NATIONAL R E S E A R C H COUNCIL
CANADA
DIVISION O F BUILDING RESEARCH
ERRATA S H E E T
for
N R C 7104
A b s o r p t i o n a n d T r a n s m i s s i o n of T h e r m a l R a d i a t i o n
by Single a n d Double G l a z e d Windows
by
G. P. M i t a l a s dnd D. G. S t e p h e n s o n
T h e a b s o r p t i o n and t r a n s m i s s i o n f a c t o r s f o r d i f f u s e r a d i a t i o n given in t h e s e t a b l e s
a r e j u s t the s i m p l e a v e r a g e s of t h e v a l u e s f o r i n c i d e n t a n g l e s b e t w e e n 0 " and 9 0 " . It h a s
b e e n b r o u g h t to o u r a t t e n t i o n t h a t the v a l u e s f o r d i f f u s e r a d i a t i o n s h o u l d b e e v a l ~ l a t e dby t h e
formula
n/2
T (9) . S i n 28 d e ,
and s i m i l a r l y f o r the a b s o r p t i o n f a c t o r .
T h e following table g i v e s the t r a n s m i s s i o n and a b s o r p t i o n f a c t o r s f o r diffuse
r a d i a t i o n f o r s i n g l e and double windows ( n = 1 . 52). T h e i n t e g r a t i o n h a s b e e n p e r f o l m e d by
f i t t i n g a 5th d e g r e e p o l y n o m i a l of C o s e to the t a b u l a t e d v a l u e s of t r a n s m i s s i o n a n d a b s o r p t i o n
f a c t o r s a n d i n t e g r a t i n g t h i s p o l y n o m i a l m u l t i p l i e d by S i n 28 t e r m by t e r m .
Diffuse Radiation
n = 1. 52
KL
Single G l a z e d
Window
Double G l a z e d Window
K L of I n s i d e P a n e = . 0 5
NATIONAL RESEARCH COUNCIL
CANADA
DIVISION O F BUILDING RESEARCH
ABSORPTION AND TRANSMISSION O F THERMAL
RADIATION BY SINGLE AND DOUBLE
GLAZED WINDOWS
G. P. M i t a l a s and D. G. Stephenson
R e s e a r c h P a p e r No. 173
of the
Division of Building R e s e a r c h
OTTAWA
D e c e m b e r 1962
ABSORPTION AND TRANSMISSION O F THERMAL
RADIATION BY SINGLE AND DOUBLE
GLAZED WINDOWS
by
G. P. M i t a l a s
and D, G. Stephenson
SUMMARY
T a b l e s h a v e been p r e p a r e d for the t r a n s m i s s i o n and absorption
of radiant e n e r g y by v a r i o u s types of windows,
The t a b l e s cover the
following r a n g e of t h e independent v a r i a b l e s :
Incident angle = 0 (10)
40 (5)
70 (2)
88 d e g r e e s
K L = 0.05 to 2.00 with i n c r e a s i n g i n c r e m e n t s
Index of r e f r a c t i o n = 1.52 and 1.62
Single and double glazed windows,
F o r a single sheet of g l a s s t h e p a r a l l e l and perpendicular
polarized b e a m s a r e t a b d a t e d s e p a r a t e l y , a s a r e t h e combined values
for a non-polarized incident beam.
Introduction
In t h e calculation of the heating o r cooling load for a r o o m ,
it is n e c e s s a r y t o know the f r a c t i o n of the radiation incident on t h e
outside of the window t h a t is absorbed by t h e g l a s s and t h e f r a c t i o n
that i s transmitted t o the interior of the room.
The absorptivity and
transmissivity of a window depend on the type and thickness of the glass;
on whether the window i s single or double glazed; on the angle that the
incident beam of light makes with the n o r m a l t o the surface; and on
the degree of polarization of the incident beam,
The tables presented
in this r e p o r t either give directly, or allow the simple calculation of,
the absorptivity and transmissivity of windows made of common glas s o
When a beam of radiant energy s t r i k e s an interface between
a i r and glass some of the energy i s reflected.
