NISTIR 88-3882

An Acoustical Technique

for Evaluation of Thermal

Insulation

Daniel R. Flynn, David J. Evans, and Thomas W. Bartel

U.S. DEPARTMENT OF COMMERCE

National Institute of Standards and Technology

(Formerly National Bureau of Standards)

National Engineering Laboratory

Center for Manufacturing Engineering

Gaithersburg, MD 20899

April 1989

National Bureau of Standards became the

National Institute of Standards and Technology on August 23, 1988, when the Omnibus Trade and

Competitiveness Act was signed. NIST retains

all NBS functions. Its new programs will encourage

improved use of technology by U.S. industry.

Prepared for: U.S. Department of Energy

and

Mineral Insulation Manufacturers Association

U.S. DEPARTMENT OF COMMERCE

Robert Mosbacher, Secretary

NATIONAL INSTITUTE OF STANDARDS

AND TECHNOLOGY

Raymond G. Kammer, Acting Director

Table of Contents

Page

List of Figures and Table iv

Abstract 1

1 . Introduction 1

2. General Technical Approach 2

3. Experimental Procedure 6

3.1 Acoustical Test Chamber 6

3.2 Instrumentation 9

3.3 Test Procedures 11

3.4 Test Samples 12

4. Experimental Results 13

4.1 Coverage . 13

4.2 Thermal Resistance 27

5. Prospects for Field Use 27

6. Conclusions 38

7 . Acknowledgments 39

8. References 40

List of Figures

Fig. 1 Instantaneous sound pressure (arbitrary units) versus time

for a 40-kHz sine wave 4

Fig. 2 Conceptual schematic of an acoustic plane wave traveling from

a sound source through a porous insulation to a sound receiver . . 7

Fig. 3 Schematic drawing of a compact source projecting sound downward to a parabolic reflector, upward through the sample to

