61,99 €
Mehr erfahren.
- Herausgeber: Wiley-VCH
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
While the first volume on building physics deals with the physical principles of heat, air and moisture behaviour of buildings, building structures and components, this second volume on applied building physics focuses on the question of what the desired performance of buildings consists of. To achieve this, knowledge of the external environmental effects and the internal live loads to which buildings are subjected is a necessary first step. Subsequently, the performance requirements and the physical correspondences are deepened with the determination of their physical parameters, at the levels of buildings, building structures and building components.
Compared to the second edition, the discussion of criteria is not limited to thermal comfort, but also includes acoustic, visual and olfactory aspects. Likewise, the indoor air quality is considered in a broader way. Analyses and calculations result in sustainable buildings with a comfortable indoor climate from functional and durable building constructions.
Compared to the second edition, the text for the third edition has been reorganised, corrected, revised and expanded where appropriate. A useful appendix for quick reference contains standard values of material properties for a wide range of building materials.
The analyses and calculations described in this book result in sustainable buildings made of functional and durable building constructions, with comfortable and healthy indoor climate and air quality.
Compared to the second edition the text in this third edition has been reshuffled, corrected, reworked and extended where appropriate.
Sie lesen das E-Book in den Legimi-Apps auf:
Seitenzahl: 549
Veröffentlichungsjahr: 2023
Ähnliche
Table of Contents
Cover
Table of Contents
Title Page
Copyright
Dedication
Preface
Acknowledgements
About the Author
List of Units and Symbols
Units
Symbols
Introduction
Subject of the Book
Further Reading
1 Ambient Conditions Out- and Indoors
1.1 Overview
1.2 Outdoors
1.3 Indoors
Annex: Solar Radiation at Uccle, Belgium (50° 51′ N, 4° 21′ E)
Further Reading
2 Performance Metrics and Arrays
2.1 Definitions
2.2 Functional Demands
2.3 Performance Requirements
2.4 A Short History
2.5 Performance Arrays
Further Reading
3 Performance Demands at the Whole Building Level
3.1 In Brief
3.2 Thermal, Acoustical, Visual and Olfactory Comfort
3.3 Health and Indoor Environmental Quality (IEQ)
3.4 Energy Efficiency
3.5 Durability
3.6 Economics
3.7 Sustainability
3.8 High-performance Buildings
Further Reading
4 Heat, Air, Moisture (HAM) Metrics at the Building Assembly Level
4.1 Introduction
4.2 Airtightness
4.3 Thermal Transmittance
4.4 Transient Thermal Response
4.5 Moisture Tolerance
4.6 Thermal Bridging
4.7 Contact Coefficients
4.8 Hygrothermal Stress and Strain
4.9 Transparent Parts: Solar Transmittance
Further Reading
5 The Envelope Parts Heat Air Moisture (HAM) Performances applied to Timber-Frame
5.1 In General
5.2 Assembly
5.3 Performance Evaluation
Further Reading
Appendix: Heat, Air, Moisture (HAM) Material Properties
A.1 Heat Related, Standard Values; Applicable In- and Outside of the Thermal Insulation
A.2 Heat Related, Standard Values; Differentiating Between In- and Outside of the Thermal Insulation
A.3 Air-Related, Measured Values
A.4 Water Vapour Related: Vapour Resistance Factor, Standard Values
Index
End User License Agreement
List of Tables
List of Units and Symbols
Table 1 List with symbols and quantities.
Table 2 List with suffixes and notations.
Chapter 1
Table 1.1 Monthly average dry bulb temperature at Uccle and Sint Joost, Brus...
Table 1.2 The thirty years based monthly mean air temperatures at several lo...
Table 1.3 Uccle, multiplier
f
mo
for the total monthly diffuse radiation.
Table 1.4 Uccle, total solar radiation on a horizontal surface (MJ/(m
2
mo)),...
Table 1.5 Monthly total solar irradiation on a horizontal surface in Europe ...
Table 1.6 Monthly mean RH (%) and vapour pressure (Pa) for locations across ...
Table 1.7 Uccle, of time wind comes from different directions (monthly mea...
Table 1.8 Wind pressure coefficients for an exposed three floors high rectan...
Table 1.9 Precipitation: duration and amounts per month, means for Uccle (19...
Table 1.10 Wind-driven rain on an 18-storey block of flats in Munich as meas...
Table 1.11 Monthly mean TRYs for Belgium (average, cold, warm).
Table 1.12 Energy performance legislation, reference year for Flanders, Belg...
Table 1.13 Uccle: cold winter (declination −17.7°) and hot summer...
Table 1.14 Moisture reference years for interstitial condensation.
Table 1.15 Uccle, ,
C
(
t
).
Table 1.16 Uccle, equivalent temperature for condensation and drying (
a
K
= 1...
Table 1.17 Operative temperatures needed according to DIN 4701 and EN 12831....
Table 1.18 Measured weekly mean air temperatures ().
Table 1.19 Dwellings, daily vapour release, depending on the number of famil...
Table 1.20 Dwellings, vapour release linked to metabolism, activity and othe...
Table 1.21 Dwellings, vapour release during a weekday by a family of two and...
Table 1.22 Daily vapour release in relation to the number of family members ...
Table 1.23 Measured weekly indoor to outdoor vapour pressure differences and...
Table 1.24 Natatoriums, weekly mean indoor/outdoor vapour pressure differenc...
Table 1.25 Belgium, indoor climate classes (
θ
e,m
: gli...
Table 1.26 Belgium, pivots between the ICC's recalculated (if <0, se...
Table 1.27 Finland and Estonia, indoor climate, pivots (weekly means).
Table 1.28 EN-ISO 13788, indoor climate classes, pivot values.
Table A1 Beam radiation under clear sky conditions on a surface perpendicula...
Table A2 Diffuse solar radiation under clear sky conditions on a horizontal ...
Table A3 Solar radiation under clear sky conditions for the 15th of each mon...
Table A4 Beam and diffuse solar radiation under permanent clear sky conditio...
Table A5 Beam, diffuse and reflected solar radiation under permanent clear s...
Chapter 2
Table 2.1 Level 0, the built environment, performance array.
Table 2.2 Level 1, whole buildings, performance array (building physics-rela...
Table 2.3 Level 2, building assemblies, performance array (building physics-...
Chapter 3
Table 3.1 Metabolic rates per unit of body area (
M
A
, W/m
2
).
Table 3.2 Clo-values.
Table 3.3 Thermal sensation scale.
Table 3.4 Permitted mean temperature of a radiant ceiling.
Table 3.5 Floor temperature and contact duration, floor covers listed from l...
Table 3.6 ASHRAE 55-2017.
Table 3.7 ISO EN 7730-2005.
Table 3.8 Speech audibility.
Table 3.9 Hearing problems caused by too loud, too long-lasting noises.
Table 3.10 Perception deafness risk, up as
F
(age), down due to continuous l...
Table 3.11 Equivalent sound pressure level indoors in dB(A), seen as comfort...
Table 3.12 Illuminances needed or experienced.
Table 3.13 Mean skull width of rodents and insectivores.
Table 3.14 CO
2
impact on human decision-making (O 600 ppm; X 1000 ppm; Y 250...
Table 3.15 MAC- and AIC values for carbon dioxide ().
Table 3.16 Ventilation flow as a function of activity.
