SIST EN ISO 17201-4:2006
(Main)Acoustics - Noise from shooting ranges - Part 4: Prediction of projectile sound (ISO 17201-4:2006)
Acoustics - Noise from shooting ranges - Part 4: Prediction of projectile sound (ISO 17201-4:2006)
This part of ISO 17201 provides a computational model for determining the acoustical source level of projectile sound and its one-third-octave-band spectrum, expressed as the sound exposure level for nominal mid-band frequencies from 12,5 Hz to 10 kHz. It also gives guidance on how to use this source level to calculate the sound exposure level at a receiver position. This part of ISO 17201 is intended for calibres of less than 20 mm, but can also be applied for large calibres. Additionally, the data can be used to compare sound emission from different types of ammunition used with the same weapon. This part of ISO 17201 is meant for weapons used in civil shooting ranges, but is also applicable to military weapons. The computational method can be used as a basis for environmental noise assessment studies. The prediction method applies to outdoor conditions, straight projectile trajectories, and streamlined projectile shapes. Because of the latter, it cannot be applied to pellets. Default values of parameters used in this part of ISO 17201 are given for a temperature of 10 °C, 80 % relative humidity, and a pressure of 1 013 hPa. Annex A can be used for calculations in other atmospheric conditions. Particularly for calibres 20 mm, the spectrum is dominated by high frequency components. As air absorption is rather high for these frequency components, calculations are performed in one-third-octave-bands, in order to allow a more accurate result for air absorption to be obtained.
Akustik - Geräusche von Schießplätzen - Teil 4: Abschätzung des Geschossgeräusches (ISO 17201-4:2006)
Dieser Teil von ISO 17201 stellt ein Rechenmodell zur Bestimmung des Schallpegels des Geschossgeräusches und dessen Terzspektrum, ausgedrückt als Schallexpositionspegel für Bandmittenfrequenzen von 12,5 Hz bis 10 kHz, bereit. Außerdem werden Leitlinien angegeben, wie dieser Quellpegel zur Berechnung des Schallexpositionspegels am Empfangsort angewendet werden kann.
Dieser Teil von ISO 17201 ist für Kaliber unter 20 mm bestimmt. Dieser Teil kann jedoch auch bei großen Kalibern angewendet werden. Außerdem können die Daten genutzt werden, um die Schallemission unterschiedlicher Munitionsarten zu vergleichen, die in derselben Waffe verwendet werden. Dieser Teil von ISO 17201 ist für Waffen vorgesehen, die auf zivilen Schießplätzen eingesetzt werden, sie kann jedoch auch auf Militärwaffen angewendet werden.
Das Berechnungsverfahren kann als Grundlage für Untersuchungen zur Bewertung von Umgebungsgeräuschen angewendet werden.
Das Prognoseverfahren gilt im Freien, gerade Geschossflugbahnen und stromlinienförmige Projektile. Auf Grund der letztgenannten Bedingung kann die Norm nicht auf Schrote angewendet werden. Die in diesem Teil von ISO 17201 verwendeten Parameter Standardwerte sind für eine Temperatur von 10 °C, eine relative Feuchte von 80 % und einen Druck von 1 013 hPa angegeben. Anhang A kann für Berechnungen bei anderen atmosphärischen Bedingungen angewendet werden. Besonders bei Kalibern unter 20 mm herrschen im Spektrum hochfrequente Komponenten vor. Da die Luftabsorption bei diesen Frequenzkomponenten relativ hoch ist, werden die Berechnungen in Terzbändern durchgeführt, um ein genaueres Ergebnis für die Luftabsorption zu erhalten.
Acoustique - Bruit des stands de tir - Partie 4: Estimation du bruit du projectile (ISO 17201-4:2006)
L'ISO 17201-4:2006 fournit un modèle de calcul permettant de déterminer le niveau d'émission acoustique du bruit du projectile et son spectre de tiers d'octave exprimé en tant que niveau d'exposition sonore pour des fréquences nominales à mi-bande comprises entre 12,5 Hz et 10 kHz. Elle donne également des lignes directrices sur la manière d'utiliser ce niveau d'émission pour calculer le niveau d'exposition sonore à l'emplacement du récepteur.
