Acoustics - Noise from shooting ranges - Part 1: Determination of muzzle blast by measurement (ISO 17201-1:2005)

ISO 17201-1:2005 specifies a method to determine the acoustic source energy of the muzzle blast for calibres of less than 20 mm or explosive charges of less than 50 g TNT equivalent. It is applicable at distances where peak pressures less than 1 kPa (equivalent to a peak sound pressure level of 154 dB) are observed. The source energy, directivity of the source and their spectral structure determined by this procedure can be used as input data to sound propagation programmes, enabling prediction of shooting noise in the neighbourhood of shooting ranges. Additionally, the data can be used to compare sound emission from different types of guns or different types of ammunition used with the same gun.
ISO 17201-1:2005 is applicable to guns used in civil shooting ranges but it can also be applied to military guns. It is not applicable to the assessment of hearing damage or sound levels in the non-linear region.

Akustik - Geräusche von Schießplätzen - Teil 1: Bestimmung des Mündungsknalls durch Messung (ISO 17201-1:2005)

Dieser Teil von ISO 17201 legt ein Verfahren zur Bestimmung der akustischen Schallenergie des Mündungsknalls für Kaliber kleiner als 20 mm und Treibladungen von weniger als 50 g TNT-Äquivalent fest. Das Verfahren ist in Entfernungen anwendbar, in denen Spitzenwerte der Schalldrücke von weniger als 1 kPa (?154 dB) beobachtet werden. Die nach diesem Verfahren ermittelte Schallenergie, die Richtwirkung der Quelle und deren spektrale Zusammensetzung können als Eingangsdaten für Schallausbreitungsprogramme verwendet werden, mit denen die Prognose von Schießgeräuschen in der Nachbarschaft von Schießplätzen ermöglicht wird. Zusätzlich können die Daten zum Vergleich der Schallemission verschiedener Arten von Schusswaffen oder verschiedener Arten von Munition mit derselben Waffe verwendet werden.
Dieser Teil von ISO 17201 ist anwendbar für Schusswaffen ziviler Schießplätze und kann auch auf militärische Schusswaffen angewendet werden. Er ist nicht anwendbar zur Beurteilung von Gehörschädigungen oder Schallpegeln innerhalb des nichtlinearen Bereichs

Acoustique - Bruit des stands de tir - Partie 1: Mesurage de l'énergie sonore en sortie de bouche (ISO 17201-1:2005)

L'ISO 17201-1:2005 spécifie une méthode permettant de déterminer l'énergie sonore émise en sortie de bouche pour des armes de calibres inférieurs à 20 mm ou des charges explosives de moins de 50 g d'équivalent TNT. Elle est applicable à des distances où les valeurs de crête de pression acoustique observées sont inférieures à 1 kPa (équivalent à un niveau de pression acoustique de crête de 154 dB). L'énergie sonore émise, la directivité de la source et leur structure spectrale, déterminées par ce mode opératoire, peuvent être utilisées en tant que données d'entrée pour les modes de propagation du son permettant la prédiction du bruit généré par les tirs au voisinage des stands de tir. En outre, les données peuvent servir à comparer le bruit émis par différents types d'armes ou différents types de munitions utilisées par la même arme.
L'ISO 17201-1:2005 concerne les armes utilisées dans les stands de tir mais elle peut également s'appliquer aux armes utilisées à usage militaire. Elle n'est pas applicable pour les besoins d'une évaluation des dommages auditifs ou des niveaux sonores dans la zone non linéaire.

Akustika – Hrup strelskih poligonov – 1. del: Določanje poka strelnih orožij z merjenjem (ISO 17201-1:2005)

General Information

Status
Withdrawn
Publication Date
31-Oct-2005
Withdrawal Date
03-Feb-2019
Technical Committee
Current Stage
9900 - Withdrawal (Adopted Project)
Start Date
01-Feb-2019
Due Date
24-Feb-2019
Completion Date
04-Feb-2019

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SLOVENSKI STANDARD
SIST EN ISO 17201-1:2005
01-november-2005
$NXVWLND±+UXSVWUHOVNLKSROLJRQRY±GHO'RORþDQMHSRNDVWUHOQLKRURåLM]
PHUMHQMHP ,62
Acoustics - Noise from shooting ranges - Part 1: Determination of muzzle blast by
measurement (ISO 17201-1:2005)
Akustik - Geräusche von Schießplätzen - Teil 1: Bestimmung des Mündungsknalls durch
Messung (ISO 17201-1:2005)
Acoustique - Bruit des stands de tir - Partie 1: Mesurage de l'énergie sonore en sortie de
bouche (ISO 17201-1:2005)
Ta slovenski standard je istoveten z: EN ISO 17201-1:2005
ICS:
17.140.20 Emisija hrupa naprav in Noise emitted by machines
opreme and equipment
95.020 Vojaška tehnika. Vojaške Military engineering. Military
zadeve. Orožje affairs. Weapons
97.220.10 Športni objekti Sports facilities
SIST EN ISO 17201-1:2005 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 17201-1:2005

