Tiêu chuẩn iso 17201 2 2006

Microsoft Word C030577e doc Reference number ISO 17201 2 2006(E) © ISO 2006 INTERNATIONAL STANDARD ISO 17201 2 First edition 2006 07 01 Acoustics — Noise from shooting ranges — Part 2 Estimation of mu[.]

General

3.1.1 air density ρ density of air for the estimation conditions

NOTE The air density is expressed in kilograms per cubic metre (kg/m 3 )

3.1.2 angular frequency ωfrequency multiplied by 2π

NOTE The angular frequency is expressed in radians per second (rad/s) in all formulae

The coordinate system in the (x, y) plane is essential for describing geometry, where the x-axis represents the line of fire, with x = 0 positioned at the muzzle The y-axis measures the perpendicular distance from this line of fire in any plane surrounding it.

NOTE 1 The sound field of projectile sound is rotational symmetric around the line of fire

NOTE 2 The coordinates are given in metres (m)

3.1.4 cosine-coefficients c 1,2…N coefficients of the cosine-transform used to describe the directivity of the angular source energy

3.1.5 deceleration angle ε difference between the radiation angle at the beginning and end of a part of the trajectory

NOTE The deceleration angle is expressed in radians (rad) in all formulae

3.1.6 specific chemical energy u specific chemical energy content of the propellant

NOTE The specific chemical energy is usually expressed in joules per kilogram (J/kg)

3.1.7 line of fire continuation of the axis of the barrel

NOTE Ballistic trajectories can be described as a sequence of straight lines Then the methods apply to each segment Corrections of the aiming device are ignored

Copyright International Organization for Standardization

Figure 1 — Line of fire and line of sight

Q p acoustic energy from a trajectory length of one metre

NOTE 1 The projectile sound source energy is expressed in joules (J)

3.1.9 propellant mass m c mass of the propellant

NOTE The propellant mass is expressed in kilograms (kg)

3.1.10 radiation angle ξ angle between the line of fire and the wave number vector describing the local direction of the propagation of the projectile sound

NOTE 1 The radiation angle is expressed in radians (rad) in all formulae

NOTE 2 ξ is the 90° complement of the Mach angle

3.1.11 angle alpha α angle between the line of fire and a line from the muzzle to the receiver

NOTE 2 The angle alpha is expressed in radians (rad) in all formulae

E time integral of frequency-weighted squared instantaneous sound pressure over the event duration time

NOTE The sound exposure is expressed in pascal-squared seconds (Pa 2 ⋅s)

L E ten times the logarithm to the base 10 of the ratio of the sound exposure to a reference value

NOTE 1 The sound exposure level is expressed in decibels

NOTE 3 The sound exposure level of a single burst of sound or transient sound with duration time is given by the formula

⎣∫ ⎦dB where p(t) is the instantaneous sound pressure as a function of time; p 0 2 T 0 is the reference value [(20 àPa) 2 ì 1 s]

3.1.14 speed of sound in air c speed of sound for the estimation condition

NOTE The speed of sound in air is expressed in metres per second (m/s)

S S size of the area at a certain distance from the trajectory through which the sound radiated from the respective path of the trajectory is propagating

NOTE The divergent area is expressed in square metres (m 2 )

3.1.16 propagation distance r S distance between the source point of projectile sound, P S , and the receiver point, P R ,

NOTE The propagation distance is expressed in metres (m)

R W radius of an equivalent radiating sphere of the “simple model of explosion”

NOTE The Weber radius is expressed in metres (m)

Weber pressure p W sound pressure at the surface of the Weber sphere

NOTE The Weber pressure is expressed in pascals (Pa).

Directivity

3.2.1 correction factor due to source directivity c S correction taking into account that different orders of Fourier functions contribute differently to the energy

Y(α) directivity function in the direction of α

Energy

3.3.1 effective angular source energy distribution

Q Y (α) effective energy radiated into the direction α, weighted by directivity

NOTE The effective angular source energy distribution is expressed in joules per steradian (J/sr)

Q e total acoustic energy after integration of Q Y (α) over the whole sphere

NOTE The total acoustic energy is expressed in joules (J)

3.3.3 energy in the propellant gas

Q g energy in the gaseous efflux of the propellant at the muzzle

NOTE The energy in the propellant gas is expressed in joules (J)