The ratio of the intensity
of the reflected beam t o the incident beam i s given by F r e s n e l r s formulae
tan
-
tan
sin
-
sin
where r
//
and r
L
2
2
2
2
- GZ)
(el + Q2)
(0,
- Q2)
(el + G2)
(8,
a r e the reflectivity of the interface for radiation
that i s polarized with the electric vector parallel and perpendicular
respectively to the plane that contains the incident beam and a normal
t o the interface, and 8
1
and 8 a r e the angles that the beam makes with
2
the normal t o the interface in the a i r and in the glass respectively.
They a r e related with the index of refraction of the glass n by Snellts law
Sine
1
= nSin8
2
F o r normal incidence
@1
=
e2
=
0
and
L
r//
-
2
n-t 1
The energy that i s not reflected at the a i r -glass interface
e n t e r s the glass, where i t i s partially absorbed a s it p a s s e s through,
The absorption may be described by
where
I i s the intensity of the beam,
X i s distance measured in the direction of the beam, and
K i s an absorption coefficient,
Thus i f the intensity of a beam incident on the surface of a sheet of glass
i s unity, the intensity of the beam that penetrates to a depth L measured
along a normal to the surface i s
i
I,
= (1 - r ) e
-3
- ~ K L / \ ] n6
-
-3
L
sin Q 1
The fraction of the energy that i s absorbed i s
Since r
depends on the polarization a does also.
The beam that reaches the second glass -air interface h a s
the intensity I
L=
A fraction r
of this i s reflected back into the glass
and the r e s t p a s s e s out of the glass into the room,
The internally
reflected beam i s again partially absorbed before reaching the out side
glass -air interface where i t i s again partially reflected.
The transmitted
portion of this beam goes into the outside air and adds to the beam that
was reflected back into the air initially a t that interface,
The over -all effect of the multiple reflections in the glass
i s that the over -all reflectivity, absorptivity and transmissivity a r e
related to the p a r a m e t e r s defined above by
1
and
T =
-r
L
-
a)'
2
(1-r) (1-a)
2
2
1 - r
(1-a)
Each of these quantities h a s a different value for parallel and perpendicular
polarization.
Tables 1 and 11 contain values of A
N * T / / v*
2,
A and T for incident angles from 0 to 88 degrees for glasses with
indices of refraction of 1 - 5 2 and 1.62 and values of the absorption
parameter K L ranging f r o m 0.05 to 2.00,
If the incident b e a m i s
polarized i t can be represented by parallel and perpendicular polarized
components.
The transmission and absorption of each component can.
be evaluated separately and then combined to give the over -all effect
for the polarized beam.
When the incident beam i s not polarized (i. e.
the p a r a l l e l and perpendicular components a r e equal) the over -all
absorption and transmission a r e given by the T and A values without
subscripts.
Double Glazing
F o r a double glazed window the radiation incident on the
Inner pane (i. e. the radiation transmitted by the outer pane) i s
p a r t i a l l y polarized, even though the original incident beam was not,
The p a r a l l e l and perpendicular components, therefore, a r e t r e a t e d
separately and only combined for the over -all value for the complete
window.
The total absorption (considering reflections between the
panes a s well a s multiple reflections in each ~ a n e by
) the outer pane
of a double window i s
and the total absorption by the inner sheet of a double window i s
r):
A2
-
A2Tl ,
1 -R R
1 2
where the quantities without super s c r i p t s apply to the panes considered
separately, subscript 1 meaning the outer pane and subscript 2 meaning
the inner one,
The over -all t r a n s m i s s i o n of the double window i s given by
*
F o r a polarized incident beam the A
*
A and T
1 " 2
* can be
evaluated separately for the p a r a l l e l and perpendicular components using
t h e s e formulae and t h e data given in Tables I o r 11, Table I11 gives the
a v e r a g e of the values for t h e two components, and hence i s directly
applicable when the incident beam i s not polarized, for the v e r y common
c a s e of a double window with an inner pane KL = 0 - 0 5 (i. e, ordinary
window glass).
This table covers t h e s a m e r a n g e of incident angle
and KL for the outer pane a s T a b l e s I and 11.
Diffuse Radiation
T h e radiation incident on a window consists of the d i r e c t
solar beam and diffuse radiation from t h e sky and reflected f r o m the
ground.
