Chapter 5Energy and Light

NBC 2016 (SP 7:2016) Volume 1

2016 · PDF page 1161

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5.1 Energy and Thermal Properties of Glass

5.1.1 General

The energy and thermal properties of glass is defined by light transmission, internal and external reflection, solar heat gain coefficient and U-value. The performance requirement for glazing shall be suitably selected. Minimum performance requirement is mentioned in the Annex A.

Specific methods of calculating light and energy factors for glass in buildings are covered here and their characteristic data can serve as a basis for light, heating and ventilation calculations of rooms and can permit comparison between different types of glazing. It is applicable to all flat glass material.

5.2Light Reflectance

5.2.1 External Light Reflectance of Glazing

External light reflectance corresponds to the amount of sunlight reflected by the external glass surface. The

amount of light reflection depends on the type of base glass (substrate tint) and the position of coating on the glass surface.

The external light reflectance of glazing $\rho_{\mathrm{v,o}}$ shall be calculated using the following formula:

\rho_ {\mathrm{v,o}} = \frac {\sum_ {\lambda = 3 8 0 \mathrm{nm}} ^ {7 8 0 \mathrm{nm}} \rho_ {\mathrm{o}} (\lambda) D _ {\lambda} V (\lambda) \Delta \lambda}{\sum_ {\lambda = 3 8 0 \mathrm{nm}} ^ {7 8 0 \mathrm{nm}} \mathrm{D} _ {\lambda} V (\lambda) \Delta \lambda}

where

$\rho_{0}(\lambda) =$ spectral external reflectance of glazing, and $D_{\lambda}, V(\lambda), \Delta \lambda$ and the integration procedure are defined in 5.1.11.4.

For multiple glazing, the calculation of the spectral external reflectance $\rho_{\mathrm{o}}(\lambda)$ shall be performed using the same methods as given in 5.1.11.4 for the calculation of the spectral transmittance $\tau (\lambda)$ .

For the spectral external reflectance $\rho_{\mathrm{o}}(\lambda)$ as a function of the spectral characteristics of the individual components of the unit, the following formulae are applied:

a) For double glazing;

\rho_ {\mathrm{o}} (\lambda) = \rho_ {1} (\lambda) + \frac {\tau_ {1} ^ {2} (\lambda) \rho_ {2} (\lambda)}{1 - \rho_ {1} ^ {\prime} (\lambda) \rho_ {2} (\lambda)}

b) For triple glazing:

\rho_ {\mathrm{o}} (\lambda) = \rho_ {1} (\lambda) + \frac {\tau_ {1} ^ {2} (\lambda) \rho_ {2} (\lambda) \left[ 1 - \rho_ {2} ^ {\prime} (\lambda) \rho_ {3} (\lambda) \right] +}{\left[ 1 - \rho_ {1} ^ {\prime} (\lambda) \rho_ {2} (\lambda) \right] \cdot \left[ 1 - \rho_ {2} ^ {\prime} (\lambda) \rho_ {3} (\lambda) \right]} - \tau_ {2} ^ {2} (\lambda) \rho_ {1} ^ {\prime} (\lambda) \rho_ {3} (\lambda)

For multiple glazing with more than three components, relationships similar to above equations are found to calculate $\rho_{\mathrm{o}}(\lambda)$ of such glazing from the spectral characteristics of the individual components.

As an example for calculating $\rho_{\mathrm{o}}(\lambda)$ , a glazing composed of five components may be treated in the same way as described in 5.1.11.4.

5.2.2 Internal Light Reflectance of Glazing

Internal light reflectance corresponds to the amount of light reflected by the inner glass surface. The amount of light reflection depends on the type of base glass (substrate tint) and the position of coating on the glass surface.

