Bsi bs en 13363 2 2005 (2006)

BRITISH STANDARD

Solar protection
devices combined with
glazing — Calculation
of total solar energy
transmittance and light
transmittance —
Part 2: Detailed calculation method

The European Standard EN 13363-2:2005 has the status of a
British Standard

ICS 17.180.20; 91.120.10

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BS EN
13363-2:2005


BS EN 13363-2:2005

National foreword
This British Standard is the official English language version of
EN 13363-2:2005, including corrigendum April 2006.
The UK participation in its preparation was entrusted to Technical Committee
B/540, Energy performance of materials, components and buildings, which has
the responsibility to:
—

aid enquirers to understand the text;

—

present to the responsible international/European committee any
enquiries on the interpretation, or proposals for change, and keep
UK interests informed;

—

monitor related international and European developments and
promulgate them in the UK.

A list of organizations represented on this committee can be obtained on
request to its secretary.
Cross-references
The British Standards which implement international or European
publications referred to in this document may be found in the BSI Catalogue
under the section entitled “International Standards Correspondence Index”, or
by using the “Search” facility of the BSI Electronic Catalogue or of British
Standards Online.
This publication does not purport to include all the necessary provisions of a
contract. Users are responsible for its correct application.
Compliance with a British Standard does not of itself confer immunity
from legal obligations.

Summary of pages
This document comprises a front cover, an inside front cover, the EN title page,
pages 2 to 24, an inside back cover and a back cover.
The BSI copyright notice displayed in this document indicates when the

document was last issued.

This British Standard was
published under the authority
of the Standards Policy and
Strategy Committee
on 30 June 2006

Amendments issued since publication
Amd. No.

Date

Comments

© BSI 2006

ISBN 0 580 48616 8

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EUROPEAN STANDARD

EN 13363-2

NORME EUROPÉENNE
EUROPÄISCHE NORM

April 2005

ICS 17.180.20; 91.120.10

English version

Solar protection devices combined with glazing — Calculation of
total solar energy transmittance and light transmittance — Part 2:
Detailed calculation method
Dispositifs de protection solaire combinés à des vitrages —
Calcul du facteur de transmission solaire et lumineuse —
Partie 2: Méthode de calcul détaillée

Sonnenschutzeinrichtungen in Kombination mit
Verglasungen — Berechnung der Solarstrahlung und des
Lichttransmissionsgrades — Teil 2: Detailliertes
Berechnungsverfahren

This European Standard was approved by CEN on 24 February 2005.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the Central Secretariat or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the Central Secretariat has the same status as the official
versions.

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ

CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia,
Slovenia, Spain, Sweden, Switzerland and United Kingdom.

EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG

Management Centre: rue de Stassart, 36

© 2005 CEN

All rights of exploitation in any form and by any means reserved
worldwide for CEN national Members.

B-1050 Brussels

Ref. No. EN 13363-2:2005: E


EN 13363-2:2005 (E)

Contents
Page
Foreword......................................................................................................................................................................3
1

Scope ..............................................................................................................................................................4

2

Normative references ....................................................................................................................................4

3
3.1
3.2

Terms, definitions, symbols and units ........................................................................................................4
Terms and definitions ...................................................................................................................................4
Symbols and units .........................................................................................................................................5

4
4.1
4.2

Characteristic data.........................................................................................................................................6
Solid layers.....................................................................................................................................................6
Gas spaces .....................................................................................................................................................6

5
5.1
5.2
5.3
5.4

Principles of calculation ...............................................................................................................................6
General............................................................................................................................................................6
Solar radiation and light................................................................................................................................7
Heat transfer...................................................................................................................................................9
Energy balance ............................................................................................................................................13

6
6.1

6.2

Boundary conditions ...................................................................................................................................13
Reference and summer conditions............................................................................................................13
Report ...........................................................................................................................................................14

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ

Annex A (normative) Determination of equivalent solar and light optical characteristics for louvres or
venetian blinds.............................................................................................................................................16
A.1
Assumptions ................................................................................................................................................16
A.2
Symbols ........................................................................................................................................................16
A.3
Direct radiation.............................................................................................................................................17
A.4
Diffuse radiation...........................................................................................................................................17
A.5
Thermal radiation.........................................................................................................................................17
A.6
Global radiation............................................................................................................................................17
A.7
Example ........................................................................................................................................................18
Annex B (normative) Stack effect ..........................................................................................................................19
B.1
General..........................................................................................................................................................19
B.2
Pressure loss factors ..................................................................................................................................20
Annex C (informative) Example..............................................................................................................................22