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SIST EN ISO 17201-1:2005
EUROPEAN STANDARD
EN ISO 17201-1
NORME EUROPÉENNE
EUROPÄISCHE NORM
August 2005
ICS 95.020; 17.140.20; 97.220.10

English Version
Acoustics - Noise from shooting ranges - Part 1: Determination
of muzzle blast by measurement (ISO 17201-1:2005)
Acoustique - Bruit des stands de tir - Partie 1: Mesurage de Akustik - Geräusche von Schießplätzen - Teil 1:
l'énergie sonore en sortie de bouche (ISO 17201-1:2005) Bestimmung des Mündungsknalls durch Messung (ISO
17201-1:2005)
This European Standard was approved by CEN on 31 July 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.
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.
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COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2005 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 17201-1:2005: E
worldwide for CEN national Members.

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SIST EN ISO 17201-1:2005

EN ISO 17201-1:2005 (E)





Foreword


This document (EN ISO 17201-1:2005) has been prepared by Technical Committee ISO/TC 43
"Acoustics" in collaboration with Technical Committee CEN/TC 211 "Acoustics", the secretariat
of which is held by DS.

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 February 2006, and conflicting national
standards shall be withdrawn at the latest by February 2006.

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.



Endorsement notice

The text of ISO 17201-1:2005 has been approved by CEN as EN ISO 17201-1:2005 without any
modifications.

2

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SIST EN ISO 17201-1:2005

INTERNATIONAL ISO
STANDARD 17201-1
First edition
2005-08-01


Acoustics — Noise from shooting
ranges —
Part 1:
Determination of muzzle blast by
measurement
Acoustique — Bruit des stands de tir —
Partie 1: Mesurage de l'énergie sonore en sortie de bouche





Reference number
ISO 17201-1:2005(E)
©
ISO 2005

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SIST EN ISO 17201-1:2005
ISO 17201-1:2005(E)
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©  ISO 2005
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ii © ISO 2005 – All rights reserved

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SIST EN ISO 17201-1:2005
ISO 17201-1:2005(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 1
4 Gun and ammunition. 5
4.1 General. 5
4.2 Gun. 5
4.3 Ammunition . 6
4.4 Ballistic parameters. 6
4.5 Test situation. 7
4.6 Other features . 7
5 Basic concept for measurement and analysis . 8
5.1 General. 8
5.2 Quantity to be measured. 8
5.3 Angular source energy distribution level. 10
5.4 Interpolated angular source energy distribution level. 10
5.5 Source energy level. 11
5.6 Directivity. 11
6 Measurement site. 11
6.1 Site. 11
6.2 Weather conditions. 11
7 Measurement planning. 12
7.1 General remarks. 12
7.2 Gun. 12
7.3 Measurement position. 12
7.4 Measurement equipment . 12
7.5 Dealing with projectile sound. 13
8 Calibration and validation. 13
9 Measurement procedures . 13
9.1 General. 13
9.2 Ground reflection correction . 14
10 Control of measurement layout. 14
11 Measurement uncertainty . 14
11.1 General. 14
11.2 Empirical part . 15
12 Report . 16
Annex A (informative) Small arms glossary . 17
Annex B (informative) Example . 30
Annex C (informative) Guidance on the measurement uncertainty. 37
Bibliography . 40

© ISO 2005 – All rights reserved iii

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SIST EN ISO 17201-1:2005
ISO 17201-1:2005(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 17201-1 was prepared by Technical Committee ISO/TC 43, Acoustics, Subcommittee SC 1, Noise.
ISO 17201 consists of the following parts, under the general title Acoustics — Noise from shooting ranges:
⎯ Part 1: Determination of muzzle blast by measurement
⎯ Part 2: Estimation of muzzle blast and projectile sound by calculation
⎯ Part 4: Prediction of projectile sound
The following parts are under preparation:
⎯ Part 3: Guidelines for sound propagation calculation
⎯ Part 5: Noise management
The initiative to prepare a standard on impulse noise from shooting ranges was taken by AFEMS, the
Association of European Manufacturers of Sporting Ammunition, in April 1996, by the submission of a formal
proposal to CEN. After consultation in CEN in 1998, CEN/TC 211, Acoustics, asked ISO/TC 43/SC 1, Noise,
to prepare the ISO 17201 series.
iv © ISO 2005 – All rights reserved