Table 3.17 The four indoor air quality classes.
Table 3.18 The four indoor air quality classes: decipols.
Table 3.19 Ventilation in non-residential buildings according to EN 13779.
Table 3.20 Ventilation in residential buildings, design values, Belgian stan...
Table 3.21 Annual end energy use in 201 dwellings built in the twentieth cen...
Table 3.22 Annual end energy for appliances and lighting.
Table 3.23 Electricity used for appliances and lighting as measured in 26 ho...
Table 3.24 Appliances and lighting in office buildings.
Table 3.25 Central heating, system efficiency.
Table 3.26 Parameters impacting the annual net heating demand of residences....
Table 3.27 Reference year.
Table 3.28 Adventitious ventilation rates in ach by window airing.
Table 3.29 Glass types.
Table 3.30 Impact of thermal inertia on net heating demand.
Table 3.31 Airtightness and ventilation.
Table 3.32 Factors influencing the annual net cooling demand.
Table 3.33 Factors of influence on the annual end energy use.
Table 3.34 Charateristics of the eight audited schools.
Table 3.35 Compactness, mean envelope thermal transmittance.
Table 3.36 Airtightness of separate classes (exterior walls only).
Table 3.37 Normalized measured end energy versus the calculated reference, r...
Table 3.38 Critical saturation degree for frost of some materials.
Table 3.39 Bricks and stone, links between class and application.
Table 3.40 Solubility of salts in water.
Table 3.41 Crystallization pressures.
Table 3.42 Hydration pressure for CaSO
4
(MPa).
Table 3.43 Metals: voltage series compared to a hydrogen electrode.
Table 3.44 The five residence types 1–5, see also Figure 3.73.
Table 3.45 Non-insulated reference, thermal transmittances.
Table 3.46 Minimum and maximum insulation thickness, step, glazing.
Table 3.47 Cases per dwelling.
Table 3.48 Optimal choices.
Table 3.49 Life-cycle inventory at the building level: in- and outflows cate...
Table 3.50 CO
2
emissions per kWh heat produced.
Table 3.51 Checks with weight per category.
Chapter 4
Table 4.1 Examples of thermal transmittance requirements (
U
max
).
Table 4.2 Infiltration percentages found in literature and as measured.
Table 4.3 EN-ISO 13788, indoor climate classes, pivot values.
Table 4.4 Month-based time function
C
(
t
).
Table 4.5 Acceptable time-averaged RH in floor coverings.
Table 4.6 Bricks and masonry: vapour diffusion thickness.
Table 4.7 Brick and veneer wall: air permeance
.
Chapter 5
Table 5.1 Apparent thermal transmittance measured on the inside face, air in...
Table 5.2 ICC1, month of January, interstitial condensation?
Table 5.3 ICC2 and ICC3, interstitial condensation?
List of Illustrations
Chapter 1
Figure 1.1 Global warming, (a) increase in the world's average annual temper...
Figure 1.2 Thermometer hut.
Figure 1.3 Air temperature: annual course, one and two harmonics; left: Kiru...
Figure 1.4 Leuven, Belgium, weather station: air temperatures between 1996 a...
Figure 1.5 Solar spectrums before (upper line) and after passing the atmosph...
Figure 1.6 Solar angles.
Figure 1.7
L
distance traversed through the atmosphere from the sun at solar...
Figure 1.8 Direct radiation on a surface with slope
s
s
.
Figure 1.9 Annual solar irradiation on a horizontal surface.
Figure 1.10 Rime formation on a well-insulated pitched roof due to under-coo...
Figure 1.11 Clear sky emissivity; left: according to (1) and (2); right: to ...
Figure 1.12 Lightweight low-sloped roof,
U
= 0.2 ...
Figure 1.13 Monthly mean RH and vapour pressure in (a) Kiruna (Sweden), a co...
Figure 1.14 Sea-based wind turbines producing renewable electricity.
Figure 1.15 Typical wind rose for Uccle, Belgium.
Figure 1.16 Precipitation: monthly amounts and duration for 1961–1970 at Ucc...
Figure 1.17 Final fall velocity of raindrops in windless weather.
Figure 1.18 SW façade of a test building: calculated lines (middle) of equal...
Figure 1.19 Average rain rose for Uccle.
Figure 1.20 Poorly insulated dwellings: weekly mean air temperature in dayti...
Figure 1.21 Natatoriums: weekly mean temperatures indoors.
Figure 1.22 Poorly insulated homes: difference in weekly mean indoor to outd...
Figure 1.23 UK, 1065 living rooms (left) and 916 bedrooms (right): indoor to...
Figure 1.24 Germany, 10 homes, living room: lowest, highest, and mean indoor...
Figure 1.25 Monthly mean indoor to outdoor vapour pressure difference in rel...
Figure 1.26 Natatoriums: weekly mean indoor to outdoor vapour pressure diffe...
Figure 1.27 Natatoriums; left: weekly mean relative humidity indoors in rela...
Figure 1.28 Belgium, pivots between the four indoor climate classes.
Figure 1.29 Finland and Estonia indoor climate: differences in indoor to out...
Figure 1.30 Medium rise office building, air flow caused by thermal stack.
Chapter 2
Figure 2.1 First performance guide, part 1, for the whole building published...
Figure 2.2 The IEA-EBC annex 32 final report; BREEAM logo.
Figure 2.3 Fire propagation should be enabled or reduced in buildings and al...
Chapter 3
Figure 3.1 P.O. Fanger.
Figure 3.2 Top: PPD versus PMV according to P. O. Fanger (equation [3.22]). ...
Figure 3.3 The blue dot shows the result of a comfort enquiry in an air cond...
Figure 3.4 The body parts.
Figure 3.5 Seated persons, temperature difference between head and ankles, %...
Figure 3.6 (a) Vertical radiant asymmetry, percentage of dissatisfied (PD); ...
Figure 3.7 Wearing shoes, long floor contact, percentage of dissatisfied (PD...
Figure 3.8 Adaptation; (a) ASHRAE 55-2017; (b) ISO EN 7730-2005.
Figure 3.9 Office in the upper corner of a building,
V
=...
Figure 3.10 The human ear (Encyclopedia Britannica).
Figure 3.11 Preferred Speech Interference Level (PSIL) as a function of dist...
Figure 3.12 Masking curves for a 1000 Hz disturbing noise with increasing lo...
Figure 3.13 The human eye.
Figure 3.14 Eye sensitivity.
Figure 3.15 The daylight factor.
Figure 3.16 The human nose.
Figure 3.17 Straw bale construction.
Figure 3.18 VOC-concentration in the air after application of a wet finish....
Figure 3.19 Oriented strand board (OSB); (a) the effect of RH; (b) the effec...
Figure 3.20 The Spanish flu pandemic.
Figure 3.21 Isopleth fixing the lowest growth rate of a mould species.
Figure 3.22 Critical relative humidity for the dust mite
Dermatophilosis far
...
Figure 3.23 Water vapour released by people.
Figure 3.24 Airborne contaminants in tobacco smoke.
Figure 3.25 The predicted number of dissatisfied (PD) versus decipol.
Figure 3.26 Secondary school, classroom, perceived IAQ, PD based on the meas...
Figure 3.27 Relative symptom prevalence versus ventilation, mean curve; the ...
Figure 3.28 CO
2
-concentrations measured in classrooms.