C.1
Input data......................................................................................................................................................22
C.2
Results ..........................................................................................................................................................22
Annex D (informative) Physical properties of gases ...........................................................................................23
Bibliography ..............................................................................................................................................................24

2
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EN 13363-2:2005 (E)

Foreword
This document (EN 13363-2:2005) has been prepared by Technical Committee CEN/TC 89 “Thermal performance
of buildings and building components”, the secretariat of which is held by SIS.
This European Standard shall be given the status of a national standard, either by publication of an identical text or
by endorsement, at the latest by October 2005, and conflicting national standards shall be withdrawn at the latest
by October 2005.
EN 13363 with the general title Solar protection devices combined with glazing - Calculation of solar and light
transmittance consists of two parts:

− Part 1: Simplified method;
− Part 2: Detailed calculation method.
This document includes a Bibliography.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,
Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ

3


EN 13363-2:2005 (E)

1

Scope

This document specifies a detailed method, based on the spectral transmission data of the materials, comprising
the solar protection devices and the glazing, to determine the total solar energy transmittance and other relevant
solar-optical data of the combination. If spectral data are not available the methodology can be adapted to use integrated data.
The method is valid for all types of solar protection devices parallel to the glazing such as louvres, or venetian, or
roller blinds. The blind may be located internally, externally, or enclosed between the panes of the glazing.
Ventilation of the blind is allowed for in each of these positions in determining the solar energy absorbed by the
glazing or blind components, for vertical orientation of the glazing.
The blind component materials may be transparent, translucent or opaque, combined with glazing components with
known solar transmittance and reflectance and with known emissivity for thermal radiation.
The method is based on a normal incidence of radiation and does not take into account an angular dependence of
transmittance or reflectance of the materials. Diffuse irradiation or radiation diffused by solar protection devices is
treated as if it were direct. Louvres or venetian blinds are treated as homogenous materials by equivalent solar
optical characteristics, which may depend on the angle of the incidence radiation. For situations outside the scope
of this document; ISO 15099 covers a wider range of situations.
The document also gives certain normalised situations, additional assumptions and necessary boundary
conditions.

2

Normative references

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ

The following referenced documents are indispensable for the application of this document. For dated references,
only the edition cited applies. For undated references, the latest edition of the referenced document (including any
amendments) applies.
EN 410, Glass in building – Determination of luminous and solar characteristics of glazing
EN 673, Glass in building – Determination of thermal transmittance (U value) – Calculation method
EN ISO 7345:1995, Thermal insulation – Physical quantities and definitions (ISO 7345:1987)
EN ISO 9288:1996, Thermal insulation – Heat transfer by radiation – Physical quantities and definitions
(ISO 9288:1989)

3

Terms, definitions, symbols and units

3.1

Terms and definitions

For the purposes of this document, the terms and definitions given in EN ISO 7345:1995, EN ISO 9288:1996 and
the following apply.
3.1.1
solar radiation and light
radiation in the whole solar spectrum or any part of it, comprising ultra-violet, visible and near infra-red radiation in
the wavelength range of 0,3 µm to 2,5 µm
NOTE

Sometimes called shortwave radiation, see EN ISO 9488.

4

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EN 13363-2:2005 (E)

3.1.2
thermal radiation
radiation emitted by any surface at or near ambient temperature in the far infrared in the wavelength range of
3 µm to 100 µm
NOTE 1

The definition deviates from EN ISO 9288.

NOTE 2

Sometimes called longwave radiation, see EN ISO 9488.