Q l difference in projectile energy of the translatory motion on a part of the trajectory of 1 m length due to air drag NOTE The kinetic energy loss is expressed in joules (J)

Q m total acoustic energy of the muzzle blast

NOTE The muzzle source energy is expressed in joules (J)

Q p product of the kinetic energy loss, Q l ,and the acoustical efficiency, σ ac

NOTE 1 The projectile sound source energy is expressed in joules (J)

Q p0 kinetic energy of the projectile at the muzzle

NOTE The projectile muzzle kinetic energy is expressed in joules (J)

Q c total chemical energy of the propellant

NOTE The propellant energy is expressed in joules (J)

Q W energy density of a Weber source with a Weber radius of 1 m

NOTE The Weber energy is expressed in joules per cubic metre (J/m 3 )

Weber energy for a mass of propellant having a Weber radius of 1 m

NOTE The reference Weber energy is expressed in joules (J)

S q (α) acoustic energy radiated from the source into the far field per unit solid angle

NOTE 1 The acoustic energy radiated by the source within a narrow cone centred around the direction α is

= Ω where Ω is the solid angle in steradian (sr)

NOTE 2 The angular source energy distribution is expressed in joules per steradian (J/sr).

Fraction

3.4.1 kinetic fraction σ cp ratio of the projectile kinetic energy, Q p , to propellant energy, Q c

NOTE The efficiency is the kinetic fraction, expressed as percentage

3.4.2 gas fraction σ cg ratio of the energy in the exhausted gases, Q g , of the propellant after the shot to the propellant energy, Q c

3.4.3 acoustical efficiency σ ac ratio of an energy that converts into acoustic energy

Projectile

3.5.1 projectile diameter d p diameter at the maximum cross section of the projectile

NOTE The projectile diameter is expressed in metres (m)

3.5.2 projectile launch speed v p0 speed of the projectile at the muzzle

NOTE The projectile launch speed is expressed in metres per second (m/s)

3.5.3 projectile length l p total length of the projectile

NOTE The projectile length is expressed in metres (m)

3.5.4 projectile mass m p mass of the projectile, for shotguns the total mass of the pellets

NOTE The projectile mass is expressed in kilograms (kg)

3.5.5 projectile speed v p speed of the projectile along the trajectory

NOTE The projectile speed is expressed in metres per second (m/s)

3.5.6 projectile speed change κ local change of projectile speed along the trajectory per length unit of trajectory

NOTE The projectile speed change is expressed in reciprocal seconds [(m/s)/m = 1/s]

M ratio of projectile speed to local sound speed

4 Estimation model for source data of the muzzle blast

General

If possible, the muzzle blast source data should be determined according to ISO 17201-1

This clause outlines the techniques for estimating acoustic source data related to muzzle blasts and explosions The muzzle blast from firearms is notably directional, with both the angular distribution of source energy and the spectrum changing based on the angle relative to the line of fire.

Propagation calculations necessitate frequency and angle-dependent source data as input However, detailed emission data, measured per ISO 17201-1, is often unavailable for many weapons and ammunition, prompting the need to estimate this data from other technical information This estimation method can also be utilized for explosives In cases of muzzle blasts, linear acoustics is applicable when the peak pressure is below 1 kPa.

This method may not be appropriate for firearms equipped with muzzle devices, such as muzzle brakes, which alter the blast field by redirecting propellant gas flow upon exiting the muzzle.

The method consists of two main steps: estimating the acoustic energy of the shot and applying the directional pattern of the source to calculate the spectrum This approach accommodates both general and specific data, enabling more accurate results Consequently, it allows for the use of default values or tailored parameters as needed.

A flow chart is utilized to outline the procedure steps and associated equations, as illustrated in Figure 2 The left section of the flow chart details the estimation of muzzle source energy, which is essential for determining acoustical source data on the right side Alternative branches are indicated by the logical sign “or” (⊕), while the sign for “and” (⊗) signifies that both sets of information are required to proceed The symbol ˆx represents a default input value for the parameter x, which can be used if the actual value is unknown Equation reference numbers are displayed at the top of the boxes.

To obtain the standard estimation, follow the outlined scheme (refer to Figure 2) using the specified default parameters for all coefficients This estimation is essential for the report, and any deviations from the default values must be justified.

