertaken by BBRI to compare the transmittances of
solar collectors under hemisphere ambient illuminance and normal incidence illuminance conditions.
Carter [7] referred and used the transmission values for light pipe solar collector and diffusers given by
Love et al [22]. However, these values were not found in Love et al's work. Therefore, it is more likely
that the findings of BBRI [20] are more accurate and can be used with higher confidence than the latter
one.
It was not explainedin BBRI's report [20] why no comparisonbetweenthe transmittancesof diffusers
under real and laboratorial testing conditions was undertaken.This may be due to the highly dynamic
and complicatedoutput of illuminance transmittedby light pipe tube, which makesthe comparison
difficult to implement. It hasbeenaddressedin Section2.4 that the working mechanismof light pipe
diffusers is complex. The attemptto evaluateits performanceseparatelyfrom other componentsof
light pipe systemdoesnot necessarilylead to an applicableresult. Light pipe diffuser is an integral part
of light pipe system;thereforeit may be more practical to assessits performancewith other
componentsas an entirety.
59
Efficiencies of light pipe tube
Zastrow et al [4] gave a simply equation to describe the transmittance of light pipe tube. However, as
pointed out by Swift et al [5], "the reliance of the transmission on the three parameters p (aspect ratio),
R (reflectance) and 0 (the incidence anlge) does not allow a straightforward statement about the
conditions under which the theory of Zastrow et al is a good approximation". It was further commented
by Swift that in the main however Zastrow et al's model "is valid under the conditions of low p, high R
it
is
low
0",
"for
the
transmitted
anticipated
and
colour
coordinates
spectrum
calculations
of
and
and
that the theory of Zastrow and Wittwer will give incorrect values".
Calculatedresultsdue to Eq. 3.2 given by Swift et al were comparedagainstmeasureddata.It was
is
0.967 and was
in
by
"the
Swift
these
that,
results
of
used
et al
value reflectivity
noticed
as reported
determinedby fitting the experimentalresultsto the correspondingtheoretical calculation.The
theoretical calculation are sensitiveto the choice of reflectivity, with changesin R of 0.001 resulting in
noticeabledifference in the calculatedcurve." It was noticed that the reflectivity of the reflective sheet
3M Silverlux was found to be 0.972, which is about 0.005 higher than the fitted value. Although Swift
et al pointed out that due to dust and aging, the reflectanceof the sheetusedin light pipe tubesmight be
expectedto be slightly lower; this apposesthe questionon the accuracyof Eq. 3.2. Equation 3.2 is not
integrable,and the transmittanceof light pipe tubesmust be obtainedusing numerical techniques.
Equation 3.3 given by Edmondsenabledthe relative comparisonof the transmittedpower by light pipe
tubesunder different sun elevation angle,aspectratio and reflectanceconditions. However, Eq. 3.3 is
112/R,
basedon a key weighting-factor (R2-X2)
which was usedwhen averagingover rays equally spaced
acrossthe tube. A main weaknessof Edmondset al's Eq. 3.3 is it is not validated by comparison
betweentheoretical valuesand measureddata.According to Eq. 3.3, Edmondset al gave theoretical
plot showing the relative transmittedpower as a function of sun elevation, surfacereflectanceand
aspectratio. However, it was reportedthat the plots were madeby normalising to the power transmitted
when the sun elevation equals90 degrees.This implies that although the plot showsthe effects of sun
60
elevation, surfacereflectanceand aspectratio, it cannotbe used directly in real light pipe design,
becausethesefigures cannotgive absolutevalues.
The efficiency of light pipe bends
Oakley et al comparedthe illuminances due to two light pipes one with and the other without bends,
and basedon a rough calculation,gave 86% as the transmittanceof one light pipe tube bend. However,
the illuminances were not measuredseparatelyfor the two light pipes, and consideringthe changingof
external environmentand the non-uniform interior layout, it is difficult to quantify the reliability of the
results.This restricts the application of this result to real designs.
Love et al's study is more sophisticatedand provided the evaluationof the efficiency of bendsin more
details. It was realizedby Love et al however, that the geometryof light pipe (SunScope)systemwith
elbow joints was too complicatedto allow for any specific conclusions.Nevertheless,Love et al
pointed out that the transmittanceof a single elbow joints is about 10 percentlower than the
transmittanceof a single straight sectionof 330 mm light pipe (SunScope).It is noticeablethat the
figure of 10 percent(indicating a transmittanceof 90%) however contradictsto the averaged
transmittanceof 80% given by the author. It was also concludedthat the transmittanceof a light bend
was found to be affectedby sky conditions, solar altitude and the geometricalconfiguration of the
bend. This implies that the light transmissionwithin light pipe bendscan be complex, and it may be
more practical to assessbends' performanceas one integral part of the whole light pipe system.
3.4 THE DESIGN OF LIGHT PIPES
The designof light pipes shouldbaseon methodsthat can predict the performanceof the whole light
pipe systemunder all weatherconditions. Designersneedto know the values of illuminance on certain
working plane or at other designatedpoints due to light pipes, Till this project, no mathematicalmethod
that takes accountof the effect of external and internal environmentalfactors and light pipe
configurationshasbeenmade available.However, Carter's work [7] put forward three chartsas a
designtool for light pipe applicationsunder overcastsky conditions.
61
3.4.1 Carter's design charts for light pipes
Using the techniquesof luminous flux measurementsand calculation,the relationship of pipe
efficiency and aspectratio for 25 pipes, variously of 330,450 and 530 imn diameterwas investigated.
Pipe input was calculatedas a function of externalhorizontal illuminance and pipe cross-sectionarea.
Pipe output was either measuredor calculatedusing protometric integrator.A designchart was given
by Carter to show the attenuationof light output with aspectratio under overcastskies for vertical pipe
systemsincluding a clear light capturedome and an opal diffuser. Carter used Love et al's resultsas the
designtool for light pipe bendsunder overcastsky conditions.
Experimentswere undertakento measurethe luminous intensity in the vertical plane for the quadrant0
degrees.
90
Measurements
for
diameter
light
330
two
were
undertaken
mm
pipes, one 610 mm in
length and the other 1220mm. Readingswere taken (not continuously) through the months from
Septemberto November. It was noted however, that the sky conditions for the testingperiod were
predominatelyovercastor cloudy with externalhorizontal illuminance only exceeding25 000 lux for
about 10% of the readings.
3.4.2 Design method based on Coefficients of Utilization
A designmethodsbasedon Coefficients of Utilization (CU) was proposedby Tsangrassoulis[23]
basedon the work of Tregenza[24]. This method treatsthe light pipe's apertureas a fixture and
assumesthat light pipes useperfectly diffuse emitter. The methodwas developedto estimatequickly
the number of light pipes neededto light a room at a given level of lux. It was found by the author that
CU dependedon the geometric form of the light pipes (aspectratio, areaof admittance),the material
properties(reflectance,specularity),the angle of incident of the solar radiation and the dimensionof
the room, the room's surfacereflectance.It was concludedthat the number of light pipe could thus be
expressedas a function of CU, designilluminance, the areaof the working plane and light loss factors
(LLF). It was pointed out that the method was by the time still in its developmentstage,and it could be
performedby a small piece of code quite easily.
62
Carter's designtool was testedby comparingthe calculatedinternal illuminances due to light pipes
againstmeasuredvalues.Good agreementhasbeenseenbetweenthe predicted and measuredvalues.
However, it is noticed that the measuredinternal illuminanceswere mostly lessthan 30 lux. The
maximum external illuminance for the validations were found to be 14 000 lux. 'Me maximum internal
to external illuminance ratio was found to be 0.225%, obtained I rn under light pipe diffuser. This
implies that the designtool given by Carter was only validatedunder heavily overcastsky conditions.
In real applications,light pipes deliver more light in clear or part-overcastsky conditions. Shaoet al's
study [11reportedthat in caseswhere light pipes with moderateaspectratios were installed, good
illuminance of up to 450 lux was obtainedwith internal/externalilluminance ratios around 1%.
It is thereforemadeclear that the application of Carter's designtool is to a considerableextent limited
to overcastsky conditions. '11iisis due to the fact that the main designchartsgiven by Carter were
generatedbasedon datameasuredunder overcastsky conditions. Studiesby Swift et al [5] and
Edmondset al [61 showedthat, under clear sky conditionsthe transmissionof light pipes is affectedby
solar altitude. According to Edmondset al, for a light pipe of an aspectratio of 3, the variation of
transmissioncan be 100%when the solar altitude changesfrom 25 degreesto 40 degrees.Swift et al
presenteddifferent curvesto describethe transmissionas a function of solar altitude for different aspect
ratio.
It hasbeenaddressedin Section2.4 that the transmissionof sky diffuse illuminance and sunlight
illuminance in light pipe systemare different. Therefore,the applicability of a designguideline mainly
for overcastsky conditions when sky diffuse illuminance is the dominant componentof externalglobal
illuminance cannotbe automatically extendedto other sky conditions.
The Coefficients of Utilization (CU) methodproposedby Tsangrassoulis[23] is mainly for estimating
the number of light pipes that are neededto meet a certain lighting requirements.However, to put the
method in to practical use, the relationship betweenCU and various geometricaland climatic factors
has to be expressedin an explicit mathematicalmanner.Further substantialprogressin this respectis
thereforeessentialfor the developmentof the CU method.
63
3.5 SUMMARY
In this chapter, previous works on daylighting perfonnance of light pipes in real buildings, working
mechanismof light pipes, transmissionefficiency of light pipes and the designguidancefor light pipe
systemshave beenreportedand critically appraised.
Previousworks on daylighting performanceof light pipe showedthat light pipe is a complex system
that requiresextensiveresearchto provide quantitative evaluationsof its performance.The
performanceof light pipe systemnot only dependson the geometricalconfigurationsof the system,but
also dependson externalmeteorologicaland geographicalconditions. It is thereforebelieved that to
reveal the relationship betweenvarious internal and external factors, and the performanceof light
pipes, vast databasethat can provide necessaryinformation on both light pipe itself and its ambient
internal and external environmentis needed.It is also revealedthat insteadof conventionaldaylight
factor, the ratio betweeninternal illuminance and external illuminance shall be usedto measurethe
daylighting performanceof light pipes.As the indicator of light pipe daylighting performance,the ratio
shall be defined as a dimensionalvariety that can describethe internal illuminance distribution due to
the light pipes. Due to the draw backsof measurementsof light pipes performancein real applications,
it is believed that mathematicalmodelling shouldbe basedon measurementsundertakenin
laboratories.Measurementson light pipes of various configurationsunder all weatherconditions shall
be undertaketo enablethe mathematicalmodelling to the purposeof generatinga generalperformance
evaluationmodel.
The efficiency of light pipe tube shouldbe investigatedunder real sky conditions.Theoretical
equationsgiven by Zastrow et al [4], Swift et al [51 and Edmonds[6] do not take accountof diffused
light and due to their respectdrawbacks,cannotbe used in real applications.Light pipe diffuser is an
integral part of light pipe system;thereforeit may be more practical to assessits performancewith
other componentsas an entirety. It was also found that the transmittanceof a light bend was affectedby
sky conditions, solar altitude and the geometricalconfiguration of the bend. This implies that the light
transmissionwithin light pipe bendscan be complex, and it may be more practical to assessbends'
performanceas one integral part of the whole light pipe system.
64
The designtool given by Carterwas only validatedunder heavy overcastsky conditions. It is made
clear that the application of Carter's designtool is to a considerableextent limited to overcastsky
conditions. The applicability of Carter's designtool, which is mainly for overcastsky conditions when
sky diffuse illuminance is the dominant componentof externalglobal illuminance cannotbe
automatically extendedto other sky conditions.Design tools should enabledesignersto know the
values of illuminance on certain working plane due to light pipe installation under all weather
conditions, especiallywhen the sky is clear and the systemdelivers more daylight into buildings. As a
conclusion,sophisticatedmathematicalperformancepredicting modelsthat takesaccountof the effect
of externaland internal environmentalfactors and light pipe configurationsis needed.
65
REFERENCES
1. Shao,L. (1988) Mirror lightpipes: Daylighting performancein real buildings Lighting Researchand
Technology,30 (1), 37-44
2. Yohannes,1.(2001) Evaluation of the PerformanceofLight pipes Usedin Qjfices, PhD Thesis,
Nottingham, Nottingham University
159-174
4. Zastrow, A. and Wittwer, V. (1987) Daylighting with mirror lightpipes and with fluorescentplanar
concentratorsProceedingsofSpie - the International Societyfor Optical Engineering, 692,227-234
5. Swift, P. D. and Smith, G. B. (1995) Cylindrical mirror light pipes Solar Energy Material and Solar
Cells, 36(2), 159-168
6. Edmonds,1.R., Moore, G. L, Smith, G. B. and Swift, P. D. (1995) Daylighting enhancementwith
light pipes coupledto laser-cutlight-deflecting panelsLighting Researchand Technology,27(l), 27-35
7. Carter,D. J. (2002) The measuredand predictedperformanceof passivesolar light pipe systems
Lighting Researchand Techonology,34 (1)
8. Whitehead,L. A. (1987) Large scalecore daylighting by meansof a light pipe, Sunworld, 11(l), 1415
9. McCluney, R. (1990) Color-renderingof daylight from water-filled light pipes, Solar Energy
Material, 21,191-206
10. Edmonds,I. R. (1992) Performanceof lasercut light deflecting panelsin daylighting applications,
Solar Energy Materials and Solar Cells, 29,1-26
11. Edmonds,1.R., Reppel,J., Jardine,P. (1997) Extractorsand emitters for light distribution from
hollow light guides,Lighting Researchand Technology,29(l), 23-32.
12. Aizenberg, J. B., Aleshina, N. A., Pyatigorskii, V. M. (1996) Arched hollow light guidesat the
ChkalovskayaMoscow subwaystation,Light and Engineering,4(3), 1-4.
13. Aizenberg, J. B., Buob, W., Signer, R., Korobko, A. A., Pyatigorsky, V. M. (1996) Solar and
artificial lighting of a schoolbuilding with hollow light guide system"Heliobus", Light and
Engineering, 4(3), 41-54.
66
---4
14. Shao,L. and Riffat, S. B. (2000) Daylighting using light pipes and its integration with solar heating
and natural ventilation, Lighting Researchand Technology,32(3), 133-139.
15. Oakely, G., Smith, S. J., Shao,L. (2000) Triple Save- the investigationand monitoring of a
combinednatural daylighting and stackventilation system,Internal report provided by Dr L. Shao,
Institute of Building Technology,School of the Built Environment,University of Nottingham.
16. Smith, S. J., Elmualim, A. A., Riffat, S. B., Shao,L. (1999) Evaluation of dichroic material for
enhancinglight pipe/naturalventilation and daylighting in an integratedsystem,C,4ST, 1.
17. Surapong,C., Siriwat, C. and Liu, R. (2000) Daylighting through light pipe in the topics, Solar
Energy, 69(4), 331-341
18. Hansen,V. G., Edmonds,I., Hyde, R. (2002), Proceedingsof the International ExpertsMeeting on
Daylighting Conference,CIBSE, Singapore.
19 Callow, J. M., Shao,L. (2002), Air-clad optical rod daylighting system,internal report from
Institute of Building Techonology,Nottingham University, UK.
20. Loncour, X., Schouwenaars,S., L'heureux, D., Soenen,S., Voordecker,P., Wouters,P. (2000)
Performanceof the Monodraught systemsWindcatcherand Sunpipe,BBRI - Belgian Building
ResearchInstitute
21. Muneer, T., Fairooz, F. and Zhang, X. (2001) Sky Luminance and RadianceDistributions -A
comparisonbasedon datafrom Bahrain,Japanand EuropeCIBSESingapore Conferenceon Tropical
Daylighting
22. Love, J. A., Arch, D., Eng, P. and Dratnal P. (1995) Photometriccomparisonof mirror light pipe
systems,unpublishedreport preparedfor CIFManagementCalgary,The University of Calgary, Alberta,
Canada
23. Tsangrassoulis,A. (2002) CIE TC 3-38 Tubular dayligbting guidancesystems(TDGS), internal
report submittedto CIE TC 3-38.
67
/\
VA U
Horizon
darkening
effect
Horizon
brightening
effect
Figure 3.1 Representation of the sky luminance distribution under non-overcast conditions
68
ý2-5*
0"
(a)
(b)
c;n-
5.
?2.5*
0"
(c)
(d)
Figure 3.2 Vector presentation of Bahrain sky radiance distribution: (a) clear sky kt=0.7, (b)
part-overcast sky kt=0.5, (c) thin overcast sky kt=0.35 and (d) heavy overcast sky kt=0.2
69
4. RELEVANT
THEORIES
Passivetubular solar light pipe is a daylighting device that transmitsexternal daylight into buildings.
To evaluateand predict the daylighting performanceof light pipes, an explicit term that can specify its
daylighting performancemust be defined first. Daylight factor hasbeenwidely used as an industrial
standardin daylighting design.However, becauselight pipes utilize both sky diffuse and sunlight
radiation, the method of daylight factor is not suitableto measurethe performanceof light pipes. With
the developmentof various innovative daylighting devices,it is necessaryto use new conceptthat
measuresdevices' perforinancein delivering both sky diffuse light and sunlight. Daylight penetration
factor (DPF) is henceintroducedin this study to specify, and as an index to evaluatethe performance
of light pipes.
The introduction of the conceptof DPF forms the basison which the daylighting performanceof light
pipes can be modelled.The proposedDPF modelsare built to predict the daylight delivery efficiency
and the internal distribution by light pipe systemsof various configurationsunder all weather
conditions.The core task of the proposedDPF model is to predict transmissionof daylight (sky difftise
light + sunlight) through light pipe systems.Light pipes use external daylight as input and produce
diffused daylight as output. However, the input and output for light pipes are complex, thereforethe
proposedDPF model should incorporateother modelsso as to accountfor the complexity of input and
output of light pipe system.
As shown in Section3.2, daylighting performanceof light pipes varies with the changingof external
weatherconditions. Sincethe proposedDPF model aims to predict the daylighting performanceunder
all weatherconditions, factors that describethe dynamic externalweathercondition have to be
incorporatedinto the DPF model. Thus the input of light pipe systemscan be described.Light pipes use
diffusers to producediffused light and spreadit into buildings. The internal illuminance distribution
resulting from light pipe's output dependson the amountof the daylight delivered by light pipe and the
propertiesof the diffusers. The proposedDPF model aims to predict the daylight level at any points of
interest.To achievethis, internal illuminance distribution modelshave to be produced,and
incorporatedinto the proposedDPF model.
70
4.1 DAYLIGHT
PENETRATION
FACTOR
In designstudiesit hasbeenconventionalto specify interior daylighting in terms of daylight factor
(DF). DF is defined as the ratio of the internal illuminance to the external diffuse illuminance available
simultaneouslyand usually expressedas a percentage.Daylight factor is divided into three
components,namely the sky component,the externally reflected componentand the internally reflected
components.The sky componentis the ratio of illuminance at any given point that is receivedfrom a
sky of known luminancedistribution, to the horizontal illuminance under an unobstructedsky
hemisphere.The external and internal reflected componentsare, respectivelythe ratios of the
illuminance receivedafter reflections from externaland internal surfacesto the horizontal illuminance
under an unobstructedsky hemisphere.
BecauseDF cannotspecify the transmissionof sunlight into buildings, light pipe daylight penetration
factor (DPF) is introduced.DPF is defined as the ratio of the internal illuminance (due to light pipe
daylight penetration)to the externalglobal horizontal illuminance available simultaneously.Light pipe
DPF has two components,namely the sky diffuse component(DPFdiff,,,,
) and the sunlight (DPFbeam)
component.When light pipe's efficiencies in transmitting sky diffuse light and sunlight are identical,
DPF is a product of externalglobal horizontal illuminance and the transmittanceof light pipe (Eq. 4.1).
DPF =E/E
(4.1)
where Ej,, nýjis the internal illuminance at a given point and Eg is the total external illuminance. In
generalDPF can be describedusing Eq. 4.2:
DPF = (Evd x
DPFdiffuse
+ (E, g-
Evd
)x
DPFbeam)/
Eg
(4.2)
The definitions of DPFdiff.. and DPFbe. are shown in Eqs.4.3 and 4.4 respectively.
DPFdiffuse =E
DPFbc=
=E
/E
intemal-diffuse
(4.3)
vd
(E
intemal-beam/
vg -E
vd)
(4.4)
71
internal
illuminance
E
diffiise
illuminance,
horizontal
the
is
Evd
at a given
the
external
where
intunal-diffuse
internal
illuminance
light
E
by
light
diffuse
due
the
transmitted
at a
to
the
pipe,
sky
point
intemal-beam
given point due to the sunlight by light pipe.
Using DPF, the internal illuminance at a given point with coordinates(x, y, z) due to a given light pipe
can be obtained,as shown in Eq. 4.5.
intcmal (x, y, z)
= DPF(,,,
y,,) x
where E intemal (x, y, z)
is
Eextemal
(4.5)
the internal illuminance at the given point P(x,y,,), and DPF(x,y,,) is the light pipe
Daylight PenetrationFactor for the given point.
By including key parametersthat presentlight pipe geometricand intemal/extemalenvironmental
factors into the proposedDPF model, the effectsof thesefactorson light pipe daylighting performance
can be taken into account.Geometricfactorsthat may determinethe performanceof light pipe are the
light
The
length
diameter
including
tube
the
the
the
so
on.
pipe
and
of
and
of
system
configurations
direct
beam
diffuse
irradiance
by
light
has
irradiance
two
and
components:
sky
captured
pipe
external
irradiance.The split betweenthesetwo componentscan be dictatedby the numerical value of the sky
clearnessindex k, [I]. Sky clearnessindex (defined as the ratio of global to the extra-terrestrial
irradiance)hasbeenwidely used to specify weatherconditions.However, k, is not an independent
factor, other factors such as solar altitude ((x,) that is usually usedto index the position of the sun on its
track through the sky canopycan also have effect on light pipe daylighting performance.'Me internal
illuminance distribution can also be affectedby the internal geometricfactors such asthe position of
the point of interest(due to the inversesquarelaw and cosinelaw). Other factors such as the room
shape,room dimensionsand the internal reflection within a room lit by light pipes will also affect the
internal illuminance distribution. However, becausepresentlythe main aim of the project is to evaluate
light pipe's daylighting performance,internal reflection is discussedin later part of the thesis(Section
6.6.5). As a conclusion,DPF model can be expressedas a function of light pipe configurationsfactors
(F,), external environmentalfactors (F.) and internal distribution geometric factors (F),
72
DPF
y,,)
(4.6)
f( FF Fc, Fi)
,,
4.2 TRANSMISSION
OF SKY DIFFUSE LIGHT AND SUNLIGHT WITHIN
LIGHT PIPES
It hasbeen explainedin Section3.2 that light pipe transmitssky diffuse light and sunlight in different
diffuse
beam
irradiance.
Sky
diffuse
different
due
This
is
to
the
and
natureof sky
mainly
mechanism.
irradianceis from all angular directionswithin the 271solid anglerange while sunlight is parallel with
its direction dependenton the position of the sun. Thereforeit is logic to supposethat the
transmittancesof sky diffuse and beamilluminance through light pipe systemcan be different. The
theoreticalmethodsfor calculating the transmittancesof sky diffuse and beam illuminance through
light pipe tube are presentedin this section.
4.2.1 Transmission of sunlight within light pipe tube
Basedon physical reasoningpresentedin Section3.2, it is possibleto show that a light pipe's
transmittanceis a function of the number of reflections required for a ray of light to descendthe pipe
light
is
incident
intensity
I
(Fig.
4.1).
If
its
on
a
pipe tube of
ct
and
elevation
sunlight
of
and reflectance
light
is
At
input
length
in
Fig.
4.1
L
R
the
then
the
each
reflection
7clR2sin(x.
power
as
and
radius
descendsa distance2Rtan(xand the number of reflections is L/(2Rtan(x).However, abovecalculation is
light
For
light
In
for
three-dimensional.
two-dimension
tube.
a
pipes
are
a
real
applications,
only
pipe
three-dimensionlight pipe tube, most light is not incident normally to the reflection surfaceof the tube
and thereforewill require more reflections to descendthe tube.
Figure 4.2 showsa projectedview along the axis of a straight tubular light pipe tube. Light incident on
the apertureat a distancex from the axis is incident on the reflecting surfaceat angle i. Then the
number of reflections required to descendthe light pipe tube is N,
N=L/(2Rcosi tana)
(4.7)
If the reflectance of the reflecting surface is p then the transmission of a ray is pý4.The energy entering
the aperture in the internal between x and x+ Ax is proportional to Ax (R 2_X2)". Therefore the
73
transmissionof the light pipe tube for sunlight (defined as the ratio of output to input beamirradiance)
can be obtainedas:
f,, [(R 2_
X2
1/2
IR
])OL/McositanOd
(4.8)
x
4.2.2 Transmission of sky diffuse light within light pipe tube
The transmissionof sky difftise light is more complex. However, by dividing the sky vault into a series
of patches,the calculation can be carried out. Figure 4.3 showsan isotropic sky vault divided into 21
patches.Presumethe radiancedistribution is uniform and for a given sky patch, its azimuth angle is y
and altitude cc,then the horizontal diffuse illuminance (AIL) entering light pipe tube due to the sky
patch can be obtainedas:
AIL=L da dy sina
(4.9)
where doc and dy are the spanof the given sky patch in altitude and azimuth dimensions.
The total horizontal diffuse illuminance (Evd)input into light pipe tube can be obtainedby either
summingup the contributions of all relevant sky patchesor by measurements.Say IL, is the horizontal
diffuse illuminance entering light pipe tube due to a given sky patch, and Tn is the transmissionof IL,,
) can be
within the light pipe tube, then the total transmissionof the sky difftise illuminance (Tdiffus,
obtainedas:
21
Tdiffuse
IL,, T,,) /
ý(E
Evd
(4.10)
n=l
in which IL,, can be obtainedusing Eq. 4.9 and T,, can be calculatedusing Eq. 4.8. Above calculation
on Tdiff,,,,in Equation is basedon the consumptionthat the sky luminancedistribution is uniform, i.e.
an isotropic model is used to provide the input illuminance value for light pipes. However, it is well
known that the sky illuminance distribution is not uniform. Therefore, to calculate Tdim,,
with a higher
74
accuracyrequiresthe application of zenith luminancemodelsthat can describeunisotropic sky
luminancedistributions. This is explainedin Section4.3.
4.3 ZENITH
LUMINANCE
MODELS
It hasbeen addressedin Section4.2.2 that to calculatethe theoretical transmissionof sky diffuse
illuminance within light pipe tube, sky luminancedistribution shouldbe madeknown first. Sincethe
sky luminancedistribution is not uniform, it is a more accurateprocedureto apply unisotropic sky
models that can describethe luminancedistribution acrossthe sky vault to the theoreticalcalculation.
Zenith luminance,L,,, describesthe luminous intensity of the circular part that is on the top of the sky
vault. Using zenith luminancemodels,the luminanceof other parts of the sky can be directly related to
L,,. This has two important bearing on the designof light pipes. Firstly, in real applicationsa light pipe
can be installed in sucha condition that its solar energycollector can only have a view of part of sky.
The use of zenith luminancemodels enableslighting designersto know the estimatedsky diffuse
illuminance availableto light pipe as input, so as to predict the internal illuminances due to the light
pipe. Secondly,the transmissionof the illuminance from different parts of sky that have varying
elevationand luminanceintensity can be calculated,leading to a more accurateresult than that obtained
basedon an isotropic sky model.
4.3.1 Moon and Spencer's overcast sky model
Lighting designersoften refer to CIE standardovercastsky condition when undertakinginterior
daylighting designas this sort of sky condition is regardedas a worst-casescenario.Overcastsky can
be defined as the sky conditions that the sun is completely blocked by cloud. It hasbeen found by
measurementsthat when the sky is overcast,the zenith part of the sky vault tendsto be brighter than
other part of the sky whose altitude is ct. The brightnessof sky patchesincreaseswhen its (x increases.
The ratio of the luminanceof any sky patch, L, ()to zenith luminance,L,,, was found to be a function of
luminancedistribution index, b, and the altitude of the sky patch (x.Moon and Spencer[2] described
aboverelationshipas:
75
L, / L,, = (1+b sin a) /(I + b)
O
(4.11)
Moon and Spencerfound that for overcastskies, the best value for b was 2. CommissionInternational
de Eclairage(CIE) hasbeenusing this b value of 2 as the standardreferencevalue for overcastskies.
4.3.2 Muneer's model
Muneer [3] hasusedEq. 4.11 to establisha relationship betweenslope diffuse irradianceand horizontal
diffuse irradiance.Muneer's model is given by Eq. 4.12,
D,8/D = cos2(,612) + [2b I z(3 + 2b)][sin, 6-, 6cosg -; rsin 2(,6/2)]
(4.12)
diffuse
hourly
horizontal
is
for
D
hourly
diffuse
irradiance
is
Dp
the
the
surface,
a
sloped
where
irradiance, P is the tilt of the slopedsurface.
