SIST EN 13032-5:2019
(Main)Light and lighting - Measurement and presentation of photometric data of lamps and luminaires - Part 5: Presentation of data for luminaires used for road lighting
Light and lighting - Measurement and presentation of photometric data of lamps and luminaires - Part 5: Presentation of data for luminaires used for road lighting
This document defines the presentation of utilances or utilization factors respectively for luminaires used for road lighting.
Licht und Beleuchtung - Messung und Darstellung photometrischer Daten von Lampen und Leuchten - Teil 5: Darstellung von Daten von Leuchten für den Einsatz in der Straßenbeleuchtung
Dieses Dokument legt die Darstellung von Utilanzen bzw. Beleuchtungswirkungsgraden von Leuchten für den Einsatz in der Straßenbeleuchtung fest.
Lumière et éclairage - Mesurage et présentation des données photométriques des lampes et des luminaires - Partie 5 : Présentation des données relatives aux luminaires utilisés pour l'éclairage public
Le présent document définit la présentation des utilances ou des facteurs d’utilisation, respectivement, pour les luminaires utilisés pour l’éclairage public.
Svetloba in razsvetljava - Merjenje in podajanje fotometričnih podatkov sijalk in svetilk - 5. del: Predstavitev podatkov za svetilke za cestno razsvetljavo
Ta dokument opredeljuje predstavitev porabe oziroma faktorjev izkoristka za svetilke, ki se uporabljajo za cestno razsvetljavo.
General Information
Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN 13032-5:2019
01-marec-2019
6YHWOREDLQUD]VYHWOMDYD0HUMHQMHLQSRGDMDQMHIRWRPHWULþQLKSRGDWNRYVLMDONLQ
VYHWLONGHO 3UHGVWDYLWHYSRGDWNRY]DVYHWLONH]DFHVWQRUD]VYHWOMDYR
Light and lighting - Measurement and presentation of photometric data of lamps and
luminaires - Part 5: Presentation of data for luminaires used for road lighting
Licht und Beleuchtung - Messung und Darstellung photometrischer Daten von Lampen
und Leuchten - Teil 5: Darstellung von Daten von Leuchten für den Einsatz in der
Straßenbeleuchtung
Lumière et éclairage - Mesurage et présentation des données photométriques des
lampes et des luminaires - Partie 5 : Présentation des données relatives aux luminaires
utilisés pour l'éclairage public
Ta slovenski standard je istoveten z: EN 13032-5:2018
ICS:
93.080.40 &HVWQDUD]VYHWOMDYDLQ Street lighting and related
SULSDGDMRþDRSUHPD equipment
SIST EN 13032-5:2019 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST EN 13032-5:2019
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SIST EN 13032-5:2019
EN 13032-5
EUROPEAN STANDARD
NORME EUROPÉENNE
November 2018
EUROPÄISCHE NORM
ICS 93.080.40
English Version
Light and lighting - Measurement and presentation of
photometric data of lamps and luminaires - Part 5:
Presentation of data for luminaires used for road lighting
Lumière et éclairage - Mesurage et présentation des Licht und Beleuchtung - Messung und Darstellung
données photométriques des lampes et des luminaires photometrischer Daten von Lampen und Leuchten -
- Partie 5 : Présentation des données relatives aux Teil 5: Darstellung von Daten von Leuchten für den
luminaires utilisés pour l'éclairage public Einsatz in der Straßenbeleuchtung
This European Standard was approved by CEN on 18 June 2018.
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 CEN-CENELEC Management Centre 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 CEN-CENELEC Management
Centre has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2018 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 13032-5:2018 E
worldwide for CEN national Members.
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SIST EN 13032-5:2019
EN 13032-5:2018 (E)
Contents Page
European foreword . 3
Introduction . 4
1 Scope . 5
2 Normative references . 5
3 Terms and definitions . 5
4 Utilances road lighting and utilization factor road lighting. 6
4.1 General . 6
4.2 General assumptions . 6
4.3 Calculation of utilance by interpolation in an utilance table . 7
4.4 Utilance road lighting table . 8
5 Application . 10
5.1 General . 10
5.2 Accumulated utilances road lighting . 10
5.3 Limitations . 11
Annex A (informative) Determination of edge illuminance ratio . 12
Annex ZA (informative) Relationship between this European Standard and the ecodesign
requirements of Commission Regulation (EC) No 245/2009, as amended by
Regulation (EU) No 347/2010, aimed to be covered . 16
Bibliography . 18
2
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SIST EN 13032-5:2019
EN 13032-5:2018 (E)
European foreword
This document (EN 13032-5:2018) has been prepared by Technical Committee CEN/TC 169 “Light and
Lighting”, the secretariat of which is held by DIN.
