Energy Efficient Buildings
Windows and Solar Heat Gain
Introduction
A major pathway of heat loss and gains into buildings is through windows. Heat is lost and
gained through windows through:



conduction
solar radiation
air infiltration through cracks/leaks
This chapter discusses:
 physical mechanisms of these pathways
 high performance window construction
 Uwin (conduction)
 SHGC (solar heat gain coefficient)
Thermal Properties of Windows
Single Pane
R T  R hi  R g  R ho
3/32"
Tia
 .68 
3 32/12  .17  .68  .0174  .17
.45
 Btu 
 .87
2
 hr  ft  F 
Toa
1
Single Pane & Storm Window
3/32"
R T  R hi  R g  R space  R g  R ho
3/32"
Tia
 .68  .0174  1.01  .0174  .17
Toa
 Btu 
 1.89 
2
 hr  ft  F 
1
>¾"
Storm
1
Rules of Thumb:
Single Glaze: R = 1 (hr-ft2-F/Btu)
Double Glaze: R = 2 (hr-ft2-F/Btu)
Triple Glaze: R = 3 (hr-ft2-F/Btu)
These calculations show that heat loss/gain through windows is 5 to 15 times greater than
through walls. This provides strong motivation to develop high performance windows
High Performance Windows
1st task is to stop air movement between panes
 Air movement from leakage reduces Rspace = 1.01 above, and essentially makes
storm windows the same as a single pane window
 Air movement between panes causes a convection cell which increases heat
transfer
 When the space between windows < 1-inch then Fviscous > Fbuoyant
 air doesn’t move and have conduction instead of convection
 Increasing space decreases conduction, but increases convection
 Optimum appears to be 0.5-1.0 inches (Pella windows are 14 " ~ 1 " )
2
32
2nd task is to find & stop greatest heat loss
 Btu 
σ  .1714  10 8 
2
4
 hr  ft  R 
ε glass ~ .94
 Btu  in 
k air  .18 
2
 hr  ft  F 
Case 1 Regular glass, air
σ T14  T24  .1714  10 8  (530 4  480 4 )
 Btu 
q rad 

 39.2 2 
1 1
1
1
 ft  hr 
 1

1
ε1 ε2
.94 .94
q conduction 
q win  q rad
kΔ .18  50
 Btu 

 18.0  2 
Δx
.5
 ft  hr 
 Btu 
 q conduction  57.2 2
 ft  hr 
T1 70F
70460530R
T2 20F
20460480R
½"
2
Case 2 Low ε, air (ε = .10)
.1714  10 8  (530 4  480 4 )
 Btu 
 2.3 2
1 1
 ft  hr 
 1
.1 .1
 Btu 
q cond  18.0  2
 ft  hr 
 Btu 
q win  q rad  q conduction  20.3 2
 ft  hr 
q rad 
Case 3 Low ε, argon (ε = .10, kargon = .108)
 Btu 
q rad  2.3 2
 ft  hr 
q cond 
.108  50  10.8
.5
q win  q rad  q conduction
Btu 
 ft 2  hr 
 Btu 
 13.1 2
 ft  hr 
The center-of-glass U value would be:
Q/A = U dT
U = Q/A dt = 13.1 Btu/ft2-hr / 50 F = 0.26 Btu/hr-ft2-F
Source: ASHRAE Fundamentals
3
Total Conductive Heat Loss/Gain through Windows
Thermal resistances of:



Wall
center-of-glass (cg)
edge-of-glass (eg)
frame (f)
are different.
Awin
Thus, the total conductance of the window must include all
three. In general, Ueg > Ucg > Uframe.
Uwin 
Frame
Aglass
Double glazing
Metal spaces
UA cg  UA eg  UA f
A win
Thus, the conduction heat transfer through a window is