It i s usually a s s u m e d that the radiation other than the d i r e c t
solar beam h a s equal intensity at a l l incident angles, s o that the
absorptivity and t r a n s m i s s i v i t y for t h i s radiation is t h e average for a l l
angles of incidence.
The data for each value of KL in Tables I , I1 and
I11 have been averaged over incident angles f r o m 0 t o 90 degrees.
These
values f o r diffuse radiation a r e given i n the l a s t section of Tables I ,
I1 and 111.
Sample Application of T a b l e s
Problem I :
Find the absorption and t r a n s m i s s i o n of a double window for
a non-polarized incident beam with an incident angle of 65 degrees.
T h e K L f o r the inner pane i s 0.05; KL for outer pane i s 1.00 and the
index of r e f r a c t i o n for both panes i s 1. 52.
Solution:
The a n s w e r s for t h i s situation can b e taken directly f r o m
Table 1x1, but to i l l u s t r a t e the u s e of the tables the a n s w e r s a r e
obtained using the data i n Table I.
(a)
F o r the p a r a l l e l polarized b e a m
(b)
F o r the perpendicular polarized beam
Hence
Since t h e incident b e a m is non polarized (i, e, t h e perpendicular
and p a r a l l e l components a r e equal) the t o t a l absorptivity and t r a n s m i s s i v i t y of t h e window is t h e a v e r a g e of the values for t h e two
components.
Therefor e
T h e s e a r e the values given in Table 111.
Application of T a b l e s t o Solar Radiation
The radiation f r o m t h e sun that r e a c h e s t h e s u r f a c e of the
e a r t h is a l m o s t a l l i n t h e wavelength region between 0.3 and 3 m i c r o n s .
T h e absorption coefficient K of n o r m a l window g l a s s v a r i e s g r e a t l y with
wavelength, s o that t h e r e i s not a single value of KL that can b e applied
f o r s o l a r radiation.
Instead t h e s o l a r s p e c t r u m m u s t b e subdivided into
r e l a t i v e l y n a r r o w wavelength bands and t h e a p p r o p r i a t e K value of
t h e g l a s s determined f o r each band,
T h e over -all t r a n s m i s s i v i t y and
absorptivity of a window f o r s o l a r radiation i s t h e a v e r a g e of the
values a p p r o p r i a t e f o r the KL of each band, weighted i n a c c o r d a n c e
with the energy content i n each wavelength band.
The s o l a r s p e c t r u m can b e divided into t e n bands, each of
which contains 10 p e r cent of t h e e n e r g y i n t h e total s o l a r spectrum,
T h e boundary wavelengths of t h e s e bands a r e : 0.30, 0,46, 0-52, 0.58,
0, 65, 0, 72, 0-80, O , 9 O , 1. 05, 1.27 and 3, 00 m i c r o n s , T h e s e values
by integrating t h e data contained in
T a b l e 81 5 of the Smithsoniari P h y s i c a l T a b l e s ,
w e r e obtained/1954, "Solar I r r a d i a t i o n a t Sea Level with Surface P e r p e n d i c u l a r to
Sun's Rays, m = 2.
"
Thus i f the t r a n s m i s s i v i t y and absorptivity of
g l a s s a r e known a t t h e s e wavelength bands the s i m p l e a v e r a g e of the
10 values gives the value that i s a p p r o p r i a t e for s o l a r radiation.
The infor mation that i s generally available f o r window g l a s s e s
i s a curve of t r a n s m i s s i v i t y for monochromatic radiation a t n o r m a l
incidence,
known.
In addition t h e r e f r a c t i v e index of t h e g l a s s i s u s u a l l y
( T h e variation of n with wavelength i s s m a l l for wavelengths
between 0 - 3 and 3. 00 m i c r o n s . ) Values of t r a n s m i s s i v i t y f o r n o r m a l
incidence and corresponding values of KL can b e extracted f r o m T a b l e s
I and 11. T h e s e data and the t r a n s m i s s i v i t y curve f o r the g l a s s indicate
t h e wavelengths that c o r r e s p o n d t o the tabulated KL values.