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 May 2019, and conflicting national standards shall be
withdrawn at the latest by May 2019.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document has been prepared under a standardization request given to CEN by the European
Commission and the European Free Trade Association, and supports essential requirements of
Commission Regulation (EC) No 245/2009, as amended by Regulation (EU) No 347/2010.
For relationship with Commission Regulation (EC) No 245/2009, as amended by Regulation (EU)
No 347/2010, see informative Annex ZA, which is an integral part of this document.
According to the CEN-CENELEC Internal Regulations, the national standards organisations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia,
Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands,
Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
the United Kingdom.
3
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SIST EN 13032-5:2019
EN 13032-5:2018 (E)
Introduction
The Eco-design Directive 2009/125/EC requires a reduction of energy consumption of fluorescent lamps
without integrated ballast, for high intensity discharge lamps, for LED light sources, and for ballasts and
luminaires able to operate such lamps and light sources.
Utilance is a measurement of the efficiency of the luminous intensity distribution of a luminaire to spread
its luminous flux onto a specified surface provided other quality requirements of EN 13201 series are
met.
There are many lighting solutions that can satisfy the road lighting criteria specified in EN 13201-2. To
design these solutions, photometric data of the equipment is required.
The use and application of utilance can serve as a tool for the pre-selection of adequate luminaires to
fulfil the lighting requirements of EN 13201-2.
The knowledge of the utilance road lighting is needed for the calculation of the installation luminous
efficacy as described in EN 13201-5.
This document specifies the presentation of tables of utilances and utilization factors of luminaires used
for road lighting.
Utilance is used in place of utilization factors because it can be applied to luminaires with replaceable or
non-replaceable lamps/light sources.
4
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SIST EN 13032-5:2019
EN 13032-5:2018 (E)
1 Scope
This document defines the presentation of utilances or utilization factors respectively for luminaires used
for road lighting.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements 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 12665, Light and lighting — Basic terms and criteria for specifying lighting requirements
EN 13201-2, Road lighting — Part 2: Performance requirements
EN 13201-3, Road lighting — Part 3: Calculation of performance
EN 13201-5, Road lighting — Part 5: Energy performance indicators
3 Terms and definitions
For the purposes of this document, the terms and definitions given in EN 12665 and the following apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http://www.electropedia.org/
— ISO Online browsing platform: available at http://www.iso.org/obp
3.1
utilization factor (of an installation, for a reference area)
F
U
ratio of the luminous flux received by the reference area to the sum of the individual luminous fluxes of
the lamps /light sources of the installation
3.2
utilance (of an installation, for a reference area)
U
ratio of the luminous flux received by the reference area to the sum of the individual total fluxes of the
luminaires of the installation
3.3
utilization factor road lighting
F
U,rl
ratio of the luminous flux received by one or more parallel strips along the road to the sum of the
individual total fluxes of the lamps / light sources of the installation
Note 1 to entry: “Along the road” is considered parallel to that of the kerb following in the same direction as any
adjacent luminaires.
3.4
utilance road lighting
U
rl
ratio of the luminous flux received by one or more parallel strips along the road to the sum of the
individual total fluxes of the luminaires of the installation
5
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SIST EN 13032-5:2019
EN 13032-5:2018 (E)
Note 1 to entry: “Along the road” is considered parallel to that of the kerb following in the same direction as any
adjacent luminaires.
4 Utilances road lighting and utilization factor road lighting
4.1 General
In this standard the average illuminance on a reference area, a longitudinal strip of a road, representing,
for example, the carriageway, a single lane, a cycle path, or a footpath, can be calculated as:
−−11
EU= ⋅⋅f Φ ⋅ W⋅ S (1)
rl M Lum
where
is the maintained average illuminance in lx on the strip under consideration;
E
U is the utilance road lighting:
rl
f is the overall maintenance factor;
M
ϕ is the luminaire luminous flux in lm;
Lum
W is the width of reference area, in m;
S is the luminaire spacing in m.
NOTE If the luminaire luminous flux is not known it can be determined from the knowledge of the total
luminous flux of the light sources in the luminaire and the light output ratio of the luminaire.