The internal light reflectance of glazing $\rho_{\mathrm{v,i}}$ shall be calculated using the following formula:

ρ_{v, i} = \frac{\sum_{λ = 380 n m}^{780 n m} ρ_{i} (λ) D_{λ} V (λ) Δ λ}{\sum_{λ = 380 n m}^{780 n m} D_{λ}}

5.3.2Division of Incident Solar Radiation Flux

The incident solar radiant flux per unit area $\varphi_{\mathrm{e}}$ is divided into the following three parts (see Fig. 7):

a) Transmitted part, $\tau_{\mathrm{c}}\varrho_{\mathrm{e}}$ :

b) Reflected part, $\rho_{\mathrm{e}}\varphi_{\mathrm{c}}$ ; and

c) Absorbed part, $\alpha_{\mathrm{e}}\varphi_{\mathrm{e}}$

where

$\tau_{\mathrm{e}} =$ solar direct transmittance,

$\rho_{\mathrm{e}} =$ solar direct reflectance, and

$\alpha_{\mathrm{e}} =$ solar direct absorptances.

The relationship between the three characteristics is:

\tau_ {\mathrm{e}} + \rho_ {\mathrm{e}} + \alpha_ {\mathrm{e}} = 1

SUN

FIG. 6 SOLAR HEAT GAIN COEFFICIENT

KEY

1 OUTER PANE

2 SECOND INNER PANE

3 \text {UNIT INCIDENT RADIANT FLUX}

\rho_ {\mathbf {e}} = 0. 3 8; q _ {\mathbf {e}} = 0. 1 7;

\tau_ {e} = 0. 4 1; q _ {i} = 0. 0 4; \text {therefore} g = 0. 4 5

FIG. 7 COMPONENTS OF INCIDENT SOLAR RADIANT FLUX

PART 6 STRUCTURAL DESIGN — SECTION 8 GLASS AND GLAZING

The absorbed part $\alpha_{\mathrm{e}}\varphi_{\mathrm{e}}$ is subsequently divided into two parts $q_{\mathrm{i}}\varphi_{\mathrm{e}}$ and , which are energy transferred to the inside and outside, respectively:

\alpha_ {\mathrm{e}} = q _ {\mathrm{i}} + q _ {\mathrm{e}}

where

$q_{\mathrm{i}} =$ secondary heat transfer factor of the glazing towards the inside; and

$q_{e}$ = secondary heat transfer factor of the glazing towards the outside.

5.3.4Solar Direct Reflectance

The solar direct reflectance $\rho_{e}$ of the glazing shall be calculated using the following formula:

\rho_ {\mathrm{e}} = \frac {\sum_ {\lambda = 3 0 0 \mathrm{nm}} ^ {2 5 0 0 \mathrm{nm}} \rho_ {\mathrm{o}} (\lambda) S _ {\lambda} \Delta \lambda}{\sum_ {\lambda = 3 0 0 \mathrm{nm}} ^ {2 5 0 0 \mathrm{nm}} S _ {\lambda} \Delta \lambda}

where

$S_{\lambda}$ = relative spectral distribution of the solar radiation (see 5.3.3);

$\rho_{\mathrm{o}}(\lambda) =$ spectral external reflectance of the glazing; and

$\Delta\lambda$ = integration procedure are the same as in light transmittance except that the data points shall be chosen at the wavelengths given in Table 11.

In the case of multiple glazing, the spectral external reflectance $\rho_{\mathrm{o}}(\lambda)$ is calculated in accordance with 5.2.1.

Table 11Normalized Relative Spectral Distribution of Global Solar Radiation (Clauses 5.3.3, 5.3.4, 5.3.6.3 and 5.3.6.4)

lnm(1)	$S_{\lambda}\Delta\lambda$ (2)
300	0
305	0.000 057
310	0.000 236
315	0.000 554
320	0.000 916
325	0.001 309
330	0.001 914
335	0.002 018
340	0.002 189
345	0.000 260
350	0.002 445
355	0.002 555
360	0.002 683
365	0.003 020
370	0.003 359
375	0.003 509
380	0.003 600
385	0.003 529
390	0.003 551
395	0.004 294
400	0.007 812
410	0.011 638
420	0.011 877
430	0.011 347
440	0.013 245
450	0.015 343
460	0.016 166
470	0.016 178

5.3.5Solar Direct Absorptance

The solar direct absorptance $\alpha_{\mathrm{e}}$ shall be calculated from the following formula:

\tau_ {\mathrm{e}} + \rho_ {\mathrm{e}} + \alpha_ {\mathrm{e}} = 1

5.3.6 Secondary Heat Transfer Factor Towards the Inside

5.3.6.1 Boundary conditions

For the calculation of the secondary heat transfer factor towards the inside, $q_{i}$ , the heat transfer coefficients of the glazing towards the outside, $h_{e}$ , and towards the inside, $h_{i}$ , are needed. These values mainly depend on the position of the glazing, wind velocity, inside and outside temperatures and, furthermore, on the temperature of the two external glazing surfaces.