Table
I or I1 can then be u s e d to indicate the t r a n s r n i s s i v i t y and absorptivity
of a window for any angle of incidence,
T h e s e r e s u l t s can b e used t o
construct a graph of absorptivity and t r a n s m i s s i v i t y v e r s u s waveValues of the absorptivity and t r a n s m i s s i v i t y can then be r e a d
length,
f r o m t h i s graph for t h e t e n 10 p e r cent bands of the s o l a r s p e c t r u m ,
and t h e a v e r a g e of t h e s e i s the value for the window that i s a p p r o p r i a t e
f o r s o l a r radiation.
T h i s p r o c e d u r e is i l l u s t r a t e d b y t h e following s a m p l e problem:
Problem II :
Find t h e over -all absorptivity (A ) and t r a n s m i s s i v i t y (T )
S
s
of a single pane of heat absorbing g l a s s f o r d i r e c t s o l a r radiation a t
an incident angle of 70 degrees.
The g l a s s h a s an index of r e f r a c t i o n
n = 1. 52 and a t r a n s m i s s i v i t y for monochromatic light a t n o r m a l
incidence a s given i n Fig. 1,
Solution:
The t r a n s m i s s i v i t y data (Fig. 1) and Table I indicate that the
g l a s s h a s t h e tabulated values of KL a t t h e following values of wavelength:
F r o m Table I
KL
T
(e = 0 0 )
F r o m Fig. 1
T (8 = 0")
Wavelength
micron
T h e t r a n s m i s s i v i t y and a b s o r p t i v i t y f o r t h e s e w a v e l e n g t h s
and 8 = 70 d e g r e e s a r e ( f r o m T a b l e I )
Wavelength
m i c r on
A g r a p h i c a l i n t e r p o l a t i o n of t h e s e v a l u e s g i v e s t h e following
r e s u l t s for the t e n s o l a r bands:
S o l a r e n e r g y band
0.30
0.46
0, 52
0. 58
0.65
0.72
0.80
0.90
1.05
l,27
-
A
T
0.46 m i c r o n
-
0. 5 2 m i c r o n
-
0. 72 m i c r o n
-
0.90 m i c r o n
0.58 m i c r o n
0.65 m i c r o n
0.80 m i c r o n
1. 05 m i c r o n
1.27 m i c r o n
3. 00 m i c r o n
T h e s e a r e t h e v a l u e s f o r t h i s window t h a t a r e a p p r o p r i a t e
f o r s o l a r radiation.
F o r a double window i t is only n e c e s s a r y to obtain the
values a p p r o p r i a t e for s o l a r radiation for each pane and each
polarization component s e p a r a t e l y i n t h e m a n n e r indicated in example
p r o b l e m s I and I1 and then t o combine p a r a l l e l and perpendicular
components.
S I T GLAZED
n=1.52
WINDOW
45.
50.
55.
GG.
65.
.I358
.I004
OEGO
.0349
.0106
.
.3628
.3440
.3147
.2670
1819
GO.
10.
20.
33.
40,
.8327
.832(?
C333
.8310
,8240
.
.I241
.I 220
. I 1 59
.I060
.0328
.a327
.a355
.a443
.R586
-8776
- 1 241
.I228
.I1 94
- 1 1 39
-1067
.a327
.8342
.a388
-8452
.8512
.I241
.I224
.I176
.lo99
.0997
60.
62.
€4.
Ci.
86.
.4378
.3730
-2983
.2125
-1137
-0149
-0106
.GO66
.0033
.0009
.7214
.6479
-5497
.4184
.2413
-0424
.0334
-0234
.0132
.0043
.5796
.5105
-4240
-3155
,1775
-0286
.0220
.0150
.0083
.0026
I'
All
T~~
DIFFUSE
ICL
RADIATION
*l
A
T
GO.
10.
20.
30.
40.
GO.
10,
23.
30.
40.
4s.
50.
55.
GO.
65.
70.
72.
74.
76.
'Is.
45.
50.
55.
GO.
65.
.7947
-7792
.7568
7247
.6793
DIFFUSE RADIATION
KL of Inside Pane = .05
OC.
10'
20.
30.
40.
45.
5055.
GO.
65.
45.
50.
55.
GO.
65.