The utilance road lighting U (see Figure 2) is given by the ratio of the luminous flux emitted by the
rl
luminaire within a specified solid angle to the total luminous flux emitted by the same luminaire, whereas
the utilization factor road lighting F is given by the ratio of the luminous flux emitted by the luminaire
u,rl
within a specified solid angle to the total luminous flux of the light source(s) in the same luminaire. The
utilization factor road lighting can be expressed as utilance road lighting multiplied by the light output
ratio:
F UR⋅ (2)
U,rl rl LO
where
is the light output ratio (of a luminaire).
R
LO
The utilance can be derived from the luminous intensity distribution of the luminaire (measured
according to EN 13032-1 or EN 13032-4, including uncertainties) and should be provided in an
appropriate format (see example in Table 1).
4.2 General assumptions
The tables are applicable for regular arrangements with constant overhang and mounting height on
straight sections of roads.
The luminous intensity distribution of the luminaire is part of the basic data needed for installation
performance calculations. This data should be given for luminaires used in road lighting in the format
specified in EN 13201-3.
With the photometric centre of luminaire as origin and the reference area of the road between two lines
parallel to its axis (which extends in principle from -∞ to +∞) a solid angle is defined. The position of the
6
=
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SIST EN 13032-5:2019
EN 13032-5:2018 (E)
two circumscribing lines is given by their transverse angle. It is common practice to choose one of these
circumscriptions at a transverse distance equal to zero.
A reference area represents one or more carriageways, footpaths, cycle paths, emergency lanes and other
road areas lying separately or adjacent to a carriageway, strips just outside or inside a carriageway (for
the evaluation of the edge illuminance ratio), etc. (see Figure 1).
Each area is to be lit to the lighting requirements as defined in EN 13201-2.
Further, it is assumed that the areas are illuminated by a lighting installation with luminaires / lamps /
light sources of the same type in one or more rows that are parallel to the above-mentioned lines that
confine the areas.
The basic conventions made in the mathematical procedures are described in EN 13201-3:2015, 4.1 and
4.2.
4.3 Calculation of utilance by interpolation in an utilance table
The limiting lines of a reference area (strip) in relation to a row of luminaires are shown in Figure 1. The
limiting lines are part of the inclined planes B and B which pass through both the limiting lines and the
1 2
-1 -1
luminaire. The angles of inclination of the planes B and B are given by tan (t / H) and tan (t / H)
1 2 1 2
respectively, where t and t are the transverse distances to the limiting lines and H is the luminaire
1 2
mounting height (centre point of light above the reference area).
Key
O overhang (position of the photometric centre of the luminaire) with respect to the reference area in m;
v
W width of the reference area in m;
H luminaire mounting height in m;
δ angle of tilt of the luminaire for calculation; (in this example δ = 0˚)
t t transverse distances to the limiting lines
1, 2
B1, B2 angles of inclined limiting planes to vertical plane B = 0°
1 reference area
2 vertical plane B = 0°
Figure 1 — Basic position of reference area relative to a luminaire in a row of lumin
...
SLOVENSKI STANDARD
oSIST prEN 13032-5:2017
01-april-2017
6YHWOREDLQUD]VYHWOMDYD0HUMHQMHLQSRGDMDQMHIRWRPHWULþQLKSRGDWNRYVLMDONLQ
VYHWLOGHO 3UHGVWDYLWHYSRGDWNRY]DVYHWLOD]DFHVWQRUD]VYHWOMDYR
Light and lighting - Measurement and presentation of photometric data of lamps and
luminaires - Part 5: Presentation of data for luminaires used for road lighting
Licht und Beleuchtung - Messung und Darstellung photometrischer Daten von Lampen
und Leuchten - Teil 5: Darstellung von Daten von Leuchten für den Einsatz in der
Straßenbeleuchtung
Lumière et éclairage - Mesurage et présentation des données photométriques des
lampes et des luminaires - Partie 5 : Présentation des données relatives aux luminaires
utilisés pour l'éclairage public
Ta slovenski standard je istoveten z: prEN 13032-5
ICS:
93.080.40 &HVWQDUD]VYHWOMDYDLQ Street lighting and related
SULSDGDMRþDRSUHPD equipment
oSIST prEN 13032-5:2017 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
---------------------- Page: 1 ----------------------
oSIST prEN 13032-5:2017
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oSIST prEN 13032-5:2017
DRAFT
EUROPEAN STANDARD
prEN 13032-5
NORME EUROPÉENNE
EUROPÄISCHE NORM
January 2017
ICS 93.080.40
English Version
Light and lighting - Measurement and presentation of
photometric data of lamps and luminaires - Part 5:
Presentation of data for luminaires used for road lighting
Lumière et éclairage - Mesurage et présentation des Licht und Beleuchtung - Messung und Darstellung
données photométriques des lampes et des luminaires photometrischer Daten von Lampen und Leuchten -
- Partie 5 : Présentation des données relatives aux Teil 5: Darstellung von Daten von Leuchten für den
luminaires utilisés pour l'éclairage public Einsatz in der Straßenbeleuchtung
This draft European Standard is submitted to CEN members for enquiry. It has been drawn up by the Technical Committee
CEN/TC 169.
