PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Road Traffic Noise Prediction Model “ASJ RTN-Model 2018”
Proposed by The Acoustical Society of Japan– Part 3: Calculation model of sound propagation
Akinori FUKUSHIMA1; Shinichi SAKAMOTO2; Yosuke YASUDA3; Takatoshi YOKOTA4
1
2
3

NEWS Environmental Design Inc., Japan

Institute of Industrial Science, The University of Tokyo, Japan

Kanagawa University, Japan

4

Kobayasi Institute of Physical Research, Japan

ABSTRACTAs the third part of “ASJ RTN-Model 2018”, calculation model of sound propagation is presented. Thismodel is basically developed as a practical calculation model based on Geometrical Acoustics. The
calculation equations in this model are defined on the basis of experimental or numerical analysis data. The
overall values of the A-weighted sound pressure level of noise propagating from a vehicle are directly
calculated by considering the frequency characteristics of vehicle noise. This calculation model consists ofshielding effects by several type barriers, excess attenuation due to ground surface, atmospheric absorption
effect, sound reflection and meteorological effect. Based on newly obtained knowledge, several
improvements were made on the calculation method to develop the model.
Keywords: Road Traffic Noise, Prediction Model, ASJ RTN-Model 2018, Sound Propagation

1. INTRODUCTION
The calculation method of sound propagation in the road traffic noise prediction model "ASJ
RTN-Model 2018" is an engineering one for calculating “the unit pattern“, a time history ofA-weighted sound pressure level LA for a driving vehicle. This method is based on sound propagationin hemi-free space and various attenuations such as diffraction effect and ground effect are corrected,
and the LA as the summation of all frequency components is directly obtained. The calculation methodof sound propagation has been updated every five years by modifying the previous model based on
newly obtained knowledge since "ASJ Model 1998" [1] had been published at 1999.
In this version of the model, several components of calculation method of sound propagation are
modified from and newly added to the previous version [2]. As for the diffraction effect, values of theparameters to calculate sound diffraction of vehicle noise were improved or newly added underconsideration of sound source characteristics of recent road traffic noise. The calculation method for
diffraction effects at a wedge with an opening angle as seen in a building and an embankment was
newly added, and the effects for thick barrier or overhung barrier were modified based on the results of
the wave-based numerical analysis. As for the ground effect, treatment of porous asphalt pavement
was newly added based on measurement results.

2. BASIC EQUATIONS OF SOUND PROPAGATION
Considering attenuation due to various factors in the sound propagation from an point source set ona center of driving lane, the A-weighted sound pressure level LA,i [dB] for vehicle noise propagatingfrom the i th source Si to the prediction point P is calculated as follows:
LA,i = LWA,i − 8 − 20 lg ri + ΔLcor,i(1)where LWA,i is the A-weighted sound power level of the source Si [dB] and ri is the distance from S i to
P [m]. ΔLcor,i denotes the correction related to various attenuation factors in the sound propagation
1
3

3704

fuku-new@wonder.ocn.ne.jp
yyasuda@kanagawa-u.ac.jp

24sakamo@iis.u-tokyo.ac.jp
t-yokota@kobayasi-riken.or.jp

from Si to P [dB] and is given by
ΔLcor,i = ΔLdif,i + ΔLgrnd,i + ΔLair,i(2)where ΔLdif,i is the correction term for diffraction [dB], ΔLgrnd,i is the correction term for the groundeffect [dB] and ΔLair,i is the correction term for atmospheric absorption [dB].

