Insulation materials made of renewable raw materials for the sound insulation
prognosis of building components
Simon MECKING(1) ; Andreas RABOLD(1) ; Anton HUBER(1)(1) Technical University of Applied Sciences Rosenheim, Germany, simon.mecking@th-rosenheim.de

Abstract

In order to increase the application possibilities in the building sector for insulating materials made from renewable raw materials, a project was initiated by the Fachagentur Nachwachsende Rohstoffe e.V. which shows thedifferent requirements for these insulating materials and provides planning and verification options. In the fieldof sound insulation, building component catalogues for these insulating materials are expanded, test methods
for the material properties of the insulating materials are defined and prediction models are further developed.
The airborne and impact sound transmissions of the components are predicted in order to investigate the influence of the different insulating materials from renewable raw materials in comparison to conventional insulating
materials. Component measurements indicate that a characterization of the cavity-insulation alone by the flow
resistance is insufficient. Using a semi-analytical calculation approach with an equivalent fluid, further insulation material properties can be taken into account in the prognosis of two-shell structural elements. The input
data for the prognosis calculation are determined by measurements of the transmission properties and comparedwith results of other calculation models based on the flow resistance. By validating the first prediction resultswith measurements, it should be shown to what extent the conventional measured variables are sufficient.
Keywords: Double shell, Transmission, Prediction models, Renewable, Insulation

1

INTRODUCTION

A significant part of the insulation materials used in the construction industry comes from non-renewable raw
materials. With regard to adequate recycling and the use of energy during production, insulating materials madefrom renewable raw materials have some environmental advantages. Within the research project, it will be
investigated to what extent the acoustic properties of these insulating materials influence the transmission of
airborne sound when used in building components compared to conventional insulating materials.

2

COMPONENT MEASUREMENTS

In a recent project [1] the airborne sound insulation of double walls with various cavity insulations made ofrenewable raw materials was measured. In addition, the flow resistance (r) and the bulk density (ρ) of theinsulating materials were determined. Figure 1 shows the measurement results. The wood fibre and hemp fibre
are panel-shaped insulating materials. The cellulose was blown-in and the sea weed was placed manually as
loose insulating material.
The measurement results using wood fibre and cellulose show the same weighted sound reduction index despite
very different flow resistance. In contrast, hemp fibre and seaweed have the same flow resistance, but sea weed
has an airborne sound insulation that is 6 dB smaller. The low frequency transmission loss of the double studwall with the sea weed is very similar to the variant without insulation material in the cavity. It is assumed
that the stiffness of the fibre-skeleton at low frequencies was responsible for the drop in sound insulation.
The results in Fig. 1 show no correlation between the length-related flow resistance and the weighted soundreduction index. This indicates that the acoustic quality of a fibre insulation material is inadequate described
purely on the basis of this parameter.

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90

80

70
Transmission loss in dB

A and C
60

50

B and D40
A: Rw = 70 dB; wood fibre
B: Rw = 70 dB; cellulose
C: Rw = 68 dB; hemp fibre
D: Rw = 62 dB; sea weed
E: Rw = 56 dB; without

30

20
63

125

250 500
1k
Frequency in Hz

2k

E

4k

Figure 1. Transmission loss of double stud walls with variation of cavity insulation with measured characteristics(A: r = 9 kPa s/m2 , ρ = 46 kg/m3 ; B: r = 36 kPa s/m2 , ρ = 58 kg/m3 ; C: r = 3 kPa s/m2 , ρ = 63 kg/m3 ; D:r = 3 kPa s/m2 , ρ = 75 kg/m3 ). The double wall consists of wooden studs with two layers 12.5 mm and 10 mmof gypsum fibre boards on each side. The cavity depth is d ≈ 140 mm. The measurements were realized at ift
Rosenheim [2].

3

PROGNOSIS FOR DOUBLE-SHELL STRUCTURES WITHOUT CONNECTION

A characteristic parameter in the calculation of sound insulation of double wall constructions is the mass-springmass resonance ( f 0 ), which can be calculated according to (1). Thereby m0 is the mass per unit area of the twoshells and s0 is the dynamic stiffness of the cavity filled with insulating material in N/m3 .
r 
1
1
1 
f0 =
s0
+
(1)
2π
m0 1 m0 2
In a fully description of a porous absorber, the dynamic stiffness is represented by the parts of the skeleton andthe fluid in (2) [3].
s0 = s0 s + s0 a
(2)
The stiffness of air in the pores depends on the dynamic compression modulus (K) and shell distance (d).
s0 a =

Re{K}dwith ps ≤ Re{K} ≤ γ ps

(3)

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For isothermal compression, Re{K} is equal to the static pressure ps . This can be assumed for fibrous insulating materials at low frequencies. At high frequencies the compression is adiabatic, increasing Re{K} by the
adiabatic coefficient (air: γ ≈ 1.402).
3.1 Semi-analytic model
The calculation of the sound insulation for a double wall with sufficient damped cavity can be approximatedwith (4) and (5) from the transmisson loss of the individual shell [cf. 4, 5]. Both measured values and predictedvalues of the transmisson loss for the individual panels can be used as input data. The first term in (4) corresponds to Berger’s mass law for vertical incidence of sound waves. The sound insulation depends substantiallyon the mass per unit area of the shells m0 i and the impedance of the air Z a . The 5 dB in the second term take
into account a correction for a practical, diffuse sound field.
R = 20 lg