If this draft becomes a European Standard, 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.
This draft European Standard was established by CEN 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 CEN-CENELEC
Management Centre has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and United Kingdom.
Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of which they are
aware and to provide supporting documentation.
Warning : This document is not a European Standard. It is distributed for review and comments. It is subject to change without
notice and shall not be referred to as a European Standard.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2017 CEN All rights of exploitation in any form and by any means reserved Ref. No. prEN 13032-5:2017 E
worldwide for CEN national Members.
---------------------- Page: 3 ----------------------
oSIST prEN 13032-5:2017
prEN 13032-5:2017 (E)
Contents Page
European foreword . 3
Introduction . 4
1 Scope . 5
2 Normative references . 5
3 Terms and definitions . 5
4 Utilances road lighting and utilization factor road lighting. 5
4.1 General . 5
4.2 General assumptions . 6
4.3 Calculation of utilance by interpolation in an utilance table . 6
4.4 Utilance road lighting table . 8
5 Application . 9
5.1 General . 9
5.2 Accumulated utilances road lighting . 9
5.3 Limitations . 10
Annex A (informative) Determination of edge illuminance ratio . 11
Annex ZA (informative) Relationship between this European Standard and the ecodesign
requirements of Commission Regulation (EC) No 245/2009, as amended by
Regulation (EU) No 347/2010, aimed to be covered . 15
Bibliography . 17
2
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oSIST prEN 13032-5:2017
prEN 13032-5:2017 (E)
European foreword
This document (prEN 13032-5:2017) has been prepared by Technical Committee CEN/TC 169 “Light and
Lighting”, the secretariat of which is held by DIN.
This document is currently submitted to the CEN Enquiry.
This document has been prepared under a mandate given to CEN by the European Commission and the
European Free Trade Association, and supports essential requirements of Commission Regulation (EC)
No 245/2009, as amended by Regulation (EU) No 347/2010.
For relationship with Commission Regulation (EC) No 245/2009, as amended by Regulation (EU) No
347/2010, see informative Annex ZA, which is an integral part of this document.
3
---------------------- Page: 5 ----------------------
oSIST prEN 13032-5:2017
prEN 13032-5:2017 (E)
Introduction
The Eco-design Directive 2009/125/EC requires a reduction of energy consumption of fluorescent lamps
without integrated ballast, for high intensity discharge lamps, for LED light sources, and for ballasts and
luminaires able to operate such lamps and light sources.
“Utilance is a measurement of the efficiency of the luminous intensity distribution of a luminaire to
spread its luminous flux onto a specified surface provided other quality requirements of EN 13201 are
met.”
There are many lighting solutions that can satisfy the road lighting criteria specified in EN 13201-2. To
design these solutions, photometric data of the equipment are required.
The use and application of utilance can serve as a tool for the pre-selection of adequate luminaires to
fulfil the lighting requirements of EN 13201-2.
The knowledge of the utilance is required for the calculation of the installation luminous efficacy as
described in EN 13201-5.
This document specifies the presentation of tables of utilances and utilization factors of luminaires used
for road lighting.
Utilance is followed in place of utilization factors because it can be applied to luminaires using
conventional or integrated light sources.
4
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oSIST prEN 13032-5:2017
prEN 13032-5:2017 (E)
1 Scope
This document defines the presentation of utilances or utilization factors respectively for luminaires used
for road lighting.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
EN 12665, Light and lighting - Basic terms and criteria for specifying lighting requirements
EN 13201-2, Road lighting - Part 2: Performance requirements
EN 13201-3, Road lighting - Part 3: Calculation of performance
EN 13201-5, Road lighting - Part 5: Energy performance indicators
3 Terms and definitions
For the purposes of this document, the terms and definitions given in EN 12665 and the following apply.