3. Correction for Diffraction ∆Ldif
Correction terms for various types of diffraction are listed in Table 1. The correction for diffraction
due to acoustical obstacles, ΔLdif, is calculated using fundamental correction term ΔLd,k or ΔLd,r [dB] asa function of the diffraction path difference δ [m]. In this version of the ASJ RTN-Model, two
fundamental correction terms, ΔLd,k and ΔLd,r , are introduced. ΔLd,k is applied for diffraction around aknife wedge such as a barrier, and it was determined from Maekawa's chart for diffraction [3,4] andthe frequency characteristics of the recent road traffic noise. ΔLd,r is another fundamental correction
term for diffraction around wedge with an opening angle which is applied to a building or an
embankment road, and is newly added based on the results by numerical analysis [5]. Note that thesymbol ΔLdif is a generic term used to represent the correction terms in Table 1. When the shielding
effect of acoustical obstacles exceeds approximately 30 dB, it may not be so large as to be indicated by
the calculated values because of the influence of actual wind conditions.
3.1 Fundamental correction term for diffraction, ∆Ld,k and ∆Ld,r
The fundamental correction terms for diffraction ΔLd,k and ΔLd,r are calculated as a function of thepath difference δ [m] shown in Figure 1 for diffraction considering the point source S, the prediction
point P and the diffraction point O:⎧ −20 − 10lg(c δ )cspecδ ≥ 1
spec⎪⎪
ΔLd,k = ⎨ −5 − 17.0 ⋅ sinh −1 cspecδ 0.415
0 ≤ cspecδ < 1(3)⎪⎪ min ⎡ 0, − 5 + 17.0 ⋅ sinh −1 cspec δ 0.415 ⎤
cspecδ < 0⎣⎦⎩⎧−17.5 − 10lg(c δ )cspecδ ≥ 1
spec
⎪
⎪
0.415
−1
ΔLd,r = ⎨−2.5 − 17.0 ⋅ sinh cspecδ0 ≤ cspecδ < 1(4)⎪⎪min ⎡0, − 2.5 + 17.0 ⋅ sinh −1 cspec δ 0.415 ⎤
cspecδ < 0⎣⎦⎩
where the path difference δ is defined as a negative value when S is visible from P. The function
min[a,b] in the Eqs.(3),(4) gives the smallest value of a and b. The coefficient c spec is defined as shownin Table 2. ΔLd,k and ΔLd,r are illustrated in Figure 2 as a function of δ.

(

)

(

(

)

)

(

PurposeFundamental term)

Table 1 – Symbols of correction terms for various types of diffraction.
SymbolSummary

Simple barrier(Single diffraction)
Embankment
Double barriers
Thick barrier
Barrier with overhang(Overhung barrier)Edge-modified
barrier
Low-height barrier
Transmission throughbarrier

ΔLd,k
ΔLd,r
ΔLdif,sb
Cdif,abs
ΔLdif,rw
ΔLdif,db
ΔLdif,tb

ΔLdif,ob
Cdif,ob
ΔLdif,emb

ΔLdif,hb
Cdif,emb
ΔLdif,low

ΔLdif,transFundamental term for various types of diffraction
for a knife wedge
for a wedge with an opening angle
Single diffraction around a simple barrier considering an infinite half-screen
Absorption effect of the standard metallic absorptive- type barrier
Single diffraction at an edge of a shoulder on an embankment road
Double diffractions due to double barriers
Double diffractions around a thick barrier, including an embankment or abuilding
Diffractions around a barrier with an overhang
Overhang effect (Additional correction term by an overhung barrier)Diffraction around a barrier with acoustic device on the top edge to reduce
diffracted soundDiffraction around a hypothetical simple barrier
Additional correction term by edge-modified barrier
Single diffraction around a low-height barrier with a height of 1 m or less ina flat terrain
Summation of diffraction over a barrier and transmission through a barrier

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P
O

O
P

S

S

(b) For S visible from P, δ = - (L – R)(a) For S invisible from P, δ = L – R
Figure 1 – Direct path R = SP, diffraction path L = SO + OP and path difference δ.
Table 2 – Coefficient cspec values
Classification of noise
Dense asphalt pavement
Noise from running vehicles Porous asphalt pavement
Gap-graded asphalt pavement
Structure-borne noise from viaducts (Independent of viaduct type)
-30

-20
-15

-25
-20

ΔLd,r [dB]-25

ΔLd,k [dB]-30

Dense asphalt
Porous asphalt
Gap-graded asphalt
Structure-borne soundInvisible (δ > 0)

-10
-5

0.01
0.1
1
Diffraction pass difference δ [m]Dense asphalt
Porous asphalt
Gap-graded asphalt
Structure-borne sound

-15
-10

Invisible (δ > 0)

-5

Visible (δ < 0)

0
0.001

cspec
1.00
0.75
0.96
0.60

10

0
0.001

Visible (δ < 0)

0.01
0.1
1
Diffraction pass difference δ [m]10(b). ΔLd,r for wedge with an opening angle(a). ΔLd,k for knife wedge
Figure 2 – Fundamental correction termΔLd,k and ΔLd,r as a function of path difference δ.
3.2Single diffraction