Q
win  UA win Tia  Toa   U win A win Tia  Toa 
Iα
Use Toa instead of Tsa since Tsa  Toa   Toa and α << 1.
h
Window Types
Window type influences air leakage and frame fraction. For passive solar, look for windows
that seal shut, such as casement or awning windows rather than sliding windows to reduce
air leakage. Also look for windows with high ratios of Aglass / Awin to maximize Qsol and
reduce edge-of-glass heat loss. Finally, choose high quality wood or vinyl frames since lowquality frames can warp and allow air and moisture (condensation) between glazings.
4
5
6
Window Thermal Performance Data
DESIGNER SERIES : CLAD CASEMENT WINDOWS
Types of Glazing
SMARTSASH II SYSTEM
3/32" Clear with 3/32" low-E DGP
SMARTSASH III SYSTEM
5/8" InsulShield IG with 3/32" glass
5/8" InsulShield IG with 3/32" low-E DGP
INSULSHIELD IX GLAZING
5/8" InsulShield HM IG with 3/32" low-E DGP
Winter CenterGlass "U" Value
Total-Unit "U" Value
Total-Unit "R" Value
LBL Damage
Function
% Visible Light
Center-Glass
Transmission
Air
Infiltration
A
B
A
B
0.38
0.40
0.40
2.48*
2.51
0.52
75
0.03
0.24
0.15
0.35
0.26
0.33
0.24
2.9
3.85**
3.06
4.17
0.33
0.26
73
61
0.03
0.03
55
0.03
0.11
0.23
0.21
A = 36" x 60" frame size
B = 48" x 72" frame size
Unit size and type are based on ASTM E1423-91
4.35
4.76
0.18
* costs approximately $275
** costs approximately $340
Data Source: Pella
Solar Heat Gain Coefficient
All solar radiation incident on a window is absorbed, transmitted or reflected. From an
energy balance, the sum of the absorbtivity, transmittance and reflectivity equals 1.0
I
       1.0
Iα
I
I
Solar transmittance of glass is a function of wavelength and the angle of incidence. In
general, glass transmits visible light, but is opaque to infrared light. Since most of the
radiation from the sun lies in the visible part of the spectrum, windows transmit most of the
energy in solar radiation into the building. After the solar radiation is absorbed by building
surfaces, the surfaces reradiate the heat as low temperature infrared radiation. Since glass
is opaque to infrared radiation, this radiation remains inside the building
The transmittance of glass is also highly dependent of the angle of incidence; at
perpendicular angles most of the light is transmitted and at low angles of incidence most of
the light is reflected.
7
Solar heat gain coefficient, SHGC, is the fraction of solar radiation incident on fenestration
that is transmitted into the building. SHGC includes fraction of solar transmitted plus
fraction of solar that is absorbed by glass and radiated into the building:
SHGC  τ  fα
Solar heat gain coefficients are shown in the tables below.
8
9
In the Tables above, note that the transmittance of visible light, labeled as “Center Glazing
Tv” is different than the “Center of Glazing” SHGCs. Most daylighting applications seek to
maximize the transmittance of visible light.
In the Tables above, note that “Total Window” SHGC is proportionally less than the “Center
of Glazing” SHGC by the proportion of glass area to total window area (Aglass / Awin). Thus,
to calculate solar heat gain using the total window area Awin use the “Total Window” SHGC.
The SHGC reported on window labels in the “Total Window SHGC at Normal Incidence”.
The SHGC is different for diffuse solar radiation, which is spread evenly over the sky, and
beam solar radiation which is directional. Thus, the total solar energy into a building, Qsol,
is:
Q sol  A win  SHGC beam  Ibeam   SHGC diffuse  Idiffuse 
In the northern hemisphere, most solar radiation is from the south. Thus, to simplify
calculations, the average solar heat gain coefficient SHGC can be approximated as:
SHGC
N
1.0
.75
W
E
Beam
Diffuse
Average
.50
S
Solar path with Qs
as length of line
.25
θ
SHGC  .9 SHGC normal
Thus, using the average solar heat gain coefficient, the solar heat gain through a window
can be calculated as:
  A  SHGC  I
Q
sol
win
total
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Selective and Non-Selective Low-e Coatings
While low-e coatings and multiple glazings significantly reduce U, they also significantly
reduce SHGC. This is good for commercial buildings, warm climates, and E,W windows that
allow more Qsol in summer than winter. But it is bad for passive-solar heating applications.
Original low-e coatings had higher SHGCs. But new low-e coatings are “selective” and
reduce transmittance in the IR range, thus reducing SHGC. Fortunately, old-style, nonselective, low-e coatings are available if specified in the US, or as the standard, in Canada.
Center of Glass Figure of Merit for various types of glazing as a function of k-value commercially
available (Data sorted for k=2)
GLAZING TYPE
U-Value
SHGC
NON-COATED GLASS
Single Pane
1.11
0.85
Dual Pane IGU 1/8"g, 3/4" IG Air
0.49
0.75
Dual Pane IGU 1/8"g, 3/4" IG Argon
0.46
0.75
Tripane IGU
0.32
0.68
SELECTIVE LOW-E COATINGS
Marvin Low E2 (Dual Pane)
Cardinal Low E2 - 145 (Anderson)(Dual Pane)
Cardinal Low E2 - 171 (Anderson)(Dual Pane)
Loewen Heat Smart Plus 1 (Tripane)
Loewen Heat Smart Plus 2 (Tripane)
Marvin High R Tripane
Loewen Heat Smart Plus 3 (Tripane)
Super Quad SC (4-Pane - 2 suspended PET films)
