# 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)

ISO 17201-4:2006 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.

ISO 17201-4:2006 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.

## 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.

---------------------- Page: 1 ----------------------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 undGeschossgeräusches 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.---------------------- Page: 2 ----------------------

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 noticeThe text of ISO 17201-4:2006 has been approved by CEN as EN ISO 17201-4:2006 without any

modifications.---------------------- Page: 3 ----------------------

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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electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or

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Published in Switzerland

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---------------------- Page: 6 ----------------------

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

calculationISO 17201-1, Acoustics — Noise from shooting ranges — Part 1: Determination of muzzle blast by

measurementGuide 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.

3.1streamlined 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 < lNOTE For the definition of effective projectile length, l , see 3.2.

3.2

effective projectile length

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)

d maximum diameter of projectile (m)

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

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.

3.5characteristic frequency

inverse of the duration time, T

f =

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 fireNOTE 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

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 turbulenceNOTE The coherence distance is expressed in metres (m).

3.8

Mach number

ratio of projectile speed to local sound speed

3.9

source sound exposure level

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

speed of the projectile at the muzzle

NOTE The muzzle velocity is expressed in metres per second (m/s).

3.12

projectile speed

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.

3.13end speed

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 propagationNOTE The fluctuating effective sound speed is expressed in metres per second (m/s).

3.16standard deviation of the fluctuating acoustical index of refraction

standard deviation of the ratio of the reference sound speed to the fluctuating effective sound speed

2 –5NOTE In accordance with [5], a value of µ = 10 is used within the context of this part of ISO 17201 [see

Equation (12)].3.17

projectile speed change

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 egiven by Equation (2):

⎛⎞ ⎛⎞

am am

ξξ==arccos⎜⎟ and arccos⎜⎟ (2)

⎜⎟ ⎜⎟

p0 pe

⎝⎠ ⎝⎠

where

v is the projectile speed at the end of the trajectory, in metres per second (m/s);

c is the speed of sound in metres per second (m/s).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

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

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

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):

xx−⋅v+κκx+c ⋅v+ x−c =c y() ( )

sp0 s am p0 s am am

(4)

cv−

am p0

with 0< 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):

⎛⎞ 94d ⎢⎥

p M

LL=+10 lg dB+ 10 lg dB (5)

E,s,bb 0

34 9/4 3 4

⎝⎠ M −1

where

L [re (20 µPa) s] = 161,9 dB (see A.2);

M = v/c the local Mach number of the projectile at the source point with the projectile speed

determined from Equation (1) and the speed of sound from Equation (3) for theambient air temperature applicable to the prediction of the sound source exposure

level for the projectile;r = 1 m.

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).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

higher frequencies:M −1

() l

ff= (6)

34 14

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).

NOTE Equation (6) shows that the characteristic frequency, f , decreases as distance, r, increases. This is a

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-

band filters, and with the characteristic frequency, f , calculated according to Equation (6), the one-third-

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

Cf=+2,5 db 28 lg dB if < 0,65f (8)

ii c

⎝⎠c

Cf=−5,0 dB − 12 lg dB if W 0,65f (9)

ii c

C 10

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 = 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 iaccount 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 iand 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

divdivergence 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

nlinprojectile sound near the source point, expressed in decibels;

A (f) is the attenuation caused by absorption processes in the atmosphere as the sound

atm ipropagates 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 irefraction 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.

divIn region II, the geometric attenuation varies between 10 lg (r/r ) dB and 25 lg (r/r ) dB, where r is the

0 0distance 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

cohdominates. 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 .

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

⎡⎤3

ll M −1

0t()

(1Ml−)()2

1 2

⎪⎪t

R = min , (12)

coh

222

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

where the local Mach number has decreased to 1,01, expressed in metres (m);l = 1,1 m, see bibliographical reference [5];

2 –5

µ = 10 ;

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

metres per second (m/s).The geometric attenuation for region II is given by Equations (13) and (14):

rk+−r M 1

( )

A = 10 lg dB for r < R (13)

div,II coh

rk+−r M 1

00()

Rk+−R M 1

coh coh ⎛⎞

A=+10 lg dB 25 lg dB for r W R (14)

div,II coh

coh

rk+−r M 1 ⎝⎠

00()

where

k = –κ /c ;

r = 1 m.

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 2max()rR,

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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