EN ISO 17201-4:2025

SLOVENSKI STANDARD
01-oktober-2025
Nadomešča:
SIST EN ISO 17201-4:2006
Akustika - Hrup s strelišč - 4. del: Izračun zvoka izstrelka (ISO 17201-4:2025)
Acoustics - Noise from shooting ranges - Part 4: Calculation of projectile sound (ISO
17201-4:2025)
Akustik - Geräusche von Schießplätzen - Teil4: Berechnung des Geschossgeräusches
(ISO 17201-4:2025)
Acoustique - Bruit des stands de tir - Partie 4: Calcul du bruit du projectile (ISO 17201-
4:2025)
Ta slovenski standard je istoveten z: EN ISO 17201-4:2025
ICS:
17.140.20 Emisija hrupa naprav in Noise emitted by machines
opreme and equipment
95.020 Vojaštvo na splošno Military in general
97.220.10 Športni objekti Sports facilities
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 17201-4
EUROPEAN STANDARD
NORME EUROPÉENNE
August 2025
EUROPÄISCHE NORM
ICS 17.140.20; 95.020; 97.220.10 Supersedes EN ISO 17201-4:2006
English Version
Acoustics - Noise from shooting ranges - Part 4:
Calculation of projectile sound (ISO 17201-4:2025)
Acoustique - Bruit des stands de tir - Partie 4: Calcul du Akustik - Geräusche von Schießplätzen - Teil4:
bruit du projectile (ISO 17201-4:2025) Berechnung des Geschossgeräusches (ISO 17201-
4:2025)
This European Standard was approved by CEN on 11 July 2025.

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.

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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
© 2025 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 17201-4:2025 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
This document (EN ISO 17201-4:2025) 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 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 February 2026, and conflicting national standards
shall be withdrawn at the latest by February 2026.
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 supersedes EN ISO 17201-4:2006.
Any feedback and questions on this document should be directed to the users’ national standards
body/national committee. A complete listing of these bodies can be found on the CEN website.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and the
United Kingdom.
Endorsement notice
The text of ISO 17201-4:2025 has been approved by CEN as EN ISO 17201-4:2025 without any
modification.
International
Standard
ISO 17201-4
Second edition
Acoustics — Noise from shooting
2025-07
ranges —
Part 4:
Calculation of projectile sound
Acoustique — Bruit des stands de tir —
Partie 4: Calcul du bruit du projectile
Reference number
ISO 17201-4:2025(en) © ISO 2025

ISO 17201-4:2025(en)
© ISO 2025
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
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Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
ISO 17201-4:2025(en)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Projectile sound . 5
4.1 General .5
4.2 Regions .5
4.3 Spectrum of an N-wave .6
5 Source description . 7
5.1 Source point .7
5.2 Source sound exposure level for streamlined projectiles.7
5.3 Source sound exposure level for non-streamlined projectiles .8
5.4 Spectrum of the source sound exposure level .11
6 Calculating the sound exposure level at a receiver location .11
6.1 Basic formula .11
6.2 Calculation of the attenuation terms . 12
6.2.1 Geometric attenuation . 12
6.2.2 Non-linear attenuation . .14
6.2.3 Non-linear shift of the spectrum . 15
6.2.4 Atmospheric absorption, excess attenuation and barrier effects .16
7 Uncertainty in source description and propagation .16
7.1 Overview .16
7.2 Uncertainties in source description .17
7.2.1 General .17
7.2.2 Source point location .17
7.2.3 Broadband source sound exposure level for streamlined projectiles .17
7.2.4 Source sound exposure level for non-streamlined projectiles .18
7.2.5 Characteristic frequency of the N-wave .19
7.2.6 Spectrum of the source sound exposure level .19
7.3 Uncertainties in determining the sound exposure level at a receiver location .19
7.3.1 General .19
7.3.2 The uncertainties at a receiver location for non-streamlined projectiles .19
Annex A (informative) Derivation of constants and consideration of barrier and other effects .20
Annex B (informative) Calculation of projectile sound for projectiles on ballistic trajectories .24
Annex C (informative) Estimation of projectile velocity change.27
Annex D (informative) Calculation examples .30
Bibliography . 41