0.32
0.27
0.24
0.24
0.18
0.14
0.12
0.08
0.41
0.32
0.41
0.41
0.37
0.34
0.34
0.24
NON SELECTIVE LOW-E COATINGS
Clear HM TC88 1/8" g 3/4" IG (HURD) (Dual Pane)
Dual 3mm, Super Spacer, 1 Ar 1 PPG SG 500 (Accurate Dorwin)
LOF Energy Advantage (3)" 3/32" g 5/8" IG Air (Dual Pane)
Cardinal Low E2 - 178 (Andersen) (Dual Pane)
Clear HM TC88 1/8" g 1" IG (Dual Pane)
Clear HM TC88 1/4" g 1 1/2' IG (Dual Pane)
PPG Sungale E-500 (3)" 3/32" g 3/4" IG (Dual Pane)
Loewen Heat Smart ER 1 (Tripane)
LOF Energy Advantage (3)" 1/8" g 3/4" IG Argon (Dual Pane)
Super Quad TC (4-Pane 2 suspended PET films)
Loewen Heat Smart ER 2 (Tripane)
Tripane, 3mm, SuperSpacer, 2 Ar, 1 PPG SG 500 (Accurate Dorwin)
Loewen Heat Smart ER 3 (Tripane)
Tripane, 3mm, SuperSpacer, 2 Ar, 2 PPG SG 500 (Accurate Dorwin)
0.28
0.35
0.37
0.26
0.21
0.18
0.3
0.27
0.28
0.1
0.2
0.21
0.14
0.17
0.5
0.65
0.73
0.58
0.5
0.47
0.74
0.69
0.71
0.41
0.62
0.65
0.55
0.61
Selective data from: Ellison, Tim, American Solar Energy Society Annual Conference,
Madison WI, 2000.
11
The Efficient Windows Collaborative (www.efficientwindows.org) characterizes window
performance into three groups according to solar gain: low, mid and high. In many
temperature U.S. climates, engineers often specify high SHGC windows for south-facing
exposures and low SHCG windows for all other exposures. This enhances solar gain during
winter when the sun Is primarily in the south, and reduces solar gain during summer when
the sun hits north, east and west exposures.
Center-of-glass properties are:
Solar Gain Type
U-Factor
SHGC
VT
Low
0.25
0.39
0.71
Medium
0.27
0.58
0.78
High
0.29
0.71
0.75
Whole window properties are:
Whole Window Properties
Double-Glazed with Low-Solar-Gain Low-E Glass, Argon/Krypton Gas
Aluminum
Wood
Vinyl
Insulated Vinyl
Frame
U-Factor
0.59
0.34
0.34
0.26
SHGC
0.37
0.30
0.30
0.31
VT
0.59
0.51
0.51
0.55
Note: The thermal performance properties of specific glazings and frames can vary depending on
product design and materials. The results presented here are averages. Consult specific
manufacturers for NFRC rated U-factors and SHGCs for products of interest.
Whole Window Properties
Double-Glazed with Moderate-Solar-Gain Low-E Glass, Argon/Krypton Gas
Frame
Aluminum
Wood
Vinyl
Insulated Vinyl
U-Factor
0.60
0.35
0.35
0.27
SHGC
0.53
0.44
0.44
0.46
VT
0.65
0.56
0.56
0.60
Note: The thermal performance properties of specific glazings and frames can vary depending on
product design and materials. The results presented here are averages. Consult specific
manufacturers for NFRC rated U-factors and SHGCs for products of interest.
12
Whole Window Properties
Double-Glazed with High-Solar-Gain Low-E Glass, Argon/Krypton Gas
Aluminum
Wood
Vinyl
Insulated Vinyl
Frame
U-Factor
0.61
0.37
0.37
0.29
SHGC
0.64
0.53
0.53
0.56
VT
0.62
0.54
0.54
0.58
Note: The thermal performance properties of specific glazings and frames can vary depending on
product design and materials. The results presented here are averages. Consult specific
manufacturers for NFRC rated U-factors and SHGCs for products of interest.
National Fenestration Rating Council (http://www.nfrc.org)
The National Fenestration Rating Council (NFRC) energy
performance label can help you determine how well a
product will perform the functions of helping to cool
your building in the summer, warm your building in the
winter, keep out wind, and resist condensation. All
energy performance values on the label represent the
rating of windows/doors as whole systems (glazing and
frame) for 48-in by 59-in gross window size.
U-Factor
The rate of heat loss is indicated in terms of the Ufactor (U-value) of a window assembly. In U.S. units UFactor ratings generally fall between 0.20 and 1.20
Btu/hr-ft2-F. The lower the U-value, the greater a
window's resistance to heat flow and the better its
insulating value.
Solar Heat Gain Coefficient
The SHGC is the fraction of incident solar radiation admitted through a window (both
directly transmitted and absorbed) and subsequently released inward. SHGC is expressed as
a number between 0 and 1. The lower a window's solar heat gain coefficient, the less solar
heat it transmits in the house.
Visible Transmittance
Visible Transmittance (VT) measures how much light is transmitted through a product. VT is
expressed as a number between 0 and 1. The higher the VT, the more light is transmitted.
Air Leakage*
Air Leakage (AL) is indicated by an air leakage rating expressed as the equivalent cubic feet
of air passing through a square foot of window area (cfm/sq ft). The lower the AL, the less
air will pass through cracks in the window assembly.
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Condensation Resistance*
Condensation Resistance (CR) measures the ability of a product to resist the formation of
condensation on the interior surface of that product. The higher the CR rating, the better
that product is at resisting condensation formation. CR is a number between 0 and 100.
Net Heat Transfer Through Windows
Thus, the net heat transfer through a window, not including air leakage due to infiltration,
can be calculated as the sum of the solar and conduction heat transfer:



Q
net,in  Q sol  Q win,out  [A win  SHGC  I total ] - [U win A win Tia  Toa ]
Example: Calculate the net heat gain into a building through a south-facing window. The
total area of the window is 6 ft2, the total U value of the window is 0.30 Btu/hr-ft2-F, the
total normal SHCG of the window is 0.70. The outdoor air temperature is 30 F. The indoor
air temperature is 70 F. The total solar radiation on each of a south exposure is 150 Btu/hrft2.
Input
Awin (ft2)
U (Btu/hr-ft2-F)
SHGC
Toa (F)
Tia (F)
Isouth (Btu/hr-ft2)
Calculations
SHGCavg = SHGC x .9
Qsol,in (Btu/hr) = Awin x SHGCavg x Isouth
Qwin,out (Btu/hr) = Awin x U x (Tia-Toa)
Qnet,in (Btu/hr) = Qsol,in - Qwin,out
6
0.3
0.7
30
70
150
0.63
567
72
495
Windows and Overhangs
In the Northern hemisphere, the sun makes a path across the southern sky; thus, southfacing exposures on buildings get much sunlight than other exposures. In addition, in the
summer the sun takes a higher path across the sky than in the winter. The seasonal
variation in the path of the sun across the sky can be utilized to maximize solar gain during
winter and minimize it during summer. In the Northern Hemisphere, overhangs on south
facing windows create shade in the summer, but allow direct sunlight to hit the windows in
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the winter. Thus, overhangs on south facing windows are highly effective at reducing solar
heat gain during summer and facilitating solar heat gain during winter.
Source: http://www.byexample.com/library/illustrations/seasonal_sun/illustration_sun.jpg)
The path of the sun across the sky varies with latitude as well as with the season (see Figure
below). At locations near the equator, the sun path is high in the sky and the sunset and
sunrise are about 12 hours apart all year long. At locations far from the equator, the sun
path is low in the sky and the number of daylight hours are large in the summer and small in
the winter.
Altitude Angle Azimuth Angle Sunset (hours
at Noon
at Sunset
after noon)
Vishakhapatnam India Latitude = 18 N
21-Jun
85
115
6.54
21-Dec
49
65
5.46
Dayton Ohio Latitude = 43 N
21-Jun
70
123
7.59
21-Dec
24
57
4.41
Fairbanks Alaska Latitude = 65 N
21-Jun
48
160
10.56
21-Dec
2
20
1.44
(CollectorSpacing_SunPosition.xlsx)
To estimate shading, it is necessary to know the position of the sun in the sky. The position
of the sun in the sky can be calculated for any latitude at any given date and time (see for
example: Duffie and Beckman, Solar Engineering of Thermal Processes, John Wiley and
Sons, 2013). This position can be plotted in sun path charts. For example, at 40 north
15
latitude, the sun has an altitude angle of about 57 at 60 west of south on July 21 at 2 pm
(see chart below).
The position of the sun in the sky can be calculated for any latitude at any given date and
time. WeaTran calculates this position, and uses it to determine solar gain on any exposure.
WeaTran can also calculate net solar gain minus shading from overhangs and wings when
the geometry of the overhang or wing is specified by enabling the “Advanced Solar Options
button” If the windows are protected by horizontal overhangs or vertical fins along their
sides, enter the height of the window “hc”, the protrusion of the overhang or wing “po”,
and the gap between overhang/fin and window “gapo” as shown in the figure below.
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po
gapo
z
y
hc
17