Estimation of chemical energy

To estimate the acoustic energy, the total chemical energy, denoted as \$Q_c\$, is crucial In cases where \$Q_c\$ is unknown, there are two alternative methods to determine it One approach involves utilizing the kinetic energy of the projectile.

The initial energy of a projectile, denoted as Q p0, can be determined directly or calculated using its mass and launch speed, as outlined in Equation (1) in Figure 2 The energy attributed to the projectile represents a portion of the total energy, and if the fraction σ cp is unknown, a default value of 35% should be applied Subsequently, Equation (2) in Figure 2 calculates Q c The right-hand branch of the equation utilizes the mass of the propellant or explosives, with the conversion factor, u, varying based on the propellant type (e.g., 4,310 J/kg for TNT or 5,860 J/kg for PETN) In cases where the specific chemical energy, u, is not available, a standard value of 4,500 J/kg should be used.

Estimation of acoustic energy

The energy $ Q_c $ is partially transformed into heat and the kinetic energy of the remaining gas $ Q_g $, as well as the kinetic energy of the projectile $ Q_{p0} $ In the context of firearms, inner ballistics plays a crucial role in determining this energy balance It is suggested that 45% of $ Q_c $ be considered the default value for $ Q_g $, which serves as the sole energy source for the muzzle blast The efficiency of converting the energy in the propellant gas $ Q_g $ into the total acoustic energy of the muzzle blast $ Q_m $ is represented in Equation (5).

Estimation of the Weber energy

The right side of Figure 2 illustrates the flow chart utilized to calculate the Weber energy, denoted as \$Q_W\$, representing the energy density of a Weber source with a radius of 1 meter.

Estimation of directivity

For rotational symmetric radiation around the line of fire, the source's directional pattern is represented by a Fourier series based on the angle α In cases where the directivity pattern, $ c_n $, is unknown, default values for various weapons can be found in the matrix presented as Equation (6) in Figure 2 By applying the directivity, $ Y $, to $ Q_e $ in Equation (10) in Figure 2, one can determine the energy flowing through the slice, which incorporates the source's directional pattern.

Estimation of the spectrum

The acoustical model of explosions in air, as outlined in Equations (11) and (12) in Figure 2, facilitates the estimation of the Fourier-spectrum of the angular source energy distribution, with α representing the direction as detailed in Annex A and Reference [8] The model parameters are validated default values that should only be modified if pertinent information is available It is important to note that the integral in Equation (12) requires numerical integration, as no analytical solution exists Additionally, this estimation method is not suitable for predicting peak pressure values or similar metrics.

NOTE Numbers at above right of the boxes are the numbers of the equations, as referenced in the text For additional information with regard to Equations (11) and (12), see Annex A

Figure 2 — Flow chart of estimation procedure for muzzle blast source data

5 Estimation model for projectile sound

General

If possible, the projectile sound source data should be determined according to ISO 17201-4

To calculate the free field sound exposure level of projectile sound, ISO 17201-4 should be utilized, provided that the parameters of the shot are known In cases where these parameters are unavailable, an alternative procedure can be employed.

This estimation procedure posits that a portion of the kinetic energy from a supersonic projectile is converted into a shock wave, allowing for the prediction of acoustic energy generated by the shock wave The sound exposure is then calculated based on this energy, with linear acoustics applied under the condition that the peak pressure remains below 100 Pa for N-waves.

The trajectories are assumed to be a straight line, however, this method also applies to ballistic trajectories which can be approximated by a set of straight lines

Standard estimation is derived using a specific scheme, as illustrated in Figure 3, based on the default parameters for all coefficients This estimation is essential for the report, and any deviation from the default values for coefficients must be justified.

Estimation of projectile sound source energy

To estimate the projectile sound source energy, denoted as \$Q_p\$, one must consider the kinetic energy loss, \$Q_l\$, multiplied by the acoustical efficiency, \$\sigma_{ac}\$ If the acoustical efficiency for the specific projectile is available, it should be utilized; otherwise, a default value of \$\sigma_{ac} = 0.25\$ should be applied.

Knowing the values of κ, v, and p0, along with the muzzle position, allows us to determine the projectile's speed and trajectory using Equation (13) in Figure 3 Additionally, Equation (14) quantifies the kinetic energy loss per meter, while Equation (15) describes the source energy of the projectile's sound.