iii
ISO 17201-4:2025(en)
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.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types
of ISO document should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
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For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 43, Acoustics, Subcommittee SC 1, Noise, in
collaboration with the European Committee for Standardization (CEN) Technical Committee CEN/TC 211,
Acoustics, in accordance with the Agreement on technical cooperation between ISO and CEN (Vienna
Agreement).
This second edition cancels and replaces the first edition (ISO 17201-4:2006), which has been technically
revised.
The main changes are as follows:
— restructure of the document into new clauses: Projectile sound, Source description, Sound exposure
level at the receiver, and Uncertainty;
— separation of source and propagation terms;
— inclusion (from ISO 17201-2) and update of the source level for non-streamlined projectiles;
— expansion of the Clause on uncertainty;
— addition of Annex B on ballistic trajectories;
— addition of Annex C on projectile velocity change;
— addition of Annex D with informative examples.
A list of all parts in the ISO 17201 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

iv
ISO 17201-4:2025(en)
Introduction
Shooting sound registered around shooting ranges consists in general of three components: muzzle blast
sound, impact sound and projectile sound. This document deals solely with the projectile sound from
supersonic projectiles. It specifies a method for calculating the source sound exposure level of projectile
sound. It also provides a method for calculating the propagation of projectile sound, accounting for its
distinct characteristics that set it apart from the propagation of sound originating from other sources.
This document is intended for calibres of less than 20 mm but can also be used for larger calibres.
Projectile sound is described as originating from a specific point on the projectile trajectory, the “source point.”
The source sound exposure level is calculated from the geometric properties and the speed of the projectile
along its trajectory. Methods are given on how the sound exposure level at a receiver location is to be
calculated from this source sound exposure level, taking into account geometrical attenuation, atmospheric
absorption and attenuation and frequency shift due to non-linear effects. In addition, the effects on the
sound exposure level due to the decrease of the projectile speed and atmospheric turbulence are taken into
account.
In a restricted region, the Mach region (region II – see 4.2), the projectile sound exposure level is significant
compared to the muzzle blast sound exposure level. Outside this region only diffracted or scattered projectile
sound is received, with considerably lower levels than in this Mach region. Projectile sound behind the Mach
region (region I) is negligible compared to muzzle sound, except for contributions due to reflections from
other regions. In this document, a computational scheme for the levels in regions II and III is provided. The
levels in region III are typically 10 dB to 15 dB lower than those in region II.
Two computational methods are given to be able to calculate the projectile sound for streamlined and
non-streamlined projectiles such as pellets. Default values of parameters used in this document 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 for other atmospheric conditions. For calibres < 20 mm, the source 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 obtain more accurate results.
For projectiles with a speed just above the speed of sound the computational methods are less accurate.
Guidance is given how to deal with this increased uncertainty.

v
International Standard ISO 17201-4:2025(en)
Acoustics — Noise from shooting ranges —
Part 4:
Calculation of projectile sound
1 Scope
This document specifies computational methods 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 specifies a method on how to use this source level to calculate the
sound exposure level at a receiver position.
Results obtained with this document can be used as a basis for assessment of projectile sound from shooting
ranges. Additionally, the data can be used to determine sound emission or immission from different types
of ammunition and weapons. The prediction methods are applicable to outdoor conditions and straight
projectile trajectories. Two computational methods are given to determine the acoustical source level: one
for streamlined projectile shapes and one for non-streamlined shapes, such as pellets.
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.
ISO 80000-8, Quantities and units — Part 8: Acoustics
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 80000-8 and the following apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
streamlined projectile
projectile that has a shape that can be described as a 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 < x < l
p
Note 1 to entry: For the definition of effective projectile length, l , see 3.3.
p
3.2
non-streamlined projectile
projectiles that have a body different from streamlined projectiles (3.1)
Note 1 to entry: These can be multi part projectiles, such as shotgun pellets, or single part projectiles with a non-
streamlined form, such as shotguns slugs (see Figure 1).