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SIST EN ISO 17201-1:2005
ISO 17201-1:2005(E)
Introduction
To obtain reliable data for the prediction of shooting sound levels at a reception point, the energy of sound
emission produced by the muzzle blast is needed. The muzzle blast is produced by the propellant gas
expelled from the barrel of a weapon; in most cases the gas has a supersonic fluid speed. Close to the muzzle,
the sound pressure is very high and cannot be described with linear acoustics. For the purposes of this part of
ISO 17201, the non-linear region is defined by the observation of a peak sound pressure level of 154 dB or
more. This part of ISO 17201 defines how the sound source energy and directivity of the muzzle blast can be
obtained from the measurement of sound exposure levels and how these measurements are to be carried out.
The source energy, its directivity and spectral structure may be used as input for sound propagation models
for environmental noise assessment. This cannot be used for calculations of sound exposure levels close to
the weapon, for instance to estimate injury to people or animals.

© ISO 2005 – All rights reserved v

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SIST EN ISO 17201-1:2005

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SIST EN ISO 17201-1:2005
INTERNATIONAL STANDARD ISO 17201-1:2005(E)

Acoustics — Noise from shooting ranges —
Part 1:
Determination of muzzle blast by measurement
1 Scope
This part of ISO 17201 specifies a method to determine the acoustic source energy of the muzzle blast for
calibres of less than 20 mm or explosive charges of less than 50 g TNT equivalent. It is applicable at
distances where peak pressures less than 1 kPa (equivalent to a peak sound pressure level of 154 dB) are
observed. The source energy, directivity of the source and their spectral structure determined by this
procedure can be used as input data to sound propagation programmes, enabling prediction of shooting noise
in the neighbourhood of shooting ranges. Additionally, the data can be used to compare sound emission from
different types of guns or different types of ammunition used with the same gun.
This part of ISO 17201 is applicable to guns used in civil shooting ranges but it can also be applied to military
guns. It is not applicable to the assessment of hearing damage or sound levels in the non-linear region.
2 Normative references
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.
ISO 9613-1, Acoustics — Attenuation of sound during propagation outdoors — Part 1: Calculation of the
absorption of sound by the atmosphere
IEC 60942:2003, Electroacoustics — Sound calibrators
1)
IEC 61672-1:2002, Electroacoustics — Sound level meters — Part 1: Specifications
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
instantaneous sound pressure
p
total instantaneous pressure at a point, in the presence of a sound wave, minus the atmospheric pressure at
that point
NOTE The instantaneous sound pressure is expressed in pascals.

1) Amalgamated revision of IEC 60651 and IEC 60804.
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SIST EN ISO 17201-1:2005
ISO 17201-1:2005(E)
3.2
sound pressure level
L
p
ten times the logarithm to the base of 10 of the square of the ratio of a given root-mean-square sound
pressure to the reference sound pressure
NOTE 1 The reference sound pressure is 20 µPa.
NOTE 2 The sound pressure level is expressed in decibels.
NOTE 3 The sound pressure level can be frequency weighted and time weighted.
3.3
peak sound pressure
p
peak
maximum absolute value of the instantaneous sound pressure during a stated time interval
NOTE The peak sound pressure is expressed in pascals.
3.4
peak sound pressure level
L
peak
ten times the logarithm to the base of 10 of the square of the ratio of the peak sound pressure to the reference
sound pressure of 20 µPa
NOTE The peak sound pressure level is expressed in decibels.
3.5
event duration
T
stated time interval, long enough to encompass all significant sound of a stated event
NOTE The event duration is expressed in seconds.
3.6
sound exposure
E
time integral of frequency-weighted squared instantaneous sound pressure
2
E = pt dt (1)
()

T
2
NOTE The sound exposure is expressed in pascal-squared seconds (Pa s).
3.7
sound exposure level
L
E
ten times the logarithm to the base 10 of the ratio of the sound exposure, E, to the reference sound exposure,
E , the sound exposure being the time integral of the time-varying square of the frequency-weighted
0
instantaneous sound pressure over a stated time interval, T, or an event
⎛⎞E
L = 10 lg dB (2)
E ⎜⎟
E
0
⎝⎠
NOTE E is equal to the square of the reference sound pressure of 20 µPa multiplied by the time interval of 1 s
0
2
(400 µPa ·1 s).
2 © ISO 2005 – All rights reserved