Muneer'smodel treatsthe shadedand sunlit surfacesseparatelyand further distinguishesbetween
found
for
his
for
Bracknell,
Muneer
Based
that
a shaded
on
study
and
non-overcast
conditions.
overcast
surface(facing away from sun) the 'best'value of b was 5.73; for a sunlit surfaceunder overcastsky
conditions b=1.68; and for a sunlit surfaceunder non-overcastsky conditions b= -0.62.
Applying the b value of 2 to Eq. 4.11, it can be seenthat under overcastsky conditions,the ratio of the
luminanceof the zenithal part of sky to that of the horizontal part is 3. Applying the b value of -0.62
for southernsky vault under non-overcastsky conditions, the ratio of the luminanceof the zenithal part
of sky to that of the horizontal part is 0.38. Shaoet al [4] have reportedthe phenomenonthat under
overcastsky the efficiency of light pipe seemsto be higher than that under clear sky conditions.This
may be explainedbasedon abovebrief analysis.When the sky is overcast,the direct view of the
zenithal part of the sky, which has the highest luminance,is transmittedby light pipe with high
efficiency. While under clear sky conditions, luminanceemitting from the brightest part of sky is
transmittedby light pipe with lower efficiency due to the multiple reflections, resulting in lower overall
transmittanceof daylight.
76
4.3.3 Perez all-sky model
The Perezet al model [5] computesL,, defined as the ratio betweenthe sky luminanceat the
function
luminance
Lp
the
of the zenith angle
point,
as
a
reference
an
arbitrary
of
and
point
considered
The
between
the
the
the
of
sun.
the
and
position
point
the
considered
angle
consideredpoint and
of
formula is given in Eq. 4.13.
L, =f (ý, y) = [1 +a exp(b/ cos0] [1 +c exp(dy) +e cos' y]
between
the consideredpoint and
4
is
the
the
the
y
angle
and
point,
of
considered
angle
zenith
where
the position of the sun. The parametera, b, c, d and e are adjustablecoefficients, functions of insolation
256-combination
the
is
the
[5].
The
values
of
of
the
as
a
represented
parameters
of
scheme
conditions
brightness
index
factor,
isotropic
the
the
sky's
the
and
clearness
sky's
correction
zenith angle of sun,
index [6].
4.3.4 Kittler,
Darula and Perez's standard sky model
Basedon Perezmodel, Kittler, Darula and Perezproposeda new range of standardskies.This is a set
different
luminance
distribution
15
describe
formulae
the
that
to
sky
under
are used
of mathematical
conditions.
The equationfor relative sky luminancedistribution to the zenith luminance is defined as a function of
ý, the zenith angle of the consideredpoint and y, the anglebetweenthe consideredpoint and the
position of the sun.
L,,
f(7)9(ý)
g
_
L,,., f (Z, )9(0)
P(gý
p(O)
-I+a
exp(b / cos
I+ a expb
(4.14)
(4.15)
77
in which the function f is the scatteringindex that relatesthe luminanceat a point to its distancefrom
the sun.
f(o
2)]
+e
exp(d)r/
c[exp(do
=I+
-
4.4 INTERNAL
ILLUMINANCE
COS2
ý
DISTRIBUTION
To determinethe internal illuminance distribution due to light pipe using the proposedDPF model, the
model must be able to predict the illuminance receivedby a given point from light pipe diffuser. The
theoreticalcalculation of a given point due to a certain light sourceoften involves two laws, which are
the Inverse SquareLaw and the CosineLaw. According to the property of the light source,the
procedureof applying Inverse SquareLaw and Lambert'sCosineLaw differs. Particularly, when the
output of light pipe is assumedto be uniform diffuse light, the approachof "radiative view factors" can
also be used to determinethe illuminance receivedat a given point from light pipe.
4.4.1 Lambertian
Surface and Lambert's
Cosine Law
A Lambertiansurfaceis a surfaceof perfectly matteproperties,which meansthat it adheresto
Lambert'scosine Iaw. Lambert'scosinelaw statesthat the reflected or transmittedluminous intensity in
any direction from an elementof a perfectly diffusing surfacevaries asthe cosineof the anglebetween
that direction and the normal vector of the surface.As a consequence,the luminanceof that surfaceis
the sameregardlessof the viewing angle.It is further illustrated by Fig. 4.4 that the intensity of
radiation along a direction that has angle 0 with the normal to a radiation-emitting surfaceis,
10= 1"COSO
(4.17)
where I,, is the intensity of radiation in normal direction. The intensity of radiation is defined as the rate
of emitted energy from unit surface area through unit solid angle.
78
4.4.2 The Inverse Square Law
Distant lights appear fainter than nearby lights of the same intrinsic brightness. However, the true
brightness of an object (its luminosity), must be distinguished from its apparent brightness. The term of
luminosity is defined as the amount of energy radiated per second by an object. Ile
intensity of light
observed from a source of constant intrinsic luminosity falls off as the square of the distance from the
object. This is known as the inverse square law for light intensity. Figure 4.5 illustrates the inverse
square law. The entire light through the I square-foot first area goes through the second one, which is
100 times larger; hence the light intensity per square foot is 100 times smaller in the second area. 'Me
intensity drops as I/R2.
4.4.3 Radiative view factor method
The view factor betweenany two surfacesis defined as that fraction of the radiative energyleaving an
emitting surfacethat is interceptedby the receiving surface.The method for calculating the view
factors from differential areasto sphericalsegmentswas given by Naraghi [7]. Figure 4.6 illustrates
that accordingto the relative position of a given point to a energyemitting hemispheresurface,the
calculation of view factor for the given point usesdifferent formulae as shownbelow by Eqs.4.18
(Appendix 1).
4.5 STATISTICAL
METHODS FOR EVALUATION
OF MODEL PERFORMANCE
As noted in Section4.1, mathematicalDPF model that enablesthe prediction of the daylighting
performanceof passivesolar tubular light pipe under all weatherconditions will be developedin this
work. In order to ensurethe computationalreliability of the proposedDPF model, validation methods
have to be applied to assessthe model's validity.
Model validation is conductedthroughoutthis body of work with the aid of establishedstatistical
methods.In theory, data can be manipulatedto produceresults from which almost any conclusioncan
be drawn. Therefore,rather than to rely on a single statisticalprocedure,model evaluationis to be
carried out using various statisticalprocedures.A summaryof the statistical tools usedthroughout this
work is presentedforthwith.
79
4.5.1 Mean bias error (MBE)
The meanbias error (MBE) of a model indicatesthe model's ability to replicate data.In anotherword,
the MBE tells whether or not a given model tendsto overestimateor underestimatethe measureddata.
In present study, the MBE is defined as:
'"(Eestimated- Eactuad
Mean Bias Error, MBE =
no. of observatims
(4.19)
is the estimatedinternal illuminance due to light pipe, Eactual
the measuredinternal
where Iýcstimated
illuminance, and "no. of observations"meansnumber of datapoints.
A lower value of MBE indicatesbetter model performance.A0 value MBE indicatesoptimal model
performance.A positive MBE indicatesan overestimationof measureddata.The converseapplies for
underestimation.Equation4.18 showsthe meanabsolutevalue of the difference betweenthe measured
and predicted data.Therefore,the physical deviation can often be misinterpreted,particularly when it is
usedto describemodel perfon-nanceagainstmeasureddataof low magnitude.
4.5.2 Root mean square error (RMSE)
Root mean square error (RMSE) is widely used to indicate the degree of scatter of the computed data
comparedagainstthe actual data.In this study RMSE is defined as:
Root Mean Square Error, RMSE
Eestimated- Eactual )2
-T(
(4.20)
no. of observations
is the estimated internal illuminance due to light pipe, Eactual
where Esthnated
the measured internal
illuminance, and "no. of observations"meansnumber of datapoints.
80
The greaterthe deviation betweenEestimated
the greaterthe sum of the squareof the
and Eactual
,
difference will be. A low RMSE is indicative of better model performance.A larger RMSE indicates
greaterdispersionof data.
4.5.3 Percentage average deviation (PAD)
As addressed in Section 4.5.1, in some cases MBE can be misinterpreted. For example, for two
mathematical models A and B, when both model have the same MBE, the performance of them can be
different. This is because that the magnitude of the data that the two models handle can be different. If
the data that model A handles is in average several times to that of model B, then the perfon-nance of
does
0
being
MBE
better
The
to
is
B.
A
than
not necessarily
equal
value
of
model
actually
model
indicate a good performance model. Suppose a model predicts largely overestimated value for half of
the observations and gives heavily underestimated value for the other half, the MBE will also be found
to be zero which can lead to erroneous conclusions such as the model is performing exceptionally well.
To overcomethe drawbackof MBE, a suitableaccompanyingstatisticalreinforcementshall be found.
PAD is thereforeintroduced in this study, which is defined as:
Percentage Average Deviation, PAD= -P(100*
I feslimaled-Eaclual II Eeslimaled)
no. of observatims
4.5.4 Slope and the value of the coefficient of determination of predicted versus measured
illuminance
In caseof regressionalanalysis,the techniqueused in the presentwork to fit models aroundmeasured
data,the use of scatterplot of calculatedversusactual data,and the slope of the fitted trend line and the
value of the coefficient of determinationare advisedto provide insight into the performanceof models.
The slope value is indicative of the validity of the model under test. The degreeof validity increasesas
the slope approaches unity. In the case of present study, a slope value lower than I implies that the
model tends to underestimate internal illuminance values due to light pipe, and the converse applies for
81
overestimation.However, the slope value cannotbe usedsolely to evaluatethe performanceof a
model. A model that producelarge scattercan producea unity slope trend line, although the
performanceof the model is actually not well. Therefore,the combineduse of slope and the coefficient
of determination(R) shall be applied to determinethe performance.The value of R2rangesfrom 0 to
1, and it indicatesthe percentageof datapoints that the model can describe.
4.5.5 Histogram of errors
Besidesscatterplot, anotherwidely usedvalidation method is histogram.Histogram plots of
percentagedeviation can be used to comparethe performancesof models.The histogramspresent
graphical representationsof the frequencydistribution of the percentageerror. A given model's
performanceis examinedin two ways. Firstly, the histogramprovides a check regardingthe proportion
of datapoints that fall within specific rangeof percentageerror and secondly,it allows an examination
of the rangeof errors.
Percentageerror = 100 *IE,,
imated-
Eactual I/ Eactual
(4.22)
is the estimatedinternal illuminance due to light pipe, Ea, the measuredinternal
where Eestiniated
njal
illuminance.
82
REFERENCES
1. Lopez, G., Batlles, F. J., Martinez, M., Perez, M. and Tovar, J. (1998) Estimation of hourly beam
solar fiom measured global solar irradiance in Spain, Proceedings of the World Renewable Energy
Conference, 1998
2. Moon, P., and Spencer, D. E. (1942) Illumination from a non-uniform sky Trans. Illum. Eng. Soc.,
37,707-725
3. Muneer, T. (1990) Solar Radiation Model for Europe Building Serv. Eng. Res. Technol., 11(4), 153163
4. Shao, L. (1988) Mirror lightpipes: Daylighting performance in real buildings Lighting Research and
Technology, 30 (1), 37 - 44
5. Perez, R., Seals, R. and Michalsky, J. (1992) Modelling skylight angular luminance distribution from
routine irradiance measurements, IESNA transmission of the 1992 IESNA annual conference
6. Muneer, T. and Zhang, X. (2002) A new method for correcting shadow band diffuse irradiance data,
Journal ofSolar Energy Engineering: ASME, 124
7. Naraghi, M. H. N. (1987) Engineering Notes: American Institution ofAeronautics and Astronautics
83
......... ......
ot
2
2
Figure 4.1 Sunlight of intensity I and elevation ccdescending a 2-D straight light pipe
Figure 4.2 A projected view along the axis of a straight tubular light pipe tube, with light
entering at distance x from the axis followed by its incident on the internal surface at projected
angle I and travels distance d between reflections
84
Figure 4.3 The uniform overcast sky vault devided into 21 patches
Ii
Figure 4.4 Emitted radiation from a surface
85
asl2r
Figure 4.5 The inverse square law
86
ing point
Figure 4.6 The calculation of view factors between a point and a hemisphere surface
87
5. MEASUREMENTS
AND DATA PROCESSING
To enablethe modelling of the daylighting performanceof light pipes, data on the internal illuminances
due to light pipes of various geometricalconfigurationsunder all weatherconditions needto be
obtained.The proposedDPF model (Eq. 4.6) expressedthe daylighting performanceof light pipes as a
function of light pipe configurationsfactors (F.), externalenvironmentalfactors (F,) and internal
distribution geometric factors (Fi). It hasbeenaddressedin 3.5 that to build the proposedmathematical
model, vast datashouldbe measuredin laboratoryenvironmentso as to eliminate the effects of other
factors rather than F., F, and Fj factors.
Other factors rather than F., F, and Fi factors,which can affect the daylighting performanceof light
pipes may include the blocked sky view and shadedsunlight causedby surroundingnatural or artificial
objects,internal reflection related factors (e.g. the colour of the ceiling and walls), the shadingcaused
by interior furniture layout and so on. Once a basic and generaldaylighting performancemodel of light
pipes has beengenerated,the effects of abovefactors can be incorporatedinto or addedto the model.
Therefore,presentstudy focuseson Fg,F, and Fi factors,aiming to producea fundamentalDPF model
of wide applicability.
Before the commenceof large scaleand long term measurements,a trial test on single light pipe was
undertakento preliminarily identify the key factorsthat affect the performanceof light pipes. This trial
test was undertakenin a real building room - the Currie test room. After the key factorsbeing
identified, daylighting performancemeasurementswere undertakenin two sites,namely the
Craighousetest room and the Merchiston test room.
The developmentof light pipe systemhasbeen an on-going process.More monitoring was therefore
carried out to determinethe performanceof newly developedlight pipes so as to examinethe
applicability and adaptability of the proposedDPF model. The latest developedlight pipes
(Monodraught)use a group of new diffusers, which enhancesthe daylight penetrationinto buildings.
Effects of different light pipe diffusers on internal illuminance distribution were investigatedand
correspondingmeasurementswere carried out in Currie test room.
88
5.1 NAPIER SOLAR STATION
Napier University solar station is locatedon the roof the main building at Merchiston campus,Napier
University, Edinburgh. Edinburgh experiencesa temperateclimate and the averagesunshineduration is
1351hours.Merchiston campus,Napier University is situatedon a main road, approximately2 km to
the south-westof Edinburgh.In a5 km radius aroundthe campus,80% of land comprisesof urban and
suburbanhousing and offices whilst the remainderis a mixture of farmland and natural features[1].
Napier University solar station was built as a part of the international daylight measurement
(CIE).
The
de
I'Eclairage
by
Commission
International
launched
(IDMP)
that
the
was
programme
latitude and longitude of the solar station are 55.95N and 3.20'W respectively.The height of the solar
station abovesealevel is I 10m.The local time for Edinburgh is GMT + 0.
The following instrumentation was installed at Napier University solar station. Illuminances are taken
at one-minuteintervals, and are recordedin a PC station.A taperecorderis installed in to the PC so as
to enablethe backup of massivedata sets.
Illuminances
Global horizontal: PRC Krochmann 910GV
Diffuse horizontal: PRC Krochmann 91OS
North-vertical: PRC Krochmann 91OGV
East-vertical:PRC Krochmann 91OGV
South-vertical:PRC Krochmann 91OGV
West-vertical: PRC Krochmann 910GV
89
Shadowband specifications
Napier University solar station employs a Kipp & Zonen CM 121 shadowring with the German
manufacturerKrochmann'sdiffuse illuminance sensor.Adjustment of the shadowring is required for
eachmeasuringday and diffuse illuminance correction factor for the obstruction of the shadering has
to be applied. The shadowband has a radius of 3 I. Ocrnand a width of 5.5.
Figure 5.1 showsthe views of the Napier University solar station.Figure 5.1(a) showsa close-upview
of the installation and the relative position of the instrumentation.The sky diffuse illuminance sensor
and shadowband are shown in the backgroundand the horizontal global and vertical illuminances
sensorsare shown in foreground.Figure 5.1(b) representsa macro view of the stationwith the global
horizontal and vertical illuminance sensorsand sky diffuse illuminance sensorand shadowband
respectivelyshown on the right- and left-hand side of the frame.
5.2 INTERNAL
ILLUMINANCE
SENSORS, DATA-LOGGER
AND STANDS
One Kipp & Zonen pyranometerCM1 1 global irradiancesensorwas used to measurethe global
incident energyto the light pipe installed in Currie test room. The Kipp and Zonen CM1 1 global
irradiancesensoris classified as a "secondarystandard"sensoraccordingto the classification of the
World Meterological Organization.The rangethe CM II is 0- 1400W/m2 with a sensitivity of 4.6
pV/Wnf2. The CM1 I global irradiancesensorhad been calibratedin November 1999by the UK
Meteorological Office.
Six sensorsof two types were usedto measurethe internal illuminancesdue to light pipes. Three
sensorsof SeleniumPhoto-ElectricCells Type-B were suppliedby Megatron Ltd, London. The active
areaand the sensitivity of Magetron Type-B photoelectric sensorsare 3.5 cm2and 0.245 [LA/lux.
Magetron Type-B photoelectricsensorsare of a dimensionof 42MM diameter and 20mm high with
integral cable 2m long. The advantageof seleniumphotovoltaic cells over other cells is that their
responseis very close to that of the humaneye; this makesthem particularly suitablefor use in light
measuringinstruments.Their efficiency as energyconvertersof the total spectrumis not as high as
someother photocells,and so they are not usedas solar cells [2]. The three Magetron Type-B
90
photoelectric sensorsemployedin this study use amplifier that requiresexternal 4.5 Volts AC-DC
power-supply.
The other three sensors were supplied by Kipp & Zonen [3]; the actual component supplied was a Lux
Lite illuminance meter, 54mm diameter x 35mm high with integral cable 3m long. Ile
Lux Lite
consists of a photodiode, a filter, a diffuser and a housing. A resistance shunts the photodiode; this is
done to generate a voltage output. The photodiode, the filter and the diffuser on top determine the
spectral specifications. The diffuser ensures a field of view of 180 degrees, and that angular
characteristics fulfil the so-called cosine response. The sensitivities of the three Lux Lite sensors are
given as 10.32 pV/Iux (±l%), 9.68pV/Iux (±I%) and 10.11pV/Iux (±I%) respectively. The ranges of
the sensors are the same, namely 5±lklx.
A 20-channeldata-loggerwas installed to record the measurementstransmittedfrom the sensors.The
actual componentwas a Squirrel SQ1000Seriesdata-loggersuppliedby Grant Instruments
(Cambridge)Ltd, England [4]. Squirrel SQ1000Seriesdata-loggerreliably measureand record inputs
from a variety and member of sensors,making them suitablefor a wide range of tasksin many
industrial, scientific and researchapplications.SQ1000Squirrel data-loggercan be used as a portable
meter, stand-alonedata-loggeror as a PC baseddataacquisition system.
To enablethe measurementof internal illuminance achievedby various light pipes with bends,one
standon which photoelectricsensorscould be mountedwas used.The use of the adjustablestand
ensuredthat photoelectric sensorsmeasuredthe illuminancesreceivedby a plane that was parallel to
the crosssection of the light pipe tube (end section).The adjustablestandconsistedof two components,
a commonly availablephotographer'stripod and a table. The flexibility offered by the tripod madethe
slope and the distanceof the plane where illuminance sensorswere mountedadjustable.The table was
manufacturedfrom a piece of high-density polystyrene25mm thick, Im wide and 1.5mlong. Prior to
use, the table was painted with a matt black finish to eliminate any light reflection into areaswithin the
sensors'range.This standwas used in Craighousetest room. Another standwas madeto measurethe
internal daylight distribution due to light pipes. This standwas madesimilar to the one used in
91
Craighousetest room, but in a smaller dimensionto be adaptableto Merchiston test room that is
smaller than Craighousetest room.
5.3 DAYLIGHTING PERFORMANCE MONITORING IN REAL BUILDING CURRIE TEST
ROOM
A trial measurementwas first carried out to determinethe decisive factors that directly affect the
performanceof light pipe. The obtaineddatawere to be analysedto reveal the influencesof Fg,F, and
Fj factors on light pipe DPFs.A simple DPF model on the performanceof a single straight light pipe
can thus be built upon the dataobtainedin the trial measurement.The performanceof this simple
model was used as a pre-checkof the sufficiency and validity of the large-scalemeasurementto be
undertakenin Craighouseand Merchiston test rooms.
Since September1999,a 330-mm diameterlight pipe provided by Monodraughthasbeeninstalled on
the roof of a two-storey detachedhousein Currie, I Okmsouth-westof City Centre,Edinburgh. The
roof is free of obstructions.The light pipe is allocatedin a child's bedroom on the top floor. The
bedroom areais a rectangular-shapedspaceof 3.7 x 2.1 x 2.3 m (length x breadth x height). Figure 5.2
showsthe dimensionsof the room and the measurementschemeundertaken.The room has four walls,
all of them coveredwith yellowish-white wallpaper.A small window on wall I (Fig. 5.2 refers) has a
westernaspect.The sizesof the window's two panesare 32 x 71 CM2and 26 x 65 cm,; and the height
of the window's sight line (sill level) is 126cmfrom the floor. Near a comer of the room, there is a door
on wall 2, which is oppositeto wall 1. Two piecesof yellow wooden furniture are locatedalong wall 3.
In anothercomer and along wall 4, a bed is placedunder the diffuser of the light pipe.
The light pipe on test was installed on a north-facing roof, which has a slope of 29* (Fig. 5.3). The
length of the light pipe is 121cm (measuredfrom the top edgeto the bottom rim of the mirror pipe).
The horizontal distancesfrom the diffuser centreto wall 1,2,3 and 4 are 225cm, 146cm, 13lcm and
79cm respectively.
From l't -7 th of May and from 26 th-31"
of May 200 1, monitoring was carried out to record the
external global illuminance and internal illuminance data. For this experiment, the window was
92
coveredwith a thick dark cotton towel, and the door was sealedto prevent any light entering from
outdoors.One Kipp and Zonen CM II global irradiancesensorwas fixed on the ridge of the roof to
measurethe global incident energyof the light pipe under test. Three Megatron indoor illuminance
sensorswere employedto record the internal illuminance in different positions of the room. These
sensorswere fixed horizontally on threestands,all of height = 0.7m; and there was no obstruction
betweenthe light pipe diffuser and thesesensors.During the measurementprogramme,positions of
thesesensorswere changedeachday and correspondingdistancesrecorded.
External global irradiancedataand internal illuminance datawere recordedby a Grant (Squirrel) datalogger on a minute-by-minutebasisthroughoutthe day. In the two weeksof measurementabout 23490
points of datawere obtained,which provides a sufficient databasefor the trial mathematicalmodelling
procedureto be carried out.
The measurement carried out included external global irradiance, internal illuminance and distances
from survey points to light pipe diffuser, with corresponding date and time recorded. Sky clearness
index and solar altitude were calculated using the algorithm provided by Muneer [5]. To ensure the
database reliability, data were discarded for solar altitude less than 10', or for k, ý! 1. Out of the 23490
data points, 21147 data were selected to develop and validate the proposed model.
5.4 DAYLIGHTING
CRAIGHOUSE
PERFORMANCE
MONITORING
UNDER ALL SKY CONDITIONS -
TEST ROOM
A purposebuilt test facility was establishedwithin the Craighousecampusof Napier University.
Within the opengroundsthe test room was locatedon flat ground with an open southernaspect.The
test room was 3.Omlong x 2.4m wide with a height of 2.5m. Inside the test room all four sidesand the
roof had hardboardcladding nailed to the frame. All edgesand the door surroundswere coveredwith
heavy papertape to seal the inside spacefrom ingressof daylight. Sophisticateddata-logging
equipmentinside the room was protected from the effects of weather.Ile room was equippedwith
power supply unit to support a PC, data-loggerand multiple indoor illuminance sensors.
93
To enablethe performancecomparisonbetweendifferent light pipes, the test room was designedfor
easeof installation of light pipes with various designs.Initially, a total of eight light pipes with varied
configurations(straight runs plus thosewith multiple bends)were suppliedby the project co-sponsor.
The diametersof theselight pipes were 21Omm,330mm, 450mm and 530mm. All the light pipes use
clear polycarbonatedomes,610mm long silverised aluminium.tubesand opal polycarbonateddiffusers.
Continuousperformancemonitoring was undertakenover a period from 10thMay to 15thSeptember,
2000. Daylighting performanceof 15 light pipes of various configurationsunder all sky conditions
were carried out during thesefour months.Details of all testscompletedare listed in Table 5.1. The
light pipe diameter,length, numberof bendsand length of bends,if any, were noted. Illuminance
sensorswere arrangedon floor or on standswith their respectivedistancesto the centreof light pipe
diffuser recorded.External horizontal global irradiancedatafrom the pyranometer(Kipp & Zonen
CM1 1) and internal illuminance data from threephotoelectricsensors(Megatron Type-B) were
sampledevery ten secondsand the averagedminute-by-minutedatawere storedby the data-logger.
The desiccantof the Kipp & Zonen CM II pyranometerhad beencheckedbefore and during the
measurementsand changedwhen necessaryso as to ensurethe accuracyof the externalglobal
illuminance measurements.The systemtime of Grant Squirrel data-loggerwas synchronizedaccording
to solar time.
After the measurements, data obtained were processed and quality controlled. External illuminance, kt
and ot, were calculated using the algorithm provided by Muneer [5]. To ensure the database reliability,
data were discarded for cc,:ý 10', or for kt ý! 1. A total of 65 270 data points for all light pipes
configuration were made available for mathematical modelling.
94
5.5 DAYLIGHTING
MERCHISTON
PERFORMANCE
MONITORING
UNDER ALL SKY CONDITIONS
-
TEST ROOM
A new test room was built upon the roof of the main building ("Main building" roof) at Merchiston
campusof Napier University. The test room was locatedin the central part of the roof and has a
completeopen view to the southernsky, and 95 per centsof the whole sky hemisphere.The test room
was 2m wide and 2m long with a height of 2m. Inside the test room all four sidesand the roof had
hardboardcladding nailed to the frame. All edgesand the door surroundswere coveredwith heavy
paper tapeto sealthe inside spacefrom ingressof daylight. Internal illuminance sensorsand datalogger equipmentinside the room were protectedfrom the effects of externalenvironment.The room
was not equippedwith power supply, becauseGrant data-loggerusessix AA1.5V batteriesand three
Kipp & Zonon Lux Lite indoor illuminance sensorsdo not require power supply.
The test room was designedfor easeof installation of light pipes with various designs,so as to to
light
four
light
between
different
Initially,
total
the
pipes
a
of
pipes.
comparison
performance
enable
light
Omm,
diameters
21
in
The
diameters
installed
these
the
test
pipes
were
of
room.
were
with varied
330mm, 450mm and 530mm.All the light pipes use clear polycarbonatedomes,610mm long silverised
aluminium tubesand opal polycarbonateddiffusers.
Continuous performance monitoring was undertaken over a period from 28ý' May to 29h August, 200 1.
Daylighting performance of 10 light pipes of various configurations under all sky conditions were
carried out during these three months. Details of all tests completed are listed in Table 5.2. The light
pipe diameter, length, number of bends and length of bends, if any, were noted. Illuminance sensors
were arranged on floor or on stands with their respective distances to the centre of light pipe diffuser
recorded. The relative position of each testing point where each illuminance sensor seats to the light
pipe being measured was also recorded. External horizontal global iffadiance data from the
pyranometer (Kipp & Zonen CM 11) and internal illuminance data from three photoelectric sensors
(Kipp & Zonon Lux Lite) were sampled every ten seconds and the averaged minute-by-minute data
were stored by the Grant Squirrel data-logger.
95
External global horizontal illuminance datawere measuredat Napier University CIE IDMP solar
station.Napier University solar station is establishedon the "South workshop" roof at Merchiston
campus,Napier University. Both the test room on the "Main building" roof and the solar station on the
"South workshop" roof have open view to the sky hemisphere.The horizontal distancebetweenthe two
roofs is about 150 m. Napier University CIE IDMP solar station usessolar time as systemtime. The
systemtime of the Grant Squirrel data-loggerusedto record internal illuminances due to light pipes
within Merchiston Campuswas synchronizedaccordingto the systemtime of Napier University CIE
IDMP solar station.
After the measurements,dataobtainedwere processedand quality controlled. External illuminance, kt
and (x, were calculatedusing the algorithm provided by Muneer [5]. To ensurethe databasereliability,
datawere discardedfor cc,:5 10*, or for k, ý: 1. A total of 22 270 datapoints for all light pipes
configuration were made availablefor mathematicalmodelling.