5.3.6.2 Single glazing

The secondary heat transfer factor towards the inside, $q_{\mathrm{i}}$ , of single glazing shall be calculated using the following formula:

q _ {\mathrm{i}} = \alpha_ {\mathrm{e}} \frac {h _ {\mathrm{i}}}{h _ {\mathrm{e}} + h _ {\mathrm{i}}}

5.3.6.3 Double glazing

The secondary heat transfer factor towards the inside, $q_{\mathrm{i}}$ , of double glazing shall be calculated using the following formula:

q _ {\mathrm{i}} = \frac {\left(\frac {\alpha_ {\mathrm{e} 1} + \alpha_ {\mathrm{e} 2}}{h _ {\mathrm{e}}} + \frac {\alpha_ {\mathrm{e} 2}}{\Lambda}\right)}{\left(\frac {1}{\mathrm{h} _ {\mathrm{i}}} + \frac {1}{h _ {\mathrm{e}}} + \frac {1}{\Lambda}\right)}\left. \right)

5.3.6.4 Multiple glazing with $n > 2$ components

The secondary heat transfer factor towards the inside, $q_{\mathrm{i}}$ , of a multiple glazing with more than two components shall be calculated using the following formula:

q_{i} = \frac{\frac{α_{e 1} + α_{e 2} + α_{e 3} + \dots + α_{e n}}{h_{e}} + \frac{α_{e 2} + α_{e 3} + \dots + α_{}}{}}{}

5.3.6.5 Mean radiant temperature (MRT)

MRT can be calculated by various methods, among which measuring with globe thermometer is the most common and is given by:

M R T = \sqrt [ 4 ]{T _ {\mathrm{g}} ^ {4} + \frac {h _ {\mathrm{cg}}}{\varepsilon_ {\mathrm{g}} \sigma} \left(T _ {\mathrm{g}} - T _ {\mathrm{a}}\right) ^ {4}}

5.4Total Solar Energy Transmission

The total solar energy transmitted into the room per unit area of glazing $\varphi_{\mathrm{ei}}$ is given by the relationship:

\varphi_ {\mathrm{ei}} = \varphi_ {\mathrm{e}} g

where

$\varphi_{\mathrm{e}} =$ incident solar radiation flux per unit area;

g = total solar energy transmittance of the glazing; and

The values of $\varphi_{\mathrm{e}}$ can be obtained from appropriate tables in meteorological literature.

NOTE — The SHGC/SF requirement for the glazing should be selected based on the prescriptive requirements are mentioned in Annex A.

5.4.1 Additional Heat Transfer

If the room temperature $T_{\mathrm{i}}$ differs from the outside temperature $T_{\mathrm{o}}$ , an additional heat transfer occurs in addition to $\varphi_{\mathrm{ei}}$ . This additional heat flow can be calculated as follows:

5.6$U$-Value

Heat transmittance through a surface by conduction, convection, and radiation is expressed by its U-value. U-value is the amount of heat transferred that is lost or gained due to a temperature differential of 1 K through 1 m². The rate of heat transfer (U-value) is minimised by the use of double glazing, using gas inside cavity or by using low-E glass for inside pane of double glazed unit.

The $U$ -value requirement for the glazing system should be selected in accordance with the Table 13 and Annex A.