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SIST EN ISO 17201-1:2005
ISO 17201-1:2005(E)
3.8
source energy
Q
total sound source energy of the event
NOTE 1 The source energy is expressed in joules.
NOTE 2 The reference to 1 s yields the sound power L of a repeated event as defined in ISO 9613-2.
W
3.9
source energy level
L
Q
ten times the logarithm to the base 10 of the ratio of source energy, Q, to the reference source energy, Q
0
⎛⎞
Q
L = 10 lg dB (3)
⎜⎟
Q
Q
⎝⎠0
where
−12
Q = 10 J
0
NOTE The source energy level is expressed in decibels.
3.10
angular source energy distribution
S ()α
q
acoustic energy radiated from the source into the far field, per unit solid angle
NOTE 1 The acoustic energy radiated by the source within a narrow cone centred on the direction α is
dQ
S ()α = (4)
q
dΩ
NOTE 2 Ω is the solid angle expressed in steradians.
−1
NOTE 3 The angular source energy distribution S ()α is expressed in joules per steradian (J⋅sr ).
q
NOTE 4 Rotational symmetry is assumed around the line with α = 0.
3.11
interpolated angular source energy distribution
S ()α
q
continuous function in α of the source energy distribution S (α ) , derived by using a defined interpolation
q
method
−1
NOTE The interpolated angular source energy distribution, S ()α , is expressed in joules per steradian (J⋅sr ).
q
3.12
angular source energy distribution level
L ()α
q
–12
angular source energy distribution as a level relative to 10 J
⎛⎞
S ()α
q
L ()α =10lg⎜⎟ dB (5)
q
⎜⎟
S ()α
q
⎝⎠0
where
−−12 1
S ()α=⋅10 J sr
q
0
NOTE The angular source energy distribution level, L ()α , is expressed in decibels.
q
© ISO 2005 – All rights reserved 3

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SIST EN ISO 17201-1:2005
ISO 17201-1:2005(E)
3.13
interpolated angular source energy distribution level
L ()α
q
continuous function in α of the angular source energy distribution level, L ()α , derived by using a defined
q
interpolation method
NOTE The interpolated angular source energy distribution level is expressed in decibels.
3.14
angle alpha
α
angle between the line of fire and a line from the muzzle to the receiver (see Figure 3)
NOTE The angle alpha is expressed in radians in all formulae.
3.15
angle beta
β
angle describing the rotation around the line of fire, anticlockwise from the view of the shooter, as the angle
between the horizontal plane intersecting the muzzle from the right-hand side (see Figure 3)
NOTE The angle beta is expressed in radians in all formulae.
3.16
angle gamma
γ
angle describing the inclination of the line of fire from the horizontal plane (see Figure 3)
NOTE The angle gamma is expressed in radians in all formulae.
3.17
angle delta
δ
angle constituted by the projection of angle α on the horizontal plane (see Figure 3)
NOTE The angle delta is expressed in radians in all formulae.
3.18
directivity
D()α
difference between the angular source energy distribution level of the source under test and the source
energy distribution level of a monopole source with the same acoustic source energy
NOTE The directivity is expressed in decibels.
3.19
muzzle distance
r
m
distance measured from the muzzle to the microphone point (see Figure 3)
NOTE The distance is expressed in metres.
4 © ISO 2005 – All rights reserved

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SIST EN ISO 17201-1:2005
ISO 17201-1:2005(E)
4 Gun and ammunition
4.1 General
The information given in 4.2 to 4.6 is needed to unambiguously define the weapon plus ammunition
combination for which the sound exposure level of the muzzle blast is estimated (items marked by an asterisk
are mandatory). All terms have the meanings given in Reference [1] and Annex A.
4.2 Gun
The following features shall be stated:
⎯ *description or brand name;
⎯ *type of gun (shot gun, rifle, revolver, pistol, etc.);
⎯ number, type and disposition of barrels (side-to-side, superposed, drilling, etc.);
⎯ calibre;
⎯ *barrel bore;
⎯ *barrel length.
Figure 1 is a schematic view and gives the main terms used to describe the gun.