L'ISO 17201-4:2006 traite des calibres de moins de 20 mm, mais elle est également applicable à de plus gros calibres. Par ailleurs, les données peuvent permettre de comparer l'émission sonore de différents types de munitions utilisés avec la même arme. L'ISO 17201-4:2006 est destinée aux armes utilisées dans les stands de tir civils mais peut également s'appliquer aux armes militaires.
Akustika – Hrup strelskih poligonov - 4. del: Napoved zvoka izstrelka (ISO 17201-4:2006)
General Information
Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN ISO 17201-4:2006
01-julij-2006
Akustika – Hrup strelskih poligonov - 4. del: Napoved zvoka izstrelka (ISO 17201-
4:2006)
Acoustics - Noise from shooting ranges - Part 4: Prediction of projectile sound (ISO
17201-4:2006)
Akustik - Geräusche von Schießplätzen - Teil 4: Abschätzung des Geschossgeräusches
(ISO 17201-4:2006)
Acoustique - Bruit des stands de tir - Partie 4: Estimation du bruit du projectile (ISO
17201-4:2006)
Ta slovenski standard je istoveten z: EN ISO 17201-4:2006
ICS:
17.140.20
95.020
97.220.10
SIST EN ISO 17201-4:2006 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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EUROPEAN STANDARD
EN ISO 17201-4
NORME EUROPÉENNE
EUROPÄISCHE NORM
April 2006
ICS 95.020; 17.140.20; 97.220.10
English Version
Acoustics - Noise from shooting ranges - Part 4: Prediction of
projectile sound (ISO 17201-4:2006)
Acoustique - Bruit des stands de tir - Partie 4: Estimation Akustik - Geräusche von Schießplätzen - Teil 4:
du bruit du projectile (ISO 17201-4:2006) Bestimmung des Mündungsknalls und
Geschossgeräusches durch Berechnung (ISO 17201-
4:2006)
This European Standard was approved by CEN on 23 March 2006.
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, Romania,
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 B-1050 Brussels
© 2006 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 17201-4:2006: E
worldwide for CEN national Members.
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EN ISO 17201-4:2006 (E)
Foreword
This document (EN ISO 17201-4:2006) 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 October 2006, and conflicting national
standards shall be withdrawn at the latest by October 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, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
Endorsement notice
The text of ISO 17201-4:2006 has been approved by CEN as EN ISO 17201-4:2006 without any
modifications.
2
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INTERNATIONAL ISO
STANDARD 17201-4
First edition
2006-04-01
Acoustics — Noise from shooting
ranges —
Part 4:
Prediction of projectile sound
Acoustique — Bruit des stands de tir —
Partie 4: Estimation du bruit du projectile
Reference number
ISO 17201-4:2006(E)
©
ISO 2006
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ISO 17201-4:2006(E)
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ii © ISO 2006 – All rights reserved
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ISO 17201-4:2006(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 2
4 Regions. 5
5 Source description . 6
5.1 Source point . 6
5.2 Source sound exposure level. 6
6 Guidelines for calculating sound exposure levels at receiver locations. 8
6.1 Basic equation . 8
6.2 Calculation of the attenuation terms . 8
7 Uncertainty in source description and propagation . 12
Annex A (informative) Derivation of constants and consideration of barrier and other effects. 13
Annex B (informative) Guidance on prediction uncertainty . 17
Bibliography . 19
© ISO 2006 – All rights reserved iii
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ISO 17201-4:2006(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 17201-4 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 2006 – All rights reserved
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ISO 17201-4:2006(E)
Introduction
Shooting sound consists in general of three components: muzzle sound, impact sound and projectile sound.
This part of ISO 17201 deals solely with projectile sound, which only occurs if the projectile moves with
supersonic speed.
It specifies a method for calculating the source sound exposure level of projectile sound. It also gives
guidelines for calculating the propagation of projectile sound as far as it deviates from the propagation of
sound from other sources.
Projectile sound is described as originating from a certain point on the projectile trajectory, the “source point”.
The sound source exposure level is calculated from the geometric properties and the speed of the projectile
along the trajectory. As a result of non-linear effects, the frequency content of the projectile sound exposure
depends on the distance from the source point. This is taken into account. Guidance is given on how the
sound exposure level can be calculated from the sound exposure level at the receiver location, taking into
account geometrical attenuation, attenuation due to the non-linear effects, and atmospheric absorption. In
addition, the effects on the sound exposure level of the decrease of the projectile speed and of atmospheric
turbulence are taken into account.