another parabolic reflector, and then downward to a measuring

microphone 7

Fig. 4 Photograph of the test chamber with a sample basket installed. . . 8

Fig. 5 Lower half of the test chamber showing the loudspeaker, the

lower reflector, and the sound-absorbing wedges 9

iii
Page

Fig. 6 Central portion of the test chamber showing the microphone, the

region where the sample basket is installed, the wires that

support the sample basket, and the top of the downward- facing

loudspeaker 10

Fig. 7 An example data set of sound insertion loss versus frequency

for the 1/3-octave bands with center frequencies from

2.5 to 25 kHz 12

Fig. 8 Measured coverage versus sound insertion loss at 10 kHz for

the bonded fiberglass samples (both the blanket and

the blown materials) 15

Fig. 9 Measured coverage versus sound insertion loss at 10 kHz for

the blown unbonded fiberglass samples 16

Fig. 10 Measured coverage versus sound insertion loss at 10 kHz for

the blown rockwool samples 17

Fig. 11 Measured coverage versus sound insertion loss at 10 kHz for

the blown cellulose samples 19

Fig. 12 Percentage change in insertion loss, plotted versus sound

frequency, due to compressing a blown bonded fiberglass

sample to two different thicknesses 20

Fig. 13 Percentage change in insertion loss, plotted versus sound

frequency, due to compressing a blown unbonded fiberglass

sample to two different thicknesses 21

Fig. 14 Percentage change in insertion loss, plotted versus sound

frequency, due to compressing a blown rockwool sample to two

different thicknesses 22

Fig. 15 Percentage change in insertion loss, plotted versus sound

frequency, due to compressing a blown cellulose sample to two

different thicknesses 23

Fig. 16 Measured coverage plotted versus predicted coverage for the

blown fiberglass samples, both bonded and unbonded 24

Fig. 17 Measured coverage plotted versus predicted coverage for the

blown rockwool samples. The prediction equation was of the

form of Eq . (7) 25

Fig. 18 Measured coverage plotted versus predicted coverage for the

blown rockwool samples. The prediction equation is discussed

in the text 26

IV
Page

Fig. 19 Thermal conductivity versus installed density for the two

types of blown fiberglass material 28

Fig. 20 Thermal conductivity versus installed density for blown

rockwool and blown cellulose 29

Fig. 21 Thermal resistance versus sound insertion loss, at 10 kHz,

for the blown bonded and unbonded fiberglass samples 30

Fig. 22 Thermal resistance versus sound insertion loss, at 10 kHz,

for the blown rockwool and cellulose samples 31

Fig. 23 Thermal resistance computed from density and thickness versus

thermal resistance predicted from sound insertion loss and

thickness for the blown bonded and unbonded fiberglass samples . . 32

Fig. 24 Thermal resistance computed from density and thickness versus

thermal resistance predicted from sound insertion loss and

thickness for the blown rockwool samples 33

Fig. 25 Thermal resistance computed from density and thickness versus

thermal resistance predicted from sound insertion loss and thick- ness for the blown cellulose samples 34

Fig. 26 One experimental configuration for field measurements of the coverage or thermal resistance of blown- in-place attic insulation ... 35

Fig. 27 Experimental configuration for field measurements of the density

or thermal conductivity of blown- in-place attic insulation when

it is not practical to enter the attic space 36

List of Tables

Table 1 Thickness, coverage, and density of the test samples 14

v
.

-

.
Abstract

A laboratory apparatus has been constructed that enables rapid measurement of

the sound insertion loss of a sample of insulation as a function of frequency.

An extensive series of measurements of the sound insertion losses associated

with blown samples of fiberglass, rockwool, and cellulose has been completed;

the results of these acoustical measurements are highly correlated with

coverage (mass per unit area) and thermal resistance (R-value). An investigation is planned to extend the acoustical techniques used in the laboratory

apparatus to in-situ determination of the sound transmission loss through

thermal insulation installed in attics. Two possible approaches to such field

measurements are described.

KEY WORDS; acoustics, attic insulation, heat flow, heat transfer, insulation, non -destructive evaluation, non-destructive testing, sound attenuation, sound

propagation, thermal conductivity, thermal insulation, thermal resistance.

1. Introduction

There is convincing evidence that the customer may not always be getting his

money's worth when he purchases blown- in-place attic insulation, either because

the insulation is not applied properly or because the quantity of insulation

delivered is less than that purchased. In 1982, for example, the Florida state

attorney's office tested 639 homes and found [1] that about 70 percent of the

houses insulated by some contractors had less than 90 percent of the insulation

claimed to have been installed. An investigation of an insulation certification program by the state of Georgia found [2] that over two- thirds of the

"certified" homes actually had less than 90 percent of the required insulation.

In addition to the customer being short-changed at the time of purchase, the

failure to provide the specified amount of insulation leads to higher fuel

bills over the life of the building. The overall economic implications of

inadequate insulation of attics are believed to be very significant.

The present procedure for measuring the quantity of insulation installed in an attic is to send one or more workers into the attic to measure the thickness of

the insulation, using a ruler, and to measure the density of the insulation,

using a circular cutter [3] to acquire samples for weighing. This procedure is

costly, in terms of the labor requirements, and destructive, in terms of

disruption of the insulation.

Ideally, one would like to use a measurement technique that directly indicates

the thermal performance of the installed insulation. Unfortunately, a review

of possible thermal techniques for making such a measurement indicates that

direct measurement of thermal performance poses several problems. Thermal

resistance measurements inherently involve measurement of a heat flux. For

large thicknesses of attic insulation, the heat fluxes are very small and

difficult to measure accurately in the field. The problem is compounded by the

difficulty of evaluating the influence of heat flows — along the ceiling,

through framing members, and, most importantly, to or from the attic space and

1
to or from the rooms beneath the attic — that do not pass through the attic

insulation. Furthermore, the time constants involved in direct measurement of

the thermal resistance of installed attic insulation could be many hours.