3.1.3
total solar energy transmittance
total transmitted fraction of the incident solar radiation consisting of direct transmitted solar radiation and the part of
the absorbed solar radiation transferred by convection and thermal radiation to the internal environment
3.1.4
light transmittance
transmitted fraction of the incident solar radiation in the visible part of the solar spectrum, see EN 410
3.1.5
normalized radiant flow rate
radiant flow rate divided by the incident radiant flow rate

3.2

Symbols and units

The following list includes the principal symbols used. Other symbols are defined where they are used in the text.
Symbol

Physical quantity

Unit

ES

incident solar radiation flow rate, solar irradiation

W/m²

I

normalised radiant flow rate

−

H

height of a ventilated space

m

T

thermodynamic temperature

K

U

thermal transmittance

W/(m²⋅K)

g

total solar energy transmittance (solar factor)

−

h

heat transfer coefficient, or thermal conductance of gas space

W/(m²⋅K)

q

density of heat flow rate

W/m²

s

width of a space

m

z

vertical coordinate

m

ε

thermal emissivity

−

α

absorptance

−

αe

solar direct absorptance

−

λ

thermal conductivity

W/(m⋅K)

λ

wavelength

µm

ρ

reflectance of the side facing the incident radiation

−

ρ'

reflectance of the side facing away from the incident radiation

−

ρe

solar direct reflectance

−

ρv

light reflectance

−

σ

Stefan-Boltzmann constant

5,67×10 W/(m²⋅K )

τe

solar direct transmittance

−

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ

-8

4

5


EN 13363-2:2005 (E)

τv

light transmittance

−

Subscripts
a

absorbed

c

conductive/convective

d

diffuse

e

external environment

g

gas

i

internal environment

j, k

integer, number of layer or space

r

radiant

th

thermal radiation

v

ventilated

B

blind

D

direct

4
4.1

Characteristic data
Solid layers

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ

The glass panes and blinds are considered as solid layers. The relevant characteristics are:

•

for solar radiation and light: the spectral transmittance and the spectral reflectances of both sides;

•

for thermal radiation: the transmittance and the emissivities of both sides.

Usually, these values are determined directly by the most appropriate optical method1). For glazing, see the
procedures recommended for glazing materials in EN 410. However, for louvres or venetian blinds, Annex A gives
a method to calculate equivalent values based on similarly determined material properties.

4.2

Gas spaces

The thermal properties of closed spaces filled with air or gas shall be calculated in accordance with EN 673. The
spaces are described by their width and the physical properties of the gas (see Annex D, Table D.1).
Ventilated air spaces are described by the width and the height of the space and the physical properties of the air.

5
5.1

Principles of calculation
General

The combination of glazing and solar protection devices consists of a series of solid layers separated by air or gas
filled spaces. The solid layers are assumed to be homogeneous with a negligible thermal resistance. The transport
of solar radiation and heat is considered to be one-dimensional, except for ventilated spaces, where the twodimensional convection is reduced to a one-dimensional formula.

1)

See CIE Technical Report – CIE 130-1998 "Practical Methods for the measurement of reflectance and transmittance".

6
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EN 13363-2:2005 (E)

The layers and spaces are numbered by j from 1 to n, where space n represents the internal environment and
space 0 the external environment. Within the physical model the number of layers is unlimited. The basic formulae
for solar radiation and heat transfer are given to establish the energy balance of each layer. To solve the system of
equations the use of an iterative procedure is recommended, due to the non-linear interaction of temperature and
heat transport.

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ

Key
Te
Tre
ve
Ti
Tri

external air temperature
external radiant temperature
external wind velocity
internal air temperature
internal radiant temperature

1
2
3
4
5
6

external
layer 1
space 1
layer j
space j
layer n

7
8
9
10
11

internal
solar radiation
direct solar and light transmittance
direct solar and light reflectance
thermal radiation and convection
(direct and indirect)

NOTE
The internal and external environments are characterised by the air temperature and the radiant temperature; the

external environment is additionally characterised by the wind velocity.

Figure 1 — Schematic presentation of a system consisting of layers and spaces

5.2

Solar radiation and light

The solar and optical properties are independent of the intensity of the solar irradiation and temperature in the
system2). It is assumed that the spaces are completely transparent, without any absorption. Each solid layer is
characterised by the spectral transmittance and reflectance in the wavelength region between 0,3 µm and 2,5 µm.
For each wavelength λ and each layer j the following equations are valid for the normalised radiant flow rates I and
I' (see Figure 2):

I j (λ ) = τ j (λ ) ⋅ I j −1 (λ ) + ρ ′j (λ ) ⋅ I ′j (λ )
I ′j −1 (λ ) = ρ j (λ ) ⋅ I j −1 (λ ) + τ ′j (λ ) ⋅ I ′j (λ )

(1)

where

2)

There are exceptions for certain materials (photochromic, thermochromic).