5.6 INTERNAL
DAYLIGHT
DISTRIBUTION
BY LIGHT PIPES - CRAIGHOUSE
TEST ROOM
From 30thOctober2000 to 14'hJanuary2001, an eight-weektest was carried out in Craighousetest
room to investigatethe internal daylight distribution due to light pipe with different configuration and
type of diffuser. Eight testswere carried out in the measurements.Table 5.3 showsthe compositionof
the tests.
Before the commenceof the test, all the light pipes (MonodraughtSunpipe)installed in the Craighouse
test room had their diffusers coveredwith black heavy plastic sheetand securedwith adhensivetape.
The cover was removed from the light pipe to be testedand the test equipmentwas placeddirectly
beneaththe light pipe diffusers.
The diametersof the light pipes were noted and six sensors(including three Kipp & Zonen Lux Lite
sensorsand three Megatron Type-B sensors)were arrangedin an array being equispacedon the same
diameter.The six sensorswere fixed upon a table sustainedby a tripod. The table was manufactured
from a piece of high-density polystyrene25mm thick and sky-blue in colour. Prior to use, the table was
painted with a matt black finish to eliminate any light reflection into areaswithin the sensors'range.it
96
was important to have the planewhere sensorswere fixed perpendicularto the light pipe axis to ensure
that all sensorswere at an equaldistancefrom the diffuser, the adjustabletripod was usedto ensurethis
condition was achieved.
5.7 DIFFUSER COMPARISON
CURRIE TEST ROOM
-
To study the effect of light pipe diffuser type on light pipe daylighting performance,a 330 min
diameterlight pipe provided by Monodraughtwas installed in the Currie test room. The object of these
testswas to comparethe performanceof the opal diffuser againstflat designclear diffuser. The opal
diffuser takesthe form of a white polycarbonateconvex shapedome,which diffuses the light evenly
into the interior space.The flat designclear diffuser is madeof translucentplastic material with crystal
effect finish and flat end.The latter type of diffuser is usedto improve the daylight transmissionof
light pipes even further, albeit having a strongerdirectional component.
For three days from 28"' to 30'hMay 2001, the daylighting performanceof a 330 nun diameterlight
pipe with flat diffuser was monitored.The externalglobal irradianceand internal illuminancesat three
points at varying distancesto light pipe diffuser centrewere measuredsimultaneouslyon a minute-byminute basis.The three indoor Megatron illuminance sensorswere installed correspondingto the
measurementscarried out on the light pipe with the older opal diffuser (seeSection5.3). A total of 4
300 datapoints were thus obtained.Daylight penetrationfactor DPF, defined as the ratio of internal
illuminance to external illuminance for flat diffuser were calculatedfor all datapoints.
97
REFERENCES
1. Kinghorn, D. (1999) Solar illuminance modelsbasedon other meteorological data Ph.D. Thesis,
Napier University, 64
html, Megatron Ltd, London, UK
2. hn: //www. megatron.co.uk/homepaRe.
3. Kipp & Zonen B. V. (2001) Lux Lite Instruction Manual, Rontgenweg,Netherlands
4. Grant Instruments(Cambridge)Ltd. (2000) Squirrel Data-logger Manual, Cambridgeshire,UK.
5. Muneer, T., Abodahab,N., Weir, G. and Kubie, J. Windowsin buildings thermal, acoustic, visual
and solar performance. Oxford: Architectural Press,2000.
98
(a)
(b)
Figure
5.1 Napier
University
CIE First-Class
solar station
99
-
***44%w
f2l%
DOOR; %,j
--
[ -]
SUN-PIPE
DIFFUSER;
SENSOR;
WINDOW;
414
CENTRE
OF THE WINDOW
Figure 5.2 Schematic of the Currie test room and light pipe system
100
Kipp & Zonen CMI 1 Solarimeter
Mirrored light-pipe
Transparent
collector
p
Light diffuser
Figure 5.3 Light pipe system installation
in Currie, Edinburgh
(P=29')
101
Table 5.1 Designs of light pipes that were monitored in Craighouse campus, Napier University
Design
Diameter, mm
Type
1
210 straight
2
3
4
5
6
7
8
9
10
11
12
13
14
15
210 straight
210 elbowed
210 elbowed
330 straight
330 straight
330 elbowed
330 elbowed
330 elbowed
330 elbowed
420 straight
420 straight
530 straight
530 straight
530 elbowed
Length, nun Bendsnumber
60
N/A
120
60
60
60
121
60
60
60
60
120
60
60
1201
601
N/A
1
2
N/A
N/A
1
2
3
4
N/A
N/A
N/A
N/A
1
Table 5.2 Designs of light pipes that were monitored in Merchiston
Design
Diameter, nun
Type
1
210 straight
2
210 straight
3
210 elbowed
4
330 straight
5
330 straight
6
330 elbowed
7
330 elbowed
8
420 straight
,
9
420 1straight
10
530 1straight
Campus, Napier University
Length, mm Bends number
60
N/A
120
60
60
121
60
60
120
60
60
N/A
2
N/A
N/A
2
4
N
N/A
N/A
Table 5.3 Internal daylight distribution tests on light pipes installed in Craighous Campus,
Napier University
Design
Diameter, mm
Type
1
2 10 straight
2
3
41
5
6
7
8
330 straight
330 straight
420 straight
420 straight
420 straight
530 straight
5301straight
Length, cm
Diffuser type
60 Clear diffuser
60 Opal diffuser
60 Clear diffuser
60 Opal diffuser
120 Opal diffuser
120 Clear diffuser
60 Opal diffuser
601 Clear diffuser
102
6. MATHEMATICAL
MODELLING
The researchstrategyfor the mathematicalmodelling of light pipe daylighting performancein terms of
DPF (Daylight PenetrationFactor) is straightforwardand canbe divided into three main blocks:
(1) Parameterisation, to identity the most decisive factors that affect the daylighting performance
of light pipe systems;
(2) Framework, to choose a proper mathematical expression for proposed models;
(3) Formula fitting;
(4) Evaluation of models and modification to the models.
Figure 6.1 shows the system structure of the development of the proposed mathematical models and the
procedure to validate the models.
Above researchstrategytreatsa light pipe systemas a black box and doesnot care the physical model
of the system.The main approachto implement such a strategyis to combine an empirical
mathematicalexpressionwith a set of coefficients derived from a large, high-quality and versatile
highly
is
it
is
database.
The
this
that
simple,
and
of
strategy
practical
major
advantage
experimental
efficient. The possiblelimitation of this strategyis that it seemsto be a non-physicalmathematical
model. To investigatethe validity of the researchstrategyand to evadepotential involved risks, a
stagedtactic was adoptedto examinethe strategy.The main aims of the two stagesare outlined below:
(1) Stage 1. According to the proposedstrategy,a simple yet accuratemathematicalmodel for a
straight light pipe will be developed.After that, numerical error analysiswill be applied to verify the
validity of the straight light pipe model, DPF. The analysisresultsobtainedin this stagewill determine
the sufficiency and the necessityof the proposedstrategy,and hencewill decidewhether the research
led by this strategyshould go onto the secondstage.Further work to improve the performanceof DPF
model and to extent the model to all light pipes can then lead the researchinto its secondstage.
103
(2) Stage11.The secondstageis a logically extendingand deepeningof the researchcarried out
in stageI. It will include threemain blocks, they are:
Firstly, to build generalmathematicalDPF model basedon the methodologyverified in stageI.
Secondly,to target a more accurateperformanceprediction that takesaccountof the causesof system
bias identified in stageI. Advanced solar radiation theoriesand techniqueswill be applied in this stage
of research.It is intendedthat the completion of this stageof researchwill further improve the overall
accuracyand reliability of the proposedmodel. Finally, validation of and modification to the general
mathematicalmodel DPF basedon independentdata will be undertaken.
6.1 LIGHT
PIPE DESIGN AND DPF
MODELLING
A precisedesignof light pipe systemis only possiblevia a thoroughunderstandingof the illuminance
transmittanceof the system.Light pipes are designedto collect light from both the sky and the sun.
Sincethe external environmentalfactors suchas sky clarity, sky-diffuse radiancedistribution and sun's
position changedynamically, the light pipe's overall efficiency of illuminance transmissionalso
changescontinuously.
The determinationof light pipe systemconfiguration aimed at achieving a given internal illuminance
under given sky conditions would be the task of light pipe designers.It may be logical to assumethat
light pipe system'silluminance performancewould dependon: (a) geometricalfactors suchas its
length, diameter,number of bends,angle of bend and the diffuser type, and (b) the abovementioned
externalenvironmentalfactors.Thus, a mathematicalmodel that encompassesthe abovefactors would
be desirable.
The conceptof light pipe Daylight PenetrationFactor (DPF) hasbeen explainedin Chapter4, Section
4.1. DPF, (),, ) is defined as the ratio of a given point's internal illuminance to the total external
y.,
illuminance for a given point with coordinates(x, y, z),
E
internal (x, y, z)
= DPF, (x,, ) XE
external
I ()A
is
is
internal
illuminance
P(,,
E
the
the
the
total
at
given
external
where E internal
point
(x.y,z)
y,,), external
illuminance and DPF(,,, ) is the light pipe Daylight Penetration Factor for the given point.
y,,
Light pipes are daylighting devicesthat utilise both sunlight and skylight. It hasbeenreportedthat
sun's position has an effect on light pipe's perfortnance[I]. When the sky is clear, the solar altitude ct,
influencesthe transmittanceof sunlight within the light pipes. However, when the sky is overcastor
part-overcast,the influence of sun's position becomesweakersince sunlight may no longer be the
major componentof externalglobal illuminance. Hencein the presentstudy the transmittanceof light
pipes was initially consideredto be a function of cc,and the sky clearnessindex k, (defined as the ratio
of global to the extra-terrestrialirradiance).
According to the research strategy addressed in Section 6, DPF modelling for light pipes were
undertakenin two steps.The first step is to develop a DPF, model basedon the performancemodelling
of a straight light pipe [4], which is describedby Eq. 6.2,
DPF, (,,, ) =J(a, k, D)
y,,
, ,
(6.2)
where D is the distancefrom light pipe diffuser centreto a given position P(,,,y, ). Eq. 6.2 is only
for
light
for
light
designs
DPF
therefore
serve
as
model
pipe
and
cannot
a
general
applicable straight
pipes of other configurations.A generalisedperformancemodel that coverslight,pipes of all typical
factors.
design
factors
to
take
as
well
as
environmental
ought
account
of
geometrical
configurations
The secondstep is therefore,to build generalDPF modelsbasedon the performancemeasurementsof
light pipe of various designsunder all weatherconditions.This requiresone year's measureddata to
build the model and anotherone year's independentlymeasureddatato validate the model. The
building and validation of DPF models are reportedin the following sections.
105
6.2 THE DPF
OF A STRAIGHT
LIGHT PIPE
6.2.1 Parameter analysis
It may be shown from first principles [2] that the illuminance receivedat any given point from an
elementalareaof a luminous sourceof a finite size is proportional to the product of the luminous
intensity of the elementalarea(1), the respectivecosinesof the anglesof emittance(0,) and incidence
(0) and the inversesquareof the distance(D) betweenthe elementalareaand the point of incidence
(seeEq. 6.3).
IlluminanceocID2
Cos 0, Cos Oi
(6.3)
Theareaof theCurrietestroom(Section5.7)was7.8m2while thelight pipeluminousdiffuserhada
diameterof 330mm. Hence,the diffuser cannotbe consideredas a point source.Furthermore,
observationshave indicated that the diffuser was of non-uniform luminosity.
Thereforeto obtain a preciseestimateof the luminanceenvironmentof the test room under discussion,
one has to integrateEq. 6.3 point-by-point within the room, taking accountof the variation of luminous
intensity of the diffuser. However, a detailedproceduresuch as this is impracticableand unwarranted
for designpurposes,in particular by an industry that is in a stageof infancy. In view of the above
discussionand as a first approximationthe relationshipbetweenDPF
distance
is
D
the
and
y,,)
presentlyproposedas that given by Eq. 6.4,
DPF, (),, ) =A*(I/D)
y,,
(6.4)
where DPF ý (.,.y., ) is the light pipe daylight
penetration
factor at the point P (,,,
due
to
the
particular
),
y,,
straight light pipe in test, A is a parameter that is dependent on sun's position
distance from point
P (,,,
light
diffuser.
pipe
)to
6.3 is subsumed in Eq. 6.4 by adapting an empirical
and sky clarity,
Note that the integral calculation
D is the
suggested via Eq.
approach.
106
Figure 6.2 showsthe scatterplot of measuredDPF againstD. Although the generaltrend seemsto be
,
in order, the percentagedeviation for any given distanceof the daylight penetrationfactor may be very
large. Figure 6.2 thereforesuggeststhat other non-geometryfactors may be involved. Presentlythe role
of k, and (x, in improving the prediction of DPF hasbeen investigated.
To explore the relationship between DPF and cc,,data sets recorded by sensors at a distance of 155cm
,
for different time frames were selected. A total of 258 data points were employed to plot DPF as a
,
function of solar altitude. Figure 6.3 shows this scatter plot. It is evident that for any given cc,a large
scatter is generated, e.g. the percentage deviation of DPF is 120% when cc,::ý;41.5'. This behaviour
further
factor.
A
daylight
the
that
penetration
affect
weather parameters additionally
suggests
demonstration of the influence of weather condition's on DPF . is shown by plotting DPF , against sky
for
A
D=155cm.
6.4
kt
for
48.5':
Figure
index
5
<49.5'.
strong
plot
shows
such
a
scatter
(x,
clearness
relationship between the two variables is evident.
6.2.2. Modelling and validation
It was demonstrated in the above section that DPF, is influenced by D, c(, and k,. Presently, a model
given by Eq. 6.5 is proposed:
DPF, = (aoo+ aoI* cc,+ a02* lXs2+ a03* k, + a04* k, 2+ ao5* cc, *
2*k,
*
a06
(Xs
+
a07 * (Xs *kt2+
aog *a
S2
*kt
2)
/D2
(6.5)
Equation 6.5 was further simplified and its validity evaluated.The simplified model is:
DPF, = (ajo + all * (x, + a12* (x, 2+ a13* k, + a14*k, 2+ a15* ot, * k,) /D2
(6.6)
Values for the coefficients used in Eqs. 6.5 and 6.6 are listed in Table 6.1.
107
Equations6.5 and 6.6 presenta genericprocedureto associateDPF to the two widely known
parameters,namely cc,and k, that influence daylight receipt. The equationscover the entire range of k,,
i. e. from heavy overcastwhen kt ;L-0.2 to clear skieswhen kt > 0.6. Further precision may be obtained
by selectingspecific formulations for overcastand clear skies.In this respectrecommendationis made
herein for more researchwork.
Model validation was undertakenvia estimationof Mean Bias Error (MBE), Root Mean SquareError
(RMSE) and PercentageAverage Deviation (PAD):
X(Eetimated - Eactuad
no. of observatims
Root Mean Square Error, RMSE =
Percentage Average Deviation, PAD
ý:(Eesiýated - Eactual)2
:
bservatio
no. of 6
ns
E( 100
--
Equation 6.7 is usedto obtain estimatedinternal illuminance E
I/
Eactual
Eetimated
timatedno. of observations
E,,
for
P (,,, ),
a
given
position
(x,
estimated
y,z)
y,,
where G is the instantaneousexternalglobal irradiance,and KG is the global luminous efficacy
(lumen/Watt). KGis computedfrom a formulation provided by Muneer and Kinghorn (Eq. 6.8) [3]:
E
DPF
=
(x,y,z)
estimated
, (,, y, )*G*
KG = 136.6 -74.541k, +57.3421k, 2
KG
(6.7)
(6.8)
Based on above procedure using Eq. 6.5 calculated internal illuminance were plotted and regressed
against corresponding measured data to determine the model's performance. Results of this comparison
108
are shown in Fig. 6.5. The slope of the fitted trend line is 0.973, and the coefficient of determinationR2
is 0.929. The MBE was found to be -2lux and RMSE 27lux which is 5% of the maximum value of
measuredilluminance (512lux) and 20% of mean illuminance (138lux). Percentageaveragedeviation
was noted as 21%. Calculatedinternal illuminance data were once again plotted againstmeasured
values for 11 different positions within the test room. 'D' for thesepositions range from 154cmto
212cm. Figure 6.6 showsthis plot for D= 194cm.Table 6.2 showsthe slope of the regressedline and
other error statisticsfor six values of D.
Similar validation procedureswere applied to Eq. 6.6 to examineits performance.In this casethe slope
W
0.930.
The
determination
found
be
fitted
line
0.970,
the
to
the
trend
was
and
coefficient
of
was
of
MBE was -2lux and the RMSE 28lux, which is 5% of the maximum value of measuredilluminance
(512lux) and 20% of meanilluminance (138lux). Percentageaveragedeviation was once again found
to be 21%. Thus, the simple model representedby Eq. 6.6 has comparableperformanceto the more
involved model (Eq. 6.5). Table 6.3 showsthe validation resultsfor 7 positions at which internal
illuminance were recorded.
6.2.3 Summary
Measurementsof a single straight light pipe installed in a detachedhousein Edinburgh hasbeen
undertaken.Experimental analysison the effects of different factors that influence the daylighting
performanceof light pipe systemhasbeencarried out, Basedon the comparativeanalysis,the most
decisive factors havebeen identified and a "best" form of mathematicalexpressionhasbeen
determined.A DPF, model for a particular light pipe hasbeenestablished.Two articles, one on the
DPF, model and the other on light pipe performancemonitoring have beenpublishedon thejournal of
Lighting Researchand Technology (CIBSE) and on the internationalRenewableEnergy for Housing
ConferenceProceeding[4,5].
It has beenconcludedthat the internal illuminance at a given point in a room where light pipes are the
only lighting systemcan be estimatedusing Eqs. 6.5 and 6.6. Reasonablygood agreementhas been
obtainedbetweenthe predictedinternal illuminance and experimentalmeasurements.The Root Mean
SquareError (RMSE) of calculatedinternal illuminance, the Mean Bias Error (MBE) and the
109
percentage average deviation have been found to be 27lux, -2lux and 21% respectively. The slope of
the best fitted trend line was noted as 0.97 and the coefficient detennination R2was found to be 0.93.
It is henceconfirmed that the proposedresearchmethod is effective and valid. Similar measurements
and modelling procedure will be applied to all types of light pipes available to obtain a general
mathematicalmodel.
6.3 STRAIGHT
LIGHT PIPE
DPF MODEL (S-DPF)
Sincethe DPF, model hasbeenverified, DPF modelling for all straight light pipes were carried out. It
was thought that an appropriatemodel for straight light pipes with differing geometricalconfigurations
should take accountof the contribution of light pipe's length and diameteras well as a, and kt. The
proposedgeneralisedformulation that includes 12 coefficients (ao- alo and in) is given by Eq. 6.9,
S- DPF(.,, = (a, + a, k, + a, a, + a, k, a, + a,,kl2as + a, k, tr
)
Y,:)
P
(a7 +a, A, +ag cot a, +a,, A,
co'a)R
2
(HID)'
ID
s2+a,
k12 as 2
(6.9)
2
R is the radius of the light pipe, p the light pipe surfacereflectance,Ap the aspectratio (defined as the
ratio of light pipe length to diameter)and H the vertical height of light pipe diffuser abovethe working
plane. Values for the coefficients usedin Eq. 6.9 are given in Table 6.4.
It may easily be shown that DPF(,,, ) is proportional to the light pipe's sectionalareaand this accounts
y,,
for the inclusion of the R2term in Eq. 6.9. It may be recalled that the inclusion of (x, and k, and D2
tcnns has alreadybeendiscussedwith referenceto Eq. 6.5.
What follows now is a justification of the remainderof the terms included within Eq. 6.9. As a daylight
reflecting device, the light pipe's transmissionis affectedby the reflectanceof its interior coating
material. Basedon physical reasoningpresentedin Section2.4, it is possibleto show that a light pipe's
transmittanceis a function of the number of reflections required for a ray of light to descendthe pipe
and its reflectance(Fig. 6.7). The higher the reflectanceof the pipe's interior surface(p), the higher the
110
light pipe's daylight transmittance.Edmondset aL [1] reportedthat for sunlight of any given intensity,
the number of reflections required is proportional to A,, and cot(x,,where Ap is aspectratio defined as
the ratio of light pipe length to its diameterand cc,the solar altitude. Therefore,a linear function that
combinesAp and cotoc,has beenpresently employedto accountfor the number of inter-reflections
occurring within the light pipe. This explains the secondfactor in Eq. 6.9,
(a7+asAp+ag
cot a, +a, OAP cot a, )
namelyp
A considerationof the mannerof the spreadof daylight by light pipe diffusers within interior spaces
led to the adoption of the last factor in Eq. 6.9, i. e. (H I D)' ID2, where 1:ý rn: ý2. For a given point in
space,to obtain its illuminance resulting from a point or finite light source,the inversesquarelaw and
the cosine law must hold. However, if a light pipe diffuser is to be consideredas a point light source,
the cosinelaw shouldbe applied only once andhencem=1; while on the other hand if the diffuser
could be treatedas a finite light source,then the cosinelaw must be applied twice, once for the
emanationof light and the other for its incidence(or projection) on the horizontal plane. This requires
in to be equalto 2. Thus a compromisewas achievedby using a variable in. The "JID
term
embodiesthe application of the inversesquarelaw.
Using the Craighousedataset, Eq. 6.9 was fitted. Good agreementbetweenthe measureddataand
calculatedvalues was obtainedand in this respectFig. 6.8 showsthe scatterplot of the predicted
internal illuminance againstmeasureddata.The trend line was found to have a slope of 0.98 and the
coefficient of determinationwas noted to be 0.95.
Model validation was also undertakenby estimationof the Mean Bias Error (MBE), the Root Mean
SquareError (RMSE) and the PercentageAverageDeviation (PAD). The MBE was found to be -I lux.
The RMSE was 27lux which was 2% of the maximum illuminance (I 187lux) and 15% of the mean
illuminance (177lux). The PAD was found to be 12%.Resultsare summarizedin Table 6.5.
To facilitate the use of the S-DPF model, Eq. 6.9 was further simplified and its validation was
undertaken by estimation of MBE, RMSE and PAD. The simplified S-DPF model is,
III
S- DPF(ý,,, = (a, + a,k, + a, tr.,),o
)
)
(a3 +a, Ap +as Cot a, +a64p Cot a, )
R'(HID)'ID'
Values for the coefficients used in Eq. 6.10 are listed in Table 6.4. Calculatedinternal illuminance
basedon the procedureusing Eq. 6.10 were plotted and regressedagainstcorrespondingmeasureddata.
The slope of the best-fit trend line is 0.98, and the coefficient of determinationR2is 0.95. The MBE,
RMSE and PAD for the simplified S-DPF model were found to be -31ux, 29lux and 13%respectively
(Table 6.5).
6.4 ELBOWED LIGHT PIPE DPF MODEL (E-DPF)
To predict the DPF(,,, ) of elbowed light pipe systems (30-degree bends), the energy loss due to each
y,,
bend has to be considered. The length of each bend (Lb) and the number of bends (N) have been
accounted for by the use of an equivalent-length factor (fl,,,) and the energy-loss factor (/i,,,j within Eq.
6.11. Lb andfl,,, are subsumed within a modified expression for Ap,. The factor
used in
Eq. 6.11 accounts for the overall transmittance efficiency of the N bend(s),
E- DPF(.,, =(a, +a, k, + a2er.,+ a3klas+a4kl2as+a, k,a. 2 + a, k,2a.,2)
Y,
z)
(a7
+agA, +ag cot a, +a, ýA,
,D
co'a)R 2(l
-fl,,,
)"(HID)'ID
2
(L
fl,,
/
Ap,
Lb)
2R andL is thelengthof straightlightpipe,fl,, theequivalent-length
+
where =
factor, Lb the sum of the linear lengthsof all bendsand R the radius of light pipe.fl,,,, is the energy-loss
factor for each30-degreebend, most commonly usedin a light pipe system.Values for the coefficients
used in Eq. 6.11 are listed in Table 6.4.
Using an optimisation procedure,regressedcoefficients in Eq. 6.11 were determined.The "best" value
forfl, wasfoundto be 0.65andthevalueforf,.. wasfoundto be 0.2,whichis in goodagreement
with
Cater'sstudy [6].
The performance of the E-DPF model was then evaluated using MBE, RMSE and PAD. The MBE was
found to be -2lux. The RMSE was 23lux which was 2% of the maximum ilIuminance (931lux) and
112
22% of the meanilluminance (1031ux).The PAD of the estimatedinternal illuminance was found to be
25%. A scatter plot of the calculated against measured internal illuminance is shown in Fig. 6.9. The
slope of the trend line was found to be 0.97 and the coefficient of determinationwas noted as 0.97.
Eq. 6.11 was further simplified and the simplified E-DPF is given below,
E
-DPF
(.,, Y,z)=(a,
+a,
k, +a2
(a3+a4.4.
+as Cot a, "Oý
cota)R
2 (1
)N
(HID)'
s)P
ID
2
(6.12)
Values of the coefficients used in Eq. 6.12 are shown in Table 6.4. The MBE, RMSE and PAD for the
simplified E-DPF model are-31ux, 25lux and 24% respectively.The calculatedinternal illuminance
due to Eq. 6.12 were regressedagainstmeasureddata.The slope of the best-fit trend line was found to
be 0.97 and the coefficient of determinationwas noted as 0.97. Resultsare shown in Table 6.5.
6.5 LIGHT PIPE VIEW FACTOR DPF MODEL (V-DPF)
The presentlyproposedS-DPF and E-DPF modelsdescribethe internal illuminance distribution of
light pipes using the factor (H / D)' /D2. The "best-fit" value for parameterm was obtainedas 1.3.To
validate the sufficiency of the expression(H / D)' /D2 in describingthe light pipe internal illuminance
distribution characteristics,anotherapproach,namely the "radiative view factors" methodhasbeen
applied to enablea performancecomparisonbetweenthe two different approaches.
The view factor betweenany two surfacesis defined as that fraction of the radiative energyleaving an
emitting surfacethat is interceptedby the receiving surface.A V-DPF model is defined herein as a DPF
model that usesview factor method to describeinternal illuminance distribution within room. The
proposedview factor model V-DPF of a straight light pipe is shown in Eq. 6.13, where F, (,,y,,) is the
view factor betweenthe ceiling mounted light diffuser and the given point P(,,,
y,,) .
V-DPF(,.,,,
+ak,
+aa,
=(ao
)
(a, +os.4, +ag cot a, +atoA,
2
cot"')R
JO
'a,
2
la,
2)
k,
+ak, a., + ak,
+ak, a, +a,
(6.13)
113
The method for calculating the view factors from differential areasto sphericalsegmentsis given by
Naraghi [7]. The entire formulation has been provided in Section 4.4.3. However, only case numbers
III and V are of interest within the present context.
Using the Craighousetest room databasefor all straight light pipes, the view factor F, (.,,,,) for eachdata
point has beencalculatedand the value of the coefficients in Eq. 6.13 have beenre-fitted. Fig. 6.10
showsthe scatterplot of the estimatedinternal illuminancesdue to the V-DPF model againstthe
measureddata.The RMSE and MBE for the V-DPF model were found to be 52lux and -9lux,
correspondingto 27lux and -1lux for the V-DPF model (Eq. 6.13). The slope of the trend line for a plot
of calculatedversusmeasureddatawas found to be 0.94 and the coefficient of determinationwas 0.86.
The correspondingfigures for the V-DPF model (Eq. 6.9) were 0.98 and 0.95. Resultsare shown in
Table 6.5.
6.6. PARAMETRIC ANALYSIS
In the modelling process, a number of environmental and geometrical factors that influence the
daylight transmissionof light pipes have beenidentified. In this sectiona parametricanalysisof those
factors is presented.
6.6.1 Effect of (x, and kt
It was shown abovethat cc,affects the DPF by altering the number of inter-reflectionswithin light
pipes. When (x, increases,the number of inter-reflectionsdecreaseswhich results in a higher
transmittance.However, when kt changes,the extent to which a, affects DPF also changes.Figure 6.11
showsthe variation of S-DPF and E-DPF againsta, for varying weatherconditions. It was noted that
DPF showsan increasinglystrongertrend with cc,for clear sky conditions.
114
6.6.2 Effect of R and L
For any given (x, and k,, the squareof the radius of a light pipe, R2affects the light pipe's external
illuminance admittance.Furthermore,the aspectratio of light pipe A. (=L/2R) and cc,influence the
light pipe's transmittance. Figure 6.12 presents this functional variation.
6.6.3 Effect of distance D and diffuser height H
The DPF model showsthat light pipe's performancestrongly dependson D, namely the distance
distance
between
H,
betweenlight pipe diffuser centreto the given point P(,,,
the
the
vertical
and
y,,)
diffuser centreto the working plane. In Eqs. 6.9,6.10,6.11 and 6.12, the best-fit value for the
like
light
in
be
indicates
found
1.3.