Figure 3.29 Spanish flu pandemic (1918–1921); precautionary measures to cont...
Figure 3.30 Classroom, teacher infected with Covid-19, not ill yet, the risk...
Figure 3.31 January at Uccle, ventilation needed to avoid mould in a 200 m
3
...
Figure 3.32 A whole-body suit with dust mask.
Figure 3.33 Mouth masks.
Figure 3.34 Flanders, Belgium, residential and equivalents: share in the ann...
Figure 3.35 Measured annual electricity use for lighting and appliances in 1...
Figure 3.36 Zones as nodes.
Figure 3.37 Horizontal protrusions and a vertical overhang, related angles (
Figure 3.38 Envelope part, the first 10 cm from inside as heat storage (left...
Figure 3.39 Zonal node model.
Figure 3.40 Zone model, transmitted solar radiation is mainly absorbed by th...
Figure 3.41 CVM, control volume in an air-tight layer.
Figure 3.42 Non-insulated villa, low energy detached house, end energy for h...
Figure 3.43 Reference, best fit.
Figure 3.44 Measured normalized annual end energy for heating in 1050 homes ...
Figure 3.45 Statistically best fitting rebound factor.
Figure 3.46 Rebound factor; (a) The Netherlands; (b) Germany.
Figure 3.47 Estate built in the 1950s, primary energy for lighting and appli...
Figure 3.48 PV on the roof of a dwelling, electricity produced (measured dat...
Figure 3.49 Dwelling,
V
= 799 m
3
, gro...
Figure 3.50 Compactness and absolute compactness as function of volume.
Figure 3.51 Compactness as function of the number of floors in a tall buildi...
Figure 3.52 Stepwise renovation of an end of the row house, annual end energ...
Figure 3.53 Detached dwelling, decreasing benefit of higher mean insulation ...
Figure 3.54 The energy used for heating over a period of 30 years versus the...
Figure 3.55 Electric analogy.
Figure 3.56 Blower door.
Figure 3.57 Energy use, impact of the embodied part.
Figure 3.58 School 8, class 2, difference in indoor/outdoor vapour pressure,...
Figure 3.59 Natatorium; (a) collapsed roof beam; (b) collapsed roof deck; bo...
Figure 3.60 Low-sloped roof particle board deck turning wet by interstitial ...
Figure 3.61 Low-sloped roof above a wood kiln, irreversible deformation of t...
Figure 3.62 Aerated concrete, hygric expansion.
Figure 3.63 Cracking.
Figure 3.64 Fungi.
Figure 3.65 Wood bugs: (a) longicorn, (b) larva, (c) anobia.
Figure 3.66 Termites.
Figure 3.67 (a) Rodent nest in glass wool (b); mineral fibre pecked by birds...
Figure 3.68 (a) Stucco, algae above the terrace floor (b); stone wall with g...
Figure 3.69 Brick wall, frost damage.
Figure 3.70 Salt efflorescence.
Figure 3.71 (a) CaCO
3
efflorescence (b); damage by crypto-efflorescence.
Figure 3.72 Degraded concrete due to steel bar corrosion.
Figure 3.73 The five residence types 1–5, see also Table 3.44.
Figure 3.74 Detached two-storey house 2, investment in a hydronic central he...
Figure 3.75 Residence 2, low-e argon filled double glass, natural ventilatio...
Figure 3.76 From top left: megatons of CO
2
emitted since 1965; evolution of ...
Figure 3.77 Building materials, embodied CO
2
(kg/kg), global values.
Figure 3.78 Construction material pyramid, embodied CO
2
(kg
eq
/m
3
).
Figure 3.79 Energy efficient renovation, impact of embodied CO
2
on the GWG e...
Figure 3.80 Leed certification.
Chapter 4
Figure 4.1 Cavity wall filled with 10 cm thick PUR boards. Left is an air la...
Figure 4.2 Floor on grade, the braces show the free perimeter, the hatched l...
Figure 4.3 Window surface.
Figure 4.4 Twofold window.
Figure 4.5 Low-sloped roof, thermal transmittance depending on insulation th...
Figure 4.6 Compactness (
C
) versus envelope mean thermal transmittance....
Figure 4.7 Former German mean envelope thermal transmittance requirements.
Figure 4.8 The <thermal resistance
R
1
/capacitance Σ...
Figure 4.9 Construction moisture due to rain during construction.
Figure 4.10 First stage drying flux in a newly plastered 4 × ...
Figure 4.11 Vapour-tight inside finish applied too early, moistens the dry p...
Figure 4.12 Rain leakage wetting part of the inner face at an outside door....
Figure 4.13 End of the row house with 2 rain gauges attached to the NW-fa...
Figure 4.14 Rain control: run-off, storage and transmission.
Figure 4.15 New building, sloping façade, true risk to get rain infi...
Figure 4.16 From (a) roof overhang, tiles, façade without overhangs ...
Figure 4.17 Rain control by buffering.
Figure 4.18 Rain control by front drainage only.
Figure 4.19 Filled cavity wall, two-step rain control.
Figure 4.20 Rising damp as cause of extensive mould growth.
Figure 4.21 Unpainted 30 cm thick homogeneous partition. Dampness height at ...
Figure 4.22 A homogeneous partition with both sides painted (diffusion th...
Figure 4.23 Gypsum plaster short-circuiting the mortar joints.
Figure 4.24 Tray mounted to exclude rising damp in the inside leaf.
Figure 4.25 Injection.
Figure 4.26 Leaking swimming pool enclosure.
Figure 4.27 Drainage.
Figure 4.28 Timber frame, damage caused by a leaky hot water pipe built in a...
Figure 4.29 Sorption/desorption isotherm.
Figure 4.30 Surface condensation.
Figure 4.31 Two person bedroom with volume 4 × 4 ...
Figure 4.32 Damage caused by interstitial condensation due to design flaws....
Figure 4.33 Front façade, outside insulation mounted the way described.
Figure 4.34 Façade retrofit, only vapour diffusion. (a) the temperature curv...
Figure 4.35 The vapour pressure curve for the situation with vapour retarder...
Figure 4.36 The vapour pressure curve for the situation without vapour retar...
Figure 4.37 Façade retrofit, air exfiltration; the air pressure curve...
Figure 4.38 Air exfiltration; the vapour pressure curve for the situation ...
Figure 4.39 Metal claddings as outside finish.
Figure 4.40 Dry cup vapour resistance factors as measured on 30 bricks from ...
Figure 4.41 Filled cavity walls: real versus the modelled dummy.
Figure 4.42 Concrete block veneer wall: head joints seeping, evolution.
Figure 4.43 Cavity side run-off measured on site for a cavity wall with conc...
Figure 4.44 (a) The building, (b) moisture spots, (c) leakage along window s...
Figure 4.45 (a) the building at the street side; (b) lime deposit on the gla...
Figure 4.46 The house with sloping garden, and rising damp in a partition.
Figure 4.47 Geometrical thermal bridges; (a) the edge between two outer wall...
Figure 4.48 (a) cracking disturbing the appearance of a black painted stucco...
Chapter 5
Figure 5.1 Timber-frame outer wall.
Figure 5.2 Timber frame, some view on how construction proceeds.
Figure 5.3 Air flux across the wall (leaks assumed smeared out).
Figure 5.4 Clear and whole wall thermal transmittance.