In December, 1984, the Mineral Insulation Manufacturers Association (MIMA)

informed [4] the National Institute of Standards and Technology (NIST), then

known as the National Bureau of Standards, that "...there is a national need to

develop a field measurement technique to determine the installed loose fill Rvalues of thermal insulation. Other legal requirements such as the FTC Home

Insulation Rule require a reliable measurement technique. The installer,

builder, utility, code official and, most importantly, the consumer need a means to measure installed R-values. The technique should be accurate, fast,

nondestructive and economical. Recent efforts in the industry, and elsewhere,

to devise a measurement technique have not been satisfactory." MIMA went on to

ask NIST to address this measurement need.

Following meetings between MIMA and NIST technical personnel, a "Workshop on New Methods to Measure the R-Value of Thermal Insulation" was held at the

National Association of Homebuilders in Washington, D.C., in June of 1985, with

approximately 70 people in attendance. At this workshop, there was extensive

discussion of the nature of the problem and a general endorsement of the need

for improved measurement procedures. NIST staff then described an acoustical

technique for indirect measurement of either the coverage (mass per unit area)

or the thermal resistance (R-value) of installed attic insulation by passing

sound waves through a sample of material and measuring the sound insertion loss

(i.e., the decrease in sound pressure level) caused by the insulation. A live

demonstration of one simple implementation of this acoustical technique was given at the Workshop. NIST indicated that the development of such a technique

as a practical field device would require considerable effort but that the

preliminary analysis and results looked quite encouraging.

The present paper (1) describes the acoustic technique that was proposed in

1985 by NIST, (2) presents the results of a pilot study (funded by MIMA, the

U.S. Department of Energy, and NIST) to examine the feasibility of this

technique for measurement of insulation coverage (or density) and thermal

performance, and (3) indicates how this technique could be extended to enable

practical field measurements of the adequacy of installed insulation.

2. General Technical Approach

When a sound wave passes through a porous material, such as loose-fill insulation, the sound wave undergoes both amplitude attenuation and a phase shift

that depend on the nature of the material and on the frequency of the incident

sound wave. For example, the sound attenuation characteristics of fibrous

materials are dependent upon, in addition to the frequency of the sound wave,

the type of fiber, the distribution of fiber diameters, the surface condition

of the fibers, the binder, the installed density, and the type and density of

the gas filling the pores of the material. There is an extensive literature

devoted to theoretical and empirical relationships between these factors and

the sound attenuation characteristics of fibrous materials. The same factors

2
which affect the propagation of sound in a fibrous material also affect thermal

conductivity, and hence R-value.

The time-dependent sound pressure associated with an ideal plane acoustic wave traveling in the positive x-direction in a porous medium can be expressed as

p = p (x , t ) = p(0 , t) exp (~7x) , (1)

where p(0,t) is the sound pressure that would exist, independent of position,

in the absence of attenuation, t is time, and 7 is the complex propagation

coefficient, which can be written as

7 = q + , (2)

where the real part a is called the attenuation coefficient and the imaginary

part (3 is the phase coefficient. The attenuation coefficient, which is a property of the porous medium and of the frequency of the sound wave, determines

the decay of the sound pressure with distance in the medium. The phase coefficient, which also is a property of the medium and the sound frequency,

describes the speed of sound propagation through the medium.

Figure 1 illustrates the behavior described by Eq . ( 1 ). The solid curve represents the sound pressure observed when an acoustic sine wave passed

through air from a 40 -kilohertz source to a receiving microphone. The curve designated by long dashes represents the received sound pressure when a sample

of R-ll fiberglass insulation was interposed between the source and the receiving microphone, while the curve shown as short dashes illustrates the received

sound pressure when two pieces of R-ll insulation were interposed. It is seen

that as additional absorptive material is placed in the sound path, the amplitude of the sinusoidal sound wave decreases, the change being described by the

attenuation coefficient (a), and the phase of the sine wave is shifted, by an amount described by the phase coefficient (f)) .