Key
1 stock 7 front sight
2 trigger guard 8 rear sight
3 trigger 9 bolt
4 magazine (inside) 10 receiver
5 barrel 11 safety lock
6 muzzle 12 bolt handle
Figure 1 — Main terms used to describe the gun (schematic view)
The main parts of smooth-bore barrel and a rifled barrel are given in Annex A.
Special features such as
⎯ choke,
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SIST EN ISO 17201-1:2005
ISO 17201-1:2005(E)
⎯ reload system,
⎯ *flame shield, and
⎯ *muzzle brake
should be mentioned.
4.3 Ammunition
The following information is needed:
⎯ *description or brand name;
⎯ *projectile calibre;
⎯ type and mass or chemical energy of propellant;
⎯ type of projectile (ball, pellets or blank);
⎯ *projectile mass.
In the case of shot guns:
⎯ total length of the cartridge;
⎯ type of tube;
⎯ type of wad;
⎯ *type, number, size and weight or type-number of pellets;
⎯ type of crimping.
Schematic views of bullet projectiles and shot gun cartridges are shown in Figure 2 with the names of their
main components.
4.4 Ballistic parameters
State parameters like
⎯ *muzzle speed (speed of the projectile close to the muzzle),
as result of a gun/ammunition combination as specified by the manufacturer.
NOTE Muzzle speed is a calculated value that corresponds to the speed of the projectile itself for rifles, or to
the speed of the centre of gravity of the cloud of pellets close to the muzzle of a shot gun.
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SIST EN ISO 17201-1:2005
ISO 17201-1:2005(E)

Key
1 projectile (bullet) for rifle 6 tube
2 projectile (bullet) for pistol 7 shot pellets
3 case 8 plastic cylinder
4 powder 9 wad
5 primer 10 case head
NOTE The measurements can be influenced by conditions such as the heating of the barrel during repetitive
shooting, the temperature, the humidity and the age of the ammunition.
Figure 2 — Schematic view of bullet projectiles and a shot gun cartridge
4.5 Test situation
Any object that can cause reflections or shield the muzzle blast shall be mentioned. Such objects can, for
example, be a part of the weapon, the support of the weapon or part of this support. Also the gunman can be
seen as a part of the weapon system that can shield the muzzle blast. All these elements, which are
commonly used under normal operation of the weapon, shall be present during the measurement and should
be mentioned in the report. Other circumstances which may affect the noise source data should also be
reported. The gun shall be positioned as it would be under normal operating conditions. If the gun is put on a
high support and fired with a rope, the shielding effect of the gunman is not taken into account. Therefore it
should be ensured that the experimental set up is as close to normal operation conditions as possible (see
also 7.2).
4.6 Other features
All other information concerning the test conditions or anything that may affect measured source data shall be
reported.
EXAMPLES
⎯ the barrel in use in the case of a combination firearm, if the barrels have different features, especially bore,
⎯ special features, like silencers, muzzle brakes, etc., and
⎯ storage conditions of the ammunition (temperature, humidity, duration, etc.).
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SIST EN ISO 17201-1:2005
ISO 17201-1:2005(E)
5 Basic concept for measurement and analysis
5.1 General
For the measurement of the muzzle blast, it is assumed that radiation of sound is rotationally symmetrical
around the line of fire. This assumption is used to define spherical coordinates, r , α and β which are centred
m
at the muzzle. The angles are defined in Clause 3 and are shown in Figure 3.
As the muzzle blast can be directional, measurements may be carried out in a circle. The goal is to measure
the level and also the directivity pattern. An equal distance between measuring points makes it easier to use
interpolation algorithms to get a continuous function for directivity pattern.
The measurements and the analyses shall yield spectral information in at least octave bands (preferably in
one-third-octave-bands) from 31,5 Hz to 8 kHz.
The calculation method given in 5.2 to 5.6 applies to broadband analysis as well as octave-band or one-third-
octave-band analysis.
5.2 Quantity to be measured
The basic quantity to be measured is the sound exposure level measured at a distance r and angles α and β:
m
2
pr t,,αβ
()
m,
Lr ,,αβ = 10 lg dt dB (6)
()
E m

2
pT
00
T
Assuming rotational symmetry, the sound exposure level is a function of r and α alone.
m
However, due to ground reflections when measuring above ground, the sound exposure level L will also
E
depend on β. The corrections to remove ground reflections are described in 9.2. After the corrections, the
sound exposure level is assumed to depend on the distance r and angle α only.
m
8 © ISO 2005 – All rights reserved

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SIST EN ISO 17201-1:2005
ISO 17201-1:2005(E)

Key
1 gun
2 muzzle
3 microphone
4 line of fire
5 ground plane
NOTE If the height of the microphone above ground is not the same as the height of the gun above ground, the angle
α is not the same as the angle δ. The relation between these angles is given below for cases where the barrel is
positioned horizontally:
⎛⎞
r cos(δ )
⎜⎟p
α = arccos
⎜⎟
22
⎜⎟rh+−()h
pm g
⎝⎠
where
r is the projected distance on the ground plane from the muzzle to the microphone;

p
r is the distance from the muzzle to the microphone;

m
h is the height of the microphone above ground;
m
h is the height of the muzzle of the gun above ground.
g
Figure 3 — Angles α, β, γ and δ
© ISO
...

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