7


EN 13363-2:2005 (E)

τj(λ)

is the spectral transmittance of the side facing the incident radiation;

τ'j(λ)

is the spectral transmittance of the side facing away from the interior3);

ρj(λ)

is the spectral reflectance of the side facing the incident radiation;

ρ'j(λ)

is the spectral reflectance of the side facing away from the incident radiation;

Ij(λ)

is the spectral normalised radiant flow rate inwards;

I'j(λ)

is the spectral normalised radiant flow rate outwards.

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ
Figure 2 — Schematic presentation of the characteristic data of layer j and the spectral flow rates
Equation (1) is solved with the boundary conditions: I 0 (λ ) = 1;

I n′ (λ ) = 0

(2)

If the spectral normalised radiant flow rates I j (λ ) and I ′j (λ ) are known for each j, the spectral data of the system
result in:
the spectral transmittance: τ (λ ) = I n (λ )

(3)

the spectral reflectance of the side facing the incident radiation: ρ (λ ) = I 0′ (λ )

(4)

the spectral absorptance of layer j:

α j (λ ) = (1 − ρ j (λ ) − τ j (λ ) )⋅ I j −1 (λ ) + (1 − ρ ′j (λ ) − τ ′j (λ ) )⋅I ′ j (λ )

(5)

The solar direct transmittance τ e , the solar direct reflectance ρ e and the solar direct absorptance α e, j of each
layer j shall be calculated from the spectral data according to the procedure given in EN 410. Similarly, the light
transmittance τ v and the light reflectance ρ v can be calculated.
If the spectral reflectance ρ ' (λ ) of the system facing the interior is required, solve Equation (1) with the boundary
conditions I 0 (λ ) = 0 ; I n′ (λ ) = 1 and use ρ ′(λ ) = I n (λ ) .

3)

For light scattering materials the transmittances τ(λ) and τ'(λ) might be different.

8
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EN 13363-2:2005 (E)

If spectral data are not available, the calculation can be done with integrated data, taking note that the accuracy is
reduced for materials where the wavelength-dependent properties are different.

5.3

Heat transfer

5.3.1

Thermal radiation

The heat flow by thermal radiation depends on the temperatures in the system, and is coupled with other heat flows
within the system. A separate solution is not possible in a normalised form.
For thermal radiation it is convenient to use the emissivity instead of the reflectance, thus each layer j is
characterised by (see Figure 3):
temperature;

Tj

τth,j transmittance for thermal radiation;
εj

effective emissivity of the side facing the exterior;

ε 'j

effective emissivity of the side facing the interior;

qth

radiative heat flow density inwards;

q'th radiative heat flow density outwards.

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ

Figure 3 — Schematic presentation of the characteristic data of layer j and the thermal radiative heat flow
density

Most solid layers are opaque in the region of thermal radiation (5 µm to 50 µm) and are described by an integrated
value, the corrected emissivity ε. This emissivity is determined by the measurement of the spectral normal
reflectance. The evaluation uses a correction for the hemispherical emission and assumes no transparency as
described in EN 673.
For infrared transparent materials such as some plastic films, opaque layers with holes, and louvre systems, the
characteristics shall be determined by an appropriate procedure. For louvres see Annex A.
For each layer j the following set of equations for the radiative heat flow densities is valid:
q th, j = τ th, j ⋅ q th, j − 1 + (1 − ε ′j − τ th, j ) ⋅ q ′th, j + ε ′j ⋅ σ ⋅ T j4
q ' th, j − 1 = (1 − ε j − τ th, j ) ⋅ q th, j − 1 + τ th, j ⋅ q ′th, j + ε j ⋅ σ ⋅ T j4

(6)

9


EN 13363-2:2005 (E)

The boundary conditions are given by the external and internal radiant temperatures Tr,e and Tr,i respectively:
q th,0 = σ ⋅ Tr,4e

;

q' th, n = σ ⋅ Tr,4i

(7)

Assuming the temperatures Tj are known, the system gives:


the net radiant heat flow to the exterior

q th, e = q ' th, 0 −q th, 0


(8)

the net radiant heat flow to the interior
q th, i = q th, n − q ' th, n



(9)

the net absorbed heat (transferred by thermal radiation) in the layer j
q th, a, j = ε j ⋅ q th, j − 1 + ε ′j ⋅ q ′th, j −  ε j + ε ′j  ⋅ σ ⋅ T j 4



5.3.2

(10)