There are various methods to estimate the parameters illustrated in the flow chart of Figure 3 For instance, if the projectile's speed, denoted as \$v_p\$, is measured at various distances, the parameter \$\kappa\$ can be estimated through linear regression analysis.

NOTE 1 Numbers at above right of the boxes are the equation numbers, as referenced in the text

Figure 3 — Flow chart for estimating projectile sound source energy

The sound exposure depends on the path length from the source position to the reception point (see Figure 4):

E r =∫ p r t t (16) where subscript S denotes all parameters which relate the source position on the trajectory to the reception position

Key x line of fire y perpendicular direction to the line of fire in any direction around the line of fire

P t position of target or point on trajectory of fire where projectile becomes subsonic

Figure 4 — Shock front geometry for two time periods, I and II

Key x line of fire y perpendicular direction to the line of fire in any direction around the line of fire

P t position of target or point on trajectory of fire where projectile becomes subsonic

NOTE For more information, see Figure 4

Figure 5 — Shock front geometry at period II

To ensure that linear acoustics apply, the distance $ r_S $ must be sufficiently large so that the peak pressure levels remain below 100 Pa The sound pressure at the source, $ P_S $, at point $ x_S $ is crucial for determining the exposure level at the reception point, $ P_R $ The energy of the sound source is directly proportional to the energy loss at the source point, $ P_S $, over a specific trajectory length Additionally, the sound exposure at $ P_R $ is inversely proportional to the divergent area $ S_S $, as illustrated in Figures 4 and 5, where $ S_S $ corresponds to $ S(x_S, r_S) $.

At the reception point $ P_R $, the value of $ x_S $ is determined In Figures 4 and 5, the angle $ \xi $ represents the radiation angle at $ x = x_S - \Delta x $ The energy is emitted from the element $ \Delta x $ along the trajectory through the divergent area $ S(x_S, r) $, which illustrates the conditions at $ P_R $ For this analysis, $ \Delta x $ is assumed to be 1 meter, as depicted in Figures 4 and 5.

NOTE 1 No analytical solution for x S is known

NOTE 2 κ is negative if the projectile is not self-propelled

From Figure 5, Equation (19) is obtained:

The area of divergence S S is dependent on ξ S , ε S and r S This area is given by Equation (20):

⎝ ⎠ (21) where v p,S′ is the speed of the projectile at point x S – ∆x

⎝ ⎠ ⎝ ⎠ (22) where v p,S′ is the speed of the projectile at point x S – ∆x; v p,S is the speed of the projectile at point x S

Then, the sound exposure is given by Equation (23): p

This estimation is valid as long as the projectile speed is greater than the speed of sound

As the change of projectile speed is assumed to be linear, E r S S ( ) can be estimated using Equation (24):

NOTE 3 Equation (24) can be applied for Mach numbers greater than 1,01

NOTE 4 Equation (24) does not depend on the choice of ∆x

The third octave band (nominal mid-band frequency f i ) sound exposure level of the source is given by

The nominal mid-band frequency of the one-third-octave band is represented by \$f_i / 10 \text{ Hz}\$, where \$i = 11\$ corresponds to a mid-band frequency of 12.5 Hz, and \$i = 40\$ corresponds to a mid-band frequency of 10 kHz.

10 kHz); f c is the critical frequency estimated from Equation (26) c clin f 1

− (27) where M is the Mach number

NOTE 5 The estimation of the spectrum does not yield the dips in the spectra that necessarily occur according to the

N-wave one-third octave spectrum For comparison to experimental data, in particular if the test data include ground reflection, this approach should be considered too simplistic

NOTE 6 1/f c describes the N-wave duration

The accuracy of source data estimations is influenced by the uncertainties in the acoustic input data Due to the complexity of the estimation processes, it is essential to assess the uncertainties of the acoustic source data by varying the input data and observing the resulting changes The methods primarily depend on energy concepts, making the estimation of energy-equivalent acoustic parameters in decibels more reliable than that of non-energy-equivalent features, such as the directivity of the muzzle blast.

Each shot in a series can exhibit a greater variation in directivity pattern compared to the fluctuations in acoustical energy The results of the procedure provide an average representation of this pattern.