Table 12Normalized Relative Spectral Distribution of Global Solar Radiation (Clause 5.5)

Sl No.	$\lambda$ nm(2)	${\mathrm{S}}_{\lambda }\Delta \lambda$ (3)
i)	300	0
ii)	305	0.001 859
iii)	310	0.007 665
iv)	315	0.017 961
v)	320	0.029 732
vi)	325	0.042 466
vii)	330	0.062 108
viii)	335	0.065 462
ix)	340	0.071 020
x)	345	0.073 326
xi)	350	0.079 330
xii)	355	0.082 894
xiii)	360	0.087 039
xiv)	365	0.097 963
xv)	370	0.108 987
xvi)	375	0.113 837
xvii)	380	0.058 351

NOTE — The values in this table are calculated according to the trapezoidal rule.

Table 13Thermal Performance of Different Glass Shading Devices (Clause 5.6)

Sl No.(1)	Name of the Shading Device(2)	Transmittance,U-Value(3)	Shade Factor(4)
i)	Plain glass sheet (3.0 mm thick)	5.23	1.00
ii)	Plain glass + Wire mesh outside	5.00	0.65
iii)	Painted glass:a) White paintb) Yellow paintc) Green paint	5.225.225.22	0.350.370.40
iv)	Heat absorbing glass	4.65	0.45
v)	Plain glass sheet + Venetian blind inside:a) Light colourb) Dark colour	3.14	0.350.40
vi)	Plain glass sheet which is,a) 100 percent shadedb) 75 percent shadedc) 60 percent shaded	5.23	0.140.340.56
NOTE — Indicative values, actual value of the system to be measured using either approved simulation software or testing laboratory

(

λ

)

Δ

λ

∑λ=380nm780nmρo(λ)DλV(λ)Δλ

1−ρ1′(λ)ρ2(λ)τ12(λ)ρ2(λ)

o

(

λ

)

=

ρ1(λ)+

[1−ρ1′(λ)ρ2(λ)]⋅[1−ρ2′(λ)ρ3(λ)]τ12(λ)ρ2(λ)[1−ρ2′(λ)ρ−

τ22(λ)ρ1′(λ)ρ3(λ)

ρ_{v, i} = \frac{\sum _{λ = 380 nm}^{780 nm} ρ _{i} ( λ ) D _{λ} V ( λ ) Δ λ}{\sum _{λ = 380 nm}^{780 nm} D _{λ} V ( λ ) Δ λ}

where

$\rho_{i}(\lambda) = \text{spectral internal reflectance of glazing, and } D\lambda, V(\lambda), \Delta\lambda \text{ and the integration procedure are as defined in light transmittance.}$

For multiple glazing, the calculation of the spectral internal reflectance $\rho_{\mathrm{i}}(\lambda)$ shall be performed using the same methods as given in 5.1.11.4 for the calculation of the spectral transmittance $\tau (\lambda)$ .

For the spectral internal reflectance $\rho_{\mathrm{i}}(\lambda)$ as a function of the spectral characteristics of the individual components of the unit, the following formulae are applied.

a) For double glazing:

\rho_ {\mathrm{i}} (\lambda) = \rho_ {2} ^ {\prime} (\lambda) + \frac {\tau_ {2} ^ {2} (\lambda) \rho_ {1} ^ {\prime} (\lambda)}{1 - \rho_ {1} ^ {\prime} (\lambda) \rho_ {2} (\lambda)}

b) For triple glazing:

\rho_ {i} (\lambda) = \rho_ {3} ^ {\prime} (\lambda) + \frac {\tau_ {3} ^ {2} (\lambda) \rho_ {2} ^ {\prime} (\lambda) \left[ 1 - \rho_ {2} (\lambda) \rho_ {1} ^ {\prime} (\lambda) \right] +}{\left[ 1 - \rho_ {3} (\lambda) \rho_ {2} ^ {\prime} (\lambda) \right] \cdot \left[ 1 - \rho_ {2} (\lambda) \rho_ {1} ^ {\prime} (\lambda) \right]} - \tau_ {2} ^ {2} (\lambda) \rho_ {3} (\lambda) \rho_ {1} ^ {\prime} (\lambda)

For multiple glazing with more than three components, relationships similar to above expressions are found to calculate $\rho_{\mathrm{i}}(\lambda)$ of such glazing from the spectral characteristics of the individual components.