Conductive and convective heat transfer in closed spaces

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ

Key

λj

thermal conductivity of the gas in space j at temperature (Tj+ Tj+1 )/2
width of space j
thermal conductance of the gas in space j
conductive-convective density of heat flow rate from layer j to layer j + 1

sj
hg,j
qc,j

1
2
3

layer j
space j
layer j + 1

Figure 4 — Schematic presentation of the characteristic data of a closed space and the conductionconvective density of heat flow rate

The thermal conductance of the gas in a closed space j is given by (see Figure 4):
hg, j = Nu j ⋅

λj

(11)

sj

where

10
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EN 13363-2:2005 (E)

λj

is the thermal conductivity of the gas in space j;

sj

is the width of space j;

Nu j

is the Nusselt number in accordance with EN 673.

The external boundary conditions are given by the external air temperature and the external convective heat
transfer coefficient:
T0 = Te ; hg,0 = hc,e

(12)

Similarly, the internal boundary conditions are given by the internal air temperature and the internal convective heat
transfer coefficient:
Tn +1 = Ti ;

hg, n = hc,i

(13)

Assuming the temperatures are known for each layer, the net absorbed heat (transferred by conductionconvection) in the layer j is given by:

(

)

(

qc,a, j = hg, j −1 ⋅ T j −1 − T j + hg, j ⋅ T j +1 − T j

)

(14)

The convective density of the heat flow rate to the external environment is given by:

qc, e = qc, a,0 = hg,0 ⋅ (T1 − Te )

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ

(15)

and from the internal environment, by:
qc,i = qc, a, n = hg, n ⋅ (Ti − Tn )
5.3.3

(16)

Ventilated air spaces

Air spaces may be connected to the external or internal environment or to other spaces. Assuming the mean
velocity of the air in the space is known, the temperature profile and the heat flow may be calculated by a simple
model. The mean air velocity can be directly calculated if the air space is mechanically ventilated, or calculated
using Annex B if it is naturally ventilated.
Due to the airflow through the space, the air temperature in the space varies with height (see Figure 5). The
temperature profile depends on the air velocity in the space and the heat transfer coefficient to both layers. The air
temperature at height z in the ventilated space j is given by:

T j ( z ) = Tm, j − (Tm, j − T1, j ) ⋅ e

− z / H TP, j

0≤ z≤Hj

(17)

where
Hj

is the height of space j;

H TP, j is the characteristic height (temperature penetration length), see Equation (18);
T1, j

is the temperature of the incoming air;

Tm, j

is the mean temperature of layers j and j+1: Tm, j = (T j + T j +1 ) / 2 .

11


EN 13363-2:2005 (E)

Figure 5 — Schematic presentation of the characteristic data of a ventilated space and the internal
temperature profile assuming the incoming air is warmed up

The temperature penetration length is defined by:

H TP, j =
where

ρ j ⋅cj ⋅sj ⋅vj

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ

2 ⋅ hc, j

(18)

ρ j is the density of the air at temperature Tg, j ;
cj

is the specific heat capacity of the air;

sj

is the width of the space j;

vj

is the mean velocity of the air flow in the space, calculated using Annex B if the space is naturally ventilated;

hc, j is the convective heat transfer coefficient for space j:
hc, j = 2 ⋅ hg, j + a ⋅ v

(19)

where
hg, j is the thermal conductance of a closed space, see 5.3.2;
a

3

is the velocity coefficient (4 W⋅s/(m ⋅K)).

The temperature of the air leaving the space is given by

T2, j = Tm, j − (Tm, j − T1, j ) ⋅ e

− H j / H TP , j

12
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(20)


EN 13363-2:2005 (E)

The equivalent temperature of the air (gas) in space j is defined by Tg, j =

Tg, j = Tm, j −

H TP, j
Hj

1
Hj

Hj

∫ T j ( z)dz

and that results in:

0

(T2, j − T1, j )

(21)

The absorbed heat in the layers j and j+1 in contact with the ventilated air space is given by:
qc, a, j = hc, j ⋅ (Tg, j − T j )

(22)

qc, a, j +1 = hc, j ⋅ (Tg, j − T j +1 )

(23)

and the heat flow from space j to the connected space k (e.g. the external and internal environments) as a result of
air movement is given by:
qv, a, k = qc, a, j + qc, a, j +1

5.4

(24)

Energy balance

Assuming steady-state, the system of equations described before shall be solved for each layer j assuming:

α e, j ⋅ ES + qth, a, j + qc, a, j = 0

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ

where

6
6.1

(25)

ES

is the solar irradiation;

α e, j

is the solar absorptance of layer j;

qth, a, j

is the absorbed thermal radiation;

qc, a, j

is the absorbed heat by conduction/convection.