Simple blast model for estimation of sound energy and its spectrum

The so-called Weber model, published in 1939 [13] , has been validated in the acoustic far field for a variety of explosions in air for charge weights, starting at 0,5 g to 20 kg [8], [9]

The model describes a spherical volume of compressed gas that expands rapidly during an explosion Initially, the expanding sphere cannot emit sound, as its growth outpaces any sound waves As the explosion progresses, the sphere's volume increases while its expansion speed decreases Once the expansion speed matches the speed of sound, the sphere begins to radiate sound.

The radiation emitted is influenced by the particle velocity at the sphere's surface, which matches the speed of sound, resulting in a constant radiation per unit area Consequently, the sphere's surface area dictates the total amount of acoustic energy radiated.

The differential Equation (A.1) describes the model: d ( ) p ( )d p t ω = −α ω (A.1) where ω is the angular frequency

The function α ω( ) in Equation (A.1) is given by Equation (A.2):

(A.2) where c is the speed of sound;

R W is the radius of the sphere, the Weber radius of the source

The time history of the pressure is expressed by Equation (A.3):

Equation (A.1) defines the Fourier spectrum of a blast In order to archive a one-third octave spectrum the

Fourier spectrum must be integrated over the range from ω 1 to ω 2 for each one-third octave band defined

Figure A.1 illustrates a Weber spectrum, which is symmetric around a center frequency as described in Equation (A.1) However, the one-third octave spectrum, due to its logarithmic scale, loses this symmetry In this presentation, the spectrum exhibits a 30 dB increase in levels per frequency decade at lower frequencies, while showing a 10 dB decrease per frequency decade at higher frequencies.

Figure A.1 — One-third octave spectrum of a Weber blast

B.1 Mass of explosives — Weber radius — Source energy level

Figure B.1 illustrates the correlation between explosive mass, Weber radius, and the measured source energy level, encompassing firearms and small explosions as defined by ISO 17201 It also presents examples of blasts from devices not covered by this standard to highlight the inherent uncertainty in this relationship The central straight line represents the regression line, while the additional lines flanking it denote the +3 dB and -3 dB limits of the average.

The three axes at the right of the graph are scales corresponding to the respective source energy level, unweighted, C-weighted and A-weighted

The abscissa of the graph in Figure B.1 indicates the mass of explosives For firearms, the effective mass accounts for the directivity of the blast

Measurements shown in Figure B.1 were taken at various distances and heights of the sources Small arms were fired from a height of approximately 1.5 m, at distances ranging from 7.5 m to 10 m, while larger weapons were typically fired from a distance of 250 m The uncertainty indicated in Figure B.1 is approximately ± 3 dB.

Key m effective mass of explosive

L LE source energy level, unweighted

L CE source energy level, C-weighted

L AE source energy level, A-weighted

10 300 full metal jacket Winchester rifle

Figure B.1 — Weber radius versus effective mass of explosives

B.2 Lateral kinetic energy — Mass of propellant

Figure B.2 illustrates the relationship between the lateral kinetic energy of a projectile at the muzzle and the mass of propellant across different types of firearm ammunition, with data sourced from ammunition catalogues [14].

Q p0 kinetic energy of projectile (J) m mass of propellant (g)

Figure B.2 — Mass of propellant versus lateral kinetic energy of the projectile [14]

The efficiency increases approximately 10 % (0,5 dB) for a temperature rise of 50 K

B.4 Weber radius — Sound exposure measurements

The uncertainty in describing a measured muzzle blast using the Weber model cannot be captured by a single value due to two main factors: the Weber radius predicts a complete spectrum but is more reliable in specific frequency ranges, and additional uncertainties arise from ground reflections and projectile sound signatures Consequently, Annex C highlights the various influences and uncertainties involved in determining a Weber spectrum from a single event measurement, using a 300 Winchester muzzle blast as an example.

Examples for estimation of muzzle blast

C.1 Estimation procedure for muzzle blast source data, according to Figure 2 flowchart C.1.1 Test plan

Tiêu đề	Acoustics — Noise From Shooting Ranges — Part 2: Estimation Of Muzzle Blast And Projectile Sound By Calculation
Trường học	International Organization for Standardization
Chuyên ngành	Acoustics
Thể loại	tiêu chuẩn
Năm xuất bản	2006
Thành phố	Geneva

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