1

e

q_{\mathrm{e}}\varphi_{\mathrm{e}}

∑λ=300nm2500nmρo(λ)SλΔλ

As the purpose of this Section is to provide basic information on the performance of glazing, the following conventional conditions have been stated for simplicity:

a) Position of the glazing: vertical;

b) Outside surface: wind velocity approximately 4 m/s; corrected emissivity 0.837;

c) Inside surface: natural convection; emissivity optional; and

d) Air spaces are unventilated.

Under these conventional, average conditions, standard values for $h_{\mathrm{e}}$ and $h_{\mathrm{i}}$ are obtained:

h _ {\mathrm{e}} = 2 3 \mathrm{W/m} ^ {2} \mathrm{K}

h _ {\mathrm{i}} = \left(3. 6 + \frac {4 . 4 \varepsilon_ {i}}{0 . 8 3 7}\right) \mathrm{W/m} ^ {2} K

where

$\varepsilon_{i}$ = corrected emissivity of the inside surface [for soda lime glass, $\varepsilon_{i}$ = 0.837 and $h_{i}$ = 8 W/m²K].

If other boundary conditions are used to meet special requirements they shall be stated in the test report.

Values for $\varepsilon_{\mathrm{i}}$ lower than 0.837 (due to surface coatings with higher reflectance in the far infrared) should only to be taken into account if condensation on the coated surface can be excluded.

e

he+hihi

where

$\alpha_{\mathrm{e}} =$ solar direct absorptance obtained from the in accordance with 5.3.2, and

$h_{e}, h_{i} =$ heat transfer coefficients towards the outside and inside, respectively, in accordance with 7.6.1.

i

=

(hi1+he1+Λ1)(heαe1+αe2+)

where

$\alpha_{e1} = \text{ solar direct absorptance of the outer (first) pane within the double glazing; }$

$\alpha_{\mathrm{e2}} =$ solar direct absorptance of the second pane within the double glazing;

$\Lambda$ = thermal conductance between the outer surface and the innermost surface of the double glazing (see Fig. 8), in Watt Per square metre per Kelvin (W/m $^{2}$ K); and

PART 6 STRUCTURAL DESIGN — SECTION 8 GLASS AND GLAZING

KEY 1 PANE 1 2 PANE 2 3 OUTSIDE 4 INSIDE

FIG. 8 ILLUSTRATION OF THE MEANING OF THERMAL CONDUCTANCE, Λ

$h_{e}, h_{i} =$ heat transfer coefficients towards the outside and the inside, respectively in accordance with 5.3.6.1.

Characteristics $\alpha_{\mathrm{e1}}$ and $\alpha_{\mathrm{e2}}$ are calculated as follows:

\alpha_ {\mathrm{e} 1} = \frac {\sum_ {\lambda = 3 0 0 \mathrm{nm}} ^ {2 5 0 0 \mathrm{nm}} \left\{\alpha_ {1} (\lambda) + \frac {\alpha_ {1} ^ {\prime} (\lambda) \tau_ {1} (\lambda) \rho_ {2} (\lambda)}{1 - \rho_ {1} ^ {\prime} (\lambda) \rho_ {2} (\lambda)} \right\} S _ {\lambda} \Delta \lambda}{\sum_ {\lambda = 3 0 0 \mathrm{nm}} ^ {2 5 0 0 \mathrm{nm}} S _ {\lambda} \Delta \lambda}

\alpha_ {\mathrm{c} 2} = \frac {\sum_ {\lambda = 3 0 0 \mathrm{nm}} ^ {2 5 0 0 \mathrm{nm}} \left\{\frac {\alpha_ {2} (\lambda) \tau_ {1} (\lambda)}{1 - \rho_ {1} ^ {\prime} (\lambda) \rho_ {2} (\lambda)} \right\} S _ {\lambda} \Delta \lambda}{\sum_ {\lambda = 3 0 0 \mathrm{nm}} ^ {2 5 0 0 \mathrm{nm}} S _ {\lambda} \Delta \lambda}

where

$\tau_{1}(\lambda),\tau_{2}(\lambda),\rho_{1}(\lambda),\rho^{\prime}_{1}(\lambda)$ and $\rho_{2}(\lambda)$ are as defined in light transmittance.