Boundary conditions
Reference and summer conditions

Two sets of boundary conditions are given for the vertical position of the glazing and the blind.

a)

Reference conditions:

These boundary conditions are consistent with the general assumptions of EN 410. They shall be used for
product comparison and average solar gain calculations during the heating period.
b)

Summer conditions:

These boundary conditions are representative of more extreme conditions. They are to be used for comfort
evaluations and cooling load calculations.

13


EN 13363-2:2005 (E)

Reference conditions

External:
air temperature

Te

278 K (5 °C)

radiant temperature4)

Tr,e

278 K (5 °C)

convective heat transfer coefficient5)

hc,e

18 W/(m²⋅K)

incident solar radiation flow rate

ES

300 W/m²

air temperature

Ti

293 K (20 °C)

radiant temperature

Tr,i

293 K (20 °C)

convective heat transfer coefficient6)

hc,i

3,6 W/(m²⋅K)

air temperature

Te

25 °C

radiant temperature4)

Tr,e

25 °C

convective heat transfer coefficient7)

hc,e

8 W/(m²⋅K)

incident solar radiation flow rate

ES

500 W/m²

Ti

25 °C

radiant temperature

Tr,i

25 °C

convective heat transfer coefficient8)

hc,i

2,5 W/(m²⋅K)

Internal:

Summer conditions

External:

Internal:
air temperature

6.2

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ

Report

6.2.1

Input data

The report shall contain the names of the products and all the input data used for the calculation. The report of
spectral data may be omitted; in that case the source of the data and the integrated solar optical properties shall be
given.
The report shall include:


a figure representing the thickness and the sequence of layers and spaces from the exterior to the interior;



solar optical properties of each layer, type and position of coating;



type of gas of each space and the type of ventilation;

4)

For comparison the emissivity of the external surface shall be set to 0,837 for glass and 0,9 for other products.

5)

The value corresponds to an external heat transfer coefficient of 23 W/(m²⋅K).

6)

The value corresponds to a temperature difference of 10 K.

7)

The value corresponds to an air velocity of 1 m/s.

8)

The value corresponds to a temperature difference of 5 K.

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EN 13363-2:2005 (E)



for a louvre or venetian blind system according to Annex A the geometry and the solar optical properties of the
material;



for the ventilated space according to Annex B the height and the geometry of the apertures and openness
factor of fabric;



the boundary conditions;

and if possible:


characteristics of the glazing, e.g. U-value, g-value;



characteristics of the blind system.

6.2.2

Results

The three parts of the secondary internal heat transfer factor are defined as the difference of the secondary heat
flow rate with and without solar radiation divided by the incident solar radiation flow rate.
The characteristic values shall be quoted to three decimal places, except for the total solar energy transmittance,
which is rounded to two decimal places.
Table 1 — Presentation of results
Item Energy to the interior by

Symbol

Reference

1

direct solar transmittance

τe

2

thermal radiation factor

g th

3

convection factor

gc

4

ventilation factor

gv

5

secondary internal heat
transfer factor

qi

sum of items 2,3,4

6

total solar energy transmittance

g

sum of items 1,2,3,4

τ(λ) (Equation (3)) evaluated according EN 410
g th =

q th ( E S ) − q th (0)
ES

gc =

q c ( E S ) − qc (0)
ES

(Equation (16))

gv =

q v ( E S ) − q v (0)
ES

(Equation (24))

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ
(Equation (9))

15


EN 13363-2:2005 (E)

Annex A
(normative)
Determination of equivalent solar and light optical characteristics for
louvres or venetian blinds

A.1 Assumptions
It is assumed that:
•

louvres or venetian blinds are adjusted to eliminate direct transmission of the solar beam;

•

reflectance and transmittance of the blind material are diffuse.

A.2 Symbols
Φi,j

view factor from zone i to zone j (see Figure A.1)9)

τ

transmittance of the blind material

ρ

reflectance of the side of blind facing the incident radiation

ρ'

reflectance of the side of blind facing away from the incident radiation

τS

transmittance of the system

ρS

reflectance of the system to the exterior

NOTE

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ

Zones c to h refer to the view factors Φi,j.