This
that
to
a
work
more
pipes
real
applications,
m
was
coefficient
light
by
internal
illuminance
finite
The
light
than
a
pipe
achieved
a
area.
a
source
of
point
sourcerather
systemwith an opal diffuser is proportional to (H/D)113and inverselyproportional to D2.
6.6.4 Effect of light pipe bends
In Eqs. 6.11 and 6.12, the best fitted value forf,.. was found to be 0.20, which meansthat each30degreebend looses20% of energyduring daylight transmission.For a light pipe with N bends,the total
wherefjý,s= 0.2. The use of bends
energytransmittanceof light pipe bendsis therefore(I_fICSS)N,
increasesthe value of the aspectratio and thus it reducesthe daylight transmittance.Figure 6.13 shows
the comparisonof DPF for a 600mm-long,520nim-diameterstraight light pipe with an increasing
number of bends.
6.6.5 Effect of internal reflection
The internal surfaces(ceiling, roof and floor) of the Craighousetest room were painted white which
has a high reflectance,the assessmentof the contribution of internal reflected illuminance is therefore
of the contribution of internal reflection on DPF. In the absenceof
necessaryto enablean assessment
any other information regardingthe inter-reflection of diffuse as well as beam illuminance within
rooms and also bearing in mind the fact that light pipes are primarily providers of diffuse illuminance,
115
the internal reflection characteristicsof light pipes were treatedas being of similar order as windows.
Therefore, for the Craighousetest room, the contribution of internal-reflectedilluminance to the total
illuminance that is receivedat survey points can be qualitatively assessedby comparing it to that of a
window operatingunder similar conditions.
The surfacereflectanceof the test room hasbeenmatchedusing the CIBSE Lighting Guide [8] and was
found to be 0.74. By abbreviatedanalysis,the contribution of internal reflection to the light pipe DPF
of largestdiameter(0.53m) light pipe was obtainedas only 5% of the total DPF using the chart given
by Muneer [9]. Presentlyundertakenanalysisshowsthat the maximum contribution of internal
reflection to the total internal illuminance measuredon eachsurvey point in Craighousetest room will
not exceedthe level of 5%. In summary,for the presentDPF model, the effect of internal reflection is
of a low order.
6.6.6 Effect of diffuser type
During 2001-2002two new types of light pipe diffuser have beenintroducedinto the market, namely
of the new opal diffuser was not carried
new opal diffuser and clear diffuser. Performanceassessment
out due to its short life span.Figure 6.14 presentsthe daylighting performanceof two light pipe
diffuser designs:old opal and clear diffusers. The DPFs that were achievedby the light pipe with a flat
clear diffuser were higher than thoseachievedby an old opal diffuser. The performancegain ratio
rangesfrom 2 (8am, 3V May 2001) to 4 (2pm, 29h May 2001), and the averagevalue hasbeen found
to be 2.9. This factor is herein called the Diffuser Factor (fD). By applying the averagefD factor to the
internal illuminancesvaluesgiven by Eqs. 6.9,6.10,6.11 and 6.12, the internal illuminancesthat can
be achievedby a flat diffuser fitted light pipe can be determined.
Due to the irregular knurling finishing of the clear diffuser, it producesapparentlydifferent internal
daylight distributing property from that of an old opal diffuser. Figures 6.15 and 6.16 show the
difference betweenthe two types of diffusers in terms of their reflectivity and transparencyproperties.
The pictures presentedin Figs. 6.15 and 6.16 were taken in Edinburgh, Currie at about 3pm on 280'
April 2002. Figure 6.15(a) showsthat bright sunlight penetratesthe clear diffuser creating a glare
effect, while the sunlight goesthrough old opal diffuser appearsto be much weaker and dimmer.
116
Another obvious phenomenonis that opal diffuser producesmuch more uniform diffused light than
clear diffuser. The latter one producesmulti-directional and irregularly distributed light. Figure 6.16
showsthe reflected light from of a point sourcedue to the two types of diffuser.
Due to the improved transparencyproperty of the new clear diffuser, the transmissionof daylight by
light pipe hasbeen improved. As shown in Fig. 6.14, the total amountof light delivered by light pipe
with new clear difftiser is much more than that deliveredby old opal diffuser light pipe. However, at
the sametime, it was found that the uniformity of the internal light due to former kind of diffuser
seemedto be poorer than the latter one.This becomesobvious when the light pipes are applied in areas
where sunshineis abundantlyavailable.Figure 6.17 showsthat certain kind of light ring patternwas
observedwhen light pipes with new clear diffusers were installed in Bahrain. Picturesin Fig. 6.17
show that in noontime in Bahrain, clear diffuser light pipe seemto delivery pools of light insteadof
uniformly distributed internal light. This "pools of light" pattern is so strong that it causescertain
discomfortssuch as glare and undesiredlight ring on the ground. The problem was eventuallyresolved
by replacing the new clear diffusers with old opal diffusers. Occupantsare satisfiedwith both the
amount of daylight that old opal diffuser light pipe delivers and the way the pipe distributed the internal
daylight.
The Dubai project henceshowsthat, for siteswhere sunlight are abundant,the application of light pipe
with old opal diffuser can not only bring sufficient daylight into buildings but also ensurethe
uniformity of the internal daylight distribution, which is very desirable.However, for siteswhere the
weatheris dominantly part-overcastor medium overcastsky, the influence of light pipe diffusers to the
performanceof light pipe is more complicated.Measurementscarried out in Mercbiston test room
revealedthat the position and size of the ring of light due to light pipe varies during the day. By simply
physical analysis,it was found that the presentationof the ring pattern of light due to clear diffuser
light pipe is dependenton sky condition, externalsunlight intensity, the geometrical factors of light
pipe tubes,the optical property of light pipe diffusers and the sun's position. Although by applying the
Diffuser Factor (fD) of value of 2.9 to DPF models for old opal diffuser light pipes, an averaged
evaluation of the performanceof clear diffuser light pipes can be obtained,consideringthe complex
117
decisive factors that affect the performance,the evaluationcan only be regardedas a rough estimation.
Further work needto be carried out to attack the problem.
6.7 A COMPARISON BETWEEN WINDOWS DF AND LIGHT PIPE DPF
In designstudiesit hasbecomecustomaryto specify interior daylighting in terms of Daylight Factor.
The Daylight Factor (DF) is the ratio of the internal illuminance to the external diffuse illuminance,
available simultaneously. The Daylight Factor is divided into three components,the direct skylight
(sky component),SC, the externally reflected component,ERC, and the internally reflected component,
IRC. It must be bome in mind that by far the SC is the dominant componentof DF. In presentanalysis
only the SC is consideredas the contributing factor for the make-up of DF.
The CIBSE Lighting Code suggeststhat when the averageDF exceeds5 per cent in a building, which
is usedmainly during the day, electricity consumptionfor lighting shouldbe too small to justify
elaboratecontrol systemson economicgrounds,provided that switchesare sensiblylocated.When the
averageDF is between2 and 5 per cent, the electric lighting shouldbe plannedto take full advantageof
availabledaylight. Localised or local lighting may be particularly advantageous,using daylight to
provide the generallighting. When the averageDF is below 2 per cent, supplementaryelectric lighting
will be neededalmostpermanently.
DPF is the ratio of the internal illuminance to the corresponding total external illuminance. Hence when
comparing the performance of windows and light pipes the above fundamental difference ought to be
home in mind, i. e. in the main, the former exploits only the sky-diffuse, whereas the latter exploits total
(sky-diffuse + solar beam) illuminance. In this analysis an attempt is made to relate the window DF to
its counterpart, i. e. an equivalent DF for light pipes with the view to compare the performance of the
two possible sources of daylight.
For UK sites,Muneer and Saluja [12] and Muneer [13] havepresentedthe relationship betweenthe
abovetwo quantities(sky-diffuse and solar beam).'Mis type of relationship is developedusing
observedhourly diffuse ratio (sky-diffuse to total (global) horizontal illuminance) data.A validated
regressionbetweenthe aboveratio and sky clarity hasbeengiven in the above-citedreferences.It is
118
obvious that as the sky clarity reduceswith increasingcloud cover, the difftise ratio would tend to
become 1. Under such conditions a light pipe with an areaequal to that of a vertical window would
receiveat least double amountof illuminance due to its exposureto the whole sky hemisphere.As the
sky clarity increases,the light pipe would gain in performanceon two counts- whole sky exposureplus
receipt of beam illuminance. Note that with increasingsky clarity the difftise ratio decreasesand hence
vertical windows would only receivea fraction of a light pipe illuminance. Table 6.6 showsthe ratio of
the internal illuminance achievedby a light pipe with a DPF of 1% to that achievedby a window with a
DF value of the same.
Due to their very nature light pipes have exposureto the whole sky hemisphere(27Esteradiansolid
angle) and thus have an advantageover their vertical counterparts,i. e. windows within vertical facades.
The latter can, at best, have exposureto Tcsteradiansolid angle.Furthermore,windows are most often
not in receipt of sunlight, whereasthe light pipe can exploit both componentsof daylight - sunlight and
skylight. Table 6.6 is basedon the assumptionthat the window and the light pipe have equalareas.In
practice,however, a light pipe will have much smaller areathan a window.
6.8 COST AND VALUE ANALYSIS OF TUBULAR LIGHT PIPES
Prior to the analysisof cost and value analysisof light pipes, it is essentialto give definitions of 'cost'
and 'value' in this context. Cost is the price paid for a thing, object, service or utility. Value is the
worth, desirability of a thing, object, serviceor utility or the qualities on which thesedepend.In most
casesvalue can at best be estimatedin an approximatemanner.On the other hand, cost is a much more
accuratemeasure.In this sectiona discussionon the cost and value of daylight deliveredby light pipes
is presented.The material on both cost and value ought to be taken as an indicative assessmentowing
to the infancy of this technology.Using light pipes in buildings as daylighting devicescan bring multifold benefit. The application of light pipes producesgood value in terms of energyconservation,
environmentprotection, maintaining health (physical and psychological) and improving productivity
and work performance.
119
6.8.1 Energy conservation
Improvementsin daylight penetrationto the indoor environment,wherebetter design can
significantly lessenenergyconsumptionon artificial lighting systems,and where lighting
control strategiescan improve building performance[14].
Negative impactsby environmentalchangedue to global warming. Official report to be
publishedby the UK Government'sEnergy Saving Trust sayssomefive million people living
in 1.8 million homes- one in every 13 in the UK - risk being inundatedby rising seasand
increasedrainfall in the starkestofficial assessment
yet of the human cost of climate changein
Britain [15].
0
An economiccost comparisonis to be carried out for light pipes and electrical lighting for an
office environment.The following dataare available:
Condition:
Office area= 15m2
Location: London
Design illuminance for electrical lights = 425lux [16]
Design illuminance for natural lighting = 33Olux [ 16]
Capital cost of electric lights and devices= E35/m2[17]
Cost of replacementelectric: Fluorescentlamps (30Wx5) = E89 [18]
Life expectancyof Fluorescentlamps = 7500 hours [ 18]
Number of fluorescentlamps=5
Utilisation factor for lamps = 0.8
Design electrical lighting load = 15W/m2 [16]
Price of electricity including VAT = 7.22p/kwh [19]
Environmental impacts
C02 emissions= 1030g/kwb-electricity
S02 emissions= 5.32g/kwh-electricity
N02 emissions= 3.5 1g/kwh-electricity
120
Additional Envirom-nentallevy on electricity use = 15%
Light pipes
Minimum external illuminance required to provide an internal illuminance of 330lux via
use of light pipe
39klux [4];
Daylight ability
lOx365x8xO.3 = 8760 hrs [3];
Required light pipe dimensions(2-off): 1.2m long with 0.45m diameter [20]
Solution (based on a ten-year cycle):
Case I- Only electrical lighting:
Annual capital cost of electrical light fitting = L52.5
Annual running cost of electricity = E109.0
Annual C02 Penalty = E8.3 (see UK Emissions Trading Scheme, Section 6.8.3)
Total ;zýE170/year
Case11- Electrical lighting with light pipe:
Annual capital cost of light pipe fitting = L88.4
Annual running cost of electricity = E86.0
Total :zf 174/year
Conclusions:
Cost comparison:The costsfor CaseI (only electrical lighting) and CaseII (electrical
lighting with light pipe) are at the samelevel with a minute difference of E4/year;
Emissionssavedin 10 yearsdue to the use of light pipes (CaseII) are significant:
C02 emission
= 1555kg
S02
=8 kg
emission
N02 emission
=5 kg
Emission saved per hour due to the use of light pipes (Case 11):
121
C02 emission
= 177 g
S02 emission
= 0.9 g
N02 emission
= 0.6 g
6.8.2 Health
Researchhas shown that daylight has an important bearing on the humanbrain chemistry.Light
enteringvia eyesstimulatesthe nerve centreswithin brain that controls daily rhythms and moods.
"
People prefer environments with daylight conditions [2 1], and may recover from operations
and illness more quickly in environments which are dayIit, and which afford an exterior view
[22].
"
Buildings with low daylight factor create environments with homogenous lighting, having
little contrast and holding limited interest for the occupant, whereas buildings with high
daylight factor transmit more quality daylight, creating conditions likened to those found
externally, maintaining optimal mood conditions for longer [23].
"
Typically people who are exposed total daylight levels of greater than 2000 lux for only 90
minutes eachday [24] show positive mood symptoms.Light exposureis important to the inner
time keeping of humans.Through evolution, man has adaptedto rhythms such as body
temperatureto provide him with explicit knowledgeof externaltime [25]. The loss of this
connectioncan contribute to fatigue, insomnia, and SeasonalAffected Disorder (SAD).
"
It was concludedthat light is an important factor in the wellbeing of building occupantsand
lack of it can have a deleteriouseffect on them [26].
"
It hasbeenreportedthat studentswithin classrooms do benefit from higher dosagesof
daylight in terms of increasedperformanceand better generalhealth [27].
"
Researchwas carried out to reveal the relationshipbetweenSAD and light levels. Seasonal
Affective Disorder (SAD) is a disturbanceof mood and behaviour that resemblessome
seasonalchangesseenin lower mammals.SAD is thought to be related to decreasedsunlight
during winter months.SAD affectedpatientshave been successfullytreatedwith exposureto
bright artificial light of higher intensity than is usually found in the home or in the work place.
122
An open trial of bright environmentallight reversedmany of thesesymptomsand improved
mood and social functioning in the winter months [28].
6.8.3 Work performance
"
and productivity
The averagepersonreceiving more than 1000lux from natural daylight for lessthan one hour
per day, is not receiving sufficient levels to maintain optimal mood. A typical office worker
could spend50% or more of their time in environmentsof 0.1 - 100 lux [29).
"
It is recognisedthat a holistic approachto lighting designis required to provide environments
which are pleasingto the eye, comfortablefor the occupant,and which do not limit work
productivity [22].
"
Daylight, a full-spectrum light source,most closely matchesthe visual responsethat, through
evolution, humanshave cometo comparewith all other light. Daylight provides continually
human
brightness
to
the
the
allowing
eye to
workplace,
and
contrasts
values,
changing
constantlyadjust.This adjustmentreduceseye fatigue. The human eye is capableof adjusting
to high levels of luminancewithout producing discomfort [25].
Researchby Alberta Departmentof Educationconcludedthat: exposureto full-spectrum light
resultedin better attendance- 3.5 fewer days-absenta year. Studentsin ftill-spectrum rooms
had better dental records- nine times lesstooth decay;studentsin full-spectrum classrooms
grew more - more than 20-mm in two years;daylit libraries had significantly lessnoise; a
result of studentsincreasesconcentrationlevels; full-spectrum lighting inducedmore positive
moods in studentsand causedthem to perform better scholastically[30].
Researchresultsby Rudolph and Kleiner arguedthat most office environmentsare detrimental
to productivity becausethey ignore the requirementsof thosewho work in them. Office layout
can be improved by consideringchangesto office furniture, lighting and noise control [3 1].
Researchcarried out by HeschongMahone group concludedthat: 1) Overall, elementary
studentsin classroomswith the most daylight showeda 21% improvementin learning rates
comparedto studentsin classroomswith the leastdaylight. 2) A teachersurvey and teacher
bias analysisfound no assignmentbias that might have skewedthe original results.3) A grade
level analysisfound that the daylighting effect doesnot vary by grade.4) An absenteeism
123
analysisfound that physical classroomcharacteristics(daylighting, operablewindows, air
conditioning, portable classrooms)do not have an effect on studentabsenteeism.These
findings may have important implications for the designof schoolsand other buildings [32].
0
HeschongMahone group [33] revealeda clear relationshipbetweenskylighting and increasing
sale.A number of mechanismsthat can explain the effect of daylighting on salehave beenput
forward as following: a) high customerloyalty to a daylit store,b) more relaxed customersin
a daylit store,c) better visibility, d) more attractiveproductsand e) better employeemorale.A
study on the effect of daylighting to students'performancein school was also carried out the
by the samegroup. It was concludedthat a uniformly positive and statistically significant
correlation existsbetweenthe presenceof daylighting and better studenttest scores.Possible
explanationsfor this phenomenonwere given as: i) improved visibility due to higher
illumination levels; ii) improved visibility due to improved light quality, iii) Improved health,
iv) improved mood, v) higher arousallevel and vi) improved behaviour.
In this sectionthe value of daylight hasbeencategorised.An examplewas also presentedto compare
the costsassociatedwith tubular daylighting and electrical lighting devices.It would be desirableto
translatethe itemisedvalue of daylight into costsso that a 'complete' picture may emerge.Towards
this end the environmentalimpact of using electric light havebeenexpressedin monetarycost via the
Climate ChangeLevy [34] announcedby one Europeangovernment,and EmissionsTrading Scheme
by UK government[35]. However, not all of the associatedvalue of daylight can easily be converted
into cost data.For example,only rough cost estimatesmay be provided for the health and productivity
benefits obtainedthrough daylight exploitation. Hence,no attempthaspresentlybeenmadewithin the
presentdocumentto 'go all the way'. The authorsfeel that such value-to-costconversionsare best left
for the judgement of the reader.The analysispresentedare however conduciveto the researchon the
value and cost engineeringstudy on all natural daylighting techniques.
6.9 SUMMARY
Mathematical modelling activities aiming at predicting the dayligbting performance achievable by light
pipes with various configurations under all weather conditions have been undertaken. Two DPF
models, one for straight light pipes and the other for elbowed light pipes were built. The models enable
124
estimationof daylight provision of the light pipes with a high degreeof accuracy,i. e. R2values of 0.95
and 0.97 for regressionbetweenpredicted and measuredilluminance were respectivelyobtainedfor the
abovemodels.The maximum Mean Bias Error (MBE) and Root Mean SquareError (RMSE) were 2lux and 27lux.
125___
REFERENCES
1. Edmonds,I. R., Moore, G. I., Smith, G. B. and Swift, P. D. (1995) Daylighting enhancementwith
light-pipes coupledto laser-cutlight-deflecting panels.Lighting Researchand Technology,27(l), 2735
2. Siegel,R. and Howell, J. R. (1981) Thermalradiation heat transfer, McGraw Hill, New York
3. Muneer, T., Abodahab,N., Weir, G. and Kubie, J. (2000) Windowsin buildings thermal, acoustic,
visual and solar performance,Architectural Press,Oxford
4. Zhang, X. and Muneer, T. (2000) A MathematicalModel for the Performanceof Light-pipes, Light
Researchand Technology,32(3)
5. Zhang, X. and Muneer, T. (2000) Light pipes for Daylight PenetrationIndoors, Proceedingsof
RenewableEnergyfor Housing Conference,The International Solar Energy Society, ISBN: 1-87364032-3
6. Carter, D. J. (2001) The Measuredand PredictedPerformanceof PassiveSolar Light Pipe Systems.
Lighting Researchand Technology,34(l), 39-52
7. Naraghi, M. H. N. (1987) EngineeringNotes: American Institution ofAeronautics andAstronautics
8. The Society of Light and Lighting (2001) CIBSELighting Guide 11: SurfaceReflectanceand
Colour, The Society of Light and Lighting, London
9. Muneer, T. (1997) Solar radiation & daylight modelsfor the energyefficient designof buildings,
Architectural Press,Oxford
10. Loncour, X, Schouwenaars,S., L'heureux, D., Coenen,S., Voordecker,P. H. and Wouters,P.
(2000) Performanceof the Monodraught systemswindcatcherand sunpipe:A casestudy, Belgian
Building ResearchInstitute
11. Muneer, T. (2002) Brief report on the performanceof Napier's Daylight PenetrationFactor (DPF)
and its comparisonagainstother publishedwork, internal report, Napier University
12. Muneer, T. and Saluja, G. S. (1986) Correlation betweenhourly diffuse and global irradiancefor
the UK, Building Serv.Eng. Res.Techol.7(l), 37-43
13. Muneer, T. (1987) Hourly diffuse and global solar irradiation, further correlation Building Serv.
Eng. Res. Technol.8(4), 85-90
14. Zeguers,J. D. M. and Jacobs,M. J. M. (1997) Energy saving and the perception of visual comfort,
ProceedingsofLux Europa
126
15. The Independent(2002), The Independent15 September2002 No.658, UK
16. CIBSE (2001) Building ServiceJournal, December2001,22
17. Glenigan(1998) Griffiths Electrical Installations Price Book, GleniganCost Information Service,
Bournemouth,UK
18. Goodoffices(2002) www. jzoodoffices.com
19. ScottishPower (2002) www. scottishpower.co.uk
20. Zhang, X. and Muneer, T. (2002) A Design guide for performanceassessment
of solar Light-pipes
Lighting Researchand Technology,34 (2), 149-169
2 1. Wyon, D. P. and Nilsson, 1.(1980) Human experienceof windowlessenvironmentsin factories,
offices, shopsand collegesin Sweden,Building ResourcesWorldwide, Proceedingsof the 18'hCIB
conference,234-239
22. Loe, D. and Davidson,P. (1996) A holistic approachto lighting design,Energy Management,
Sep/Oct 16-18
23. Cawthome,D. (1991) Buildings, lighting and the biological clock, The Martin Centrefor
Architectural and Urban Studies,University of Cambridge
24. Savides,T. J., Messin, C., Senger,C. (1986) Natural light exposureof young adults,Physical
Behavior, 38,571-574
25. AIA, Franta,G., Anstead,K. (1993) Daylighting Offers GreatOpportunities,Daylight American
Institute of Architects, Building Connections,Energy and ResourceEfficiencies, Washington,DC,
U.S.A
26. Steemers,K. (1993) The role of lighting in the environmentalperformanceof buildings Facilities,
11(5)
27. Plympton, P., Conway, S., Epstein,K. (2000) Daylighting in schools:Improving student
performanceand Health at a price schoolscan afford, National RenewableEnergy Laboratory, U. S.A,
report presentedin American Solar Energy Society ConferenceMadison, Wisconsin, 2000
28. Truesun (1987) http://www. truesun.com/main/articles.htm, SeasonalAffective Disorder: A Review
of the Syndromeand it's Public Health Implications, American Journal ofPublic Health, 77(l), 57-60
29. Espiritu, R. C. (1994) Low illumination experiencedby SanDeigo adults: associationwith atypical
depressivesymptoms,Biological Psychiatry, 35,403-407
127
30. ADE - Alberta Departmentof Education(1992) Study into the effects of Light on Children of
ElementarySchool Age: A Caseof Daylight Robbery,Alberta Departmentof Education,Source:
ht!p://www. huvco.com/studies.htm
3 1. Rudolph, P. A. and Kleiner, B. H. (1990) Building an Effective Office Space,Work Study,39(3)
32. HeschongMahone Group (1999a)Daylighting in school: An investigation into the relationship
betweendaylighting and humanperformance(condensedreport)
33. HeschongMahone Group (I 999b) Skylighting and retail sales:An investigation into the
(condensed
between
daylighting
human
report)
and
performance
relationship
34. EEBPP(Energy Efficiency Best PracticeProgramme)2002, hl! p://www. enerpy-efficiency.gov.uk/
35. ProfessionalEngineering, 27 November 2002, UK, pp32
128
CIN
.m
W
4ý
"o
t4
ý4
2
-0
cu
=
"a
E
(D
9.1
.=
q
c
0
10
En
C/)
cd
0
C'n
U
cn
3M
U
,0EZ
5
(D
r.
cu
U
ci
*E
m
"C
0
-2 r.
E
12 -0
( ý)
eu
cn
=t.
En Z ;6
>
Ld
ý
- E5
- v
2 0. ýý
.0 -0
"Ci
,
r.
n4
ýc5
=
U2
(1)
CD
rn
rn
w
ui
cri
CZ.(1
rA
ce
CIS
r.
M ce
Cli
cu
;3
m
(M
E
22
ce
V)
cn
cl
Cd
CL4
Z
cn
:=I
"zi
u
(n
Z
rn
=cu. cu
-
E: Cd b =
"Ci
-ýg 0.)
-0
-
CD JZm
0
-g0
cu
0
-ýý :i
ze
Ln
=E
.
;ýi
(L)
cz
m
CD-
2
lý
5
ljz
"
ZS
ý
a)
c2.
.
- C,2
ý- Ln-r,
-= ý
0.6
0.5
0.3
LM 0.2
.
>M,
0.1
0
0
50
Figure 6.2 Variation
100
150
Distance D, cm
250
200
of daylight penetration factor as a function of distance, D
0.6
0.5
$
0.4
I
$
+
$
*
I$
I
4
*
I
*
I2
*
.
0.2
1 1
*
1
En
.
0.1
0
40
41
I
I
II
42
43
44
II
45
46
I
47
48
49
Solar altitude, Degree
Figure 6.3 Daylight penetration factor variation as a function of solar altitude (D=155cm)
131
0.60
'Ile
0
0.50
*+*u0++
gv
it
4a
0
0.40
0
++
0.30
0.20
0.10
0.0040.00
0.05
0.10
0.16
0.20
0.25
0.30
0.36
Lj.
-tw
I
Sky clearness index, kt
Figure 6.4 Daylight penetration factor as a function of sky clearness index, k, (D = 155cm; solar
altitude = 49±0.5, light pipe sees only Northern part of sky vault)
600
600
cu
400
300
200
100
0
0
100
200
300
400
500
600
Measured internal illuminance, lux
Figure 6.5 Plot of calculated internal illuminance against measured internal illuminance for all
distances
132
500
400
300
L0
200
.
100
0
0
100
200
300
400
500
Measured internal illuminance, lux
Figure 6.6 Plot of calculated internal illuminance against measured internal illuminance for
D=194cm
Figure 6.7 Light entering a light pipe descendsvia a seriesof inter-reflections
133
Figure 6.8 Scatter plot of calculated due to Eq. 6.9 (Y-axis) against measured internal
illuminance (X-axis) for elbowed light pipes (units = lux)
134
135
(a)
Effect of solar altitude on S-DPF
1.8
1.6
14
.
se
kt=Ol
.
12
.
E3 kt=0.2
1.0
U:
a.
C? 0.8
0.6
0.4
0.2
A
kt=0.3
3E kt=0.5
kt=0.7
0.0
15
20
25
30
35
40
45
50
55
Solar altitude, degree
Effect of solar altitude on E-DPF
1.4 1.2 1.0 -
o
0.8
0.6
U.J
0.4
kt=O.1
kt=0.2
kt=0.3
kt=0.5
kt=0.7
0.2
0.0
20
25
30
35
40
45
50
Solar altitude, degree
55
60
Figure 6.11 DPF for 420mm-diameter light pipe as a function of a, and kt, (a) for straight light
pipe and (b) for light pipe with two bends (D=H=1.2m)
136
2.0 1.8
I-'O-a.
1.6 -
= 30'-
a, = 45' --hr- a, = 60'
1.4
;P. 1.2 1
LZ
1.0 0.8
0.60.4 0.2 0.0
24679
Aspect ratio
1.0 -
0.9i
a, 30"
aS 45' --A-- cc'= 600
0.8 -
0.7 i
0.6 U: 0.5
CL
0.4
0.3 0.2
0.1 0.0 -
36
8
10
12
Aspect ratio
Figure 6.12 Effect of aspect ratio on DPF, (a) for straight light pipe and (b) for light pipe with one
bend (420mm-diameter, D=H=1.2m)
137
Predicted IDPFsfor straight and elbowed light-pipes
25 L
:::
2.0
1
5
LL: .
a-
nobend
(a one-bend
-
-
E3
E3
1.0
A
'S
two-bend
x
three-bend
-four-bend
X
0.5 -
0.0
0.5
0.4
0.3
0.2
0.1
kt
Figure 6.13 Comparison of the predicted DPFs for straight light pipe and elbowed light pipes
H=Im)
D=1.2m,
(530mm-diameter,
four
bends
three
two,
cc,
=45",
and
with one,
Comparison of external and internal illuminance profile (lux)
100000
100001000100
10 11-1.1Internalilluminance
at 1.76mfromdiffuseron29thMay,2001.
measured
1
789
10
11
12
13
14
15
16
17
Hour
Flattranslucent
diffuser,lux
-
Domeopaldiffuser,lux
-External
global,lux
Figure 6.14 Comparison between external and internal illuminance due to different diffusers
138
AA
(a) Transparency ol'a CICM-dil-I'LISCI
"4%.