Projectile sound exposure levels are significant compared to the muzzle sound exposure level in a restricted
region, the Mach region (region II — see Clause 4). Outside this region only diffracted or scattered projectile
sound is received, with considerably lower levels than in the Mach region. Projectile sound behind the Mach
region (region I) is negligible compared to muzzle sound. In this part of ISO 17201, a computational scheme
for the levels in regions II and III is provided. In the bibliographical reference [2], measurements and
calculations were compared for a set of calibres and distances, i.e. from the source point to the receiver
location. For this set, there is a slight tendency of an overestimation of the projectile sound: on average 1,8 dB,
A-weighted.
© ISO 2006 – All rights reserved v
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INTERNATIONAL STANDARD ISO 17201-4:2006(E)
Acoustics — Noise from shooting ranges —
Part 4:
Prediction of projectile sound
1 Scope
This part of ISO 17201 provides a computational model for determining the acoustical source level of
projectile sound and its one-third-octave-band spectrum, expressed as the sound exposure level for nominal
mid-band frequencies from 12,5 Hz to 10 kHz. It also gives guidance on how to use this source level to
calculate the sound exposure level at a receiver position.
This part of ISO 17201 is intended for calibres of less than 20 mm, but can also be applied for large calibres.
Additionally, the data can be used to compare sound emission from different types of ammunition used with
the same weapon. This part of ISO 17201 is meant for weapons used in civil shooting ranges, but is also
applicable to military weapons.
The computational method can be used as a basis for environmental noise assessment studies. The
prediction method applies to outdoor conditions, straight projectile trajectories, and streamlined projectile
shapes. Because of the latter, it cannot be applied to pellets. Default values of parameters used in this part of
ISO 17201 are given for a temperature of 10 °C, 80 % relative humidity, and a pressure of 1 013 hPa.
Annex A can be used for calculations in other atmospheric conditions. Particularly for calibres < 20 mm, the
spectrum is dominated by high frequency components. As air absorption is rather high for these frequency
components, calculations are performed in one-third-octave-bands, in order to allow a more accurate result for
air absorption to be obtained.
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 9613-2, Acoustics — Attenuation of sound during propagation outdoors — Part 2: General method of
calculation
ISO 17201-1, Acoustics — Noise from shooting ranges — Part 1: Determination of muzzle blast by
measurement
Guide to the expression of uncertainty in measurement (GUM). BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML,
first edition, 1993, corrected and reprinted in 1995.
© ISO 2006 – All rights reserved 1
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ISO 17201-4:2006(E)
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 17201-1 and the following apply.
3.1
streamlined projectile
body of revolution of which the first derivative of the cross-sectional area A(x) at a distance x behind the nose
of the body is continuous for 0 u x < l
p
NOTE For the definition of effective projectile length, l , see 3.2.
p
3.2
effective projectile length
l
p
distance between the nose and the cross-section with the maximum diameter of the projectile
See Figure 1.
NOTE The effective length of the projectile is measured along the length-axis of the projectile and is expressed in
metres (m).
Key
l effective projectile length (m)
p
d maximum diameter of projectile (m)
p
Figure 1 — Effective projectile length
3.3
N-wave
sound pressure having a variation with time described by a sudden initial increase to a maximum followed by
a linear decay to a minimum and ending with a sudden increase to the initial sound pressure
See Figure 2.
Key
t time
p sound pressure
Figure 2 — Assumed N-shaped waveform for sound of supersonic projectile
at 1 m from source point on projectile’s trajectory
2 © ISO 2006 – All rights reserved
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ISO 17201-4:2006(E)
3.4
duration time
T
c
time between two pressure increases of the N-wave
NOTE 1 The duration time is expressed in seconds (s).
NOTE 2 Resulting from the non-linear acoustic effects, T , for the N-wave along the sound path will change.
c
3.5
characteristic frequency
f
c
inverse of the duration time, T
c
1
f =
c
T
c
NOTE The characteristic frequency is expressed in Hertz (Hz).
3.6
coordinate system (x, y)
plane co-ordinate system describing geometry, where the x-axis denotes the line of fire with x = 0 at the
muzzle, and the y-axis measures the perpendicular distance from the line of fire in any plane around the line
of fire
NOTE 1 The sound field of projectile sound is rotational symmetric around the line of fire.