Figure 5.5 I-shaped engineered stud.
Figure 5.6 Timber frame wall: temperature damping and thermal admittance.
Figure 5.7 Timber-frame dwelling with veneer wall as outside finish, the con...
Figure 5.8 Building paper.
Figure 5.9 Timber-frame wall finished with brick veneer.
Figure 5.10 Timber-frame wall with brick veneer as outer finish, diffusion f...
Figure 5.11 Condensation risk at the back of the plywood for ICC2 conditions...
Figure 5.12 Condensation risk at the back of the plywood for ICC3 conditions...
Figure 5.13 Convection + diffusion in ICC2.
Figure 5.14 The deposits the one cold week gives at Uccle.
Figure 5.15 Condensation by combined diffusion + convection; (a) impact of t...
Figure 5.16 A taped OSB inside finish as air and vapour retarder.
Figure 5.17 ICC2, wet brick veneer, moisture deposit at the back of the plyw...
Figure 5.18 ICC2, relative humidity at the back of the gypsum board inner li...
Figure 5.19 Timber-frame outer wall, ICC3, hygric inertia of the plywood acc...
Guide
Cover
Table of Contents
Title Page
Copyright
Dedication
Preface
About the Author
List of Units and Symbols
Begin Reading
Appendix: Heat, Air, Moisture (HAM) Material Properties
Index
End User License Agreement
Pages
iii
iv
v
vi
xv
xvi
xvii
xviii
xix
xx
xxi
xxii
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
337
338
339
340
341
342
343
344
345
346
Applied Building Physics
Ambient Conditions, Functional Demands, and Building Part Requirements
Hugo Hens
Third, revised Edition
AuthorProf. em. Hugo Hens, PhDUniversity of LeuvenDepartment of Civil EngineeringKasteelpark Arenberg3001 HeverleeBelgium
Cover: Renovated two-family housedating from the 1950s: up to low energyPhoto: Hugo Hens
All books published by Ernst & Sohn are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
Library of Congress Card No.: applied for
British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library.
Bibliographic information published by the Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.d-nb.de.
© 2024 Ernst & Sohn GmbH, Rotherstraße 21, 10245 Berlin, Germany
All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.
Print ISBN: 978-3-433-03423-1ePDF ISBN: 978-3-433-61189-0ePub ISBN: 978-3-433-61188-3oBook ISBN: 978-3-433-61190-6
Coverdesign: Petra Franke/Ernst & Sohn GmbH using a design by Sophie Bleifuß, Berlin, Germany
To my wife, children and grandchildren
In remembrance of Professor A. de Grave, a civil engineer who introduced building physics as a new discipline at the University of Leuven, Belgium, in 1952.
Preface
While the first volume on Building Physics looked to the fundamentals governing the heat, air, moisture response of building parts and whole buildings, this second volume on Applied Building Physics shows how building physics may help in upgrading building and building part design and construction by applying the discipline related performance rationales, requirements and metrics to guarantee a sound building quality. How, starts with the ambient conditions out‐ and indoors acting as the environmental loads buildings and building parts or assemblies face. Then a move is made to the performance fields of importance at the whole building level, after which, directly linked to the book on Building Physics, the heat, air, moisture requirements and metrics actually expected when designing and realizing building parts assemblies pass the review.
This content to a large extent reflects the 38 years of teaching Building Physics and Applied Building Physics to architectural, building and civil engineering students, that, coupled to more than 36 years of experience in building and building part performance research and more than 50 years of activity in consultancy and in curing hundreds of heat, air, moisture‐related damage cases. When and where needed, information from international sources and literature has been consulted, which is why all chapters end with an extended further reading list. The book uses SI units. It could be of help for undergraduate and graduate students in architectural and building engineering, although also practising building engineers, who want to refresh their knowledge, may benefit. Presumed anyhow is that the reader has a sound knowledge of the fundamentals treated in the first book, along with a background in construction materials and building design and construction.
Acknowledgements
The book reflects the work of many, not only of the author. Therefore, we thank the thousands of students we had during the 38 years of teaching. They gave us the opportunity to test the content. The book should also not have been written the way it is if not standing on the shoulders of those, who preceded it. Although we started our carrier as a structural engineer, our predecessor Professor Antoine de Grave planted the seeds that fed the interest in building physics. Bob Vos of TNO, the Netherlands, and Helmut Künzel of the Fraunhofer Institüt für Bauphysik, Germany, showed the importance of experimental work and field testing to understand whole building and building part or assembly performance, while Lars Erik Nevander of Lund University, Sweden, taught that solving problems in building physics does not always ask complex modelling, mainly because reality in building construction is much more complex than any model can simulate.
During the four decades at the Unit of Building Physics and Sustainable Construction within the Department of Civil Engineering of the KULeuven, several researchers, then PhD‐students, got involved. They all contributed by the topics chosen to the advancement of the research done at the unit. Most grateful I am to Gerrit Vermeir, my colleague from the start in 1975, now professor emeritus, to Staf Roels, Dirk Saelens, Hans Janssen and Bert Blocken, who succeeded me as professors at the unit.
The experience gained as a structural engineer and building site supervisor for a medium‐sized architectural office the first 4 years of my career, as building assessor during some 50 years, as operating agent of four IEA, EXCO on Energy in Buildings and Communities Annexes forced me to rethink the engineering‐based performance approach each time again. The many ideas exchanged in Canada and the United States with Kumar Kumaran of NRC, Paul Fazio of Concordia University in Montreal, Bill Brown, William B. Rose of the University of Illinois in Urbana‐Champaign, Joe Lstiburek of the Building Science Corporation, Anton Ten Wolde and those participating in ASHRAE TC 1.12 ‘Moisture management in buildings’ and TC 4.4 ‘Building materials and building envelope performance’ were also of great value.
Finally, I thank my family, my wife Lieve, who managed living together with a busy engineering professor, our three children, our children in law and our grandchildren.
Leuven, March 2023 Hugo S.L.C. Hens
About the Author
Dr. Ir. Hugo S.L.C. Hens is an emeritus professor of the University of Leuven (KU Leuven), Belgium. Until 1972, he worked as a structural engineer and site supervisor at a mid-sized architectural office. After the sudden death of his predecessor and promotor Professor A. de Grave in 1975 and after defending his PhD thesis, he stepwise built up the Unit of Building Physics at the Department of Civil Engineering.
He taught Building Physics from 1975 to 2003, performance-based building design from 1975 to 2005 and building services from 1975 to 1977 and 1990 to 2008. He authored and co-authored 68 peer-reviewed journal papers and 174 conference papers about the research done, has helped to manage hundreds of building damage cases and acted as coordinator of the CIB W40 working group on Heat and Mass Transfer in Buildings from 1983 to 1993. Between 1986 and 2008, he was operating agent of the Annexes 14, 24, 32 and 41 of the IEA EXCO on Energy in Buildings and Communities. He is a fellow of the American Society of Heating, Refrigeration and Air Conditioning Engineers (ASHRAE).