C
(b) I rallsparcllcý
Figure
ol'all old Opal diffuser
6.15 The comparison
of an old opal against
a clear diffuser
(transparency
property)
139
(;I) I i'1111Id ;' poillf li"'111Solirct, f ellected from the clear diffuser inner surface
(1)) Light Of a point liýýItI -iilýt
hIII-I
1,11,(k dh" II It It,
lllllý 1' 141-t
Figure 6.16 The comparison of an old opal against a clear diffuser (reflectivity
property)
140
light
in
Bahrain
project
pipe
light"
"pools
seen
Ring
phenomenon
6.17
of
pattern and
Figure
141
Table 6.lCoefficients used in Eqs. 6.5 & 6.6
a00
0.053
a02
ao,
0.032
alo
0.407
-0.000
all
a12
0.008
-0.149
0.002
-0.140
a14
0.266
ao6
a07
aos
0.146
-0.002
a15
0.002
results for the model represented by Eq. 6.5
155
0.96
0.93
Table 6.3 Validation
-1.878
a13
0.000
Table 6.2 Validation
Distance(cm)
Slope
R2
a03
1.952
a05
a04
167
1.13
0.96
181
0.90
0.95
176
1.16
0.95
191
1.15
0.92
212
0.90
0.96
results for the model represented by Eq. 6.6
Distance(cm)
155
167
176
181
191
194
212
Slope
0.96
1.13
1.16
0.89
1.16
0.91
0.90
R'
0.93
0.96
0.94
0.94
0.92
0.97
0.96
Table 6.4 Coefficients used in Eqs. 6.9 - 6.13
Models
ao
Eq. 6.9
356.7
-572.4
Eq. 6.10*
62.5
-17.2
-1.2
2.6
Eq. 6.11
305.0
-190.5
-2.9
Eq. 6.12**
192.5
-108.8
Eq. 6.13
356.7
-572.4
a,
a2
a3
a4
a5
a6
a7
a8
ag
alo
-10.2
42.8
0.5
-0.9
137.7
3.5
-0.5
0.5
136.0
4.3
1.1
-5.8
4.4
0.2
133.8
4.0
7.1
-2.1
-0.3
-5.3
132.4
-0.4
0.2
8.6
-2.6
-1.2
-10.2
42.8
0.5
-0.9
137.7
3.5
-0.5
0.5
Equation 6.10 is the simplified model of Eq. 6.9
Equation 6.12 is the simplified model of Eq. 6.11
142
Table 6.5 Error statistics for Eqs. 6.9 - 6.13
Models
Eq. 6.9
MBE
RMSE
RMSE/MaXnicasured
X
RMSE/MeanmeasuredI
PAD
Slope
-0-
-Ilux
27lux
2%
15%
12%
0.98
0.95
Eq. 6.10*
-3lux
29lux
2%
16%
13%
0.98
0.95
Eq. 6.11
-2lux
23lux
2%
22%
25%
0.97
0.97
Eq. 6.12"
-3lux
25lux
3%
24%
25%
0.97
0.97
Eq. 6.13
-91ux
52lux
18%
29%
25%
0.94
0.86
The maximum value of measured internal illuminance due to light pipes, lux
xMaXmCasured:
Ncan--,
d: The mean value of measured internal illuminance due to light pipes, lux
Equation6.10: the simplified model of Eq. 6.9
Equation6.12 : the simplified model of Eq. 6.11
Table 6.6 Relationship between a 'conventional' window daylight factor and an equivalent
daylight factor for a light pipe
Sky type
Heavy overcast
Thin overcast
Part overcast
Clear
Sky ClaritylRatio of external global
to diffuse illuminance
0.2
0.3
0.51
0.7
IDF
1.00
1.06
1.46ý
2.80
DPF (%) Ratio of internal
illuminance achieved
by a light pipe to that
by a window
1
2.0
1
2.1
1
2.9
1
5.6
143
7. SHADOW BAND DIFFUSE MEASUREMENTS
CORRECTION
For solar energy applicationsdesigns,global and diffuse horizontal irradianceand beamnormal
irradianceare the threemost important quantities.Global horizontal irradiance can be easily measured
using a pyranometer.As to the measurementof diffuse horizontal irradiance,the most common
approachis to use a shadowband aidedpyranometerto interceptbeam irradiance.To study the effect
installed
horizontal
light
daylighting
diffuse
to
the
roofs,
on
of
pipe
perfon-nance
radiation
of sky
horizontal diffuse irradiancemeasurementshave to be madeavailable.Moreover, consideringin real
is
illuminance
input
light
installed
total
the
not
where
on slope roofs
pipes are often
applications
horizontal global illuminance. For the latter case,true slope illuminance hasto be calculatedso as to
direct
has
illuminance
light
Slope
two
the
sun
name
major
components,
of
pipes.
performance
predict
illuminance and sky diffuse illuminance. Horizontal diffuse illuminance measurementsarebeing
from
illuminance
for
the
the
therefore
throughout
slope
calculating
method
world,
carried out
horizontal illuminance has to be used for light pipe design.In this chapter,a new method of obtaining
is
being
horizontal
diffuse
illuminance
the
than
around
reported.
method
used
prevailing
more accurate
7.1 BACKGROUND
Global (G) and diffuse (D) horizontal irradianceand beamnormal irradiance(B,,) are the three most
important quantitiesfor solar energyapplicationsdesign.The important role that diffuse irradiance
plays in a solar systemdesigncannotbe overemphasised.It was reportedby Drummond [1] and others
that the ratio of diffuse componentto the global irradiancecan be ashigh as 0.65. Therefore,to provide
a preciseestimationof the solar energyavailable for a given application, a more accuratemeasurement
of diffuse irradianceis required.
A simple relationship existsbetweenG, D and B,, (seeEq. 7.1).
D=G-B,,
sina
Therefore, diffuse irradiance can either be calculated from measurement of G and B. or measured
directly. However, in the first instance, the beam normal irradiance measurement device
144
(pyrheliometer)hasto be installed on an equatorialmount with active tracking of the sun'strail. As this
is expensive,this method hasnot beenwidely adopted.The more common approachhas thereforebeen
to use a pyranometeraidedby a shadowband to interceptbeamirradiance.The beamirradiance is then
obtainedvia subtractionof the diffuse componentfrom global irradiance.
Unfortunately, the shadowband that is usedto block the sunshinealso shadessomediffuse iffadiance
as well. It can lead to the monthly averagederror of horizontal diffuse iffadiance measurementof up to
24% of the true value [1]. Henceit is necessaryto correct the measureddiffuse iffadiance obtained
using the shadowband instrument.
The inner surfaceof a shadowband is usually paintedblack so as to eliminate any reflected irradiance
from the inner surfaceto the pyranometer.If the sky-diffuse irradiancedistribution is assumedto be
isotropic and the irradiancethat is reflectedby inner surfaceof shadowband negligible, the correction
factor of the diffuse irradiancecan be calculatedby using the simple geometricmethod given by
Drummond [I]. This geometricmethod calculatesthe proportion of the sky areathat is subtended.
by
the shadowband, P, and then derivesthe correction factor as I /(I -P).
However, as the real sky-diffuse distribution is not isotropic, an anisotropic factor must be taken into
considerationto obtain a correction factor. The necessityof applying an anisotropiccorrection factor
hasbeenwidely investigated.Kudish [2] hasreportedthat, for Beer Sheva,Israel, the anisotropic
correction factor varies from 2.9% to 20.9%, whereasthe geometric(isotropic) correction factor varies
only from 5.6% to 14.0%.Painter [3], comparedthe diffuse irradiancemeasuredby both an occulting
disc and a shadowband pyranometer.He concludedthat the anisotropic correction factor has a
significant seasonaldeviation. Eero'sstudy [4] showedthat the deviation of the monthly isotropic
correction factor with respectto total correction factor rangesfrom 1% for Decemberto 7.5% for
August.
Work relating to the developmentof an anisotropic diffuse irradiancecorrection method hasbeen
undertaken by several investigators during the past decade. Ineichen [5] reported his method of
combining two simple models to determine the total correction factor: one was the isotropic geometric
145
model and the other was basedon the diffuse radiation as a function of solar altitude. Kasten et al[6]
consideredthe influence of threeparametersthat were most relevant in determiningthe anisotropic
correction factor, namely: the ratio of the diffuse to global radiation, the solar declination and the
coefficient for beamradiation transmission.Siren'sinvestigation and evaluation [7] , basedon a twocomponentsky radiation model, showedthat the total correction factor appearedto be a function of the
shadowband geometry,location of the shadowband, and the sky radiation distribution. LeBaron et al.
[8] presenteda model employing the parameterschememethod put forward by Perez.This parameter
schemeis representedas a 256-combinationof the values of the zenith angleof sun, the isotropic
correction factor, the sky's clearnessindex and the sky's brightnessindex.
The common characterof the aboveanisotropicmethodsis that they employ different radiation
distribution modelsto obtain the ratio of diffuse irradiancesubtendedby shadowband to the total
diffuse irradiance.However, the use of a complex function and parameterschemewithin such a model
makesit more difficult to apply the model in practise.The purposeof this article is to develop a
relatively simple yet accurateanisotropicmodel that can be applied widely acrossthe global.
In this article, the developmentof a new model basedon the radiancedistribution index formulation
introducedby Moon and Spencer[9] is presented.Investigation of the relationshipbetweenthe
radiancedistribution index and sky clearnessindex, k,, is reported.The model is validatedusing data
from two siteswith disparateclimate conditions. Drummond'sisotropic model is examinedthrough
physical reasoningand numerical analysis.A comparisonof the performanceof the proposedmodel,
and Drummond's isotropic model is illustrated through the use of error histogramsand statistical
analysis.The proposedmodel hasbeen derived basedon non-site specific parameters,namely: radiance
distribution index, b and clearnessindex k, and henceshould be applicablefor all sites.
7.2 DRUMMOND'S
METHOD
7.2.1 Theory
Drummond [I] gave the following formula based on geometrical analysis to calculate the isotropic
shadow band diffuse correction factor FD:
146
FD ý 1/0-0
(7.2)
where FD is the correction factor and f is the proportion of diffuse irradiance obstructed by the shadow
band. Note that FDis to be multiplied with the uncorrectedvalue of diffuse irradianceas measuredwith
shadowband to provide the correcteddiffuse irradiance.f can be calculatedusing Eq. 73:
f=
X/T =2(Whi) cos' 5 (to sing sin5 + cosy cos5 sinto)
(7.3)
where X is the diffuse irradianceshadedby shadowband,T is the total diffuse irradiance.Eq. 7.3 is
derived from the integration of Eqs. 7.4 and 7.5 below, basedon the assumptionthat the sky-diffuse
radiancedistribution is uniform:
X=IW
Cos
I=sunset
f
3,5
sinadt
1=sunrise
T=7c 1
(7.4)
(7.5)
where I is the radiation intensity of the sky. However as real sky-diffuse irradiancedistribution is
anisotropic,to get a more accuratecorrection factor, the I value must be treatedas a variant. Such a
procedureis given below.
7.2.2 Examination of 'measured' diffuse correction factor
Measurementsof the global and diffuse sky irradiancealong with beamnormal irradiancewere usedto
examinethe validity of Drummond's method [1]. To reveal the inadequacyof Drummond's isotropic
method, comparisonof the correction factor rangeobtainedusing Drummond's method and the range
of measuredcorrection factor hasbeenundertaken.
One complete year's data (1995) for Bracknell (51.4*N, 0.8'W) in England are used to examine
Drummond's method. The data consists of hourly horizontal global, beam normal and diffuse
147
irradiancemeasuredby shadowband. Hourly irradianceon vertical surfacesfacing north, east,south,
west and a tilted surfacefacing south at the local latitude anglewere also available.Thesedata were
provided by the UK Meteorological Office, Bracknell.
To ensuredatareliability, dataare discardedif they do not satisfy simultaneouslythe following quality
control conditions:
G- Bn sina >D
uncorrected;
B,, sina < G;
B,, < E,, * earth-sundistancecorrection;
a> 10 degree
0172024DN), where DN is the Julian day number.
The earth-sundistancecorrection = 1+0.033cos(O.
is the uncorrecteddiffuse irradiance.E,,,the extra-terrestrialirradiance,is taken as 1367
Duncorrected
W/M2.A total of 3583 hours datawere thus chosento examineDrummond's correction factor against
the true correction factor.
The true correction factor, F,,,, is obtainedusing Eq. 7.6:
F
= (G - Bý,sin(y)/I)uncorrected
(7.6)
Figure 7.1 showsthat Drummond'sisotropic correction factor rangesfrom 1.010to 1.128,whereasthe
true correction factor rangesftom 1.001 to 1.480.It is thereforeconfirmed that, in the caseof hourly
diffuse irradiancemeasurement,Drummond's methodunderestimatesthe correction factor by up to
24%.
148
7.3 NEW MODEL BASED ON SKY-DIFFUSE
DISTRIBUTION
INDEX
7.3.1 Theoretical analysis
A radiancedistribution index, b, basedon the work of Moon and Spencer[9] is introducedherein to
facilitate the present modelling exercise. The model is given in Eq. 7.7,
Lo = Lz (I +b sinO)/ (I + b)
(7.7)
,
b
is
0,
is
L,
is
the
LO
the
the
and
radiance
with
an
altitude
=
zenith
radianceof a given sky patch
where
radiancedistribution index.
Muneer [10] hasused the abovemodel to establisha relationshipbetweenslope diffuse irradianceand
horizontal diffuse iffadiance. Muneer's model is given by Eq. 7.8,
Dp/D=COS2(P/2)+ [2b/TE(3+2b)] [sinp -P cosp - 7Esin2(P/2)]
(7.8)
where Dp is the hourly diffuse irradiance for a slopedsurface,D is the hourly horizontal diffuse
irradiance,P is the tilt of the slopedsurface.Muneer'smodel also treatsthe shadedand sunlit surfaces
separatelyand further distinguishesbetweenovercastand non-overcastconditions.Basedon his study
for Bracknell, Muneer found that for a shadedsurface(facing away from sun) the 'best'value of b is
5.73; for a sunlit surfaceunder overcastsky conditionsb=1.68; and for a sunlit surfaceunder nonovercastsky conditions b= -0.62.
As reportedabove,measuredvertical and slope surfaceirradiancedata for Bracknell, England were
madeavailable to the authors.Using thesedata an assessmentof the variation of V againstk, can be
madeusing Eq. 7.8. The presentlydevelopedmathematicalrelationshipbetweenb and k, is given in
Eq. 7.9,
For k, >0.2,
149
2b,
0.382- 1.11kt
=
g(3 + 2b,)
2b2
2b2)
+
T(3
,
= 0.166 + 0.105 kt
(for southemhalf of sky hemisphere)
(7.9a)
(for northem half of sky hemisphere)
(7.9b)
For k,: 5 0.2, b, =b2=1.68 (after Muneer [10]).
A point worth mentioning here is that, strictly speaking the sky radiance distribution is twodimensional
function of any given sky patch geometry (sky patch altitude and azimuth) and the
,a
position of sun. Eq. 7.9 represents a compromise between simplicity (represented by an isotropic
model) and complexity (represented by a two-dimensional model such as the one described above).
Another feature of Eq. 7.9 is that due to its relative simpler formulation it also tends to be robust
(covering all-sky conditions) and of general applicability, as shall be demonstrated herein via validation
undertaken for disparate sites, i. e. Bracknell, England (51.4'N, 0.8'W) and Beer Sheva, Israel (31.3'N,
34.8'E).
7.3.1.1 Total sky-diffuse irradiance
The total sky-diffuse irradiancecan be obtainedthrough a numerical integration basedon Moon and
Spencer'ssky-diffuse distribution model. If the zenith radianceis termed Lz, then the horizontal diffuse
irradianceD can be calculatedusing Eq. 7.10,
r/2
D=f;
0
(7r sinO cosO)(LO,+ LONO
(7.10)
Lo, is defined as the sky-diffuse
where LO,=Lz(I+blcosO)/(I+bl), and L02=Lz (I +b2COSO)1(1+b2).
radiance emanating from any given patch of the southern half of the sky vault, and L02the
correspondingradiancefrom the northernhalf of the sky hemisphere.Thus,
D= 7cLzf[
2
(sinO cosO+blsinO COS2())/(I+bl)dO]+
2
(sinO cosO+b2sinOcos20)/( I+b2)dO])
(7.11)
150
So,
D =(TcLz/6) [(3+2b,)/(I+ bl) + (3+2b2)/(I+ b2A
(7.12)
Moon and Spencer[9] showedthat using bl=b2=2 in Eq. 7.12 adequatelydescribesthe radiance
distribution of an overcastsky, and leadsto the relationship,D =77rLz/9.
7.3.1.2 Thenew correctionfactor basedon b, and b2functions (Eq. 7.9)
If FAis defined as the diffuse irradiancethat is obscuredby shadowband, then FAmay be calculated
using Eq. 7.13:
I=sunsel
f
3,5
Lo sinadt
FA: --WCOS
I= sunrise I
The result of the aboveintegration is,
FA= 2W Lz cos 38 (1, + b112) /0+
bl)
I, = cosy cos8 sinto + to sin(p sin8
12ý tOsin2cpsin'5 + 2sinto sinT cosy sin5 cos5 + cos2T Cos25 [ to/2 +(sin2to)/4]
Now, using Eqs.7.12 and 7.14, the proposedshadowband diffuse irradiancecorrection factor, Fp, can
be obtained,
Fp = 1/(I-FA / D)
(7.15)
7.3.2 Validation
The validity of the proposed model was tested by plotting the corrected hourly diffuse irradiance
against the true diffuse irradiance as obtained via Eq. 7.1. Databases of two different sites, namely:
151
Bracknell, England and Beer Sheva, Israel were used to validate the proposed model. These two sites
provide diversevariation in climatic conditions and latitude separation.
7 3.2.1 Validation using Bracknell database
7.3.2.1.1 Scatter plots and statistical analysis
The proposedmodel was applied to the culled Bracknell databasewhich was previously used to
examinethe performanceof the Drummond's method (seesection2). Correcteddiffuse irradiance
(Dcorrcacd)
datawere regressedagainsttrue values of 'measured' diffuse irradiance(D) obtainedvia
Eq. 7.1 to determinethe model's performance.Resultsof this comparisonare shown in Fig. 7.2. The
slope of the fitted trend line is 0.99, and the coefficient of determination,R2,is 0.98. Drummond's
method was also applied to this database.The result is shown in Fig. 7.2. The slope of the fitted trend
line is 0.95, and the coefficient of determinationR2is 0.97. The slope of the fitted trend line is
indicative of the validity of the model under test. The degreeof validity increasesas the slope
approachesunity. 'Me proposedmethod thus offer a better accuracy.
To enablefurther insight into the validation of the abovemodelsthe meanbias error (MBE) the root
,
meansquareerror (RMSE) and the PercentageAverage Deviation (PAD) have beenobtained.Results
are shown in Table 7.1.
Y,(D,,,,,,
-D)
Ied
no.of data points
ýE(D
Root Mean Square Error, RMSE =
D)2
.......
no. of data points
E(I 00 *1 D,,,,,,,,
Percentage Average Deviation, PAD =
I/ D,
d -D
no. of data points
orrected
152
7.3.2.1.2 Histograms
Histogram plots of percentageerror were also madeto comparethe proposedmodel's performance
againstthat of Drummond's method.The histogramspresentgraphical representationsof the frequency
distribution of the percentageerror. A given models'perfori-nanceis examinedin two ways. Firstly, the
histogram provides a check regardingthe proportion of datapoints that fall within specific range of
percentageerror and secondly,it allows an examinationof the rangeof errors.
Histogramsof the proposedmodel for all-sky conditions, and for 0< kt:5 0.2 (heavy overcast),
0.2 < k,: 5 0.6 (part-overcast)and 0.6 < k, <I (clear-sky) are shown in Fig. 7.3 respectively.
Correspondinghistogramsfor Drummond's method are given in Fig. 7.4. The results of theseanalyses
arepresentedin Table 7.2 as the number of datapoints that fall in percentageerror rangesof -3%
I %, -1% -
+1%, and +1% -
+3%. For the proposedmodel and for all-sky conditions, 70% of
correcteddiffuse value fall in the -3% -
+3% percentageerror range,while for Drummond's method
the correspondingfigure is 58%. Under clear-sky condition (0.6 < k, <1), when solar energyhas the
greatestimpact the proposedmodel is significantly better. Generally speaking,the proposedmodel
displaysa normal distribution for errors, while Drummond's model is heavily skewed,especiallyunder
clear-sky conditions.
7.3.2.2 Validation using Beer Shevadatabase
Nearly two yearsof measureddata (February,,1998-
December,1999) for Beer Sheva(31.4'N,
34.8'E) in Israel were used for further evaluationof the modelsunder discussion.The dataconsist of
hourly horizontal diffuse (measuredusing shadowbandpyranometer)and global, beam normal
irradianceand irradianceon a south facing sloping surfacewith tilt = 40 degree.Thesedatawere
provided by the Chemical EngineeringDepartmentat Ben-Gurion University. Again, the data setswere
culled using the combination of the four conditions given in Section2.
7.3.2.2.1 Scatter plots and statistical analysis
153
Diffuse irradiancedatarespectivelycorrectedvia proposedmodel and Drummond's method,were
regressedagainsttrue diffuse irradiancevalues.The resultsof this comparisonare shown in Fig. 7.5.
The slope of the fitted trend line for proposedmethodis 1.00,and the coefficient of determination,R2
is 0.99. The result obtainedfrom the applicationof Drummond's methodis shown in Fig. 7.5. The
slopeof the fitted trend line in this caseis 0.96, and the coefficient of determinationR2is 0.99. Table
7.3 showsthe MBE, RMSE and PAD statisticsfor Beer Shevadatabase.The proposedmodel produces
an RMSE of 17 W/m2, an MBE of 2W/m2and a PAD of 5%. The correspondingfigures for
Drummond's method are23 W/m2,
2 and 7% respectively.
-5W/M
7.3.2.2.2Histograms
Figure 7.6 and 7.7 show the histogramsfor different sky conditionsobtainedthrough applicationof the
proposedand Drummond's methodto Beer Sheva'sdatabase.The resultsof this analysisare presented
in Table 7.4. For all-sky conditions,41% of diffuse valuescorrectedby the proposedmethodfall in the
±3% percentageerror range,while for Drummond's method,the correspondingfigure is 21%. Once
again,the proposedmodel displaysa normal error distribution behaviour,while Drummond's method
is considerablyskewed,especiallyunder clear-skyconditions.
7.4 SUMMARY
A new anisotropicmodel to correct diffuse irradiancemeasuredby shadowband hasbeendeveloped.
This method is basedon the use of a single diffuse radiancedistribution index, b, introducedafter the
work of Moon and Spencer[9]. Clearnessindex, kt, is usedas a parameterto determinethe value of b,
and b is then usedto obtain the correction factor to accountfor the diffuse irradianceobscuredby
shadowband. The proposedmethod is validatedusing databasesfrom siteswith disparatesky
conditions. The Drummond's isotropic method,which is basedsolely on geometriccalculation is
comparedagainstthe proposedmethod that usesan anisotropicradiancedistribution. Resultsshow that
for the caseof Bracknell, England the RMSE MBE and PAD of correcteddiffuse irradianceobtained
,
using the proposedmethod are 12W/m2, -0.7 W/M2and 3% respectively.CorrespondingRMSE,
MBE and PAD due to Drummond's method are 16 W/M2, -5.6 W/M2 and 4% respectively.For the case
2
2W/M
17
W/m2,
MBE
RMSE
Sheva,
Israel,
Beer
and a
the proposedmodel producesan
an
of
of
of
154
PAD of 5%. The correspondingfigures for Drummond's methodare 23 W/mý, -5W/m2and 7%
respectively.
155
REFERENCES
1. Drummond,A. J. (1956) On the Measurementof Sky RadiationArch. Meteor. Geophys.Bioklim. 7,
413-436
2. Kudish, A. I. and Ianetz,A. (1993) Analysis of Diffuse RadiationData for Beer Sheva:Measured
(ShadowRing) VersusCalculated(Global-Horizontal Beam) Values Solar Energy, 51,495-503
3. Painter,H. E. (1981) The ShadeRing Correction for Diffuse Irradiation MeasurementsSolar
Energy, 26,361
4. Vartiainen, E. (1998) An anisotropicShadowRing CorrectionMethod for the Horizontal Diffuse
IrradianceMeasurementsRenewableEnergy, 17,311-317
5. Ineichen,P., Gremaud,J. M., Guisan,0. and Mermoud, A. (1984) Study of the correctivefactor
involved when measuringthe diffuse solar radiation by using the ring methodSolar Energy, 32,585
6. Kasten,F., Delme, K. and Brettschneider,W. (1983) Improvementof measurementof diffuse solar
radiation Solar radiation data, F.2,221
7. Siren, K. E. (1987) The shadowband correction for diffuse irradiation basedon a two-component
sky radiancemodel Solar Energy, 39,433
8. LeBaron, B. A., Michalsky, J. J. and Perez,R. (1990) A simple procedurefor correcting shadow
band data for all sky conditionsSolar Energy, 44,5,249-256
9. Moon, P. and Spencer,D. E. (1942) Illumination from a non-uniform sky Trans.Illum. Eng. Soc.,
37,707-725
10. Muneer, T. (1990) Solar Radiation Model for EuropeBuilding Serv. Eng. Res. Technol.,11(4), 153163
156
I
.0
0
cu
'a
1.01
1.06
1.31
1.21
1.11
1.26
1.16
1.41
1.36
1.46
shadow band correction factor
(a) Drummond'scorrection factor range
1
. c2
cu
Co
1.01
1.11
1.06
1.16
1.41
1.31
1.21
1.26
1.36
1.46
shadow band correction factor
(b) Actualresults
Figure 7.1 Comparison of the range of diffuse irradiance correction factor given by Drummond's
method and actual results
157
600
E 500
400
--
-Z
6-
.7-.
A: 300
CL)
=, 7
-.
200
ts
100
0
u
jv
0
100
300
200
true diffuse irradiance
400
500
1
600-
(W/M2)
600
i:z
500
400
..
..
ap
A
A7
300
4
ým 200
lu m
100
0
o0
100
200
true diffuse
400
2)
irradiance (Wlm
300
500
600
Figure 7.2 Scatter plot of true diffuse irradiance versus corrected irradiance using the proposed
(top) and Drummond's model (bottom) -Bracknell data
158
1
(a)
1
1
(D
.
C)
0
CL
0
10.0
6.0
8.0
2.0
4.0
0.0
-10.0 -8.0 -6.0 -4.0 -2.0
4.0 5.0
2.0
3.0
1.0
0.0
-5.0 -4.0 -3.0 -2.0 _1.0
percentageerror, %
percentage error, %
4011
1201
1001
ý5
m
-Q
E
(I,
C
0
a-
80
60
CD
40
20
-10.0 -8.0 -6.0 -4.0 -2.0
0.0
2.0
4-0
percentage error, %
6.0
8.0
10.0
l
o
-10.0 -8.0 -6.0 -4.0 -2.0
0.0
2.0
4.0
6.0
percentage error, %
Figure 7.3 Proposed model's error histogram under all-sky (a), heavy overcast (0 < kt: 5 0.2) (b),
(d)
data
Bracknell
kt
(0.6
kt:
0.6)
(c)
(0.2
<
5
<1)
<
conditions
and
clear-sky
part-overcast
-
159
8.0
10.0
600
(b)
500
400
m
E
2 300
S
0
CL
CL
n
(Z
200
100
0
8.0
10.0
0.0
2.0
4.0
6.0
-10.0 -8.0 -6.0 -4.0 -2.0
-5.0 -4.0 -3.0 -2.0 -1.0
0.0
1.0
2.0
3.0
4.0
5.
percentage error, %
percentageerror, %
600
(d)
(C)
500
Q)
-0
400
300
0.