NOTE 2 The co-ordinates are given in metres (m).
3.7
coherence distance
R
coh
distance between the source point on the trajectory and a receiver beyond which the contribution of different
parts of the trajectory are incoherent due to atmospheric turbulence
NOTE The coherence distance is expressed in metres (m).
3.8
Mach number
M
ratio of projectile speed to local sound speed
3.9
source sound exposure level
L
E,s
sound exposure level expected at a distance of 1 m from the source point
NOTE 1 The source sound exposure level is expressed in decibels (dB).
NOTE 2 The reference distance of 1 m is “measured” in the direction of the receiver and not perpendicular to the
trajectory.
3.10
source point
point where a line from the receiver perpendicular to the wave front intersects the projectile trajectory
NOTE In this part of ISO 17201, the source point is used to represent the trajectory that in principle is a line source
[see Equation (4)].
© ISO 2006 – All rights reserved 3
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ISO 17201-4:2006(E)
3.11
projectile launch speed
v
p0
speed of the projectile at the muzzle
NOTE The muzzle velocity is expressed in metres per second (m/s).
3.12
projectile speed
v
p
speed of the projectile along the trajectory
NOTE 1 The projectile speed is expressed in metres per second (m/s).
NOTE 2 Published data on the projectile speed as a function of distance refer to air density at sea level. For other
elevations above sea level, changes of density could have to be taken into account.
3.13
end speed
v
pe
speed of the projectile as it hits the target or at the trajectory point where the Mach number is reduced to 1,01
NOTE The end speed is expressed in metres per second (m/s).
3.14
reference sound speed
adiabatic sound speed averaged over a period of at least 10 min
NOTE The reference sound speed is expressed in metres per second (m/s).
3.15
fluctuating effective sound speed
sum of the instantaneous adiabatic sound speed and the instantaneous horizontal wind velocity component in
the direction of the sound propagation
NOTE The fluctuating effective sound speed is expressed in metres per second (m/s).
3.16
standard deviation of the fluctuating acoustical index of refraction
µ
0
standard deviation of the ratio of the reference sound speed to the fluctuating effective sound speed
2 –5
NOTE In accordance with [5], a value of µ = 10 is used within the context of this part of ISO 17201 [see
0
Equation (12)].
3.17
projectile speed change
κ
local change of projectile speed along the trajectory per length unit of trajectory
NOTE 1 The speed change is expressed in reciprocal seconds [(m/s ⋅ m) = 1/s].
NOTE 2 It is negative for non-self-propelled projectiles.
4 © ISO 2006 – All rights reserved
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ISO 17201-4:2006(E)
4 Regions
The wave front originating from the nose of the projectile has the shape of a cone (see Figure 3). The
projectile speed decreases along the projectile trajectory. As a consequence, the wave front is curved. Three
regions (I, II and III) are distinguished (see Figure 3). In regions I and III considerably lower sound exposure
levels occur compared to those in region II. In this part of ISO 17201, a computational scheme for the sound
exposure levels in regions II and III is provided. The levels in region I are negligible in comparison to the
muzzle blast. The projectile speed is locally approximated by a linear function of the distance x along the
projectile trajectory, according to Equation (1):
vx=+v κx (1)
( )
pp0
The boundaries of region II are described with the angles ξ and ξ , shown in Figure 3. These angles are
0 e
given by Equation (2):
⎛⎞ ⎛⎞
cc
am am
ξξ==arccos⎜⎟ and arccos⎜⎟ (2)
0e
⎜⎟ ⎜⎟
vv
p0 pe
⎝⎠ ⎝⎠
where
v is the projectile speed at the end of the trajectory, in metres per second (m/s);
pe
c is the speed of sound in metres per second (m/s).
am
Key
1 weapon
2 source point
3 projectile trajectory
4 wavefront
5 target
6 projectile
7 receiver
Figure 3 — The three regions for describing the sound of a projectile
© ISO 2006 – All rights reserved 5
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ISO 17201-4:2006(E)
The speed of sound is a function of the absolute temperature of the ambient air, T , in Kelvin and is given by
am
Equation (3):
1/ 2
cc= T T (3)
()
am ref am ref
where
T = 283,15 K (10 °C);
ref
c = 337,6 m/s (the speed of sound at T ).
ref ref
When the projectile speed along the trajectory decreases below the speed of sound, the angle ξ becomes
e
zero; the region III vanishes in this case. The “target” is then replaced by the trajectory point where the Mach
number is reduced to 1,01.