3.2.1 Simple barrier, ∆Ldif,sb
The correction term ΔLdif,sb for diffraction around a simple barrier [dB] is calculated as follows:
except for standard metallic absorptive-type barrier⎧⎪ ΔLd,k
ΔLdif,sb = ⎨(5)⎪⎩ ΔLd,k + C dif,abs standard metallic absorptive-type barrier
where Cdif,abs is the correction term for the absorption effect of the standard metallic absorptive-typebarrier [dB] and is calculated as [6]:⎧− 0.5 lg(1 + 20δ ) δ > 0
Cdif,abs = ⎨
(6)
δ ≤0
⎩0
In order to calculate LAeq at a prediction point around a barrier with a finite length, the “one-path”
method considering only the diffraction at the top edge of the barrier can be available. If a line segment
SP from S to P crosses a finite barrier in a plan view, ΔLdif is calculated using Eq.(5). If not, thepropagation from S to P is calculated for a terrain without a barrier.
3.2.2 Diffraction at wedge with opening angle, ∆Ldif,rw
The correction term ΔLdif,rw for single diffraction around wedge with an opening angle such as anedge of shoulder on an embankment road [dB] is calculated as follows:
ΔLdif,rw = ΔLd,r(7)
3.3

Double diffractions

3.3.1 Double barriers, ∆Ldif,db
The correction term ΔLdif,db for the diffraction around a pair of barriers [dB] with a spacing of 5 m
or more, shown in Figure 3, is calculated as follows [7]:3706δ SXP ≥ δ SYP⎧⎪ ΔLSXP,k + ΔLXYP,kΔLdif,db = ⎨(8)
δ SXP < δ SYP⎪⎩ ΔLSYP,k + ΔLSXY,kwhere ΔLABC,k is ΔLd,k for the diffraction path ABC with the path difference δABC.
Even if the two barriers are not parallel, ΔLdif,db is calculated by Eq.(8) using the coordinates ofeach diffraction point on the shortest propagation path [8]. As the attenuation due to shielding by
double barriers increases, lower frequency components are more dominant as compared with single
barrier. Therefore, when ΔLdif,db calculated by Eq.(8) becomes approximately -30 dB or less, thecalculation error becomes large.
3.3.2 Thick barrier, ∆Ldif,tb
The correction term ΔLdif,dd for the double diffraction around an acoustical obstacle such as anembankment or a building [dB], shown in Figure 4, is calculated as follows [5,9]:
δ SXP ≥ δ SYP⎧⎪ ΔLSXP,r + ΔLXYP,rΔLdif,tb = ⎨(9)δ SXP < δ SYP⎪⎩ ΔLSYP,r + ΔLSXY,rwhere ΔLABC,r is ΔLd,r for the diffraction path ABC with the path difference δABC. Even behind a thickbarrier, low frequency components become dominant as compared with a single barrier.
3.3.3 Overhung barrier, ∆Ldif,ob
The shielding effect of the overhung barrier is generally larger than that of a hypothetical thickbarrier with the same diffraction point as the overhung barrier. Furthermore, the additional shielding
effects depend on the type of the overhung barrier and frequency. In this model, calculation formulaof the additional shielding effect was determined based on the results of the numerical analysis inwhich the shielding effects of overhung barriers in A-weighted overall level for road traffic noise
were obtained.
The correction term ΔLdif,ob for the diffraction around a overhung barrier [dB], shown in Figure 5, iscalculated by the following equations [10]:ΔLdif,ob = ΔLdif,tb + Cdif,ob
(10)
C
⎧⎛
⎫
⎞
B
⎪
⎪
− 1⎬
Cdif,ob = A ⎨⎜⎟⎜ B − ΔL⎟
dif,tb ⎠
⎩⎪⎝
⎭⎪

(11)

where ΔLdif,tb is the correction term for the hypothetical thick barrier approximated as obstacle withdiffraction points X and Y using Eq.(9). Cdif,ob is the correction term for the overhang effect [dB]determined by the difference between the A-weighted sound pressure level behind the overhung
barrier and that behind the thick barrier. The coefficients A, B, and C are listed in Table 3.
3.4 Edge-modified barrier, ∆Ldif,emb
The calculation method of the correction term ΔLdif,emb for the diffraction around anedge-modified barrier [dB] follows the method of "ASJ RTN-Model 2013", and ΔLdif,emb is given as
the summation of shielding effect for hypothetical simple barrier and device-dependent efficiency ofedge-modified barrier, as follows:
P
P
X
X
Y
X
X
Y
Y
P
Y
P
S

S

X
S

S

(a) δ SXP ≥ δ SYP
Y
P S

X

S

(a) δ SXP ≥ δ SYPXYP(b) δ SXP < δ SYP
Figure 3 – Calculation of diffraction arounddouble barriers.

S

Y

Y
P S

X

P

(b) δ SXP < δ SYP
Figure 4 – Calculation of diffraction aroundthick barrier.