$\alpha_{1}(\lambda) =$ spectral direct absorptance of the outer pane, measured in the direction of the incident radiation, given by the relationship:

\alpha_ {1} (\lambda) = 1 - \tau_ {1} (\lambda) - \rho_ {1} (\lambda)

$\alpha_{1}^{\prime}(\lambda) =$ spectral direct absorptance of the outer pane, measured in the opposite direction to the incident radiation, given by the relationship: $\alpha_{1}^{\prime}(\lambda) = 1 - \tau_{1}(\lambda) - \rho_{1}^{\prime}(\lambda)$

$\alpha_{2}(\lambda) =$ spectral direct absorptance of the second

pane, measured in the direction of the incident radiation, given by the relationship:

\alpha_ {2} (\lambda) = 1 - \tau_ {2} (\lambda) - \rho_ {2} (\lambda)

$\Delta\lambda$ and the integration procedure are the same as in 5.1.11.4 except that the data points shall be chosen at the wavelengths given in Table 11.

The thermal conductance $\Lambda$ shall be determined for a temperature difference of $\Delta T = 15^{\circ}C$ across the sample and a mean temperature of the sample of $10^{\circ}C$ , or by measuring methods using the standard guarded hot plate method, or the standard heat flow metre method.

If another temperature difference $\Delta T$ across the sample and/or another mean temperature of the sample is used for the determination of the thermal conductance $\Lambda$ to meet special requirements, this shall be stated in the test report.

q_{i} = \frac{\frac{α _{e 1} + α _{e 2} + α}{h _{e}}}{\frac{\frac{α _{e 3} + \dots + α _{e n}}{Λ _{23}} + \dots +}{\frac{1}{h _{i}} + \frac{1}{h _{e}} + \frac{1}{Λ _{12}} + \frac{1}{Λ _{23}} + \dots + \frac{1}{Λ _{(n - 1) n}}}}

where

$\alpha_{e1}$ = solar direct absorptance of the outer (first) pane within the n-fold glazing;

$\alpha_{\mathrm{e2}}$ = solar direct absorptance of the second pane within the $n$ -fold glazing;

$\alpha_{\mathrm{en}} =$ solar direct absorptance of the $n^{\mathrm{th}}$ (inner) pane of the $n$ -fold glazing;

$h_{e}, h_{i} =$ heat transfer coefficients towards the outside and towards the inside, respectively in accordance with 5.3.6.1;

$\Lambda_{12}$ = thermal conductance between the outer surface of the outer (first) pane and the centre of the second pane (see Fig. 9);

$\Lambda_{(n - 1)n} =$ thermal conductance between the centre of the $(n - 1)^{\mathrm{th}}$ pane and the outer surface of the $n^{\mathrm{th}}$ (inner) pane (see Fig. 9); and

$\Lambda_{23}$ = thermal conductance between the centre of the second pane and the centre of the third pane (see Fig. 9);

The thermal conductances $\Lambda_{12}$ , $\Lambda_{23}$ ...... $\Lambda_{(n-1)_n}$ shall be determined by iteration technique. The calculation of the direct solar absorptances $\alpha_{e1}, \alpha_{e2}, \ldots, \alpha_{en}$ shall be performed using the methods given in 5.3.6.3.

FIG. 9 ILLUSTRATION OF THE MEANING OF THE THERMAL CONDUCTANCES $\Lambda_{12},\Lambda_{23}\dots \Lambda_{(n - 1)n}$

As an example for the calculation of the direct solar absorptances the following procedure is given which consist of the following $(n-1)$ steps for a glazing consisting of n components:

a) First step — Calculate the spectral characteristics of a unit consisting of $(n-1)$

components 2, 3,......n according to what has been prescribed in 5.1.11.4 and 6.1. Then combine this unit with the first (outer) pane as a double glazing.