5 Source description
5.1 Source point
The position of the source point (x , 0) for receivers in region II can be determined by iterative methods. For
s
straight trajectories this can be determined with the use of Equation (4). A co-ordinate system (x, y) is used,
with the x axis along the projectile trajectory and the origin at the muzzle, according to Equation (4):
2
22
xx−⋅v+κκx+c ⋅v+ x−c =c y
()
() ( )
sp0 s am p0 s am am
(4)
cv−
am p0
with 0<
ss
κ
where (x, y) is the position of the receiver.
In the case that the calculated source point lies beyond the target or for receivers in region III, the source
point is set at the target position.
5.2 Source sound exposure level
The (broadband) source sound exposure level, L , expressed in decibels, is given by the geometric
E,s,bb
[4]
properties of the projectile and its speed at the source point , according to Equation (5):
⎡⎤
3
⎛⎞ 94
d ⎢⎥
p M
⎜⎟
LL=+10 lg dB+ 10 lg dB (5)
⎢⎥
E,s,bb 0
34 9/4 3 4
⎜⎟
2
lr
⎢⎥
p0
⎝⎠ M −1
()
⎢⎥
⎣⎦
where
2
L [re (20 µPa) s] = 161,9 dB (see A.2);
0
M = v/c the local Mach number of the projectile at the source point with the projectile speed
am
determined from Equation (1) and the speed of sound from Equation (3) for the
ambient air temperature applicable to the prediction of the sound source exposure
level for the projectile;
r = 1 m.
0
6 © ISO 2006 – All rights reserved
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ISO 17201-4:2006(E)
In principle, the total length of the projectile can be used instead of the effective length to calculate the
(broadband) sound exposure level, but — to be consistent — then the total length should also be used to
calculate the shape factor K and from this the constant L (see Annex A).
0
When the Mach number approaches unity, the third term in Equation (5) becomes undeterminable. Therefore,
a lower limit of M = 1,01 is used in these expressions.
The spectrum of the projectile sound can be calculated as the Fourier transform of the N-wave. The one-third-
octave-band spectrum of the sound exposure level at a receiver position is assumed to have a single
characteristic frequency, f , determined in hertz, according to Equation (6), with spectral roll-offs to lower and
c
higher frequencies:
14
2
14
M −1
() l
r
p
0
ff= (6)
c0
34 14
d
Mr
p
where
r is the distance from the source point to the receiver in metres (m);
f is the reference frequency, equal to 175,2 Hz at 10 °C (see A.3).
0
NOTE Equation (6) shows that the characteristic frequency, f , decreases as distance, r, increases. This is a
c
consequence of pulse broadening due to non-linear effects.
Over the range of nominal mid-band frequencies, f , from 12,5 Hz to 10 kHz for standard one-third-octave-
i
band filters, and with the characteristic frequency, f , calculated according to Equation (6), the one-third-
c
octave-band spectrum of the sound source exposure level is given by Equation (7):
Lf=+L C−C (7)
()
Ei,s E,s,bb i tot
where
⎛⎞
f
i
Cf=+2,5 db 28 lg dB if < 0,65f (8)
⎜⎟
ii c
f
⎝⎠c
⎛⎞
f
i
Cf=−5,0 dB − 12 lg dB if W 0,65f (9)
⎜⎟
ii c
f
c
⎝⎠
40
dB
C 10
i
C = 10 lg 10 dB (10)
tot ∑
i=11
and where
i/10
f = 10 Hz, is the nominal mid-band frequency of the one-third-octave band (12,5 Hz to 10 kHz,
i
i = 11 represents a mid-band frequency of 12,5 Hz, and i = 40 represents a mid-band frequency of
10 kHz).
© ISO 2006 – All rights reserved 7
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ISO 17201-4:2006(E)
6 Guidelines for calculating sound exposure levels at receiver locations
6.1 Basic equation
The one-third-octave-band-spectrum of the sound exposure level at the receiver location, L (f ), needs to
E,r i
account for the attenuation caused by various factors that reduce the amplitude of the sound as it propagates
over the path from the 1 m reference distance to the location of the receiver at distance r. The following
expression accounts for the principal factors that need to be considered.