 ω (m0 + m0 ) 
1

2

2 Za

− 5 dB( f < f 0)

(4)

Above the mass-spring-mass resonance, the transmission loss can be calculated approximately according to (5)in case the cavity is filled with a porous absorption material [4, 5].
ω 2Z a
R ≈ R1 + R2 + 20 lg 0
( f > f 0)
s 1
(5)
≈ R1 + R2 + ∆R
The dynamic stiffness of the interlayer is s0 and can be calculated with the frequency-dependent distinction ofcases according to (6) [5], if the insulating material has flow resistance of r ≥ 5 kPa s/m2 .
(ρ a ca 2( f ≤ f d)
0
d
(6)
s ≈
ω Za
( f > f d)
The change between the calculation methods of the dynamic stiffness of the cavity depends on the wavelength
ratio to the shell distance. In [cf. 4–6] the frequency f d is calculated according (7).1 After that the transmission
loss above f d increases by 6 dB compared to the sum of the transmission loss of the two individual shells.
fd =

1 ca
55
≈
2π d
d

(7)

3.2 Modified model
In order to be able to consider the dependency of the characteristic insulation properties in the prediction of
airborne sound insulation, a rigid skeleton is assumed in the case of insulating materials that are not loaded byforce and an equivalent fluid is assumed as a substitute model. Depending on the shell distance, at medium or
higher frequencies cavity resonances ( f HR ) after (8) can occur, which reduce the sound insulation. Where c isthe complex phase velocity in the equivalent fluid.
f HR,n = n

Re{c}
2d

mit

n = 1, 2, 3...

(8)

By using a porous absorber the reduction of transmission loss can be minimised. The absorber reduces thestiffness of the air layer and attenuates cavity resonances. In the modified model, the resulting dynamic stiffness
is calculated from the superposition Ares of the individual cavity resonances multiplied by dynamic stiffness ofthe equivalent fluid acc. (3). For each resonance, a foot-point excited, damped single-mass oscillator is assumed.
1 In [5] 4 instead of 2π is given for the transition of the equations, but 2π is also used in the diagram of the source reference. The 2π also resultsfrom the crossover frequency of the two equations in (6).

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Also the bulk modulus at the mass-spring-mass resonance in (3) and (1) can be determined iteratively with theuse of the specific insulation properties of the equivalent fluid. The corresponding values from the standards are
additionally shown in Fig. 2. The loss factor (η) for the amplification function Ai of an individual resonancecan also be calculated from the dynamic bulk modulus according to (9).
Im{K}
Re{K}

η=

(9)

To correct the difference in impedance between air and the cavity filled with insulating material, a further ratio
between these impedances is added in (10). With decreasing frequency the influence of this correction on the
result increases. The difference caused by the impedance correction is exemplarily shown in Figure 3.
R ≈ R1 + R2 + 20 lg ωΦ 2ZZa a0s a Ares 1 Re{Zc }(10)≈ R1 + R2 + ∆Rmodified
3.3 Equivalent fluids
For this approach, it is assumed that the fibre-skeleton is rigid, is not shifted and the coupling between skeleton
and fluid is negligible. If there are doubts, a complete poroelastic model should be used. The dynamic bulk
modulus of the absorber is calculated according to (11) from the characteristic wave impedance (Zc ) and the
propagation coefficient (γ) or the complex phase velocity (c) [see 7, 8].
K = jωZc= c Zcγ(11)3.3.1 Semi-empiric models for fibre absorbers
The characteristic impedance and the propagation coefficient can be calculated on the basis of the flow resistanceusing semi-empirical models for fibre materials [cf. 9–11] according (12) and (13). The basis of the different
fit parameters in the models are regression analyses of measurement results from glass wool and rock wool
samples, which often show a porosity close to one.
Zc = R + jX
 f −0.754  h 
 f −0.732 i= Z a 1 + 0.0497+ j Z a − 0.0758
[9]
r
r

 f −0.632  h 
 f −0.632 i= Z a 1 + 0.0699+ j Z a − 0.107
[10]
r
r



f 6.2  h 
f 4.1 i= Z a 1 + 0.00027 2 − lg
+ j Z a − 0.0047 2 − lg
[11]rr
γ = α + jβ
 f −0.595 i ω h f −0.700 i
ωh
0.169
+j
1 + 0.0858
[9]
=
ca
r
ca
r
 f −0.618 i ω h f −0.618 i
ωh
=
0.160
+j
1 + 0.109
[10]
ca
r
ca
r

f 4.1ωhf 6.2 iω= 0.0069
2 − lg+j
1 + 0.0004 2 − lg
[11]
ca
r
ca
r

(12a)
(12b)
(12c)

(13a)
(13b)
(13c)