List of Units and Symbols
Units
The book uses the SI system, internationally mandatory since 1977, with as base units the metre (m), the kilogram (kg), the second (s), the Kelvin (K), the ampere (A) and the candela. Derived units of importance when studying applied building physics are:
Unit of force
Newton (N)
1 N = 1 kg m/s
2
Unit of pressure
Pascal (Pa)
1 Pa = 1 N/m
2
= 1 kg/(m s
2
)
Unit of energy
Joule (J)
1 J = 1 N m = 1 kg m
2
/s
2
Unit of power
Watt (W)
1 W = 1 J s
−1
= 1 kg m
2
/s
3
Symbols
For the symbols, the ISO standards (International Standardization Organization) are followed. For quantities not included, the CIB-W40 recommendations (International Council for Building Research, Studies and Documentation, Working Group ‘Heat and Moisture Transfer in Buildings’) and the list edited by Annex 24 of the IEA, EBC (International Energy Agency, Executive Committee on Energy in Buildings and Communities) apply.
Table 1 List with symbols and quantities.
Symbol
Meaning
SI units
a
Acceleration
m/s
2
a
Thermal diffusivity
m
2
/s
b
Thermal effusivity
W/(m
2
K s
0.5
)
c
Specific heat capacity
J/(kg K)
c
Concentration
kg/m
3
, g/m
3
e
Emissivity
—
f
Specific free energy
J/kg
Temperature ratio
—
g
Specific free enthalpy
J/kg
g
Acceleration by gravity
m/s
2
g
Mass flux
kg/(m
2
s)
h
Height
m
h
Specific enthalpy
J/kg
h
Surface film coefficient for heat transfer
W/(m
2
K)
k
Mass-related permeability (mass could be moisture, air, salt, etc.)
s
l
Length
m
l
Specific enthalpy of evaporation or melting
J/kg
m
Mass
kg
n
Ventilation rate
s
−1
, h
−1
p
Partial pressure
Pa
q
Heat flux
W/m
2
r
Radius
m
s
Specific entropy
J/(kg K)
t
Time
s
u
Specific latent energy
J/kg
v
Velocity
m/s
w
Moisture content
kg/m
3
x,y,z
Cartesian co-ordinates
m
A
Water sorption coefficient
kg/(m
2
s
0.5
)
A
Area
m
2
B
Water penetration coefficient
m/s
0.5
D
Diffusion coefficient
m
2
/s
D
Moisture diffusivity
m
2
/s
E
Irradiation
W/m
2
F
Free energy
J
G
Free enthalpy
J
G
Mass flow (mass = vapour, water, air, salt)
kg/s
H
Enthalpy
J
I
Radiation intensity
J/rad
K
Thermal moisture diffusion coefficient
kg/(m s K)
K
Mass permeance
s/m
K
Force
N
L
Luminosity
W/m
2
M
Emittance
W/m
2
P
Power
W
P
Thermal permeance
W/(m
2
K)
P
Total pressure
Pa
Q
Heat
J
R
Thermal resistance
m
2
K/W
R
Gas constant
J/(kg K)
S
Entropy, saturation degree
J/K, –
T
Absolute temperature
K
T
Period (of a vibration or a wave)
s, days, etc.
U
Latent energy
J
U
Thermal transmittance
W/(m
2
K)
V
Volume
m
3
W
Air resistance
m/s
X
Moisture ratio
kg/kg
Z
Diffusion resistance
m/s
α
Thermal expansion coefficient
K
−1
α
Absorptivity
—
β
Surface film coefficient for diffusion
s/m
β
Volumetric thermal expansion coefficient
K
−1
η
Dynamic viscosity
N s/m
2
θ
Temperature
°C
λ
Thermal conductivity
W/(m K)
μ
Vapour resistance factor
—
ν
Kinematic viscosity
m
2
/s
ρ
Density
kg/m
3
ρ
Reflectivity
—
σ
Surface tension
N/m
τ
Transmissivity
—
ϕ
Relative humidity
—
α, ϕ, Θ
Angle
rad
ξ
Specific moisture capacity
kg/kg per unit of moisture potential
Ψ
Porosity
—
Ψ
Volumetric moisture ratio
m
3
/m
3
Φ
Heat flow
W
Table 2 List with suffixes and notations.
Symbol
Meaning
Symbol
Meaning
Indices
A
Air
m
Moisture, maximal
c
Capillary, convection
o
Operative
e
Outside, outdoors
r
Radiant, radiation
h
Hygroscopic
sat
Saturation
i
Inside, indoors
s
Surface, area, suction
cr
Critical
v
Water vapour
CO
2
, SO
2
Chemical symbol for gasses
w
Water
ϕ
Relative humidity
Notation
Meaning
[], bold,
Matrix, array, value of a complex number
Dash (e.g.: )
Vector
Introduction
Subject of the Book
This is the second volume in a series of three:
Building Physics: Heat, Air and Moisture, Fundamentals, Engineering Methods, Material Properties and Exercises
Applied Building Physics: Ambient Conditions, Whole Building and Building Assembly Performance
Performance-Based Building Design: from Below Grade over Floors, Walls, Roofs, and Windows to Finishes
The term ‘applied’ could be perceived as a pleonasm since ‘Building Physics’ is by definition referring to a body of knowledge, whose application is essential for the correct performance of new construction and renovation. Whatever, the subjects discussed in this second book offer a link between ‘Building Physics: Heat, Air and Moisture’ and the volume on ‘Performance-Based Building Design’.
Highlighted in Chapter 1 are the climate, the indoor environment and several related design approaches. Chapter 2 advances the performance concept with its hierarchical structure, from the urban environment down to whole buildings, building assemblies, the layers assemblies consist of and the materials used. In Chapter 3, several fields of importance that fix building physics-related performance requirements at the whole building level are discussed. Chapter 4 analyses the heat, air, moisture performance metrics, to which building envelopes must comply to ensure a correct behaviour. Chapter 5 advances timber frame walls as example of a construction choice with possibly a problematic heat, air, moisture response, while for the sake of completeness, the Appendix repeats lists with material property values, already discussed in ‘Building Physics: Heat, Air and Moisture, Fundamentals, Engineering Methods, Material Properties and Exercises’.
Well known is that a performance-based approach should guarantee building quality. Of course, physical integrity is not the only value of importance in the built environment. Also, functionality, spatial quality and aesthetics, all belonging to the architect's responsibility, are, but these should never figure as arguments to neglect a correct overall structural and physical performance.
Further Reading
CIB-W40 (1975). Quantities, Symbols and Units for the description of heat and moisture transfer in Buildings: Conversion factors, IBBC-TNP, report no. BI-75-59/03.8.12, Rijs-wijk.
ISO-BIN (1985). Standards series X02-101 – X023-113.
Kumaran, K. (1996). Task 3: Material Properties, Final Report IEA EBC Annex 24, ACCO, Leuven, 135 p.
De Freitas, V. P. and Barreira, E. (2012). Heat, air and moisture transfer terminology, parameters and concepts, Report CIB W040, 52 p.
1Ambient Conditions Out- and Indoors
1.1 Overview
The role the ambient conditions have in building physics could be compared to the role loads have in structural engineering, the reason why the term ‘ambient or environmental loads’ is often used. Their knowledge is essential to make appropriate decisions when designing building envelopes and whole buildings. The components shaping the conditions out- and indoors are:
Outdoors
Indoors
Air temperature
θ
e
Air temperature
θ
i
Radiant temperature
θ
R
Relative humidity (RH)
ϕ
e
Relative humidity (RH)
ϕ
i
(Partial water) vapour pressure
p
e
(Partial water) vapour pressure
p
i
Solar radiation
E
S
Under-cooling
q
rL
Wind
v
w
Air speed
v
Rain and snow
g
r
Air pressure
P
a,e
Air pressure
P
a,i
In what follows, all are discussed separately. Bear in mind though that the greater the difference between the out- and indoor temperature and relative humidity is, the stricter the envelope and HVAC performance requirements become. If not, maintaining thermally comfortable and environmentally healthy conditions indoors will among other things require more energy than acceptable.