L (fL)=−()f A−A−A ()f−A (f) (11)
E,riE,si div nlin atmi excessi
where
L (f ) is the one-third-octave-band sound source exposure level at nominal mid-band frequency f
E,s i i
and at the 1 m reference distance from the source point [see Equation (7)], expressed in
decibels;
A is the attenuation of the level of the sound in a field free of reflections and resulting from the
div
divergence of the geometric area of the wave front as the distance increases from the 1 m
reference distance, expressed in decibels;
A is the attenuation caused by non-linear effects associated with the large initial amplitude of
nlin
projectile sound near the source point, expressed in decibels;
A (f) is the attenuation caused by absorption processes in the atmosphere as the sound
atm i
propagates over the path from the 1 m reference distance to the location of the receiver,
expressed in decibels;
A (f ) is the excess attenuation including losses due to the interaction with the ground, atmospheric
excess i
refraction and shielding by a barrier, expressed in decibels.
NOTE As the projectile sound propagates from the 1 m reference distance to a receiver at distance r, the attenuation
includes losses resulting from interaction of the sound wave with the surface of the ground, refraction or bending of the
sound path caused by gradients in the vertical profile of the sound speed of the air, and shielding by a barrier. ISO 9613-2
provides guidance on appropriate procedures to account for the additional attenuation terms in a prediction of projectile
sound. Guidance is given in A.4 for the approximation of the barrier effect.
6.2 Calculation of the attenuation terms
6.2.1 Geometric attenuation
For the computation of the geometric attenuation, A , receiver positions in regions II and III are distinguished.
div
In region II, the geometric attenuation varies between 10 lg (r/r ) dB and 25 lg (r/r ) dB, where r is the
0 0
distance from the source point to the receiver, as the consequence of two effects:
a) effect of the decrease of the projectile speed along the trajectory;
b) effect of atmospheric turbulence.
At short distances the first effect is dominant. After some coherence distance (R ), the second effect
coh
dominates. At distances greater than 10 km from the source point on the projectile trajectory, the attenuation
[5]
approaches the spherical limit 20 lg (r/r ) dB .
0
8 © ISO 2006 – All rights reserved
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ISO 17201-4:2006(E)
The coherence distance, R , in metres, is given by Equation (12):
coh
1/ 3
⎧⎫
22
⎡⎤3
2
2
ll M −1
⎪⎪
0t()
(1Ml−)()2
1 2
⎪⎪t
⎢⎥
R = min , (12)
⎨⎬
coh
⎢⎥
222
π
Mc /f M µ
⎪⎪
am c 0
⎢⎥
⎣⎦
⎪⎪
⎩⎭
where
l is the total length of the trajectory calculated for Equation (12), either to the target or to the point
t
where the local Mach number has decreased to 1,01, expressed in metres (m);
l = 1,1 m, see bibliographical reference [5];
0
2 –5
µ = 10 ;
0
M is the local Mach number at the location of the source point;
c is the speed of sound at the temperature of interest for ambient air, see Equation (3), expressed in
am
metres per second (m/s).
The geometric attenuation for region II is given by Equations (13) and (14):
22
⎡⎤
rk+−r M 1
( )
⎢⎥
A = 10 lg dB for r < R (13)
div,II coh
⎢⎥
22
rk+−r M 1
00()
⎢⎥
⎣⎦
22
⎡⎤
Rk+−R M 1
()
coh coh ⎛⎞
r
⎢⎥
A=+10 lg dB 25 lg dB for r W R (14)
⎜⎟
div,II coh
⎢⎥
22
R
coh
rk+−r M 1 ⎝⎠
00()
⎢⎥
⎣⎦
where
k = –κ /c ;
am
r = 1 m.
0
In region III, in front of the weapon, the geometric attenuation of projectile sound is approximated by a sum of
two terms, according to Equation (15), with distances r and r as shown in Figure 4:
1 2
⎡⎤
max()rR,
r
20
1
AA==()rr+20lg dBwithR=2+ (15)
⎢⎥
div,III div,II 1 0
R 100
⎢⎥0
⎣⎦
The first term on the right hand side of Equation (15) is the geometric attenuation calculated according to
Equation (13) or Equation (14), as appropriate for a location on the boundary between region II and region III
and at the distance r that is closest to the location of the receiver in region III. The additional contribution
...
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