CL
m
200
100
20
oL
J.U -t$.U -b.U -4.U -Z.U U.U
percentage
Figure
Z.U
4.U
error, %
b.U
b.U IU.U
-10.0 -8.0 -6.0 -4.0 -2.0
0.0
2.0
4.0
percentage error, %
model's error histogram
under all-sky (a), heavy overcast (0 < kt: 5 0.2)
(0.2 < kt: 5 0.6) (c) and clear-sky (0.6 < kt <1) (d) conditions
Bracknell
data
-
7.4 Drummond
(b), part-overcast
160
6.0
8.0
10.0
600
ýz 500
4,
*
+
E+*
400
a)
LA
e
300
200
ts
U 100 o
0
100
200
True diffuse
300
irradiance
400
500
600
(W/M2)
600
C14
E
k
500
LV
400
V
All
300
M 200
v
100
0
0
100
200
300
400
500
600
True diffuse irradiance (Mm)
Figure 7.5 Scatter plot of true diffuse irradiance versus corrected irradiance using the proposed
(top) and Drummond's model (bottom) - Beer Sheva data
161
(a)
(b)
k)
.o
.0
0
CL
2
ca
'a
-14.0
-10.0
-12.0
-6.0
-8.0
-2.0
-4.0
6.0
2.0
0.0
4.0
10.0
8.0
14.0
-12.0
12.0
-8.0
-10.0
0.0
-4.0
-6.0
percentage error, %
4.0
2.0
-2.0
8.0
6.0
12.0
10.0
percentage error,
(c)
(d)
ci)
-a
E
(I)
C
0
0
0
-0
101
-12.0
-8.0
-10.0
0.0
-4.0
-6.0
-2.0
4.0
2.0
percentageerror, %
8.0
6.0
12.0
10.0
-12.0
-8.0
-10.0
0.0
-4.0
-6.0
-2.0
4.0
2.0
8.0
6.0
12.0
10.0
percentageerror, %
Figure 7.6 Proposed model's error histogram under all-sky (a), heavy overcast (0 < kt: ý 0.2) (b),
part-overcast (0.2 < kt: 5 0.6) (c) and clear-sky (0.6 < kt <1) (d) conditions - Beer Sheva data
162
(b)
(a)
m
a)
.0
E
I O(A
U)
0
0.
C',
C',
im.
2
cu
oL
-14.0
-8.0
-12.0
-2.0
-6.0
-10.0
-4.0
0.0
10.0
6.0
2.0
8.0
4.0
14.0
12.0
-4.0
-8.0
-12.0
-6.0
-10.0
4.0
0.0
8.0
-2.0
10.0
6.0
2.0
percentage error, %
percentage error, %
(d)
(c)
. im
12.0
401
Co
0
CL
a
cc
'a
I oi
oL
-12.0
0
-4.0
-8.0
-10.0
-6.0
-2.0
8.0
4.0
0.0
2.0
6.0
percentageerror, %
12.0
10.0
-12.0
-4.0
-8.0
-10.0
-6.0
4.0
0.0
-2.0
2.0
8.0
6.0
percentageerror, %
Figure 7.7 Drummond model's error histogram under all-sky (a), heavy overcast (0 < kt: 5 0.2)
(b), part-overcast (0.2 < kt: 5 0.6) (c) and clear-sky (0.6 < k, <1) (d) conditions - Beer Sheva data
163
12.0
10.0
Table 7.1 Mean Bias Error (MBE), Root Mean Square Error (RMSE) and Percentage Average
Deviation (PAD) comparison of the proposed model versus Drummond's method, Bracknell
All-sky conditions
MBE
(W/mI)
Proposed
Model
Drummond
Model
-0.7
-5.6
0.6 < k, <I
0.2 < k,:5 0.6
0<k,: 5 0.2
RMSE
(W/mI)
PAD
(%)
MBE
(W/ml)
RMSE
(W/ml)
PAD
(%)
12.0
2.8
0.4
1.6
0.7
15.7
4.2
0.0
1.4
0.7
MBE
(W/mI)
RMSE
(W/mI)
PAD
-0.3
15.1
3.9
-4.8
16.7
4.9
MBE
(W/ml)
-5.2
-24.5
RMSE
(W/ml)
PAD
(%)
12.4
3.4
27.4
10.7
Table 7.2 Histogram percentage error analysis results, Bracknell. Figures given below are the
number of data points in each category
All-sky conditions
-3-4
%
-1 -1
%
1-3
211
0
547
195
94
65
503
148
-3--1
N
-1 -1
1 -3
Proposed
Model
393
1259
Drummond
Model
374
1081
0.6 < k, <1
0.2 < k,:!ý 0.6
0<k,: 5 0.2
-1 -1
1 -3
N
304
504
297
429
-3-4
N
-3-4
(%)
-1 -1
(%)
1 -3
(%)
114
89
68
19
44
8
3
3
Table 7.3 Statistical comparison of the two models under discussion - Bracknell data.
Month
RMSE
(W/M2)
Proposed
Model
January
February
March
April
May
june
July
August
September
October
November
December
MBE (W/M2)
Drummond
Proposed
Model
model
4
6
9
12
18
10
18
10
11
10
4
2
5
7
15
19
20
14
20
19
16
13
4
2
-1.5
-0.6
-1.8
-2.5
4.3
-0.3
3.7
-4.9
-3.9
-6.0
-1.2
-0.5
Percentage Average Deviation
Drummond
Proposed
model
model
-1.6
-1.0
-6.5
-10.0
-4.4
-6.0
-3.7
-14.0
-8.0
-7.6
-1.3
-0.6
Drummond
Model
2.0
1.8
5.0
5.3
5.2
3.8
4.8
6.7
4.4
4.7
2.1
1.7
2.0
1.7
3.2
3.0
3.7
2.0
3.2
2.9
3.0
3.8
2.2
1.5
164
Table 7.4 Mean Bias Error (MBE), Root Mean Square Error (RMSE) and Percentage Average
Deviation (PAD) comparison of the proposed model versus Drummond's method, Beer Sheva
All-sky conditions
Proposed
Model
Drummond
Model
NIBE
RMSE
(W/m'L
(W/m')
PAD
MBE
0.6<k, < I
0.2 < k,: 5 0.6
0<k, :50.2
RMSE
PAD
W/M2
MBE
RMSE
PAD
MBE
(W/ml)
(W/m)
(0/. )
(W/m
PAD
RMSE
2)
(w/m2)
.
2.1
17.1
5.2
3.2
5.11
3.0
5.0
17.2
4.4
-5.3
23.4
7.3
4.7
8.5
7.0
0.5
18.4
5.2
I
I
I
-0.7
20.3
6.9
-15.6
30.4
9.0
I
Table 7.5 Histogram percentage error analysis results, Beer Sheva. Figures given below are the
number of data points in each category
All-sky conditions
0.6 < k, <1
0.2 < k,: 5 0.6
0<k,:: ý 0.2
-3-4
-1 -1
N
1 -3
-3-4
N
-1 -1
1 -3
N
-3-4
-1 -1
N
1 -3
-3-1
N
-1 -1
N
1 -3
Proposed
Model
42
110
147
2
22
78
19
56
48
22
32
21
Drummond
Model
39
58
57
2
2
5
20
43
25
18
14
27
Table 7.6 Statistical comparison of the two models under discussion - Beer Sheva data.
Month
RMSE (W/mý)
Proposed
model
17
january
February
16
March
17
April
17
May
17
June
21
July
15
20
August
September 23
October
16
November 18
December 17
MBE
Drummond
model
27
23
24
23
19
22
13
18
31
29
28
27
(W/M2)
PercentageAverage Deviation
Proposed
model
-4.5
-1.0
5.5
2.8
5.5
11.7
10.8
13.4
Drummond
model
-13.6
-8.0
-2.2
-3.6
0.7
6.6
6.5
10.9
-0.5
-5.9
-10.0
-8.9
-13.9
-20.5
-21.6
-18.1
Proposed
model
4.7
3.9
4.3
4.7
4.7
4.8
7.0
7.4
7.3
5.8
6.9
5.7
Drummond
model
8.1
6.7
6.5
6.3
5.2
7.3
6.3
8.4
10.1
10.5
11.7
9.5
165
8. VALIDATION
OF DPF MODELS
The validation of DPF modelshasbeencarried out by threeapproaches.The first approachwas to
apply the DPF modelsto independentlymeasureddatain Merchiston test room, and comparethe
measuredinternal illuminance dataagainstthosepredicteddue to DPF models.The secondapproach
was to check the DPF modelsusing one of the most establishedstatisticaltechniques:residualanalysis.
The third approachwas to comparethe DPF modelsagainstresultsdue to independentresearches.
8.1 CHECKING
THE LINEAR MODEL BY STATISTICAL
TECHNIQUE - RESIDUALS PLOT
The adequacyof a fitted regressionmodel can be carried out by the methodof checkingthe residual
is
linear
fitted, no
"whenever
due
The
the
to
applies
generally
a
model
model.
residual
method
plots
(the
is
how
[I].
The
the
to
there
e
graph
of
residual
procedure
produce
a
are"
many predictors
matter
differencebetweenobservedYOand calculatedY, valuesof the dependentvariable) plotted againstthe
independentvariablesXi or the observedvalue Y,, [2].
A satisfactoryresidualsplot is one that showsa (more or less)horizontal band of points giving the
impressionof Fig. 8.1. There are many possibleunsatisfactoryplots. Three typical onesappearin
Fig. 8.2. The first of thesethree(the funnel) displaysthe band of residualswidening to the right
showing non-constantvariance.The secondis a downward trend and the third is a curve. For the funnel
type of plot, it indicatesa lack of constantvarianceof the residuals.The corrective measurein this case
is a transformationof the Y variable. A plot of the residualssuch asFig. 8.2(2) indicatesthe absenceof
an independentvariable in the model under examination.If however, a plot such as Fig. 8.2(3) is
obtained,a linear or quadraticterm would have to be added.
Becausethe residualsand the Y,, values are usually correlatedbut the residualsand the Y, are not.
Therefore,ej = (Y. - Yc)j, i=l, 2,
is usually plotted against(Y, ) j. A slope in the ej and (Yji
n
...,
indicatesthat somethingis wrong. It is possibleto evaluatetest statisticson residuals,but it is often
difficult to know if they are sufficiently deviant to require action. In practical regressionsituations,a
detailed examinationof the corresponding residualsplots is usually far more infonnative, and the plot
166
will almost certainly reveal any violations of assumption serious enough to require corrective action
Ill.
The residualsdue to the S-DPF model (Eq. 6.9) were calculatedfor eachdatapoints from Craighouse
data.It is defined that,
S= Predictedinternal illuminance - measuredinternal illuminance, lux;
Ycl= Predictedinternal illuminance, lux;
Xj= Solar altitude, degree;
X2= sky clearnessindex, ratio;
Absolute error =S= Predictedinternal illuminance - measuredinternal illuminance, lux
The residualsplot of S versusYc is shown in Fig. 8.3. It can be seenin Fig. 8.3 that the residualplot
,j
showspattern of a horizontal band. This indicatesthat generally speaking,the S-DPFmodel being
examinedis adequate.Figure 8.4 showsthe histogramof the absoluteerror (residual) due to the S-DPF
model. It is shown in Fig. 8.4 that the distribution of absoluteerror is a normal distribution with a mean
value of -2.3 lux. The standarddeviation of the absoluteerror was found to be a=28.31 lux. This
implies that the S-DPFmodel can predict the daylighting performanceof straight light pipes with a
quite high accuracy,namely more than 99 per cent of all predictionsgiven by the model are found
within the error rangeof ±501ux.The meanvalue of measuredinternal illuminance was found to be
177lux, the percentageof prediction due to S-DPFmodel that fall in the error rangeof ±17.7lux (10 per
cent of meanvalue 177lux) was then found to be 75%. Consideringthat the sensitivity of human eyes
to illuminance at the level of 50lux is in a low order, it is thereforeconcludedthat the prediction given
by the S-DPF can be usedwith high confidencein practical light pipe design.
The residualplots of S versusX, and X2 are shown in Figs. 8.5 and 8.6 respectively.Figure 8.5 shows
that the residual due to S-DPF model is generally constant,independentto the changeof solar altitude.
Figure 8.6 showsa similar trend and presentsa profile of horizontal band, which confirms that the SDPF model is adequate.For solar energy applications,especiallyfor light pipe daylighting project,
sun's position and sky conditions are the most significant variablesto be considered.Figures 8.5 and
167
8.6 confirm that the S-DPFmodel hasadequatelydescribedthe effect of abovetwo factorsto the
daylighting performanceof light pipes. It is also worthy hereto point out that since S-DPFmodel uses
only non-sitespecific factors,it is thereforeexpectedto be applicablefor global sites.
8.2 VALIDATION OF S-DPF MODEL USING MERCHISTON TEST ROOM DATA
As addressedin Section5.5 that a total of 22 270 Merchiston test room datapoints for straight
light pipes of sevenconfigurationsunder all weatherconditionshad beenmadeavailablefor S-DPF
model validation. Merchiston test room datawere further divided into three groupsto revealthe
performanceof the S-DPFmodel under different sky conditions.The whole data setwere divided into
three groupsaccordingto sky clearnessindex, namely measurementstakenunder non-heavy-overcast
sky conditions(k,>0.2), under heavy overcastsky conditions (k,:ý0.2) and under all-sky condition. The
perfornianceassessment
of S-DPFmodel under abovedifferent sky conditionswere conductedand
reportedin the following threesub-sections.
8.2.1 Case-by-caseassessmentof the S-DPF model under non-heavy-overcastsky conditions
(kt>0.2)
The S-DPFmodel was applied to sevencasesof straight light pipe configurationsto examineits
performance.The sevencasesare:
Case1: light pipe in 0.21m diameterand 0.6m long,
Case6: light pipe in 0.45m diameterand 1.2m long, and
Case Might pipe in 0.53m diameterand 0.6m long.
Internal illuminance predictions due to S-DPF model for eachof abovesevencaseswere calculated
respectively. Scatter plot of calculated internal iluminances against measured illuminances were then
data.
based
independent
The
S-DPF
the
scatter plots were
to
on
of
model
performance
assess
obtained
168
generatedwithin Excel environment,and after that the best-fit trend lines were generatedby the Excel
to examinethe accuracyof the model. By linear regression,equationsand slopesof the best-fit lines
were obtainedand correspondingcoefficient of determinationR-Squarevalueswere reported.Results
are presentedbelow.
Case 1: Figure 8.7 shows the scatter plot of predicted internal illuminance against measured internal
illuminance for a light pipe 0.2 1m in diameter and 0.6m in length. The vertical distance between light
pipe diffuser and the working plan was 1.68m. The distances between three testing points and the light
pipe diffuser centre ranged between 1.68 and 2 meters. 'llie sky clearness index varied between 0.2 and
0.8. The slope of the best-fit trend line was found to be 0.96 and the R-Square value was noted as 0.87.
The mean error was found to be Olux and the RMSE was noted as 10 lux. In this case it can be seen that
the prediction of S-DPF is quite good. A RMSE value of 10 lux means that at least about two thirds of
predicted data given by S-DPF is within an error band that is negligible (± I Olux).
Case2: Figure 8.8 showsthe scatterplot of predictedinternal illuminance againstmeasuredinternal
illuminance for a light pipe 0.21m in diameterand 1.2min length. The vertical distancebetweenlight
pipe diffuser and the working plan is 1.12m.The distancesbetweenthree testing points and the light
pipe diffuser centrerangedbetween1.28and 2.10 meters.The sky clearnessindex varied between0.2
and 0.8. The slope of the best-fit trend line was found to be 0.96 and the R-Squarevalue was noted as
0.96. The meanerror was found to be -4lux and the RMSE was noted as 9 lux. In this caseit can be
seenthat the prediction of S-DPF is also good. A RMSE value of 9 lux meansthat at least about two
thirds of predicteddatagiven by S-DPF is within an error band that is negligible (±I 8lux). The RSquarevalue is ashigh as 0.96 which meansthat 96% of datais describedby the S-DPFmodel. It is
found however, that for this case,the S-DPFmodel seemsto slightly underestimatethe internal
illuminance, with a mean error of -4 lux. This might be due to the fact that when the light pipe was
longer, to test the internal illuminance at distancesabout I and 2 meters,sensorswere put further near
to the comer of the test room where internal reflection played a more significant role and led to a
higher reading of measuredilluminance.
169
illuminance for a light pipe 0.33m in diameterand 0.6m in length. The vertical distancebetweenlight
pipe diffuser and the working plan was 1.68m.The distancesbetweenthreetestingpoints and the light
pipe diffuser centrerangedbetween1.74and 2.14 meters.The slope of the best-fit trend line was found
to be 1.0 and the R-Squarevalue was noted as 0.88. The MBE was found to be -6lux and the RMSE
was noted as 55 lux. In this case,accordingto the figure of R-Square,MBE and RMSE, which are both
larger than thoseof previous cases,the performanceseemslesssatisfactory.However, it is noted that
for this case,the averagedmeasuredinternal illuminance was found to be 200lux, while the figures for
CasesI and 2 are 44lux and 51lux respectively.The percentageof RMSE to meanmeasured
illuminance for Cases1,2 and 3 were found 23%, 18%and 27% respectively.Therefore,the valuesof
RMSEs of cases1,2 and 3 arebasically comparableand in the sameorder. It is also notedthat the
averagedexternal illuminance for the third casewas found to be 46835lux, which is 35% higher than
Case1 and 32% higher than Case2. The maximum externalilluminance recordedduring the
measurementfor the third casewas found to be ashigh as I lOklux, and correspondinglythe sky
clearnessindex monitoredduring the day rangedfrom 0.2 to 0.8. The reasonwhy the third case
producesa larger RMSE may thereforebe due to the quite dramaticvarianceof externalconditions.
illuminance for a light pipe 0.33m.in diameterand 1.2m in length. The vertical distancebetweenlight
pipe diffuser and the working plan was 0.9 in. The distancesbetweenthree testingpoints and the light
pipe diffuser centrerangedbetween 1.32and 1.71meters.The slope of the best-fit trend line was found
to be 1.04and the R-Squarevalue was noted as 0.82. The meanerror was found to be llux. and the
RMSE was noted as 55 lux. It is also noted that the averagedexternal illuminance for the third casewas
found to be 47219lux, which is 36% higher than CaseI and 33% higher than Case2. The maximum
external illuminance recordedduring the measurementfor the third casewas found to be as high as
115klux, and correspondinglythe sky clearnessindex monitored during the day rangedfrom 0.2 to 0.8.
The maximum and minimum internal illuminances were found to be 600lux and 20lux respectively.
Case 5: Figure 8.11 shows the scatter plot of predicted internal illuminance against measured internal
illuminance for a light pipe 0.45m in diameter and 0.6m in length. The vertical distance between light
170
pipe diffuser and the working plan was 1.74m. The distances between three testing points and the light
pipe diffuser centre ranged between 1.74 and 2.06 meters. The slope of the best-fit trend line was found
to be 0.93 and the R-Square value was noted as 0.74. The mean error was found to be -25lux, which
was 10% of averaged measured internal illuminance. Corresponding figures for RMSE was noted as
65lux and 26% respectively. In this case it seems that the S-DPF model underestimates the internal
illuminance.
Case6: Figure 8.12 showsthe scatterplot of predicted internal illuminance againstmeasuredinternal
pipe diffuser and the working plan was 1.18m. The distancesbetweenthree testingpoints and the light
pipe diffuser centrerangedbetween 1.30and 1.62meters.'Me slope of the best-fit trend line was found
was noted as 75 lux. The MBE was found to be 6% of the averagedinternal illuminance of 289lux, and
RMSE was 26% of the averagedinternal illuminance.
Case 7: Figure 8.13 showsthe scatterplot of predicted internal illuminance againstmeasuredinternal
pipe diffuser and the working plan was 1.18m. The distancesbetweenthree testingpoints and the light
pipe diffuser centrerangedbetween 1.30and 1.62meters.The slope of the best-fit trend line was found
was noted as 106 lux. The MBE was found to be 8% of the averagedinternal illuminance of 403lux,
and RMSE was 26% of the averagedinternal illuminance.
8.2.2 Performance assessment of the S-DPF model under heavy-overcast sky conditions (kt:50.2)
A total of 7,200 datapoints of sevenlight pipe configuration caseswere measuredunder heaveovercastsky conditions (k,:50.2). S-DPFmodel was applied to predict the internal illuminance values
due to the light pipes. Scatterplots of the measuredinternal illuminance versusvaluespredictedby SDPF model for all heavy-overcastsky condition dataand for eachof the sevencasesare shown in Figs.
8.14 - 8.21. Statisticsresultsare shown in Table 8.1.
171
Figure 8.14 showsthat the slopeof the best-fit trend line for all heavy-overcastsky condition scatter
plot was found to be 1.12and the R-squarevalue was 0.94. The RMSE and MBE were found to be
31lux and 9lux respectively.The meanvalue of measuredinternal illuminance was 106luxwith a
maximum value of 519lux and a minimum value of I Olux.The PAD (averagedpercentagedeviation)
was noted as 20%.
Figure 8.14 shows that under heave-overcast sky conditions, generally speaking the S-DPF model tends
to overestimate the internal illuminance due to light pipes. This can be due to two main reasons.
First, the measurements undertaken in Merchiston test room was one year later than that carried out in
Craighouse test room. The very same light pipes (Monodraught) were tested in the two measurements.
During the two years' time, light pipes have been transported from sites to sites, and during the tests
they were also installed and removed quite frequently according to the test schedules. It is therefore
logical to assume that certain aging effect may have taken place during the course, which can lead to
slight changes of the reflectance of internal surface of light pipe tube. Swift et al [3] pointed out that in
the mathematical modelling of light pipe's transmittance of light, the reflectance of the internal surface
of light pipe tube plays an important role. Swift found that "the theoretical calculations are sensitive to
the choice of reflectivity, with changes in R (reflectivity, author) of 0.001 resulting in noticeable
differences in the calculated curve". This therefore suggests that the method of applying the internal
reflectivity value of 0.95 that was obtained based on Craighouse data, to Merchiston data may produce
noticeable system bias.
The secondpossiblereasonthat can contribute to the overestimateis that under low illuminance levels
the measurementsby Kipp and Zonon sensorsare subjectto more errors. It was found that under heavy
overcastsky conditions, the meanvalue of measuredinternal illuminance was as low as 106lux. The
rangesof the sensorsare all 5±lklux. The sensitivitiesof the three Lux Lite sensorswere given as
10.32[tV/Iux (±I%), 9.68pV/Iux (±I%) and 10.1lgV/Iux (±I%) respectivelyby the manufacturer
(Section 5.2). Thereforeunder heavily overcastsky conditions, the measurementerror due to the
sensorscan reachashigh as ±50lux (equalsto about 1% of the range),which accountsfor almost 50%
of the mean internal illuminance value.
172
However, it shall be pointed out that as an innovative device that utilizes sunlight, light pipe contributes
most to the daylighting when the sky is clear and sunlight is available.Unfortunately, when the sky is
heavy-overcast(kt:50.2), light pipes provide a lower level of daylight, though which is sufficient
enoughto form a good backgroundinternal illuminance. Nevertheless,artificial lighting is required
under such a condition if any sophisticatedwork that requiresdetailed information on objectsis to be
carried out. Bearing this in mind, it can be seenthat the performanceof S-DPF model under heavyovercastsky conditions is adequateenoughfor generallighting designpurposes.
8.2.3 Performance assessment of the S-DPF model under all-sky conditions
To reveal the over all performanceof S-DPFmodel, it is applied to the whole data set from Merchiston
test room. Internal illuminance predictions due to S-DPFmodel for all sevencasespresentedabove in
Sections8.2.1 and 8.2.2 were calculated.Scatterplot of calculatedinternal iluminancesagainst
measuredilluminances was shown in Fig. 8.22.The slope of the best-fit trend line was found to be 1.03
and the R-Squarevalue was noted as 0.90. The MBE was found to be -5lux, the RMSE 76 lux, and the
PAD was found to be 22%. The maximum of the internal illuminance was found to be 1986lux and the
minimum found l0lux. The high R-Squarevalue of 0.90 suggeststhat the S-DPF model built using
Craighousedatarepresentsmost of the independentlymeasureddatafrom Merchiston test room. The
slope value of 1.03suggeststhat the S-DPF model can estimatethe meanvaluesof internal
illuminances due to light pipes quite precisely. It is howevernoticed that for Merchiston dataset the
RMSE was found to be 76 lux, which is higher than the RMSE value of 27 due to Craighousedata.
This can be mainly own to following threereasons.
First, the external environmentfor the two testsin Craighouseand Merchiston test rooms were not
absolutelythe same.The Merchiston test room was build on the roof of a 7- storeybuilding with an
almost completeview to the sky (more than 95% of the hemisphere).However, the view angle of the
test room in Craighouseto the sky was not the whole vault. Trees and buildings within a distanceof 20
metersblocked about 20% of the sky although the southernhemispherewas clear. Therefore,the
coefficients developedfor one site may not be the best-fit value for the other. This can be the main
reasonfor the higher value of RMSE due to Merchiston dataset.
173
The second main reason that may contribute to the up-rise of RMSE may be due to the different
geometry of the two test rooms. To enable an almost complete view of the sky hemisphere, Merchiston
test room was built upon the roof of a 7- storey building within Merchiston campus. However, on the
other hand it was afterwards found that the wind speed on the top of the building was so strong that the
size of the test room had to be minimized so as to meet the safety requirements. The dimension of the
Merchiston
test room was therefore chosen as 2x2x2
Craighouse
test room (3.0 x 2.4 x 2.5 m).
have the some colour (colour
internal reflection
although
of wood), the smaller Merchiston
than that occurred within
model developed based on Craighouse
chance of prediction
Therefore,
3
in , which was less than half of the size of the
the Craighouse
data to the Merchiston
the internal surfaces of the two huts
test room caused more significant
test room. The application
data was thus inevitably
of the S-DPF
subject to more
error.
The third possiblefactor that may contribute to the higher RMSE value of 67lux is the asymmetrical
distribution of internal daylight due to light pipes. The S-DPFmodel assumesthat the internal
illuminance distribution on a working plan below the light pipe diffuser is symmetricalto the difftiser
centreand is a function of the vertical and total distancesof one point to the diffuser centre.From 30th
October 2000 to 14thJanuary2001, a purposedmeasurementwas undertakenin Craighousetest room
to test this assumption(seeSection5.6).
Light pipes of four configurationswere tested,which were light pipe 0.21ra in diameter and 0.6m in
length, 0.33m in diameterand 0.6m in length, 0.45m in diameterand 0.6m in length and 0.45m in
diameterand 1.2min length. Unfortunately it was found that the test for the 0.2Im-diameter light pipe
was faulty.due to the leakageof rainwater into the pipe. The rest of the testsproducedgood data and a
sum of about 900 datapoints were obtained. Resultsare shown in Tables 8.2 and 8.3. Table 8.2 shows
one day's data measuredfor the 0.33m-diameterlight pipe on 18'hDec 2000. It can be seenthat the
standarddeviationsof the five measurements(one Magetron sensorwas found faulty) taken at different
positions surroundingthe centrepoint of diffuser are averagedat a value of 86lux. For the 0.33mdiameterlight pipe, the averagedratio of the standarddeviationsto the averagedilluminance
underneathlight pipe diffuser was found to be 14%.The correspondingfigures for the 0.45m-diameter
light pipes 0.6m and 1.2min length were found to be 12% and 13%respectively(Table 8.3). Therefore
174
the asymmetricaldistribution of internal illuminance althoughnot very significant, has a substantial
effect on the daylighting performanceof light pipe. It is worthy however to point out that in real
applications,especiallyfor large rooms,usually a group of light pipes needto be installed to provide an
even distribution of daylight within the space.For occasionswhere multi-light pipes are installed
symmetrically to the room layout, the effect of asymmetricaldistribution of internal illuminancescan
be reduced,and the predictionsgiven by S-DPFmodel tendsto be more accurate.
8.3 COMPARISON
OF DPF
MODELS AGAINST RESULTS DUE TO INDEPENDENT
RESEARCHES
In this section the performance of DPF models are evaluated by comparing it against other independent
researchresults.
The first comparisonis madewith the study carried out by Loncour et al [4] on behalf of Monodraught
Ltd. Figures. 8.23 and 8.24 presenttheir findings that statethat:
(a) the actual,measuredlight transmissionwithin straight run of pipe was 48% as comparedto
93% that was claimed by the manufacturer;
(b) the diffuser had a loss of 44% of the incident energy;and
(c) the straight-lengthenergyloss was found to be 29% with an extra 5% loss for pipejunction. Thus for eachmetre pipe-lengthwith a pipe-junction the loss would be 29 +5= 34%. This
figure doesnot include the effect of loss due to diffuser.
To comparethe DPF models againstthe findings by Loncour et al [41, the drop of the daylight
penetrationfactor on one point in room due to the light pipe (with a 2-meter distancefrom the point to
the diffuser centre),as a function of the length of light pipe tube (not including dome and diffuser) has
been calculated.It is found that the per meter DPF drop dependson the solar altitude, sky clearness
index and the aspectratio of light pipe tube. Ile averagevaluesof per meter DPF drop for 0.33m,
0.45m and 0.53m diameter light pipes are 0.42,0.34 and 0.29 respectively.
175
Mus the figures given by DPF model for 0.33-m pipe diameter are comparable to the results given by
Loncour et al [4]. Note that the per cent drop of 42% includes the effect of energy loss through the
diffuser and hence shows slightly higher figure than 34% for a comparable aspect ratio of 3.6 (pipe
diameter 0.33m).