Predicting the future climate outdoors remains a guess. Not only are most components not measured everywhere, but the future is never a copy of the past and does not obey the paradigm ‘the longer the data chain available, the better the forecast’. Moreover, global warming combined with the actual measures taken and future measures that will be taken to minimize the emission of global warming gasses, is loading any long-term prediction with uncertainty, see Figure 1.1.
Figure 1.1 Global warming, (a) increase in the world's average annual temperature from 1850 to 2014; (b) the same for Uccle, Belgium.
A way to bypass that uncertainty is by using reference values and reference years for any performance check requiring climate data. Many of the facts and trends illustrating this in the book come from the weather station at Uccle, Belgium (50° 51′ north, 4° 21′ east). The large number of observations available there allowed to synthetize what happened over the last century.
1.2 Outdoors
1.2.1 In General
The geographic location is what largely determines the climate: northern or southern latitude, proximity of the sea, presence of a warm or cold sea current, and height above sea level. Of course, also microclimatic factors play. In city centres, the air temperature is on average 4–6 °C higher than at the countryside, while the relative humidity (RH) is lower and the solar radiation less intense, a reality called the urban heat island effect. To illustrate, Table 1.1 lists the monthly mean dry bulb temperatures measured at Uccle and Sint Joost for the period 1901–1930, both weather stations in the Brussels region, with the Uccle one situated in a green area and the Sint Joost one in the city centre.
From the annual down to the daily fluctuations, all are linked to the earth's elliptic orbit around the sun, the earth's inclination, the rotation around its axis and at its surface, more locally, the sequence of low- and high-pressure days. As a consequence, outside the equatorial band with its wet and dry seasons, each year sees a winter, springtime, summer and autumn passing. In addition, each 24 hours, day- and night-time alternate. In temperate and cold climates, high pressure brings warmth in summer and cold in winter, while low pressure cares for more moderate but often wet weather in summer and fresh but wet weather in winter. Anyhow, the last decennia, global warming is changing these patterns. New are more heat waves in summer, sequences of days showing excessive rain fall and warmer winters.
The data needed should focus on the annual cycle, the daily cycle and the daily averages. From a meteorological point of view, the 30-year averages, for the twentieth to twenty-first century 1901–1930, 1931–1960, 1961–1990, 1991–2020, 2021–2050, figure as the annual reference. Due to long-term climate changes induced by solar activity and global warming, the consequence of a still increasing imbalance between GW-gasses released and removed from the atmosphere, the trend to warmer, just mentioned, is real. Relocation of weather stations, more accurate measuring and the way averages are calculated also impact the data. Up to 1930, as daily mean was used the average between the daily minimum and maximum temperature logged by a minimum/maximum mercury thermometer. Today, the air temperature is logged each 10′ and the daily mean is calculated as the average of the 144 values so obtained.
Table 1.1 Monthly average dry bulb temperature at Uccle and Sint Joost, Brussels (°C).
Month
J
F
M
A
M
J
J
A
S
O
N
D
Uccle
2.7
3.1
5.5
8.2
12.8
14.9
16.8
16.4
14.0
10.0
5.2
3.7
Sint Joost
3.8
4.2
6.8
9.4
14.6
16.7
18.7
18.0
15.4
11.2
6.4
4.7
1.2.2 Air Temperature
Calculating the heating and cooling load and estimating related annual end energy use requires knowledge of the outside air temperature, while the loads so quantified fix the size and the investment in the HVAC installation and the energy use as annual cost. From day to day, the air temperature further impacts the heat, air, moisture stress building enclosures endure, while high hourly values increase overheating risk indoors. As imposed by the World Meteorological Organization (WMO), the measuring accuracy in the open field, 1.5 m above grade in a thermometer hut (Figure 1.2) should be ±0.5 °C. Table 1.2 gives the 30-year monthly averages for several weather stations across Europe and North America.
An annual average with one harmonic reflects the table data quite well, although two harmonics, the second on a half a year basis, do better:
In both is the annual average and t time.
For three locations, the two harmonics gave as a result (°C, also see Figure 1.3):
A
2,1
B
2,1
A
2,2
B
2,2
Uccle
9.8
−2.4
−7.4
0.45
−0.1
Kiruna
−1.2
−4.2
−11.6
1.2
0.5
Catania
17.2
−4.1
−6.6
0.8
0.2
Figure 1.2 Thermometer hut.
Table 1.2 The thirty years based monthly mean air temperatures at several locations (°C).
Month location
J
F
M
A
M
J
J
A
S
O
N
D
Uccle (B)
2.7
3.1
5.5
8.2
12.8
14.9
16.8
16.4
14.0
10.0
5.2
3.7
Den Bilt (NL)
1.3
2.4
4.3
8.1
12.1
15.3
16.1
16.1
14.2
10.7
5.5
1.2
Aberdeen (UK)
2.5
2.7
4.5
6.8
9.0
12.1
13.7
13.3
11.9
9.3
5.3
3.7
Eskdalemuir (UK)
1.8
1.9
3.9
5.8
8.9
11.8
13.1
12.9
10.9
8.5
4.3
2.7
Kew (UK)
4.7
4.8
6.8
9.0
12.6
15.6
17.5
17.1
14.8
11.6
7.5
5.6
Kiruna (S)
−12.2
−12.4
−8.9
−3.5
2.7
9.2
12.9
10.5
5.1
−1.5
−6.8
−10.1
Malmö (S)
−0.5
−0.7
1.4
6.0
11.0
15.0
17.2
16.7
13.5
8.9
4.9
2.0
Västerås (S)
−4.1
−4.1
−1.4
4.1
10.1
14.6
17.2
15.8
11.3
6.3
1.9
−1.0
Lulea (S)
−11.4
−10.0
−5.6
−0.1
6.1
12.8
15.3
13.6
8.2
2.9
−4.0
−8.9
Oslo (N)
−4.2
−4.1
−0.2
4.6
10.8
15.0
16.5
15.2
10.8
6.1
0.8
−2.6
München (D)
−1.5
−0.4
3.4
8.1
11.9
15.6
17.5
16.7
13.9
8.8
3.6
−0.2
Potsdam (D)
−0.7
−0.3
3.5
8.0
13.1
16.6
18.1
17.5
13.8
9.2
4.1
0.9
Roma (I)
7.6
9.0
11.3
13.9
18.0
22.3
25.2
24.7
21.5
16.8
12.1
8.9
Catania (I)
10.0
10.4
12.0
14.0
18.0
22.0
25.2
25.6
23.2
18.4
15.2
11.6
Torino (I)
1.6
3.5
7.6
10.8
15.4
19.0
22.3
21.6
17.9
12.3
6.2
2.4
Bratislava (Sk)
−2.0
0.0
4.3
9.6
14.2
17.8
19.3
18.9
15.3
10.0
4.2
0.1
Copenhagen (Dk)
−0.7
−0.8
1.8
5.7
11.1
15.1
16.2
16.0
12.7
9.0
4.7
1.1
Montreal
−9.9
−8.5
−2.4
5.7
13.1
18.4
21.1
19.5
14.6
8.5
1.8
−6.5
New York
0,6
2.2
6.1
11.7
17.2
22.2
25.0
24.4
20.0
13.9
8.9
3.3
Chicago
−5,6
−3,3
2,8
9,4
15,0
20,6
23,3
22,2
18,3
11,7
4,4
−2,8
Los Angeles
15,0
14,9
20,3
17,3
18,8
20,7
22,9
23,5
22,8
20,3
16,9
14,2
Figure 1.3 Air temperature: annual course, one and two harmonics; left: Kiruna, Sweden; right: Catania, Italy.