b) Second step — Calculate the spectral characteristics of a unit consisting of the $(n-2)$ components 3, ..., n and furthermore, those of a double glazing consisting of pane 1 and pane 2. These units are then combined as a double glazing. The sum $\alpha_{e1} + \alpha_{e2}$ is then obtained. This procedure is continued up to the last $(n-1)^{\text{th}}$ step.

c) $(n - 1)^{\mathrm{th}}$ step — Combine the $(n - 1)$ panes $1,2,\dots$ $(n - 1)$ and determine the spectral characteristics of this unit. This unit is then combined with the $\mathfrak{n}^{\mathrm{th}}$ (inner) pane as a double glazing. From the second equation in 5.3.6.3, the sum $\alpha_{\mathrm{e1}},\alpha_{\mathrm{e2}}$ ... $\alpha_{\mathrm{e(n - 1)}}$ is obtained, that is with the known values $\alpha_{\mathrm{e1}},\alpha_{\mathrm{e2},\dots}\alpha_{\mathrm{e(n - 2)}}$ from the previous steps $\alpha_{\mathrm{e(n - 1)}}$ is determined. $\alpha_{\mathrm{en}}$ is obtained according to the expression of $\alpha_{\mathrm{e2}}$ in 5.3.6.3.

In the case of triple glazing for the solar absorptances $\alpha_{\mathrm{e1}}$ , $\alpha_{\mathrm{e2}}$ and $\alpha_{\mathrm{e3}}$ as a function of the spectral characteristics of the individual components of the unit, the following formulae are obtained:

\alpha_ {e 1} = \frac {\sum_ {\lambda = 3 0 0 \mathrm{nm}} ^ {2 5 0 0 \mathrm{nm}} \left\{\alpha_ {1} (\lambda) + \frac {\tau_ {1} (\lambda) \alpha_ {1} ^ {\prime} (\lambda) \rho_ {2} (\lambda) \left[ 1 - \rho_ {2} ^ {\prime} (\lambda) \rho_ {3} (\lambda) \right] + \tau_ {1} (\lambda) \tau_ {2} ^ {2} (\lambda) \alpha_ {1} ^ {\prime} (\lambda) \rho_ {3} (\lambda)}{\left[ 1 - \rho_ {1} ^ {\prime} (\lambda) \rho_ {2} (\lambda) \right] \cdot \left[ 1 - \rho_ {2} ^ {\prime} (\lambda) \rho_ {3} (\lambda) \right] - \tau_ {2} ^ {2} (\lambda) \rho_ {1} ^ {\prime} (\lambda) \rho_ {3} (\lambda)} \right\} S _ {\lambda} \Delta \lambda}{\sum_ {\lambda = 3 0 0 \mathrm{nm}} ^ {2 5 0 0 \mathrm{nm}} S _ {\lambda} \Delta \lambda} \\ \alpha_ {e 2} = \frac {\sum_ {\lambda = 3 0 0 \mathrm{nm}} ^ {2 5 0 0 \mathrm{nm}} \left\{\frac {\tau_ {1} (\lambda) \alpha_ {2} (\lambda) \left[ 1 - \rho_ {2} ^ {\prime} (\lambda) \rho_ {3} (\lambda) \right] + \tau_ {1} (\lambda) \tau_ {2} (\lambda) \alpha_ {2} ^ {\prime} (\lambda) \rho_ {3} (\lambda)}{\left[ 1 - \rho_ {1} ^ {\prime} (\lambda) \rho_ {2} (\lambda) \right] \cdot \left[ 1 - \rho_ {2} ^ {\prime} (\lambda) \rho_ {3} (\lambda) \right] - \tau_ {2} ^ {2} (\lambda) \rho_ {1} ^ {\prime} (\lambda) \rho_ {3} (\lambda)} \right\} S _ {\lambda} \Delta \lambda}{\sum_ {\lambda = 3 0 0 \mathrm{nm}} ^ {2 5 0 0 \mathrm{nm}} S _ {\lambda} \Delta \lambda} \\ \alpha_ {e 3} = \frac {\sum_ {\lambda = 3 0 0 \mathrm{nm}} ^ {2 5 0 0 \mathrm{nm}} \left\{\frac {\tau_ {1} (\lambda) \tau_ {2} (\lambda) \alpha_ {3} (\lambda)}{\left[ 1 - \rho_ {1} ^ {\prime} (\lambda) \rho_ {2} (\lambda) \right] \cdot \left[ 1 - \rho_ {2} ^ {\prime} (\lambda) \rho_ {3} (\lambda) \right] - \tau_ {2} ^ {2} (\lambda) \rho_ {1} ^ {\prime} (\lambda) \rho_ {3} (\lambda)} \right\} S _ {\lambda} \Delta \lambda}{\sum_ {\lambda = 3 0 0 \mathrm{nm}} ^ {2 5 0 0 \mathrm{nm}} S _ {\lambda} \Delta \lambda} \end{array}