Figure A.1 — Schematic presentation of a louvre or venetian blind

9) Siegel, R, Howell, J,R, (1992) Thermal radiation heat transfer, Hemisphere Publishing Corporation.

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EN 13363-2:2005 (E)

A.3 Direct radiation
τ S, D = Φ 51 ρ + Φ 61τ +

ρ S,D = Φ 52 ρ + Φ 62τ +

(Z Φ 54 ρ ' +Φ 63 τ )(Φ 31 ρ

+ Φ 41τ ) + (Z Φ 63 τ + Φ 54 ρ )(Φ 41 ρ ' + Φ 31τ )
⋅Z
Φ 34 ρ ⋅ (1 − ZZ ' )

(ZΦ 54 ρ '+Φ 63τ )(Φ 32 ρ + Φ 42τ ) + (ZΦ 63τ + Φ 54 ρ )(Φ 42 ρ '+Φ 32τ ) ⋅ Z
Φ 34 ρ ⋅ (1 − ZZ ')

(A.1)

(A.2)

where
Z=

Φ 34 ρ
;
1 − Φ 34τ

Z'=

Φ 34 ρ '
1 − Φ 34τ

(A.3)

NOTE

ρdir is the reflectance to the exterior; there is a second reflectance to the interior, which is mathematically identical if
subscript 2 is replaced by 1 in Equation (A.2).

A.4 Diffuse radiation
τ S, d = Φ 21 +

ρ S, d =

(Φ 23 ρ + Φ 24τ )(Φ 31 + Z 'Φ 41 ) + (Φ 24 ρ '+Φ 23τ )(Φ 41 + ZΦ 31 ) ⋅ Z
Φ 34 ρ ⋅ (1 − ZZ ')

(Φ 23 ρ + Φ 24τ )(Φ 32 + Z 'Φ 42 ) + (Φ 24 ρ '+Φ 23τ )(Φ 42 + ZΦ 32 ) ⋅ Z
Φ 34 ρ ⋅ (1 − ZZ ')

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ

(A.4)

(A.5)

NOTE
ρdif is the reflectance to the exterior; there is a second reflectance to the interior, which is mathematically identical if
subscript for face 2 is replaced by that for face 1 in Equation (A.5).

A.5 Thermal radiation
For thermal radiation the diffuse values are valid.
For the thermal radiation properties of the blind system Equations (A.4) and (A.5) shall be used replacing the solar
optical transmittance τ by the thermal transmittance τth and the solar optical reflectance by the thermal reflectance
ρ th = 1 − τ th − ε .

A.6 Global radiation
For global solar radiation a mixing of the direct transmittance τD and diffuse transmittance τd is recommended
according to τ = 0,85 ⋅ τ D + 0,15 ⋅ τ d .
NOTE
In particular for louvres and venetian blinds, the solar transmittance for diffuse radiation may be larger than the solar
transmittance for direct radiation. Therefore one should use the solar transmittance for global radiation with a mix of direct and
diffuse radiation suitable for the local climatic conditions.

17


EN 13363-2:2005 (E)

A.7 Example
Table A.1 gives view factors Φij for slats adjusted perpendicular to the solar beam with a spacing ratio d/l = 1,0 (see
Figure A.2).
Table A.1 – View factors

Φij

j

1

i

2

3

4

1

0,000

0,307

0,076

0,617

2

0,307

0,000

0,617

0,076

3

0,076

0,617

0,000

0,307

4

0,617

0,076

0,307

0,000

5

0,059

0,707

0,000

0,233

6

0,538

0,089

0,373

0,000

ｗｗｗ．ｂｚｆｘｗ．ｃｏｍ

Figure A.2 — Slats adjusted at 45° perpendicular to the solar beam with a spacing ratio d/l = 1,0

Table A.2 gives the resulting equivalent transmittance, and the resulting reflectance to the exterior (see Figure A.2).
Table A.2 – Equivalent transmittance and reflectance
Material of slats

τ

Direct

ρ = ρ’

Diffuse

τs,D

ρs,D

τs,d

ρs,d

0,00

0,30

0,03

0,22

0,35

0,12

0,00

0,70

0,12

0,52

0,44

0,30

0,20

0,60

0,23

0,52

0,51

0,31

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