3.1
utilization factor (of an installation, for a reference area)
F
U
ratio of the luminous flux received by the reference area to the sum of the individual luminous fluxes of
the lamps of the installation
3.2
utilance (of an installation, for a reference area)
U
ratio of the luminous flux received by the reference area to the sum of the individual total fluxes of the
luminaires of the installation
3.3
utilance road lighting
U
rl
ratio of the luminous flux received by one or more strips along the road to the sum of the individual total
fluxes of the luminaires of the installation
3.4
utilization factor road lighting
F
u,rl
ratio of the luminous flux received by one or more strips along the road to the sum of the individual total
fluxes of the luminaires of the installation
4 Utilances road lighting and utilization factor road lighting
4.1 General
In this standard the average illuminance on a reference area, a longitudinal strip of a road, representing,
for example, the carriageway, a single lane, a cycle path, or a footpath, can be calculated as:
-1 -1
E = U ⋅ f ⋅ ϕ ⋅ W ⋅ S (1)
av rl m Lum
5
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oSIST prEN 13032-5:2017
prEN 13032-5:2017 (E)
where
E is the average illuminance in lx on the strip under consideration;
av
U is the utilance road lighting:
rl
f is the overall maintenance factor;
m
ϕ is the luminaire luminous flux in lm;
Lum
W is the width of reference area, in m;
S is the luminaire spacing in m.
NOTE If the luminaire luminous flux is not known it can be determined from the knowledge of the total
luminous flux of the light sources in the luminaire and the light output ratio of the luminaire.
The utilance road lighting U is given by the ratio of the luminous flux emitted by the luminaire within a
rl
specified solid angle to the total luminous flux emitted by the same luminaire, whereas the utilization
factor road lighting F is given by the ratio of the luminous flux emitted by the luminaire within a
u,rl
specified solid angle to the total luminous flux of the light source(s) in the same luminaire. The utilization
factor road lighting can be expressed as utilance road lighting multiplied by the light output ratio.
The utilance can be derived from the luminous intensity distribution of the luminaire (measured
according to EN 13032-1 or EN 13032-4) and should be provided in an approved format.
4.2 General assumptions
The tables are applicable for regular arrangements on straight sections of roads.
The luminous intensity distribution of the luminaire is part of the basic data needed for installation
performance calculations. This data should be given for luminaires used in road lighting in the format
specified in EN 13201-3.
With the luminaire as origin and the reference area of the road between two lines parallel to its axis
(which extends in principle from -∞ to +∞) a solid angle is defined. The position of the two
circumscribing lines is given by their transverse angle. It is common practice to choose one of these
circumscriptions at a transverse distance equal to zero.
A reference area represents one or more carriageways, footpaths, cycle paths, emergency lanes and other
road areas lying separately or adjacent to a carriageway, strips just outside or inside a carriageway (for
the evaluation of the edge illuminance ratio), etc.
Each area is to be lit to the lighting requirements as defined in EN 13201-2.
Further, it is assumed that the areas are illuminated by a lighting installation with luminaires of the same
type in one or more rows that are parallel to the above-mentioned lines that confine the areas.
4.3 Calculation of utilance by interpolation in an utilance table
The limiting lines of a reference area (strip) in relation to a row of luminaires are shown in Figure 1. The
limiting lines are part of the inclined planes B and B which pass through both the limiting lines and the
1 2
-1 -1
luminaire. The angles of inclination of the planes B and B are given by tan (t / H) and tan (t / H)
1 2 1 2
respectively, where t and t are the transverse distances to the limiting lines and H is the luminaire
1 2
mounting height (centre point of light above the reference area).
6
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oSIST prEN 13032-5:2017
prEN 13032-5:2017 (E)
Key
O overhang with respect to the reference area in m;
v
W width of the reference area in m;
H luminaire mounting height in m;
δ angle of tilt of the luminaire for calculation;
U(B ) utilance as interpolated for the angle B
x x
1 vertical plane B = 0°
2 reference area
Figure 1 — Basic position of reference area relative to row of luminaires
Once the plane angles B and B have been calculated for a given installation geometry the resulting
1 2
utilance can be calculated by interpolation between tabulated utilances given as function of angle B.
For B - δ ≥ 0 and B - δ > 0;
1 2
U = U (B - δ) - U (B - δ); (2)
2 1
For B - δ < 0 and B - δ ≥ 0;
1 2
U = U (B - δ) + U (B - δ); (3)
2 1
For B - δ < 0 and B - δ ≤ 0;
1 2
U = U (B - δ) - U (B - δ); (4)
1 2
where
...
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