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ΔLdif,emb = ΔLdif,hb + Cdif,emb(12)
where ΔLdif,hb is the correction term ΔLdif,sb for single diffraction by the hypothetical simple barrier[dB] shown in Figure 6, and C dif,emb is the device-dependent efficiency of edge-modified barrier [dB].
The edge of hypothetical barrier corresponds to the intersection of the two straight lines SO and PO
in Figure 6, which are the line through the point source and the source-side edge of theedge-modified barrier, and the line through the prediction point and the receiver-side edge,
respectively.
3.5 Low-height barrier, ∆Ldif,low
The calculation method of the correction term ΔLdif,low for the diffraction around a barrier with aheight of 1 m or less [dB] follows the method of "ASJ RTN-Model 2013", and ΔLdif,low is given as theinsertion loss of the barrier:ΔLdif,low = ΔLd,k,1 − ΔLd,k,0(13)
where ΔLd,k,1 and ΔLd,k,0 are ΔLd ,k for O1 (an edge of the barrier) and O0 (an intersection of the barrier
and the ground) shown in Figure 7, respectively.
3.6 Transmission through barrier, ∆Ldif,trans
The correction term ΔLdif,trans for the transmission [dB] is obtained as a function of the diffracted
sound, the sound energy through the hypothetic opening corresponding to the width of the barrier,and the sound transmission loss of the barrier considering the A-weighted spectra of road traffic
noise.

4. Correction for Ground Effect, ∆Lgrnd
4.1 Fundamental correction term for ground effect, ∆Lg
The sound wave propagating above a ground with a finite impedance is attenuated due to theinterference of the direct wave and the reflected one on ground surfaces. The ground effect by theinterference is calculated using the fundamental correction term ΔLg [dB] determined as thedifference between the A-weighted sound pressure level propagating above the ground with a finite
impedance and that above the rigid surface, as follows [11]:X

Table 3 – Coefficient values of Cdif,obCoefficient values
Type of overhung
barrierA
B
C
T-type3.0
10
1.0
Y-type3.5
10
2.0
L-type1.5
10
1.5
Semi-Y-type
1.5
10
1.5

S
Hypotheticalobstacle

Y
P

Y

S

S

Y

P

(d) Semi-Y-type

Figure 5 – Calculation of diffraction aroundoverhung barrier.

Y

S

O1

Edge-modified
barrierUpper diffraction pathP

Road

Figure 6 – Calculation of diffraction aroundedge-modified barrier.

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X
P

P

HypotheticalbarrierP(b) L-type(c) Y-type
XYS(a) T-type

X

O

X

S
Hypotheticalbarrier

O0

GroundLower diffraction path

Figure 7 – Calculation of diffraction arounda low-height barrier.

r⎧⎪− K lgrc
ΔLg = ⎨
⎪0⎩r ≥ rc(14)r ≥ rcwhere ΔLg is the fundamental correction term for ground effect under consideration of spectral
characteristic of road traffic noise, K is a coefficient for the excess attenuation, r and rc are thepropagation distance [m] and the critical distance [m], respectively. K and rc depend on the type ofground surface. Equations for K and rc for loose soil, grassland, and compacted ground were provided
as a function of the height of propagation path in previous version of the ASJ RTN-Model. In thisversion, equations for K and rc for propagation above porous asphalt pavement is newly added [12].
4.2 Calculation method of ground effect for several road types, ∆Lgrnd
The correction term ΔLgrnd for excess attenuation by ground effect from a vehicle S to a receiver P
is calculated as the summation of fundamental correction terms ΔLg,i from S to P as shown in Figure 8:
ΔLgrnd =

n

∑ ΔL

(15)

g,i

i =1

where ΔLg,i is fundamental correction term ΔLg [dB] for ground effect due to the i th ground surface.
ΔLg =0 [dB] for road surfaces paved with dense asphalt or gap-graded asphalt pavement. When theattenuation by ground effect exceeds approximately 30 dB, it may not be so large as to be indicated by
the calculated values because of the influence of actual wind conditions.

5. Correction for Air Absorption, ∆Lair
The correction due to air absorption ΔLair is specified on the basis of the standard atmosphericcondition of 20°C temperature and of 60 % relative humidity and it is given as follows:
2

3

⎛ r ⎞
⎛ r ⎞
⎛ r ⎞
ΔLair = −6.84 ⎜⎟ + 2.01⎜⎟ − 0.345 ⎜⎟⎝ 1000 ⎠⎝ 1000 ⎠⎝ 1000 ⎠where, r is the distance [m] between a source point S and a prediction point P.