ISO 17201-4:2025(en)
Figure 1 — Examples of non-streamlined projectiles
Note 2 to entry: For the definition of effective projectile length, l , see 3.3.
p
3.3
effective projectile length
l
p
distance between the nose and the cross-section of streamlined projectiles where it reaches the maximum
diameter of the projectile
Note 1 to entry: The effective length of the projectile (see Figure 2) is measured along the length-axis of the projectile
and is expressed in metres (m).
Key
l effective projectile length, expressed in metres (m)
p
d maximum diameter of projectile, expressed in metres (m)
p
Figure 2 — Effective projectile length
Note 2 to entry: For non-streamlined projectiles: The distance between the two points on the longitudinal axis of the
projectile at which the radius of the projectile changes the most is used as the effective length for non-streamlined
projectiles. If this is not applicable due to the special shape of the projectile other methods shall be used to determine
the effective length, e.g. via sound measurements. For projectiles consisting of pellets as used mainly in shotguns, the
effective length is set to the diameter of the barrel of the shotgun.
3.4
N-wave
idealized waveform of a sound having a pressure 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 back to the initial
sound pressure
ISO 17201-4:2025(en)
NOTE The duration is the time between a and b.
Figure 3 — Assumed N-shaped waveform for sound of a supersonic projectile at 1 m from the source
point on its projectile’s trajectory
Note 1 to entry: Measurements show deviation from the idealized N-wave (see Figure 3) that is increasing with
distance.
3.5
duration time
T
c
duration between two pressure increases of the N-wave (3.4)
Note 1 to entry: See points a and b in Figure 3.
Note 2 to entry: The duration is expressed in seconds (s).
Note 3 to entry: T will change along the sound propagation path resulting from non-linear acoustic effects.
c
3.6
characteristic frequency
f
c
inverse of the duration time, T
c
f =
c
T
c
Note 1 to entry: The characteristic frequency is expressed in hertz (Hz).
3.7
co-ordinate 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 to entry: The sound field of projectile sound is rotational symmetric around the line of fire.
Note 2 to entry: The co-ordinates are given in metres (m).
3.8
coherence distance
R
coh
distance between the source point (3.11) on the projectile trajectory and a receiver beyond which the
contribution to the sound from different parts of the trajectory are incoherent due to atmospheric turbulence
Note 1 to entry: The coherence distance is expressed in metres (m).
3.9
Mach number
M
ratio of the projectile speed to the local sound speed

ISO 17201-4:2025(en)
3.10
source sound exposure level
L
E,s
sound exposure level expected at a distance of 1 m from the source point (3.11)
Note 1 to entry: The source sound exposure level is expressed in decibels (dB).
Note 2 to entry: The reference distance of 1 m is defined in the direction of the receiver and not perpendicular to the
trajectory.
3.11
source point
point where a line from the receiver perpendicular to the wave front of the projectile sound intersects the
projectile trajectory
Note 1 to entry: The projectile radiates sound along the whole trajectory and is therefore in principle a line source. In
this document, a source point is used to represent the position of the trajectory (see Formula (9)].
3.12
projectile launch speed
v
p0
speed of the projectile as it leaves the muzzle
Note 1 to entry: The muzzle velocity is expressed in metres per second (m/s).
3.13
projectile speed
v
p
speed of the projectile along the trajectory
Note 1 to entry: The projectile speed is expressed in metres per second (m/s).
Note 2 to entry: 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 shall be taken into account.
3.14
reference sound speed
c
ref
adiabatic sound speed averaged over a period of at least 10 min
Note 1 to entry: 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 1 to entry: 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
standard deviation of the ratio of the reference sound speed (3.14) to the fluctuating effective sound speed (3.15)
2 −5
Note 1 to entry: In accordance with Reference [3] a value of μ = 10 is used within the context of this document [see
Formula (20)].
3.17
projectile speed change
κ
local change of projectile speed (3.13) along the trajectory per length unit of trajectory
Note 1 to entry: The speed change is expressed in reciprocal seconds [(m/s ⋅per m) = 1/s].

ISO 17201-4:2025(en)
Note 2 to entry: It is negative for non-self-propelled projectiles.
4 Projectile sound
4.1 General
When a projectile travels at supersonic speed, it generates a shock wave with a cone-shaped wave front
originating from its nose. This is shown in Figure 3 for a constant projectile speed. However, as the projectile
speed decreases along its trajectory, the wave front becomes curved. The area around the trajectory can be
divided into three regions, each requiring different methods to calculate sound levels. This is explained in 4.2.
The time-history of the shock wave has the shape of the letter N and is therefore referred to as an N-wave.
The spectrum of this N-wave can be calculated as detailed in 4.3.
Clause 5 outlines the calculation of the source sound exposure level for both streamlined and non-
streamlined projectiles.
In Clause 6, a method is described to calculate the sound exposure level of projectile sound at a receiver position,
taking into account several attenuation terms that are subtracted from the source sound exposure level.
NOTE For the calculation of projectile sound on ballistic trajectories see Annex B.
4.2 Regions
Three regions (I, II and III) are distinguished around the trajectory to describe projectile sound (see
Figure 4). In regions I and III sound exposure levels are considerably lower than in region II. In this document,
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 Formula (1):
vx =+vxκ (1)
()
pp0
The boundaries of region II are described with the angles ξ and ξ , shown in Figure 4. These angles are
0 e
given by Formula (2):
   
c c
am am
ξξ=arccos anda= rccos (2)
   