Most scientific literature is basedon a more objective approachfor reporting energyloss in light pipes
and that is to divorce from a per metre loss and insteadreport in terms of loss (or transmission)as a
function of aspectratio (light pipe length to diameterratio). Sucha plot is shown in Fig. 8.25, produced
by a Liverpool basedresearcher,Carter [5]. Note that Carter's loss factor of 60% for an aspectratio of
3.6 is higher thanNapier's result of 42% (averagefigure). Note that Carter's data are within close
proximity to the study undertakenby Love et al (1995) in Canada.Carter has taken a figure of ±10%
difference betweendatasetsas being acceptable.A point of ftirther note in Fig. 8.25 is that there can be
variations (scatter)in the illuminance readings- internal as well as external.Figure 8.26 showsthat
Carter's estimateof energyloss in a 30-degreebend is 20% [5]. This is very close to Napier-based
measurementsthat were found to give this value as 21%. David Jenkins [6] undertook ftirther
comparativework betweenNapier and Liverpool studiesand two suchplots are shown in Fig. 8.27.
Once again this plot enablesvalidation of the DPF models.
Figure 8.28 showsthe light transmissionplot of a light pipe. The point that is worthy of note here is
that daylight is a very variable resource.Even at a one-minutefrequencythere is a significant change.
This must be bome in mind whenevermeasurementsrelatedto light pipe performanceare undertaken.
For short pipes DPF producessimilar resultsto thosefound by Shao[7] and Oakley et al [8]. Note that
Oakley quotesDPF values of 0.48%, 0.38% and 0.18% respectivelyfor aspectratios of 2.1,4.6 and
8.4.
The Napier DPF hasNOT beenevaluatedfor long pipes. Early indications basedon abbreviated
analysissuggestthat a higher loss of energytakesplace within the entrancelength of the light pipe (see
the shapeof the asymptoticcurve producedby Carter, Fig. 8.25). This is analogousto a well-known
phenomenonwithin fluid flow in pipes. Figures 8.29 and 8.30 demonstratethis concept,i. e. two
sourcesof energy loss are shown - entranceto the pipe and developing flow within the starting length.
176
At this stage it is difficult to explain this phenomenon for light flow but further research in this respect
to comparethe performanceof longer light pipes againstthat of shorterpipes could lead to new
discovery.
8.4 THE DESIGN TOOLS
The proposedmodel S-DPF (Eq. 6.9) enablesthe prediction of the internal illuminancesthat are
achievableby opal diffuser light pipes of various configurationsand under different sky conditions.As
a set of guidelinesfor practical engineeringdesign,Tables 8.4 - 8.9 provide the internal illuminances at
various distancesthat can be achievedby opal diffuser light pipes of varying geometrical
configurationsoperatingunder a set of three weatherconditions for Kew, London [9]. The tablesalso
cover a set of three seasonalvariations: summer,winter, and autumn and spring together.
Basedon E-DPF (Eq. 6.11), it hasbeenfound that light pipe's daylight transmissionreduction factor
due to the use of one 30-degreebend is around 0.2. This factor can be used as a simple guideline for
elbowed light pipe design.It hasalso beennoted that the efficiency loss due to the introduction of
bendsis a function of solar altitude, which meansthat for different weatherconditions and different
times of the year, the actual transmissionreduction factor differs. The more sophisticatedmathematical
model E-DPF (Eq. 6.11) should thereforebe applied wheremore accuratedesignfor elbowedlight
pipes is required.
To predict the achievableinternal illuminance by straight light pipes with flat diffusers, a multiplicative
factor fD is used to obtain the internal illuminancesvaluesindicated in Tables 8.4 - 8.9. For elbowed
light pipes with flat diffusers, combining the use of fo with the factor fl,,, =0.2 may be usedas a
simpler guideline. However, by applying the fD to the resultsgiven by E-DPF model (Eq. 6.11) a more
accurateperformanceassessment
may be made.
Additionally, within the Excel Visual Basic Application environment,lux plot [Courtesy:David
Jenkins,Monodraught] that can visually describethe internal illuminance distribution due to light pipes
has been constructed based on DPF models. The lux plot can be used by building or lighting designers
177
in both of their initial and final stages of design of light pipes. Figure 8.31 shows an example of such
lux plot.
8.5 UmITATIONS
OF THE DPF MODELS
Any modelhasits own limitations;DPFmodelis not anexception.It is thereforeworthyhereto
addressthe envelop of the S-DPF and E-DPF models,so as to guide the application of the models in
real designs.
S-DPF and E-DPF modelswere developedand validated using measurementson 17 different light
pipes configurationsand measurementsettings.Sinceas the basis of the modelsthe measurementshave
boundariesin various dimensions,it is believed that the DPF modelshave an envelopetoo. The
envelopestipulatesthe condition under which a given model can perform with its accuracycoherentto
the statistical evaluationof the model. The envelopof the DPF models is decidedby the boundariesof
measurementconditions. However, in developingthe DPF models,empirical mathematicalformulae
and physical reasoninghavebeenapplied, which fonris the basis on which DPF models can be
expectedto work well in a broaderrangeof conditions.
Table 8.10 showsthe measurementsettingsfor all performancemonitoring on the daylighting
performanceof light pipes with opal diffuser. Geometrically,there are mainly five dimensionsof
boundaries,which are the diameter,length, number of bendsof light pipes, and the vertical and total
distances(seeFig. 8.32) betweena given point and the centreof a light pipe diffuser. On the other
hand, the externalweathercondition producesother threeboundariesincluding the solar altitude (aj,
sky clearnessindex (k,) and the global illuminance (E,g). According to Table 8.10 and the limitations of
externalweatherconditions of ct, k, and Evp the envelop of the DPF models can be clarified, as shown
in Table 8.11.
The boundary of DPF models is constrainedby the facility availability of the project. However, the
applicability of DPF modesis not only limited to the configurationsand external conditions given in
Table 8.11. When there is an attemptto apply the DPF modelsto a broaderrangethat is beyond the
boundarybeing given in Table 8.11, an estimatedresult that is of a right order is expectableand
178
achievable. But at the same time, it is also worthy here to clarify that the accuracy of the model, where
it is applied to a condition that is out of the boundary,has not beenwell validated.
179
REFERENCES
1. Norman, R., Draper and Smith, H. (199 8) Applied Regression Analysis (Third Edition), WileyIntcrscience Publication, USA and Canada.
2. Muneer, T. (1997) Solar radiation & daylight modelsfor the energy efficient design ofbuildings,
Architectural Press, Oxford
3. Swift, P. D. and Smith, G. B. (1995) Cylindrical mirror light pipes, Solar Energy Material and Solar
Cells, 36(2), 159-168
4. Loncour, X., Schouwenaars,S., L'heureux, D., Soenen,S., Voordecker,P., Wouters,P. (2000)
Performanceof the Monodraught systemsWindcatcherand Sunpipe,BBRI - Belgian Building
ResearchInstitute
5. Carter,D. J. (2001) The Measuredand PredictedPerformanceof PassiveSolar Light Pipe Systems.
Lighting Researchand Technology,34(l), 39-52
6. Muneer, T., Zhang, X. and Jenkins,D. (2002) Brief report on the performanceof Napier's Daylight
PenetrationFactor (DPF) and its comparisonagainstother publishedwork, Report submittedto
Training CompanyProgramMeeting
7. Shao,L. (1988) Mirror lightpipes: Daylighting performancein real buildings Lighting Researchand
Technology,30 (1), 37 - 44
159-174
9. Hunt, D. R. G. (1979) Availability ofdaylight, Building ResearchEstablishment,Watford
180
-Y,,
......................
..........................................
............
Xi or Y,,
Figure 8.1 A satisfactory residuals plot
Yc
-Y.
Xi or Y,,
10
...............
.................
..........
.............
Yo
(2)
Yo
(3)
Figure 8.2 Examples of characteristics
shown by unsatisfactory
residuals behaviour
181
illuminances (Y-axis) versus predicted values (X-axis) for S-DPF model, Unit: lux
14000
12000
10000.
8000
6000
4000
Std. Dev = 28.31
2000
Mean = -2.3
,N= 25723.00
Ei=L01ý1
>e ýo,-0 ý'oý,
ý,
ý,
ýo
ý,
:
000 00
Figure 8.4 Histogram
of data points
of absolute
error
due to S-DPF
model, Unit
for X-axis:
lux, Y-axis:
number
182
illuminances (Y-axis, Unit: lux) versus solar altitude (X-axis, Unit: degree) for S-DPF model
illuminances (Y-axis, Unit: lux) versus sky clearnessindex (X-axis) for S-DPF model
183
Figure 8.7 Scatter plot of predicted internal illuminance against measured internal illuminance
(light pipe 0.21m in diameter and 0.61m in length), Unit: lux
6UU -
250 -y0.9572X
0.9641
200 A,
150 100
-
50
0
0
50
100
150
200
250
30C
184
r%r%
m
OUU
y
1.0215x
600 -R0.8759
400 200 0
0
200
400
600
800
800
y=1.0426x
600 -W=0.8235
OP
400
200 -
+IV'
0
0
200
400
600
800
Figure 8.10 Scatter plot of predicted internal illuminance (Y-axis) against measured internal
illuminance (X-axis), (light pipe 0.33m in diameter and 1.22m in length), Unit: lux
185
-7r%r%
I uu
600
500
400
300
200
100
0
100
0
200
300
400
500
600
700
1500
y=0.9987x
R2= 0.8643
1200
4V
900
600
4.
4
300
0
0
300
600
900
1200
1500
186
1600
1200
800
400
0
0
1200
800
400
1600
600
Y=1.1 199X
500 -W=0.9378
400 *+
+
300 200 -+
100 00
100
200
300
400
500
600
Figure 8.14 Validation: scatter plot of measured (X-axis) internal illuminance versus predicted
values (Y-axis) due to S-DPF model (Merchiston data, heavy-overcast sky), Unit: lux
187
8(
40 20 0 -0
Z-u
4U
bu
öu
Figure 8.15 Validation: scatter plot of measured internal illuminance (X-axis) versus predicted
in
diameter
data,
heavy-overcast
0.21m
(Merchiston
due
S-DPF
(Y-axis)
to
and
sky,
model
values
0.61m in length), unit: lux
100
80 -y2=0.9384x
so -R=0.7203
40 -
20 -+
0
0
20
40
60
80
100
values (Y-axis) due to S-DPF model (Merchiston data, heavy-overcast sky, 0.21m in diameter and
1.22m,in length), unit: lux
188
189
190
in
diameter
data,
heavy-overcast
0.53m
(Merchiston
S-DPF
due
(Y-axis)
to
sky,
and
model
values
values (Y-axis) due to S-DPF model (Merchiston data, all weather), unit: lux
191
3.3 Optical efficiency
The optical system can be split up into three parts:
" The transparent top dome
"
The highly reflective aluminium ducts
9 The enddiffuser
3.3.1 The manufacturer stated performance of the aluminium ducts
Light losses in the ducts amount to 8% per bend and 3% per meter of straight duct according
to documentation (Data Sheet No. 1, Monodraught, 1999). The light transmission of the two
installed systems can as a consequencebe calculated. To control these values the light level
at the beginning and at the ending of Sunpipe 2 were measured, giving the real light
transmission of the duct.
Theoretical
Sunpipe
Measured
Sunpipe 2
Sunpipe 2
Light transmission duct
74%
93%
48%
Global light transmission
33%
42%
22%
Table 3: Light transmission through the Sunpipe system
For the calculationof the light transmissionof the global systemthe top domeandthe diffuser
aretakeninto account.
For the theoreticalvalues the normal light transmittancewere used properties(measuredat
BBRI, resultsare given in Appendix A). Theseamountto about 50 % for the diffusersand
for the top domes. Thesewere chosenbecausethey are typically the valuesthat
about90'D/o
would be included in product specifications(although not yet included in the product data
sheet).
luxmete
Referenceluxmeter outside
Figure 21: Determination of the
hemispherical transmittance
For the measuredvalue a test was performedto
determinethe hemisphericaltransmittance(Figure
21) of the top dome and the diffuser. These
amountto 56 % for the diffuser and 80 % for the
top dome.
In this particularcase,the useof the normalvalues
insteadof the hemisphericalvalues doesnot lead
to a different result.
Renuirk:
Thesemanufacturerspecifiedvaluesseemto be quite idealistic and lead to a performancethat
is almost twice as good as the real performance.Again, more prudence in product
specifications
would be recommendable.
Aonodraught- Final report
November 2000
ISM
141
Loncour
al
by
et
15 of report
page
Scanned
of
8.23
copy
Figure
192
3.3.2 Detailed analysis of light decrease in the aluminium duct
To get a better insight in how the light flux diminishes in the duct, a detailed measurement
campaign was set-up. The decreaseof light flux through the duct was determined by on-site
measurementsin Sunpipe 2. The illuminance in the duct was measuredalong the length of
the duct and comparedwith the referenceluxmeter outdoors, under an overscastsky.
The set-up (Figure 22) is comparableto a daylight factor measurement.Figure 23 shows how
much light is left at every point of the duct with respectto the duct entrance.
The effect of the direct view of the
sky can be determined. As can be
seen it decreasesvery quickly from
0.0M
%to
100
I
%after
I
only
meter.
---(),25m
50ni
__V,
Flu\ýctcr
inside Sunpipe
0,75m
----------- ---
ReferenceILLxmctLroutside
44553WIM
1. . 7"
In
L. I
j, ------------'Jk(
- ------ 4-
The remainder of the light is the
interrcflected part, which increases
steeply in the beginning of the duct
and after 0.75 rn decreases slowly
with the absorption of light by the
duct. An extra light loss of about
5% is noticed between 1.25 and 1.5
rn, right at the point where two
junctions were made.
The average decreaseper meter of
duct, basedon the values where the
direct part is almost completely
gone (starting from 75 cm), Is in
this case 29 %, meaning that we
have a light transmission per meter
of 71 %. This is a lot worse than
the stated 3% per meter.
a '10
Figure 22: Measurement of light decreAse in Sunpipe
100% fý
wt k" atmýM 1.~
70%
60%
5os
-1
30% .
20% 10% .
os
05
0
1
1.5
LeNth
i
theoretical --
2
2.5
(-)
measured relative -
direct part -
reflected part!
Figure 23: Light decrease along the length of the Sunpipe
L%nodraugM- Final report
November 2000
16/48
141
Loncour
al
by
et
16
of report
Figure 8.24 Scanned copy of page
193
IM
-
90
80
70
60
50
eu
ui
40
30
20
-------
...............
10
0
0123456789
10
Aspect rallo
Figure 5 (a) Graph of pipe efficiency against aspect ratio. (b) Graph of pipe efficiency against aspect ratio
Figure
8.25 Scanned
copy of Figure
5 of Carter
[51
120
100
80
60
40
20
0
0
20
60
40
100
so
Bond angle
Figure 6 Graph of efficiency against bend angle for bend
length equal to pipe diameter
Figure
8.26 Scanned
copy of Figure
6 of Carter
[51
194
Comparisons
of predictions
and measurements for 330mm Sunpipe, 0.6m in length,
10/8/99
University of Liverpool results for Eh range 9900-52200lx
Predicted corresponding to external luxes recorded in experiment
350
300
250
hL
200
z
150
1A,
100
p
50
L
11
120
13 0
125
Comparisons
of predictions
135
Time of day, h
14ýO
145
150
and measurements for 330mm Sunpipe, 0.6m in length,
2917/99
500
450
,
mý
a.
a M. a
3,
Z.
400
350
300
-4 250
E
200
ISO
University of Liverpool results for Eh range 57825-102825lx
100
50
AS -- Predicted corresponding to external luxes recorded in experiment
0
12.5
13
13.5
14
Tlý
14.5
15
155
of day, h
Figure 8.27 Comparative plots showing close conformance between Liverpool
Napier's DPF model estimates
measurements and
195
100000
............
ioooo
1ON
100
10
'b
4ý1
'5
'5
(P
A
'b
Q11, z"
134
Q0
cqý
co
(Zý
zq
e
't,
Nczý
"3
'b
ý-
-IS
'b
10
113
:.5
C)
"A
'5
NQ,
Figure 8.28 Plot showing measured external and internal illuminance
lux
NIZ,
4S
NIS
NO
AAA
NI:
at Napier University,
IN
ýN
unit:
FIGURE 8.25
Entrance [Iow conditions and loss coefficient (Refs. 28. -19).
(a) Reentrant. K,
OX (b) Sharped
cdged, K, - 0.5,
wi Sll(-,Iitl I rounded.
K, -7 0.2 (see Fig.
8.27). (d) Well
rounded, K, = 0.04
(see Fig. 9.27).
Figure 8.29 Loss of flow energy at entrance to a conduit
196
Figure 8.30 Loss of flow energy during the 'starting-length'
within the conduit
Lý] File Edit View Insert FQrmat Jools Data Window Help
X Gb lftl
43
10
,w
wBz
11 IF IF aMW%,
70%
*68;'8 1iF i.ir
-ý
Figure 8.31 An example of lux plot ICourtesy: David Jenkins, Monodraught]
! ). .&ý
Figure 8.32 An illustration
of "vertical"
distance H, and "total"
distances D used in DPF model
198
(01%
'Ei
2A
ýD
-
-
\tD (=)
rýc
rn
00
cq
C,
cq
rn
ý,0
rn
kn
rn
rn
x
>Z
<
"0
r-
rq rn 0
<D
vi
10
Ici
pe
AA=,
cl
E
42
Kr)
cý
rc;
rcý
00 cý C% 0%
c; c5 2 2
ýZID
Icýri 'lý
CD -N lý
CD NZ
-d
C) - 'C '0 "C MJ 0
"C 'CJ
r.
=
Z'
"Ci "C "c "Ci
00
cý
cn
le CD "CD "0 cý
cý
clý 1:ý cý
CD CD 0
CD
r-
-5
5
Eý -5
--r,
CZ g'. r.
ýa -ciýE3
2 Ei VIEi Ei E
rn rn
n
ý 11 lý `I: v-)
C) 0 C:) (D
Rý
:4.9
2
Rý.Eý
L
.
gz
.!
im. ný $Z n.
5 A.- ý5Z ý5 15Z
.:
.
00
-
u
E-
cq
r, )
lu
u
zr V)
&)
iL)
%M r(D
(D
vlý \.0 r-
Table 8.2 Sample data of Internal illuminance
2000)
Date
Time
Sl (LUX)
S2 (LUX)
distribution
S3 (LUX)
(0.33m-diameter
S4 (LUX)
light pipe, 18th Dec
S6 (LUX)
Average lux SDV, lux
18-Dec-00
9: 22: 12
119
82
82
84
110
95
18
18-Dec-00
9: 23: 12
127
88
86
92
120
103
19
18-Dec-00
9: 24: 12
138
93
91
100
127
110
21
18-Dec-00
9: 25: 12
144
100
98
106
132
116
21
1B-Dec-00
9: 26: 12
148
104
101
113
138
121
21
1B-Dec-00
9: 27: 12
151
106
106
118
140
124
21
18-Dec-00
9: 28: 12
155
ill
110
116
139
126
20
18-Dec-00
9: 29: 12
156
115
115
109
135
126
19
18-Dec-00
9: 30: 12
155
115
115
108
137
126
20
18-Dec-00
9: 31: 12
155
114
109
113
142
127
21
18-Dec-00
9: 32: 12
161
113
109
115
141
128
22
18-Dec-00
9: 33: 12
167
120
117
116
142
132
22
18-Dec-00
9: 34: 12
174
130
125
124
150
141
21
18-Dec-00
9: 35: 12
183
135
130
134
162
149
23
18-Dec-00
9: 36: 12
194
139
135
137
171
155
26
18-Dec-00
9: 37: 12
204
145
144
143
177
163
27
18-Dec-00
9: 38: 12
213
152
145
157
184
170
28
18-Dec-00
9: 39: 12
224
156
149
168
193
178
31
18-Dec-00
9: 40: 12
239
165
158
174
206
188
34
18-Dec-00
9: 41: 12
255
177
171
189
225
203
36
18-Dec-00
9: 42: 12
272
191
186
211
245
221
37
18-Dec-00
9: 43: 12
292
208
203
230
260
239
37
18-Dec-00
9: 44: 12
306
221
221
250
275
255
37
18-Dec-00
9: 45: 12
320
234
238
270
293
271
37
18-Dec-00
9: 46: 12
336
245
251
280
305
283
38
18-Dec-00
9: 47: 12
350
255
258
290
322
295
41
18-Dec-00
9: 48: 12
370
264
263
305
337
308
47
18-Dec-00
9: 49: 12
391
281
279
315
344
322
47
18-Dec-00
9: 50: 12
410
304
303
329
360
341
45
18-Dec-00
9: 51: 12
422
317
321
362
391
363
45
18-Dec-00
9: 52: 12
443
331
340
404
422
388
50
18-Dec-00
9: 53: 12
463
345
361
433
447
410
53
18-Dec-00
9: 54: 12
490
363
379
447
468
429
56
18-Dec-00
9: 55: 12
524
389
394
444
473
445
57
18-Dec-00
9: 56: 12
545
415
407
435
468
454
56
18-Dec-00
9: 57: 12
547
424
415
438
477
460
54
18-Dec-00
9: 58: 12
554
418
413
453
494
466
59
18-Dec-00
9: 59: 12
561
411
415
470
505
472
63
18-Dec-00
10: 00: 12
568
422
434
489
518
486
60
18-Dec-00
10: 01: 12
582
438
453
507
533
503
59
18-Dec-00
10: 02: 12
600
447
466
517
549
516
62
18-Dec-00
10: 03: 12
609
451
469
521
560
522
65
18-Dec-00
10: 04: 12
609
449
463
523
565
522
67
18-Dec-00
10: 05: 12
614
446
457
525
571
523
72
18-Dec-00
10: 06: 12
629
449
455
534
580
529
78
18-Dec-00
10: 07: 12
640
457
460
553
594
541
81
18-Dec-00
10: 08: 12
653
469
476
590
619
561
84
200
Table 8.3 Summary of the Internal illuminance
distribution
test results (Craighouse test room)
Diameter,
m
Length,
M
Averaged Standard
Deviation, lux
Averaged Internal
Illuminance, lux
0.33
0.45
0.45
0.6
0.6
1.2
80
48
63
603
389
495
Ratio betweenStandard
Deviation and internal
illuminance, %
13%
12%
T 13%
201
CIA
2
rq
"CJ e
CD V)
e rq
r4 -
CD (D 0
CD 0
tA vi
rn 0., CD ýo W) C> ;ý cli
00
(11
rn -
CD V) CD CD vi 0 C> vi
11
0 "'
:: > CD
<" \O
r- ,:V')> CN
ýQ le rq V') r)
"000
E
rn
CD
In c> vý v"ý C)
11 11 r-i rq 1-
'Q 'e
11 "1, `1, ,
r"U r, 1 -
5
e
12
.
'. 12
00
-
-
4.
0
CL
?
,
vi
-
1
C> ci
00 le
v-i
0
0
V-ý CD V)
V)
vi
E =
-
CD
CD kr) V'l CD CD CD CD C> CD
c-i \m oo c> cý vi (Z rn rq
CD (Z (Z vlý vi
10 (1) 00 Ilt rq
(Z
-
CD -
00
r, 1 -
CD
v)
2
Ir
rq
C,4 -
CD
IT
0I "CJ11i t-
CD
CD
kn
(D
vi
vi
-e rn r4 v) rq %Z -
.0
CD kn CD CD kn kn 0
CD
00 *0 trý
le kn rn r, c> 0
00
cýI r, 4 -
C> vi
IZ rn
0
(11
-
Ei
-
Z
e.)
vý CD CD vl
oý, cý -0 rn
kn vi
c> r-
V) (Z
Wý
CD
V) %M C> CD rn C> 0
(Z
\ýo
VI 00 t
ýt i rq i VI i fli i -
ýt
clý -
vý
0
00 le
-
(Z
r-
cý
le
cý
\,O
-
V'l
(n
rn
cý
00
V')
V)
rn
C> rq
rl i -
CD
CD
-
"Ci
11 e
-zj
-
vl
"CJ (N
0
N
. r.
0
4.1 en
(U rn CD V) vi
11 11 Cq -e
*
ýý
cý
c5 cý
ýo rn
%Z
rq
vi ,
c-i cý
0
r-
'
00
,
ýz
C> r14
c2 0
ri V)
cý
rn
ýo rn
-2
'
vi
-
kn 0
r, ) rq
CD V'l
rq
-
-
r-
C,1 VI
rn
e
0 ,
CD
ýt <=> vlý CD 0
(D
c
CD CD CD
-0-
ý_o
"CJ
u
r)
rn
cl)
-
ýa1 V)
-
-
CD
-
V)
ce
Z-
l
-
c>
i
'n 111
Irl l',', Irl
CD
11 0
"0
-
ol o
ýo rn
vi
V)
n 0
r1) rq
Cý, c: > C> (D =ý
CD
rq V). V') V') v»i v',
rn (q -
1
Irl
CD
ý
-e> =
't
-
CD vi c> V-ý vi V-ý V-ý tn vi tA CD vi
00 e 00 ýt rq e rq - r-i - - - -
(r)
vi
10
Ici
. 9:
2.
e
u
9
t..
m
U
ce
E-
>
0
>
9 u
ý.
,U
2
>
0
4
>
u
>
o t) 4, 0 2
m A
D
,
4,
e
e
ý
m
m
cu
>
>
ý
r.
u
t
u
0
ü
.
U
P. C
> U im. CD
> U. P'L'3,
>
>
CD
o
CD
u
'im.CD
0.
0.
Cd
ce
'i I:
ý2
CD
=i
C: )
c:,
CD
22
CN
C>
CD
CD
ll)ýo
C: )
rn
-
.c,
rn
cli
I
,
7: 1
kn
C)
trl
ýo
til,
-
-
0
In
tn
en tn
rl)
C14 rn
r-
r-
kn
-
E
n
rWl
(= C) W-)
tn
r-
C)
(=
tn
C>
-1
en C*4 ell
C,4 -
tn
IT
Rzr W)
m
C>
t)
c)
r,
-
-
ýT
m
N
M
r4
CN
tn
-'ý -e- llý 9-
-
-
-
0
0
M
0
V-1 C> W) (:::, ir) CD
C14 rq
N
-
N
o
00
0
ýo
W-1 kf)
V')
"It
C>
I
IT
C)
M
C)
'T
C)
en
00
o
%,
1.0
IT
1-n
1:
C) Cli
N
C>
tt*)rqC) W)
C14 ti) C>
ýt 1 Cý>
cl) en C)
rn
-
ltý
I-
00 -
00 ýo 00 "o 'IT IC W'Trf) "It M Cq
4.
0
Q)
'a
C'4
0
kr)
C'4 N
0
N
te)
-
0
tn
C-4 -
c)
-
kn
-
o
-
5
r-
0
.0
11
u
r
"o
.
C, 11)
tn
- n n 2 2 2 2
1111
"
tn tn tf) C) o
:r
m
-
1
I
-= c> c:, %n -10 in
tn tr) tn C)
VI C> tn
C-4 en C,4 -
eq
V') V') VI vi
tn V') tf)
0M
=
C)
E5 1
cd m
(=
0
11 11 W)
%0 tn
tn C) C) C) vi
M
"t
rn
0
C'4 C*4 N
"a
r)
vi
tn
tn
tn
v
ýC-
-
tr)
tn
-
-
-
-
tn
co
V')
VI
vi
W) tn
kl-j
C13
C)
E
(D
eq
Cq -
-
-
-
-
-
Irl
11) trl
Irl
W) V') tn
V)
10
0
al
>
0
ti
0
.4
C)
C)
\0
(D
>
0
cts t: ,
M
Cý
in
M
>
.2
0
m
C*
(D
>
Q)
>
>
t:
C':
cli
2
(U
>
$ý
cl
>
0
ol
1)
>.
M
.2
t:
'd
C4
Cl
>
>
0 1U 12ý0 U a, 10 ul pýl o UI P. 10
C)
ý2
C)
ýr
C14
C)
C>
C,
en
IC
en
E
Eý
Cýl
N
C)
ý10 kn
00
-
0
C>
m 00 00
'IT
trl
C)
11 t-
I-
C14 C)
,a
5
11 -
0
(n
W)
0
It
:3
I-
7,
e-
C)
-60- "o
I tfl
ýn
0
Q)
0
tri
0ý
r-
(ý
(1)
I
5f
. cli
C's
I
-9-
I
C>
rý
cqs
-
0
'n
(n rq
W)
l
(14 en
rn
-
o
0
W)
=
C,
%C
0
ff)
t-
0
CD V-) 0
0
In
IT
0
ti,
Irl
CN
tn
kil
kn
C'4
-
-
0
14'T
V-) 0
00 0
0
r-
0
01, C4 -
I
I
I
I I
=
r
-
00
W') CD 0
r')
-
C14
cl)
0
0
C)
"
CD
tn
en t-
tf .I
-T N
tt .I
ýo
In
C14
-tT
-
I I
"0
-
C14
en 00 'IT
I
0C:,
- - -I- (=
clý -
t6l
0
,IV
m
4
C.
eq
C)
00
tn
00w)00
00
"V
Q
C:
)
110
0
M
C: ) (D
C*, tn
V'I
rn
0
"1
,
'1',
I
I
110
00
'IT
- 00
- - Clq
0
Z:
.
c
0
C) 0
(=) ('4
Lrl
"T 0
'o
o
0
:t
0
ýo
0
tn
CN
-
o
a,
00
Vn
-
1 -
Ilzr <71, ýo (14 ,N
C,4 W) C14 "r
Cý
0
en C)
r'IT
-
11 'o
1
VI
VI
ýr
-
C)
C)
E
r-L
ý=
CD
-
o
cl
o
V-)
ýo 'IT 00 <D cq en
IC
(14
.Zr
00
"tý
ý:,
00
-
101
=(=
cq V) I
11 r- W) 0
Cý
tn
C*
ýa
.