For Uccle the average difference between the monthly mean daily minimum and maximum temperature (θe,max,day − θe,min,day) during the period 1931–1960 is (°C):
J
F
M
A
M
J
J
A
S
O
N
D
5.6
6.6
7.9
9.3
10.7
10.8
10.6
10.1
9.8
8.0
6.2
5.2
A combination with the annual course gives (time in hours):
with:
(°C)
(°C)
h
1
(h)
h
2
(h)
h
3
(h)
8.4
2.8
456
−42
8
The equation assumes that the daily values fluctuate harmonically, which is not the case. Instead, the gap between the minimum and maximum value swings considerably, without even a glue of being harmonic. To give an example, in Leuven, Belgium, the differences in January and July 1973 were random, with as averages 4.0 and 8.9 °C and as standard deviation 60% in January and 39% in July.
A question of course is whether the air temperatures recorded during the past decades reflect global warming. For that, data measured between 1997 and 2013 at the outskirts of Leuven were tabulated. Figure 1.4 shows the annual means and monthly minima and maxima. The least square line through the annual is:
Figure 1.4 Leuven, Belgium, weather station: air temperatures between 1996 and 2013; left: the annual mean; right: the average, minimum, maximum, and monthly mean.
With on average 11.1 °C and a slightly negative slope, apparently, no increase appeared. Not so at Uccle, 30 km west of Leuven. There the overall average between 1901 and 1930 was 9.8 °C, i.e. 1.4 °C lower than measured from 1997 to 2013 in Leuven. From 1952 to 1971 the average in Uccle remained 9.8 °C but, since, the moving 20 years average is slowly increasing, with the highest values logged after 2001.
1.2.3 Solar Radiation
1.2.3.1 In General
The heat gains by solar radiation give less end energy needed for heating, though active cooling may loom as overheating might be the unintended consequence. Solar radiation further lifts the outside surface temperature of envelope assemblies, so enhancing drying and activating solar-driven vapour flow from rain-buffering outside finishes to inside. The concurring drop in RH may simultaneously increase the hygrothermal stress and strain in thin outside finishes.
The sun behaves as a 5762 K hot black body, ≈150 000 000 km away from the earth (=Dse). Through that distance, the rays reach the earth in parallel. Above the atmosphere, the solar spectrum coincides with the thin line in Figure 1.5, giving as irradiation:
with rs the sun's radius in km.
This 1332 W/m2 is called the average solar constant (ESTo), the mean radiation the earth should receive per m2 perpendicular to the solar beam if without atmosphere, a flow, which is quite thin. Burning 1 l of fuel gives 4.4 × 107 J. Collecting so many Joules above the atmosphere per m2 perpendicular to the moving solar beam will take nine hours, what explains why transforming solar energy into enough heat or electricity requires large collecting surfaces.
Figure 1.5 Solar spectrums before (upper line) and after passing the atmosphere (lower, up and down line).
A more exact calculation of the solar constant takes into account the annual variation in distance between earth and sun and the annual cycle in solar activity:
with d the number of days from midnight December 31/January 1. As the lower, up and down line along the spectrum in figure 1.5 shows, when crossing the atmosphere, gasses present, especially water vapour and CO2, absorb part of the solar radiation, which definitely moderates what the earth surface receives.
To fix the sun's position on the sky, either the azimuth (as) and solar height (hs) or the time angle (ω) and solar declination (δ), being the angle between both Tropics and the equator, can be used. The solar height touches 90° on December 21 when standing at zenith at the Tropic of Capricorn and on June 21 when standing at zenith at the Tropic of Cancer, see Figure 1.6. While the azimuth and solar height describe the sun's movement locally on earth, the time angle and solar declination link it to the equator.
Figure 1.6 Solar angles.
The time angle (ω) goes from 180° at midnight over 0° at noon to –180° next midnight. One hour so takes 15°. The solar declination (δ) in radians in turn equals:
where +23.45 and −23.45 are the latitudes of the tropic of Capricorn and the tropic of Cancer in degrees. The solar height in radians and the maximums (hs,max) in degrees and rad follow from:
with ϕ the latitude, positive in the northern, and negative in the southern hemisphere.
1.2.3.2 Beam Radiation
During the passage through the atmosphere, selective absorption by ozone, oxygen, hydrogen, carbon dioxide and methane muffle the solar rays, change their spectrum and scatter a part. The longer the distance so traversed, the larger these impacts, a fact the air factor m, the ratio between the distance the ray's traverse from the sun at solar height hs to sea level and the distance they traverse from the sun in zenith to any location at and above sea level, accounts for (Figure 1.7).
For a location z km above sea level, the air factor so is:
The beam radiation on a surface perpendicular to the rays consequently becomes:
Figure 1.7L distance traversed through the atmosphere from the sun at solar height hs to sea level, Lo idem but now from the sun in zenith to a location at height z.
Figure 1.8 Direct radiation on a surface with slope ss.
with TAtm the atmospheric turbidity and dR the optic factor, a measure for the scatter per meter traversed:
On a clear day with average and minimal air pollution, the atmospheric turbidity (mo = 1 for January, mo = 12 for December) touches:
The beam radiation on a sloped surface, where the perpendicular to it forms an angle χ with the solar rays, now equals (Figure 1.8):
with:
In it, as is the azimuth (south 0°, east 90°, north 180°, west –90°) and ss the slope of the surface (0° if horizontal, 90° (π/2) if vertical, 0 to 90° if sloped to, 0 to –90° (−π/2) if sloped away from the sun).
For a horizontal surface facing the sun, the formula becomes:
For a south, west, north or east looking vertical surface facing the sun, it simplifies to:
South: cos χv, south = − sin δ cos ϕ + cos δ sin ϕ cos ω
West: cos χv, west = − cos δ sin ω
North: cos χv, north = − sin δ cos ϕ − cos δ sin ϕ cos ω
East: cos χv, east = cos δ sin ω
With the beam radiation on a horizontal surface known (ESD,h), the value on any sloped surface (ESD,s) follows from:
Beam radiation so looks predictable. The true unknown however is the atmospheric turbidity (TAtm). Cloudiness, air pollution and RH, all intervene, but the impact is complex and varies from day to day.