0 e
   
v v
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
The speed of sound is a function of the absolute temperature of the ambient air, T , in Kelvin and is given by
am
Formula (3):
12/
T 
am
cc= (3)
 
am ref
T
 
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.

ISO 17201-4:2025(en)
Key
1 weapon 5 target
2 source point 6 projectile
3 projectile trajectory 7 receiver
4 wavefront
Figure 4 — Three regions for describing the sound of a projectile
4.3 Spectrum of an N-wave
To determine the spectrum of the projectile sound at a distance r from the source point a relative spectrum
s
L ( f , r ) is used based on the characteristic frequency f of the N-wave at this distance. This characteristic
E,rel i s c
frequency, determined in hertz, shall be calculated with Formula (4):
14/
14/
M −1
l
()
r
p
fr()= f (4)
cs 0
34/ 14/
d
M p r
s
where
r is the distance from the source point to the receiver (see Figure 4), expressed in metres (m);
s
f is the reference frequency, equal to 175,2 Hz at 10 °C (see A.3);
M is the Mach speed of the projectile at the source point (x ). A minimum value of M = 1,02 shall be
s
used in the formula to prevent an indeterminate result from Formulae (6) and (7).
NOTE 1 Formula (4) shows that the characteristic frequency, f , decreases with increasing distance, r . This is a
c s
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 and with the characteristic
i
frequency f , calculated according to Formula (4), the one-third octave band relative spectrum with spectral
c
roll-off to lower and higher frequencies is given by Formula (5):
Lf ;; rC= fr −Cr (5)
() () ()
Ei,rels ii stot s
where
 f 
i
Cf ;, r =+25 28lg dB if ff<06, 5 (6)
()
ii s   i c
fr()
 
cs
f
 
i
Cf();,r =−50−12lg dB if ff≥ 06, 5 (7)
ii s   i c
fr
()
 
cs
ISO 17201-4:2025(en)
Cr()
is
Cr()=10lg 10 dB (8)
tots ∑
i=11
i/10
and where f = 10 is the mid-band frequency of the one-third octave band (12,5 Hz to 10 kHz, i = 11
i
represents a mid-band frequency of 12,5 Hz, and i = 40 represents a mid-band frequency of 10 kHz).
NOTE 2 Nominal or exact frequencies (base 2 or 10) can be used.
[18] [19]
NOTE 3 The frequency range is the same as in ISO 17201-1 and ISO 17201-2 for muzzle blast sound.
5 Source description
5.1 Source point
The position of the source point (x , 0) depends on the receiver position. For receivers in region II the source
s
position can be determined by numerical methods, for straight trajectories this can be determined according
to Formula (9). A co-ordinate system (x, y) is used, with the x axis along the projectile trajectory and its
origin at the muzzle.
2 22
xx− ⋅+vxκκ+cv⋅+ xc− =cy (9)
()
() ()
sp00samp samam
10, 2cv−
am p0
with 0< ss
κ
where (x, y) is the position of the receiver.
NOTE Similar to Formula (4) a minimum value of M = 1,02 is used in Formula (9).
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 for streamlined projectiles
The (broadband) source sound exposure level, L (x ), expressed in decibels, is given by the geometric
E,s,bb s
[4]
properties of the projectile and its speed at the source point , according to Formula (10):
 