(16)

6. Calculation Methods of Sound Reflection
For the calculation methods of sound reflection, two kinds of calculation methods are prepared inthis model. One is specular reflection method applied to flat surface with sufficiently large size and theother is scattered reflection method employed to uneven surface.
6.1

Specular reflection method

6.1.1 Basic equation
This method is applied to flat surface with sufficiently large size in comparison with thewavelength. The reflection in this situation is equivalently considered as the diffraction from amirror-image source S' of a real source S to receiver P around a hypothetical absorbing barrier, which
is set complementarily to the original reflecting surface, as shown in Figure 9. The specular reflection
is calculated as
LA,refl = LWA − 8 − 20 lg r + ΔLrefl + ΔLabs(17)
where LA,refl is the A-weighted sound pressure level of the reflected sound [dB], r is the path lengthfrom S' to P [m], ΔLrefl is the correction term for reflection and ΔLabs is the correction term for the

ΔLg,2

ΔLg,3

P

ΔLg,2

r2

ΔLg,1

ΔLg,1
r1
S

S
P

Road surface

r3

P

r2

r1
P

Slope

Road surface
Ground(a) Flat (with barrier)(b) Bank
Figure 8 – Calculation of ground effects for various terrains.

Ground

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S'

S'

r
Hypothetical barrier
Semi-infinitereflecting plane

O

O
P

S

P
S

(b) Propagation from a mirror-image source(a) Reflection from a semi-infinite flat plane

Figure 9 – Calculation of sound reflection on a semi-infinite flat plane by the specular reflection method.
absorbing characteristics of the reflecting surface [dB].
6.1.2 Fundamental correction term for reflection, ∆Lr
The correction term ΔLrefl is calculated using fundamental correction term ΔLr as a function of thediffraction path difference δ [m] between the path S'OP and the path S'P. ΔLr is described as
cspecδ ≥ 1⎧⎪− 20 − 10 lg(cspecδ )ΔLr = ⎨
(18)
−1
0.33
⎪⎩− 3 − 19.3 ⋅ sinh ((cspecδ ) ) 0 ≤ cspecδ < 1
The values in Table 2 are applied to the coefficient c spec.
6.1.3 Correction term for reflection on a semi-infinite plane, ∆Lrefl
The correction term ΔLrefl for reflection from a semi-infinite plane in Figure 9(a) is calculated
considering the hypothetical barrier in Figure 9(b) as follows:
for S′ invisible from P
⎧ ΔLr
⎪
ΔLr
⎛
⎞
ΔLrefl = ⎨(19)
10
for S′ visible from P⎪10lg ⎜⎜1 − 10 ⎟⎟⎝⎠⎩6.1.4 Correction term for reflection on a finite-width plane, ∆Lrefl,slit (slit method)
As shown in Figure 10(a), we consider the flat reflective plane O1–O2 with a finite width and an
infinite length (i.e., a strip). The sound reflected on the plane is equivalently considered as thecontribution from the mirror-image source S' to the prediction point P through slit opening O1–O2 withthe same width as the strip (see Figure 10(b)).The energy of sound passing through the slit opening is
calculated as the difference between the energies of sounds diffracted around the two hypotheticalbarriers shown in Figure 10(c). The correction term ΔLrefl,slit is calculated as
ΔLrefl,1

ΔLrefl,2

ΔLrefl,slit = 10lg 10 10 − 10 10(20)

where ΔLrefl,n (n = 1,2) is defined as ΔLrefl for diffraction point On using Eq.(19).
6.2 Scattered reflection method
For a reflection on the uneven surface such as a bottom of a viaduct road with girders and structuralelements, a method of calculating scattered reflection assuming the Lambert’s cosine law is employed[13].
6.3 Correction for surface absorption, ∆Labs
The correction term for the sound absorption ΔLabs is calculated as follows:
ΔLabs = 10lg(1 − α A,RTN )(21)
where, αA,RTN is an absorption coefficient which is calculated under consideration of spectral
characteristic of road traffic noise.

7. Meteorological effect
Quantitative evaluation of meteorological effects on sound propagation is not easy because themeteorological effect is a complicated phenomenon caused by wind and temperature profiles above3710

ground. Therefore, we investigated theinfluences of the meteorological conditions
on the diffraction and the ground effects bynumerical analysis, and determined the limitof these correction values based on the
numerical results [14].

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S’

O1
Reflecting plane

O2
P

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r
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Equivalent
the Research Committee on Road Trafficslit opening
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P
3. Z. Maekawa, “Noise reduction by barriers, ”
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S'
5. A. Fukushima, S. Sakamoto and Y. Yasuda,“Practical calculation method of noise
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Hypotheticaland Vib. Acoust. Soc. Jpn., N-2018-35
barrier(2018) (in Japanese).
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Figure 10 – Calculation of reflection by the slit method.
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