1.2.3.3 Diffuse Radiation
Independently of whether the sky is blue or cloudy, the diffuse part of the solar radiation reaches the earth from sunrise to sunset. It looks as if the rays come from all directions. A simple model considers the sky as a uniformly radiating vault. Any surface, whose slope differs from horizontal, sees part of it. For the vault as black surface at constant temperature, each point on it has a same luminosity, giving as view factor with a surface:
If ESd,h is diffuse radiation on a horizontal surface, then on a sloped it equals:
Closer to reality is the sky as a vault with highest luminosity at the solar disk and lowest at the horizon. For any point P on it characterized by its azimuth aP and height hP, related luminosity writes L(aP,hP). The angle Γ between the perpendicular on a surface with slope ss and the line from the surface's centre to that point P now equals:
with 0 ≤ aP ≤ 2π and 0 ≤ hP ≤ π/2. The diffuse radiation on the surface so becomes:
with:
and:
In it, Lsd is the luminosity at the solar disk and ε the angle between the line from the centre of the sloped surface to P and the perpendicular to the vault in P coinciding with the solar beam there:
Entering this formula and the multiplier f in the upgraded equation for diffuse radiation gives:
Luminosity at the solar disk now equals:
with TAtm the atmospheric turbidity and hs (°) the solar height. On a monthly basis, this set of formulas can be simplified to:
with fmo a multiplier correcting the monthly diffuse radiation calculated with the simple model for the other luminosity at the solar disk than at the horizon. Table 1.3 gives fmo for Uccle.
Table 1.3 Uccle, multiplier fmo for the total monthly diffuse radiation.
Multiplier
f
mo
Slope
↓
Az
→
0, S
22.5
45
67.5
90, E,W
112.5
135
157.5
180, N
0
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
22.5
1.03
1.03
1.02
1.01
1.00
0.99
0.98
0.97
0.96
45
1.05
1.04
1.03
1.01
0.99
0.96
0.94
0.92
0.92
67.5
1.06
1.05
1.03
0.99
0.94
0.90
0.86
0.84
0.83
90
1.06
1.04
1.00
0.94
0.87
0.81
0.76
0.73
0.71
112.5
0.98
0.97
0.92
0.85
0.76
0.68
0.63
0.60
0.60
135
0.80
0.78
0.74
0.67
0.59
0.53
0.49
0.47
0.47
157.5
0.58
0.56
0.51
0.48
0.46
0.43
0.41
0.40
0.34
180
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1.2.3.4 Reflected Radiation
Any surface on earth reflects part of the solar radiation received. To calculate the intensity, the surroundings are considered acting as a horizontal plane with reflectivity 0.2, their albedo. Each surface so receives reflected radiation proportionally to its view factor with that plane (Fse):
A horizontal surface facing the sky does not receive reflected radiation (ss = 0), although it can in reality. A low-sloped roof for example may get reflected radiation from nearby higher buildings. Also, an albedo 0.2 is too simplistic. White snow gives much higher values.
1.2.3.5 Total Radiation
Beam, diffuse and reflected together fix the total solar a surface receives. The appendix contains tables with values for Uccle. Table 1.4 summarizes the average, minimum and maximum monthly totals measured on a horizontal surface there, together with related monthly mean cloudiness, calculated as one minus the ratio between the measured and total solar radiation on it under clear sky conditions.
Table 1.5 lists the monthly totals on a horizontal surface for several locations in Europe, while Figure 1.9 shows the annual totals. The ratio between least and most sunny location nears 2.
1.2.4 Clear Sky Long Wave Radiation
By cooling outer surfaces and the layers at the outside of the thermal insulation to below the air temperature, even to below the dewpoint outdoors, clear sky long wave radiation may induce extra heat losses. Related under-cooling so can turn the outdoor air into a moisture source causing condensation on the outer face of insulating glass and rime formation on EIFS insulated walls and on well-insulated tiled and slated roof pitches (Figure 1.10). Guilty is the long wave balance between the celestial vault, the sky, the terrestrial environment and the surface, with the sky as selective radiant surface, absorbing all but emitting only a fraction of the incident radiation.
Table 1.4 Uccle, total solar radiation on a horizontal surface (MJ/(m2 mo)), related cloudiness.
J
F
M
A
M
J
J
A
S
O
N
D
Total solar radiation (1958–1975)
Average
72
129
247
356
500
538
510
439
327
197
85
56
Min.
61
104
177
263
406
431
408
366
279
145
63
41
Max.
93
188
311
485
589
640
651
497
444
274
112
78
Related cloudiness (1958–1975)
Average
0.47
0.44
0.42
0.42
0.36
0.35
0.38
0.38
0.34
0.39
0.49
0.50
Min.
0.55
0.55
0.58
0.57
0.48
0.48
0.51
0.48
0.44
0.55
0.62
0.63
Max.
0.31
0.19
0.27
0.20
0.25
0.22
0.21
0.30
0.11
0.15
0.33
0.30
Table 1.5 Monthly total solar irradiation on a horizontal surface in Europe (MJ/(m2 mo)).
Month
J
F
M
A
M
J
J
A
S
O
N
D
Den Bilt (NL)
72
132
249
381
522
555
509
458
316
193
86
56
Eskdalemuir (UK)
55
112
209
345
458
490
445
370
244
143
70
39
Kew (UK)
67
115
244
355
496
516
501
434
311
182
88
54
Lulea (S)
6
52
182
358
528
612
589
418
211
80
14
1
Oslo (N)
44
110
268
441
616
689
624
490
391
153
57
27
Potsdam (D)
104
137
238
332
498
557
562
412
267
174
88
70
Roma (I)
182
247
404
521
670
700
750
654
498
343
205
166
Torino (I)
171
212
343
474
538
573
621
579
422
281
181
148
Bratislava (Sk)
94
159
300
464
597
635
624
544
389
233
101
72
Copenhagen (Dk)
54
114
244
407
579
622
576
479
308
159
67
38
Figure 1.9 Annual solar irradiation on a horizontal surface.
Figure 1.10 Rime formation on a well-insulated pitched roof due to under-cooling.
Calculating starts by assuming the sky to be at air temperature while having an absorptivity 1, a reflectivity 0 and an emissivity given by (or, or with pe in Pa, θe in °C):
Clear sky
Cloudy sky
(1)
(4)
ε
L
, sky
=
ε
L
, sky,
o
(1 − 0.84
c
) + 0.84
c
(2)
(3)
As water vapour is a greenhouse gas, the clear sky three gives a decreasing value at higher air temperature but an increasing value at higher vapour pressure outdoors. In the cloudy sky one, c is cloudiness, 0 for a clear, 0.125–0.875 in steps of 0.125 for a hardly to very and 1 for a totally covered sky. According to Figure 1.11, the formulas (1) and (2) give different emissivities, while formula (3) suggests that (1) applies for lower, (2) for higher outside temperatures.
The black surface emittances of the surface (Mb,s) and the terrestrial environment (Mb,t) equal:
In it, is the radiosity of the sky and Fs,t, Fs,sky, etc. are the view factors between sky, terrestrial environment and surface. Since the first two surround the surface, Fs,t + Fs,sky = 1. The view factor between the terrestrial environment and the surface in turn is so small, that the second equation does not play. This makes Ft,sky = 1, giving as radiosity of the sky:
Figure 1.11 Clear sky emissivity; left: according to (1) and (2); right: to (3).
That changes the two black surface emittance equations into:
The radiant heat flux at the surface so becomes:
The assumption the terrestrial environment is a black surface at outside air temperature simplifies this equation to:
Making the sky a black surface too at temperature θsk, e = θe − (23.8 − 0.2025θe)(1 − 0.87c), gives:
a result that fits with the equation for the radiant flux if the sky emissivity is set a little higher than assumed in Figure 1.11