 
94/
 
d
Mx()
p  
s
 
Lx =+L 10lg +10lg (10)
()
E,s,bbs 0
 
3 34/
  2
 Mx −1 
94/ ()
()ss
 4 
 
lr
p
 0 
where
L [re (20 µPa) s] = 161,9 dB (see A.2);
M(x ) = v(x )/c the local Mach number of the projectile at the source point x with the pro-
s s am s
jectile speed determined from Formula (1) and the speed of sound from Formula (3)
for the ambient air temperature;
r = 1 m.
When the Mach number approaches 1, the third term in Formula (10) becomes indeterminate. Therefore, a
lower limit of M = 1,02 is used in these expressions.
NOTE 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 is also used to calculate the shape
factor K and from this constant L (see Annex A).
ISO 17201-4:2025(en)
5.3 Source sound exposure level for non-streamlined projectiles
The computational method for non-streamlined projectiles is based on the assumption that a certain portion
of the kinetic energy of the projectile, moving with supersonic speed, is lost into a shock wave. From this
energy loss the sound exposure is calculated assuming linear acoustics.
With this method, default values are given and used for some parameters. Values deviating from the defaults
may be used if appropriate, but the reason shall be stated.
The sound source energy radiated from a specific emission point P is proportional to the energy loss over a
S
length of trajectory Δx around that emission point. The projectile energy loss is calculated as the integral of
the drag-force along the trajectory from x-Δx/2 to x + Δx/2 with the spatial stepwidth Δx of 0,01 m:
xx+Δ /2
1 s
Qx()= ρ AC ()xv ()x dx (11)
1 sW p
∫
xx−Δ /2
s
where
vx()
is the velocity, in m/s, of the projectile at position x;
p
ρ is the air density (altitude depending), in kg/m ;
A is the cross-sectional area of the projectile to the line of fire, in m ;
Cx()
is the air friction coefficient depending on the Mach number;
W
x is the position of the projectile on the x-axis; in m;
Δx is the spatial stepwidth, for which the submitted acoustical energy is calculated, in m.

ISO 17201-4:2025(en)
Key
P position of the muzzle P position of the source point
M S
P reception point P position of the target point
R T
x line of fire
y perpendicular direction to the line of fire in any direction
around the line of fire
r distance from the source point to the reception point
s
Figure 5 — Mach front geometry for one time period
In Figure 5, angle ξ denotes the radiation angle at the position x = x −Δx/2 and ξ denotes the radiation
1 S 2
angle at the position x = x +Δx/2.
S
Because Δx is small, the drag-force can be assumed constant over this small part of the trajectory.
Formula (11) reduces then to following Formula (12):
Qx() = ρAC ()xv ()xxΔ (12)
1 sW sp s
where
vx()
velocity, in m/s, of the projectile at the source point x ;
ps
s
ρ air density (altitude depending), expressed in kg/m ;
A cross-sectional area, expressed in m ;
Cx()
air friction coefficient depending on the Mach number;
W s
x position of the projectile on the x-axis, expressed in m;
s
Δx part of the trajectory for which the submitted acoustical energy is calculated, expressed in m.

ISO 17201-4:2025(en)
If C (M) is not known, but projectile speed change κ is given or measured, the projectile energy loss Q can
W 1
be calculated alternatively by Formula (13):
Qx()=−mxκΔ vx() (13)
ls pp s
with m the projectile mass in kg. See also Annex C.
p
If C (M) and κ are not known, C (M) = 1,1 for non-streamlined projectiles shall be used.
W W
NOTE The value of 1,1 was found for shotgun pellets and was derived from two typical types of shotgun pellet
ammunition (cal 16/70 and cal 12/70). For streamlined projectiles of rifles, a value of C (M) = 0,3 was found and
W
C (M) = 0,5 for projectiles of pistols.
W
The projectile sound source energy Q is the product of the projectile energy loss Q and the acoustical
p l
efficiency σ . If σ is not known for the projectile under consideration, σ = 0,25 shall be used as default.
ac ac ac
Qx =σ Qx (14)
() ()
PS ac 1 s
The energy is radiated from the element Δx on the trajectory through the divergent area S which represents
the situation for the position x on the x-axis. The area of divergence S is dependent on x , Δx, ξ and r This
s s s s
area is given by Formula (15):
Sr =2π sinsξξrxΔ in +r tan ε (15)
() () []() ()
ss ss ss
where
εξ=−ξ
s1 2
 c 
ξ =arccos
1  
vx −Δx/2
()
 s 
 c 
ξ =arccos
 
vx()+Δx/2
 
s
The sound exposure is calculated by the divergent area S, see Figure 5.
The source sound exposure is calculated at a reference distance r of 1 m perpendicular to the wave front
and is given by Formula (16):
Qx
()
ps
Ex()=ρc (16)
Ss
Sr
()
The broad band source level is defined by Formula (17):
Lx =10 lg(/Ex E ) (17)
() ()
E,,sbbs Ss 0
E = 400 μPa s [see ISO 80000-8:2020, 8-16].
This approach is valid as long as the projectile speed is greater than the speed of sound.
The flow chart in Figure 6 shows the scheme to calculate the sound exposure.