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3.3.2 Macroscopic model for fibre absorbers
A more sophisticated prognosis under consideration of further macroscopic parameters is the calculation of thecharacteristic impedance and the propagation coefficient according to Johnsen-Champoux-Allard (JCA) [8, 12]
in (14) and (15). In addition to the flow resistance, the porosity Φ, the tortuosity τ, the viscous and thethermal length (Λ, Λ0 ) of the insulating materials are also taken into account. In describing the air, the Prandtl
number Pr and the dynamic viscosity µ are also required.
"(γ − 1)r
K(ω) = γ ps γ − 0j 4 µ τ 2 Pr ρ a ω
Φr
1 + jτ Pr ρ ω 1 +
0
2
2
02
Φ Λ r
a
r
h
Φr
j 4 µ τ2 ρa ω i
ρ(ω) = ρ a τ 1 +1+
j τ ρa ωΦ2 Λ2 r2

#−1
(14)

(15)

In Fig. 2 dynamic bulk modules, loss factors and phase velocities resulting from the macroscopic and semiempirical models are presented for the parameter data sets 1 and 2 of Tab. 1.
·105
0.15

Air, adiabatic (γ ps )ISO 12354-1:2017, Gl. D.2
1

Air, isothermal (ps )

0.8

0.05

0

Delany 1970
Miki 1990
Komatsu 2008
JCA 1987-1992

0.6

0.4

0.2

0

0.1

DIN 4109-34:2016, Gl. 2

phase velocity c in m/s

dynamic bulk modulus K in Pa

1.2

loss factor η

1.4

63

125

250
500
1k
Frequency in Hz

2k

4k

63

125

250

500

1k

2k

4k

250
500
1k
Frequency in Hz

2k

4k

Air, ca = 343 m/s

300

200

100

0

63

125

Figure 2. Properties of equivalent fluids calculated acc. to empirical models [9–11] for Par. 2 and a macroscopic
model acc. to Johnson-Champoux-Allard (JCA) [12, 13] for Par. 1 from Tab. 1. The imaginary parts are grey.

3.4 Application
Figure 3 shows the influence of the cavity from the modified calculation compared to that of the semi-empiricalapproach [4, 5] and to the values [15] obtained from measurements. The modified prediction shows a better
agreement to the measurement results in the frequency range of cavity resonances. The significant reductions in1414

Table 1. Characteristics of insulation materials.

Par. 1 [14]Par. 2Par. 3 [14]rkPa s/m2
5.20
5.20
11

1.00

Λ
µm
131

Λ0
µm
187

1.40

58

122

Φ

τ

0.95
0.94

sound insulation are probably due to the fact that only the vertical sound incidence was taken into account in
the prediction. The double-shell wall consisted of two 16 mm chipboards and a mineral fibre insulation in thecavity. To calculate the equivalent fluid, the empirical model according to [11] was used with a flow resistanceof r = 5.2 kPa s/m2 (Par. 2) .
Figure 4 shows the resulting transmission loss from the measurements against two different parameter data sets
for the insulation material using the modified calculation. The type of insulation material can lead to significant
differences in transmission loss.
Measurement: R − R1 − R2 acc. (5)Modified, Par. 2, acc. (10)Modified, Par. 2, with Z a / Re{Zc } = 1
Semi-analytic, acc. (5)Cavity influence ∆R in dB

20

10

0
f HR,2−10

f HR,1

−20
f0
63

125

250 500
1k
Frequency in Hz

2k

4k

Figure 3. Cavity influence ∆R according to modified model with properties of equivalent fluid (Par. 2 from
Tab. 1) according to [11] compared to the semi-analytical approach [4, 5] and the values determined from measurements [15].

4CONCLUSIONSWith the modified prediction model, the transmission loss through the cavity resonances and the mass-springmass resonance can be calculated using amplification functions of a damped oscillator with a single degreeof freedom. The equivalent fluids used for this purpose make it possible to calculate these depending on thecharacteristics of the insulating material. This makes it possible to evaluate the acoustic quality of insulating
materials made from renewable raw materials in comparison to conventional insulating materials.
The next steps are to use insulation properties determined by measurement at PTB Braunschweig [cf. 16] as
input data for the prognosis and to compare them with component measurements. In addition, the transmission
via studs will be integrated into the prognosis.

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70

Transmission loss in dB

60

50

40

30

d = 91 mm

20

Rw = 54.1 dB, Measurement
Rw = 53.5 dB, modified, Par. 2
Rw = 50.5 dB, modified, Par. 3

10

63

125

250 500
1k
Frequency in Hz

2k

4k

Figure 4. Predicted transmission loss for two insulation material parameter datasets (Par. 2 and 3 from Tab. 1)
compared to measurements [15].

ACKNOWLEDGEMENTS
The results are from subproject 3 of the joint research project Mehr als nur Dämmung - Zusatznutzen von Dämmstoffen aus nachwachsenden Rohstoffen funded by Bundesministerium für Ernährung und Landwirtschaft (BMEL)
via Fachagentur Nachwachsende Rohstoffe e.V. (FNR) with the funding code 22005516.

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