0
it')
en C14 ý=
r,
C14 -
00
ýc
'IT -
M
-
I
9
t4l)
W)
'IT C11
C-4 -
C'j
r)
-
tn
-
-
2
cl
ti
0
M
10
C)
cf)
M
ý,o
C,4 -
Eý'In
0
r--
-
0
0
C7,
ýo
(=
N
-
ýr
ý::
c,
11
- 11
tri
en (14 'IT C11 -
CONkn en "o
C)
kn
Nr
C)
t'll
00 C14
C> (0
M N
C)
-
W)
V)
0
in
tn
0
m
ýo
cq
C14 'IT cli
III
1
til
cl
tn
cq
en (11
kr,Irl 11)
11r,
u
0
E0
E
C)
C14
11
ý
11
-9 - liz
-41) C)
tn
<ý
W) rn
-
rn
"T
Cl
ýr
kf-)
-41
C>
Cý W) M
11
4
_
0
C,
C)
r-
+
-
rtý
,-11 1 0
-
1
o0.00C,4
_j -
-
-
u
>
?
ctl
m
L)
cd
C,
U
C)
U
>
0
U5
ca
8
;ý
Ll
i
m
t's
,
oc,
ý
0
>
0
tn
-
kn
kn
C)
tn
w
cl
u
W
U
>
a)
>
(?
rp
cts
u
w
cl
03
L)
as
L)
cl
m
,ý
in
'n
C13
u
>
0
cli
cl
u pm,
ý
U)
0>
0>
0>
0>0 ýE0>0 pP
PC
.
ý
C)
C)
in
-ry)
-En
-EA
Cd
Cd
In
ID
1,
w
>
C,
- - ....
-w
-W
0
'41
C)
C)
C,
C>
0>
.0
N
N
11
wl
0
W,
'r,
C)
tn
ýo
'IT
N
rn
tf)
-
rm
ýo
ell
tn
vi
kn
C)
CD
kri
C)
=
(%1 0
rn
-
0
"
0
-
'IT 110 C) C% en Ln vi
N ýo 00 -
C,
V)
CD
-
(=
11)
kt)
C)
11
C%
tn
tt)
rn
ýo
CD
'IT
r-
Ch
eq
tri
tn
C,4 ttl
11 r- Cý vi "T
"tv Cý4
C7%eq
1
CL
.7
m
en r-
C)
ao
- C)
C\
W')
W)
C)
r-
ON C14 CD C14 CN It
\0
rN
oo
m
(D
(0
tr)
C)
'IT
C) V)
IýT C) 'T
Nr rl)
kn
W)
C)
cDce)
W,-t,- = 'o 2 C',
Ln
0
r-
W)
W) V) vi C)
C4
c
ýzr cq (w) (14
C-4 'D
M
tn
CD CD ttl
ý 7'
4 kn
--I-
*-r,"'. "I'"D"'"'
Cý ý,c
V')
o
\0
C)
CD
VII C11 tn 0
kn 00 It
0
m
m
0
0
cq
0
tn
cq
00
t4l)
C)
VI
CD
W)
t-
C)
C% ýo
N
kf)
C) tn 0 0
ON 110 en I--
C)
tn
til
C14
ý= C:,
m
C)
kf)
vi
M
V'l
C,
VI
C)
cq
tr- Cj en
rm
en
C)
C)
C)W)
0
vi
tn
>)-9- lu1100 W)
C14 ý-c *11, N 'IT rl)
0
Cý(oC>ON
Cý
R
-
C) 'IT
eq -
C)
r-
C)
C)
ýc
-
\.O t1r) C4 rcli
en r4 -
V,
C>
W)
00 til
M
W) -T (14 "T
"o
r.
-0
cl
0
0
C.
I.
11
"al
-
-
rn
cf)
m4
tn
-
0
In
-
00 'T
c)
C)
W)tf)
\o 0 \0
-
C,
C=
0
rn
11
E
C)
11
V-)
V-
C)
c)
'T
en
CD
IC
(ýý
in
V, ) tn
00
C)
kn
M
(D
cn
m
C14 -
-
V-1
re)
0
110
N
CD
tn
ýc
0
00
tn
-
C>
C)
0
kn
0
0
rl)
-
rn
ell
I
o c, tn 0 o c,
'4Zt
00
W)
Do
kn
en
ýo
C)
C)
0
00
zT
W)
C14
1:
1
CD
00 kr) r)
U
w
en, N,
C,4
<D
o
c,
-
-
-
a
VI
.
.
.
.
.
.
U
r-
It
ýo
IT
C14 'T
0 -W)0 kf) CD
C14
-
cq
-
C)
-
40.
I-
0 C)
ý,c
-
-
tf)
0
t4l)
kn
0
o
::,
%ýo
rn kn rn N m "
kn
:,
-
12
Iý
I"
"
c,
r1l -
-
-
Itz
"0
03
lu
>
w
0
C',
U
.2
cd
0
a)
6
u lpýl
o
0
V3
m
cl
0
U
>
cts
G)
>.
(1)
>
CU
>
t:
L,
'd
19
C"
o
c*
4,
>
0
v
4ý
>
U
0
10
C)
\.o
ý2
Cd
C14
CIS
0)
o
U
(U
>
C's
cl
0
' o 0
im.
1
C)
C)
cn
en
>
0
I
110
CD
cli
0
rl-
"C3
0
V'i
0
'r,
ON tn
'r,
en \X) 'IT
t",
'IT
r-
-
en tn
en C14 zT C14
'r,
Cý'
'r,
w
\0
en ('I
0.
X
El
m
It) C)
zl' In
C'4 -
C)
00
-
-
o
c)
lzr
-
c)
C)
C)
V'I
tn
(=,
C>
C)
\0
\0
C14
It
-
rf)
N
-
C14 -
oI
r-
vi
't
o
m
(ý
In
-
C)
C)
'IT 00 W) M
C>
VI)
00 -
CN -
kn
'r,
W)
t/l
tn
-
CN \0
ýo
c,
0
0
r-
tn
(01,
I
"r
C14
V')
kn
V') en
V
IV
(. I
0
11 I'll
In.
o
cq
7
1
Cý
-9-
10
11
1
cý
ell
I
I
C) C) vi o t'l t)
cq
m C14 en C14 I
I
I
I
I
tr)
-
I
o
-
c) C)
C-4 I
I
CD V -) 0
ý
-
C, tr) wl tn vl
C>
C)
C)
Cý
VI)
(ý
W) C>
(0
(=
tf)
Cl) C', cn C', 00 %lo
1
rq
o
1 -1
00
kn
N
kr)
-
It
C>
C)
CN
\C
C)
C)
tn
I
in
tr) c)
C)
In
C)
1=1
""I
C: l
'In
kr,
"r
en
kn
en
C14 m
cq
V)
Wl
In
Wl
"r)
tf)
\c
:r
r-
(3.)
I
I
'r,
41
0
(:D
C.
c)
kl') kjj
C-4 -
C>
-
kn
-
cD
-
c>
-
c)
-
-
C)
C)
kil)
C)
in
tf)
V-1 o
1-n
C)
M
CN -
N
-
-
-
-
Ln -
it)
(=)
CD
t4r)
0
11)
0
C>
-
.4
11 C,
9.1
0
"tj
N
-e-
10
oIV')
Oo V') cn V, ) en cq
C's r)
CD tn
11 11 as
-
kn
tn
kn
0
0
0
0
t--
It
r-
'IT
M
tr)
M
C-4 rn
N
-
N
-
-
W)
-
W)
In
tn
W)
V1
tn
tri
kn
kf)
V')
Ln
V)
tf)
tn
(ý
kf)
C)
tn 0
-
kn
krl
11)
Irl
11)
11)
1,1,
Irl
Ir,
I, )
tl,
V-)
kf)
tn
tf)
kn
11)
kn
kn
W)
if)
V11
U
ei
Ei
-11
" rZ C,4
kn
vi
-
-
u
cl
C-4 (=)
u. 11 11 kn W) V) 0
'jý
ý
-e- '0
rl)
cq
-
C13
u
>
>
P-4 0
<li
m
ce
8-
C)
CD
"r. ý
-E
E
tn
W) 0
Cq -
-
0
-
m
u
cc
Q
cl
U)
Cd
V,
> cl
> m
> m
>
I? U. "I (? u "' 0 u " 0
., m
m
as
Cd
>
>
m 0>
cl
0
P.
POL!
P. C)
C>
2-2
": r
C14
c: l
en
kn
kn
cl
M)
>
'I
u "' 0
C's
cl
PC,.,
,0
cli
E
C4
5
0
r-
CD
-
rl
00 r13
CD vi
00 ri
CD (D kr) kr) V)
r_ %0 (n rn ýc
tf)
CD
r, )
CD
rn
oo
CD
-e
cq
0
ýo
4n vi
00
-
rq
C> 0
CD
CD ki)
l'n
00 CD V') r4) c-i 00 V') zr r) CD
trcý
cq
2
Ch
V')
- <=>
10
rn
-
CD 5 D 2
11 r)
.
X
.
vl
(D
e
c>
vi
oo
in
ce
C>
ICJ rq -
92»
-
CD
rq
>
"0
1
CD (D
rn rAe
-
V)
0
ýt
e
e
kn
kn
\C
-
-
ý
10 .
C>
(D
t
CD
-
(n
-
(DO ýt
kn
V)
ým
rn
CD
cý
-
CD
cq
V'l
"0
tf)
rn
41) CD vi
00 V') rq
CD
CD
m
rq
CD
VI
e
rn
C, 4
e
r-1
rý
V)
vl
cý 1vi
-
1.0 rn
00
%M ýc
rn
e
C>
t)
oo
rq
kn
(=
CD
V) vi CD CD
C> CD O\ ýo
CD
kn
-
0
'In
V
r, )
CD CD
m rn CD
vi
ýt
CD
rn
V)
"0
vi C> CD CD vi
rei rq vi rn -
kn
Cl,
-
rn
CD
rg
ID
e
r, 1
CD CD er) C> CD CD kn
11 rq
r, 1
CD
V)
rq
rn
kn
oo
-
ci
CD 1.
n
-
vl
V)
vi
cý
CD
rn
-
V)
mt
CD
tf)
-
-
C, 1
-
,
"0
r.
"U
-
\. O
ýt
"0
75
m
lt
i
r, )
11
CD
11
-e-
'Im
c:> cý
Z
Pý
v'
t
L--
vli
CD
V)
V)
CD
0
0
ro) (Z
r-
rn cq -
N
CD
v)
vi
v)
-
t-
v)
c
V)
-
Cý
4n
CD
- ci
ý
-0-
IZJ
C>
n n r,V, n
00 ýt
CD V)
-
00
-
e
ýo
t, 1
rn
ýt
r, 1
rq
-
Ln CD (D
\M
t
N
-
[Z) 0
rl
(14 kf) rn
rq
r-ý
Kri wi
ýt
r, 1 kn
CD CD
fl)
r*4
V)
V)
(A
vi
V)
V -1
kn
vý
'n
tr)
tf)
(Z) vi
e
CD V)
rn
00
kn
V)
V)
CD
vi
CD
.
0
rq
ýr
1 1
kr)
"CJ
2
C>
CD
vý
0
-
-
-
v .ý
vl
0
0
,
CD vi
CD
-
-
-
(, q
(2
vi
0
-
10
w
0.
44
>
ce
.0
0
E-4
(L)
j
m
cu
>
cu
>
re
0
cu
>
cu
ce
>
tu
>
m
m
0 u
0 2 %.9 2
u , 0 u ' 0
ce
(U
>
>
>
U
c r, C» 4'. O L) '. (D u p. 0
P. CD
c
iz.
'
C:)
c>
ýc
rr2
22
CD
CD
CD
(Z
CD
ým
rn
rn
-
Table 8.10 Measurement Settings
Diameter
Length
21
21
33
33
45
45
53
53
21
21
33
33
33
33
33
33
53
61
121
61
121
61
121
61
121
61
61
61
61
61
61
61
61
61
Bendsno. Vertical distance,cm
Total distance,cm
Maximum value
Total distance,cm
Minimum value
225
233
188
193
217
180
220
186
167
219
159
192
151
140
130
158
144
119
122
98
107
166
107
168
118
124
122
94
120
85
83
87
131
102
101
102
98
107
163
102
168
93
120
114
90
120
84
72
83
102
92
0
0
0
0
0
0
0
0
1
2
1
2
3
3
4
4
1
Table 8.11 Envelop for DPF models
Boundary
Unit
Minimum
Maximum
Diameter
CM
21
53
oftube
Vertical
distance
Total
distance
CM
61
120
Cm
70
170
CM
80
230
Length
Bend
no.
0
4
a
Degree
15
57
k,
E,
0.01
0.86
Lux
1270
97270
208
9. CONCLUSIONS
AND FURTHER
WORK
The presentresearchset out to meet specific objective, iternisedin Chapter 1. The overall aim of the
researchwas to provide a generalmathematicalmodel for the prediction of light pipe daylighting
performance.Basedon two years' measurementson the daylighting performanceof light pipes, large
and reliable databaseswere obtainedwhich enabledthe mathematicalmodelling. Theseprocedureshad
previously not beencarried out.
The key points concludedthroughout the researchare now presentedin turn.
Two years' dataon light pipe daylighting performanceunder all weatherconditions were
measured.The datawere measuredon a minute-by-minutebasisand provided detailed
information on the performanceand configurationsof light pipes, weatherconditions and the
arrangementof sensorsduring the tests.The databaseenabledthe opportunity to conduct the
aimed mathematicalmodelling on light pipe. Moreover, this information haspreviously been
unavailableand can be usedby engineers,architectsand researchersalike as a foundation for
further study on light pipes.
ii.
In an attempt to establisha mathematicalmodel for light pipe daylighting performance
An analysisof independentvariableswas conductedto identify the factor exerting
assessment.
the most significant influence on the performanceof light pipes. It was found that the
daylighting performanceof light pipes is affectedby light pipe configuration factors, external
weatherconditions and the position of the point of interest.Light pipe configuration factors
include the aspectratio and sectionareaof light pipe tube, the reflectanceof the internal
surfaceof light pipe tube, number of bends,degreeof bend and types of light pipe dome and
diffuser. External weathercondition includes global horizontal illuminance, solar attitude and
sky clearnessindex. The performanceof light pipe was also found affectedby the vertical and
horizontal distancesbetweenthe point of interestand the centreof the light pipe diffuser.
Therefore,proposedmathematicalmodel were reportedas a function of above-mentioned
factors.
209
Light pipes are daylighting devices that utilise both sunlight and skylight. This is in contrast to
traditional daylighting devices such as windows, which owing to their design and orientation
limitations utilise only sky-diffuse and reflected illuminance. Therefore, a new concept of
Daylight Penetration Factor (DPF) has been introduced in present research to specify the
performance of light pipes. DPF is the ratio of the internal illuminance to the corresponding
total external illuminance at a given point. The introduction of DPF into daylighting research
enables the performance comparison between innovative and traditional daylighting devices.
iv.
Two mathematical models, S-DPF for straight light pipes and E-DPF for elbowed light pipes
have been built to assessthe performance of straight light pipes and elbowed light pipes.
Compared to S-DPF model, E-DPF model uses an extra term to account for the effects of light
pipe bend. The term is a function of bends number N, and when N is given the value of 0, EDPF collapses to the exact form of S-DPF. S-DPF and E-DPF models predict the internal
illuminances due to light pipes under all weather conditions. Since the DPF models use non
site-specific information for light pipe performance assessment, it is considered to be world
wide applicable. The DPF models were incorporated into Excel spreadsheets that facilitate the
use of the DPF models. The DPF models are based on physical analysis of the working
mechanism of light pipes and are adjustable by changing the value of coefficients employed in
the model. The DPF model method therefore provides a flexible framework that enables a
sustainable development of the mathematical modelling of light pipe daylighting performance.
By carrying out more measurement, fitting and validation procedures that were developed in
present research, the accuracy of the DPF models can be continuously improved.
V.
In addition to traditional error evaluation techniques,i. e. MBE and RMSE, PAD, slope of
best-fit trend line, coefficient of determination,a statistical residualanalysiswas also
conductedto further investigatethe robustnessof the proposedmodels. The DPF models were
further validated using independentdata set, and comparedto resultsgiven by independent
researchesin the field. Good agreementshavebeenreachedbetweenpresentfindings and
results given by other researchbodies.The validation of the DPF modelsusing independent
210
data shows that the models can predict the performance of light pipes under all weather
conditions with a good accuracy.
vi.
It was found that the type of light pipe diffuser heavily affects the daylighting perforinanceof
light pipes. Comparisonbetweenlight pipes with opal and clearsdiffuser showedthat the
amount of light delivered by the latter one was significantly more than that by the former one.
This is due to the improved transparencyof the diffuser, which allows a better daylight
penetrationinto internal space.However, it is also found that although the penetrationof
daylight is improved by using clear diffusers, the internal distribution of the penetrated
daylight is lessuniform than that due to opal diffuse light pipes. This shortcomingbecomes
apparentwhen the external illuminance is high (higher than 30klux), that is certainpattern of
"pools of light" can be observedwithin interior spacedue to the unsymmetricaldistribution of
daylight. DPF models given in presentresearchwere developedfor opal diffuse light pipes. A
Diffuser Factor (fD) hasbeen introducedto link the DPF modelsto the performanceof clear
diffuser light pipes.
vii.
Practical engineeringdesigntool have beenproducedbasedon DPF models.The guideline
takesthe form of six designtablesthat provide the internal illuminances that can be achieved
by opal diffuser light pipes of varying geometricalconfigurationsoperatingunder typical
London weatherconditions.By applying an efficiency-loss factor of 0.2, the guideline can be
adaptedto aid the designof elbowed light pipe. Additionally, within the Excel Visual Basic
Application environment,lux plot that can visually describethe internal illuminance
distribution due to light pipes hasbeenconstructedbasedon DPF models.The lux plot
[Courtesy:David Jenkins,Monodraught] canbe usedby building or lighting designersin both
of their initial and final stagesof designof light pipes. The application of the lux plot in the
initial stageof designgives a generalpicture of how many and what kinds of light pipes are
neededfor a certain designpurpose.While the application of the lux plot at the final stageof
designhelps to tune the designand provide a crosscheck.
211
viii.
A new anisotropicmodel to correct diffuse irradiancemeasuredby shadowbandhasbeen
developed.This method is basedon the use of a single diffuse radiancedistribution index, b.
Clearnessindex, k, is usedasa parameterto determinethe value of b, and b is thenusedto
obtain the correction factor to accountfor the diffuse irradianceobscuredby shadowband.
The proposedmethodis validatedusing databasesfrom siteswith disparatesky conditions.
The Drummond's isotropic method,which is basedsolely on geometriccalculation,is
comparedagainstthe proposedmethodthat usesan anisotropicradiancedistribution. Results
show that for the caseof Bracknell, Englandthe RMSE, MBE and PAD of correcteddiffuse
irradianceobtainedusing the proposedmethodare 12W/m2,-0.7 W/m2and 3% respectively.
CorrespondingRMSE, MBE and PAD due to Drummond's method are 16 W/M2,-5.6 W/mý
and 4% respectively.For the caseof Beer Sheva,Israel, the proposedmodel producesan
RMSE of 17 W/m2,an MBE of Mrný and a PAD of 5%. The correspondingfigures for
Drummond's method are23 W/m2,-5W/M2and 7% respectively.
ix.
The S-DPF model assumesthat the internal illuminance distribution on a working plan below
the light pipe diffuser is symmetricalto the diffuser centreand is a function of the vertical and
total distancesof one point to the diffuser centre.A purposedmeasurementwas undertakenin
Craighousetest room to test this assumption(Section 5.6). It was found that the asymmetrical
distribution of internal illuminance althoughnot very significant, has a substantialeffect on
the daylighting performanceof light pipe. It is worthy however to point out that in real
applications,especiallyfor large rooms, usually a group of light pipes needto be installed to
provide an even distribution of daylight within the space.For occasionswhere multi-light
pipes were installed symmetrically to the room layout, the effect of asymmetricaldistribution
of internal illuminancescan be reduced,and the predictionsgiven by S-DPFmodel tendsto be
more accurate.
In order that future researchfollow in a logical mannerfrom the presentwork, some suggestionsfor
possible work arepresentedherein.
212
A 3-D light pipe DPF model
The DPF models predict the daylighting performance of light pipes based on a validated
observation that the internal distribution of daylighting due to light pipes is approximately
symmetrical to the axis of light pipe tube. This can however, be pointed out as a weak link in
the chain of calculating the performance of light pipe system. DPF models predict not only the
daylight transmittance of light pipe system, but also the internal illuminance level at given
points. The linkage between above two functions of DPF models is the method of describing
internal illuminance distribution. It has been found that the internal distribution of daylight due
to light pipe is not always strictly symmetrical to the axis of light pipe tube. The deviation of
the internal illuminances for points at different positions but having the same distances to the
light pipe diffuser centre can be as high as 15%. This implies that the unsymmetrical internal
illuminance distribution may be a major factor causing system bias of the DPF models. It is
therefore suggested that more geometrical factors that describes the relative position of a given
point to light pipe diffuser should be included into the DPF models, so as to take into account
the effect of unsymmetrical internal illuminance distribution. One proposal that may be
adopted would be to establish a 3-D coordinate system that can describe the geometrical
relationship between the sun's position (soIar altitude and azimuth), the light pipe tube's
position and a given point's position. Once the 3-D DPF model that incorporates abovementioned additional geometrical factors is constructed, further measurements on the internal
illuminance distribution should be undertaken and the data obtained can then be used to
determinethe formal form of the 3-1) DPF model. After that, consideringpractical issuessuch
as capital and manpowerlimitations, experimentscannotbe usedto enumerateall possible
casesof light pipe applications,computer aideddesigntool suchas CAD or simulation
packagelike Matlab may be usedto build an computationalmodel so asto extrapolatethe 3-D
DPF model.
A general standard for evaluating traditional and innovative daylighting devices
Daylight factor hasbeen acceptedas an industry standardfor window design.Windows are
traditional daylighting device,but owing to their designand orientation limitations utilise only
sky-diffuse and reflected illuminance. As a comparison,innovative daylighting devicessuch
213
devices,
daylighting
both
for
innovative
light
However,
to
utilise
sunlight
and
skylight.
as
pipe
date no general method is available to assesstheir daylighting performance. Based on the
concept of light pipe daylight penetration factor, DPF, a reference method may be adopted for
an agreed standard to assessall daylighting devices. In this respect the author would like to
propose new tasks that may be included for further work. The first task is to design a method
by
be
illuminance
(L-FoM)
Figure
Merit
Pipe
Light
that
the
achieved
of
would
ratio
of
of a
dimensions.
due
light
illuminance
light
"reference"
to
to
of
prescribed
a
pipe
given
pipe
any
The second task is to design a Light Pipe to Window Figure of Merit (LW-FoM) that would be
the ratio of illuminance achieved by any light pipe to illuminance due to a "reference" window
of prescribed dimensions. The above L-FoM and LW-FoM would be evaluated under
(section
i).
3-D
the
system
above
coordinate
proposed
and
within
conditions
sky
prescribed
214
APPENDIX 1: THE METHOD FOR CALCULATING
THE VIEW FACTORS
FROM DIFFERENTIAL
AREAS TO SPHERICAL SEGMENTS BY
NARAGHI
I-LH
I: D>
v
and
(whereD=
-I<H<L
1-0
I
_fCOS-'(
IT
VD 2
+2
I-LH
-)+22
D41 - L2
,
2(1- 2L2 -D2
V(I+D
-1+2HL-(D2
+H
+H
2)L2
_
L=
-H
2+ 2HL)
2(l
-2HL)'-4D
VD2
-1+
2H
2-
(D
+D2+H2-
-L2)
2+
H2)H2
U,
IT
(tan
and
H
-+2
i
(D2 +H 2)2
2HL + 2DAF--,
2HL
[sin-'(
F')(D41
e)(Dýl
2DVI
-
H-(D
VH 222
+ (D
2+H2
- 1)(D
L2
-I+
LH)
Lý
+I-
LH)
)L
+H 2)
h]
2)
TH 2+
(D 2- 1)(D2 +H 2)
I-LH
H: D<
4-1--L?
I
H(I -D2-H
ý(l
(I +D2+H2-
x tan
D2+ H2
-sin-I(
F,
dh
H=
,
)]+2sin-'(ý
-H2
D
(4.18a)
-I<H<L
1-ýý
H2 -1
V(D'+H2-1)(1-H2)
D'+H2
H
(D 2+ H2)2
Cos-1(4D2
+ H2 -1
D
(4.18b)
215
III:
I-LH
when L>0D>
when L<0
and H< -1
7 =77
I-LH
D> 71 --e
LH -I
when D> 4-1:ý-e
I
<H<-l
and
L
and H<1
L
I
FA
I
(Cos-'(
2; r
+2
IV:
+
DII
VD 2
when L>0
when L<0
2(1-
I-LH
-1+
-
+D2+H2
2HL - (D 2+ H2)L2
DZ+H 223
I-LH
D<
r-41-e
-D+
I(I
2HL)
tan-'(
-4D
-2HL)2
2 (1
_
L2)
+ D2 + H2 - 2HL + 2DVI
N(I+D
22+H
2HL
2DIIi
-
-
Lz)(DVI
iF)(DTI
-
-
L2
LH)
+
-1
Lý +I-
LH)
H-(D'+H2)L
H
+2
COSA
(D +H2)ý
VH 2+ (D 2- 1)(D 2+H
2)
(4.18c)
and H< -I
I -LH
D<
41--p
F, -A,
u,
V:
L2
V(l
2Lý
2_H2
I
an
L
<H<-l
ý-H3
(D 2 +H 2)2
(4.18d)
LH-1
when D< T,
and H<I
L
--ýP
Fu
"
I4
2; r
V(I+D
2Lý
2 +H2
-
D2
-H2+
-2HL)2
2HL
-4D
2(l
_
L2)
(4.18e)
216
APPENDIX
11: LIST OF PUBLICATIONS
1. A MathematicalModel for the Perfonrianceof Light-pipes, X Zhang and T Muneer, Lighting
Researchand Technology,Vol. 32(3), 2000
2. A Design Guide for PerformanceAssessmentof Solar Light-pipes, X Zhang, T Muneer and J
Kubie, Lighting Researchand Technology,Vol. 34(2), 2002
3.
Light-pipes for Daylight PenetrationIndoors, X Zhang, ProceedingsofRenewableEnergyfor
Housing Conference,The UK Solar Energy Society, 20 October 2000, Perth
4.
A New Method for Correction ShadowBand Diffuse IrradianceData, T Muneer and X Zhang,
Journal ofSolar Energy Engineering,American Society of Mechanical Engineering,Vol. 124,2002
5.
Sky Luminance and RadianceDistributions -A ComparisonBasedon Data from Bahrain,
Japanand Europe,T Muneer, F Fairooz and X Zhang, Light Researchand Technology,Lighting
Researchand Technology,Specialissuefor CIBSE "An Expert's Conference:Tropical Daylight and
Buildings", Singapore,2002
6. Evaluation of An Innovative Sensorfor Measuring Global and Diffuse Irradiance,and Sunshine
duration, T Muneer, X Zhang and J Wood, submittedto InternationalJournal of Solar Energy, in
review.
7. Cost and Value Analysis of Piped Daylight, T Muneer and X Zhang, submittedto Commission
International de FEclairage(CIE) TC3-38 Committee,2002
8. Accuracy Analysis of Solar Position Algorithms Used within CIBSE Guides 'A' and 'J', CIBSE,
August, 2000, in communication.
217

- Repository@Napier

Transcription

Similar documents

Fernco Flexible Coupling Installation - Fernco

Fernco Flexible Coupling Installation - Fernco

LGOBO SALE SHEET

10` x 10` Gazebo

At the annual Gem-O-Rama gem and mineral

The Homestead Hotel and Condominium: Sanitary Drain Stack

OWNER`S MANUAL - Thaw Frozen Metal Pipes Quickly with

COMPOSITE PIPE SOLUTION FINAL SEPTEMVRI

Concrete Pipe 101 - American Concrete Pipe Association

Flowpex Technical Manual