ISO 17201-4:2025(en)
NOTE Numbers at above right of the boxes are the formulae numbers, as referenced in the text.
Figure 6 — Flow chart for calculating the sound exposure
An example is given in D.3.
5.4 Spectrum of the source sound exposure level
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 Formula (4), the one-third
c
octave band spectrum of the sound source exposure level is given by Formula (18):
Lf();;xL= ()xL+ ()fr (18)
Ei,,ss EEsb,,bs rel i 0
where
r = 1 m reference distance from the source point perpendicular to the wave front;
x source position.
s
6 Calculating the sound exposure level at a receiver location
6.1 Basic formula
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

ISO 17201-4:2025(en)
over the path from the 1 m reference distance to the location of the receiver at distance r . The following
s
expression accounts for the principal factors that need to be considered.
Lf() =Lf();;xA− ()rA− ()rA− ()fr −−Af();;rA− ()fr (19)
Ei,r Ei,ss divs nlin sSpecShift i s atmsiiexcess s

where
L ( f ,; x ) is the one-third octave band sound source exposure level at mid-band frequency f and at
E,s i s i
the 1 m reference distance from the source point [see Formula (17)], expressed in decibels;
A (r ) is the attenuation of the level of the sound in a field free of reflections and resulting from
div s
the divergence of the geometric area of the wave front as the distance increases from the
1 m reference distance, expressed in decibels;
A (r ) is the attenuation caused by non-linear effects associated with the large initial amplitude
nlin s
of projectile sound near the source point, expressed in decibels;
A ( f ; r ) is the shift of the spectrum corresponding with the non-linear propagation pulse broad-
SpecShift i s
ening of the N-wave, expressed in decibels;
A ( f ; r ) is the attenuation caused by absorption processes in the atmosphere as the sound
atm i s
propagates over the path from the 1 m reference distance to the location of the receiver,
expressed in decibels;
A ( f ; r ) is the excess attenuation including losses due to the interaction with the ground, atmos-
excess i s
pheric refraction and shielding by a barrier, expressed in decibels.
NOTE 1 As the projectile sound propagates from the 1 m reference distance to a receiver at distance r , the
s
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.
NOTE 2 See Annex D for example of L and A .
E,s SpecShift
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
div
distinguished. In region II, the geometric attenuation varies between 10 lg (r /r ) dB and 25 lg (r /r ) dB,
s 0 s 0
where r is the 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 the coherence distance (R ), the second effect
coh
dominates. At distances greater than 10 km from the source point on the projectile trajectory, the attenuation
[3]
approaches the spherical limit 20 lg (r /r ) dB .
s 0
ISO 17201-4:2025(en)
The coherence distance, R , in metres, is given by Formula (20):
coh
 13/ 
l
 
2 t 3
 22 
M −1
 
() ll M −1
 
()
0 t
 
 2 1 
 
R =min , (20)
   
coh
2 2 2
π
Mc / f M μ
   
am c 0
   
 
where
l is total length of the trajectory either to the target or to the point where the local Mach
t
number has decreased to 1, expressed in metres (m);
l = 1,1 m see Reference [3];
2 −5
μ = 10 , see 3.16;
M is the local Mach number at the location of the source point;
c is speed of sound at the temperature of interest for ambient air, see Formula (3), expressed
am
in metres per second (m/s).
The geometric attenuation for region II is given by Formulae (21) and (22):
 
rk+−rM 1
()
ss
 
A = 10 lg dB                             for r < RR (21)
div,II s coh
2 2
 
rk+−rM 1
()
0 0
 


Rk+−RM 1
()
cohcoh r
 
s
 
A = 10 lg + 25 lg dB          for rR< (22)
div,II   scoh
2 2
 
R
rk+−rM 1  
ccoh
()
0 0
 
where
k = −κ/c ;
am
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 Formula (23), with distances r and r as shown in Figure 7:
1 2
max()rR,  r
20 11
AA==rr +20lg dB with R =+2 (23)
()
div,III div,II 1 0
 
R 100
 
The fi
...