where

$\tau_{1}(\lambda),\tau_{2}(\lambda),\tau_{3}(\lambda),\rho_{1}(\lambda),\rho^{\prime}_{1}(\lambda),\rho_{2}(\lambda),\rho^{\prime}_{2}(\lambda),\rho_{3}(\lambda)$ are as defined in light transmittance;

$\alpha_{1}(\lambda),\alpha^{\prime}_{1}(\lambda)$ and $\alpha_{2}(\lambda)$ are as defined in 5.3.6.3 double glazing;

$\alpha_{2}^{\prime}(\lambda) =$ spectral direct absorptance of the second pane, measured in the opposite direction to the incident radiation, given by the relationship:

\alpha_ {2} ^ {\prime} (\lambda) = 1 - \tau_ {2} (\lambda) - \rho_ {2} ^ {\prime} (\lambda)

$\alpha_{3}(\lambda) =$ spectral direct absorptance of the third pane, measured in the direction of the incident radiation, given by the relationship:

\alpha_ {3} (\lambda) = 1 - \tau_ {3} (\lambda) - \rho_ {3} (\lambda)

$\Delta \lambda$ and the integration procedure are the same as in 5.1.11.4 except that the data points shall be chosen at the wavelengths given in Table 5.

PART 6 STRUCTURAL DESIGN — SECTION 8 GLASS AND GLAZING

For a glazing with more than three components, the formulae for the solar absorptances $\alpha_{\mathrm{e1}},\alpha_{\mathrm{e2}},\dots,\alpha_{\mathrm{en}}$ as a function of the individual components.

4

+

εgσhcg

(Tg−Ta)4

where

$T_{\mathrm{a}} =$ air temperature, in Kelvin;

$T_{g}$ = black globe temperature, in Kelvin;

$\varepsilon_{\mathrm{g}} =$ emissivity of black globe;

$\sigma =$ Stefan-Boltzmann constant; and

$h_{\mathrm{cg}} =$ convective heat transfer coefficient of the black globe.

ei

q_{z}

q _ {\mathrm{z}} = U (T _ {\mathrm{o}} - T _ {\mathrm{i}})

where $U$ is the $U$ -value (thermal transmittance) of glazing.

3

(

λ

)

]

+

(

λ

)

ρ1′

(

λ

)

(

λ

)

ρ1′

(

λ

)

]

τ32(λ)ρ2′(λ)[1−ρ2(λ)ρ1′(λ)]+

−

Λαe2

)

2500nm

{α1(λ)+1−ρ1′(λ)ρ2(λ)α1′(λ)τ1(λ)ρ2(λ)}

Sλ

Δ

λ

2500nm

{1−ρ1′(λ)ρ2(λ)α2(λ)τ1(λ)}

Sλ

Δ

λ

Λ(n−1)nαen

e3

+

…

+

αen

+

Λ12αe2+αe3+…+αen

+

5.1 Energy and Thermal Properties of Glass

5.1.1 General

5.2.1 External Light Reflectance of Glazing

5.2.2 Internal Light Reflectance of Glazing

5.3.6.1 Boundary conditions

5.3.6.2 Single glazing

5.3.6.3 Double glazing

5.3.6.4 Multiple glazing with n>2n > 2n>2 components

5.3.6.5 Mean radiant temperature (MRT)

5.4.1 Additional Heat Transfer

5.3.6.4 Multiple glazing with $n > 2$ components