The mean-square sound pressure, which is independent of time, at the position x

is given by

p

2 = p 02 exp (—

2

qx) , (3)

where p G

2 is the mean-square value of p

2 at x = 0 . The sound insertion loss,

defined as the decrease in sound pressure level in decibels (with attenuation

present) relative to the sound pressure level that would exist if there were no attenuation, is

D = -10 log ^ 0 (P

2 /P0

2

) = -1 ° l°gl 0

[ exp (—2qx)

]

= 8.686ax . ( 4 )

Thus, the sound insertion loss is proportional to the product of the attenuation coefficient and the sample thickness.

Delaney and Bazley [ 5 ] have developed empirical relationships expressing the

attenuation and phase coefficients of fibrous absorbent materials as simple

power-law functions of the ratio of the sound frequency divided by the specific

flow resistance of the material. Bies [6] has presented an empirical relation3
No insulation 1 batt, R-1

2 batts, R-1

ui

ccD

CO

(0

LU

CC

Q.

Q

O

(0

0 20 40 60 80 100

TIME (ms)

Fig. 1 Instantaneous sound pressure (arbitrary units) versus time

for a 40-kHz sine wave. The solid line corresponds to

propagation through air. The long-dash line illustrates

the attenuation and the phase shift due to interposing a 9-cm thick sample of fiberglass (1 R-ll batt) between the source and the receiver, while the short-dash line

indicates the sound pressure with 18 cm (2 R-ll batts) of

insulation in place.

ship giving the specific flow resistance of fiberglass products in terms of the

fiber diameter and the installed density of the material. Combining Delaney

and Bazley's expressions with the Bies relationship enables us, for randomly

oriented fibrous material, to express the attenuation and phase coefficients in

terms of the installed density, p, of the insulation, the average fiber

diameter, d, and the sound frequency, f. The resultant expression for the

attenuation coefficient is

a = a

o (5)

where a 0 is a reference attenuation coefficient corresponding to the values p =

p Q , d = dQ , and f = f G

. The three exponents in Eq . (5) have the approximate

U
values n ~ 0.9, v ~ 1.2, and £ ~ 0.4. These exponents vary somewhat for

different materials. The phase coefficient will not be discussed further in

the present paper.

Although there may be a considerable range of fiber diameters within a given

batch of fibrous insulation, a representative fiber diameter may be determined.

Since the sound frequency can be fixed experimentally, one can take d = dQ , f =

fQ , and Eq. (5) yields the following simple relationship between the attenuation coefficient and the installed density of the insulation:

Thus, for a given material it is not necessary to know v and £. The coverage,

or mass per unit area, of installed insulation in an attic is given by W = pi,

where i is the thickness of the insulation. Combining this equation with Eqs

.

(4) and (6), the coverage is related to the sound insertion loss by the

expression

where rj = 1/p and K is a material - dependent proportionality constant. The

parameter rj will have a value not too different from unity so that the sample

thickness, i, need not be known very accurately in order to use Eq . (7). For

the special case where rj = 1 , Eq . (7) reduces to simply W = K • D, i.e., the

coverage is proportional to the sound insertion loss.

It is well known that the effective thermal conductivity of a given loosefill

insulating material depends upon the installed density of that material. For

mineral fiber insulations, the effective thermal conductivity, A, of relatively

thick insulation can be represented in terms of the installed density, p, of

the material by an equation of the form

where A, B, and C are constants, with (approximately) A representing the

thermal conductivity of the gas (air) filling the insulation, Bp representing

heat conduction through the fibers and the interaction of that conduction with

the surrounding gas, and C/p representing the radiative heat transfer through

the porous insulation.

The thermal resistance of the sample can be expressed as

If the density of the sample is constant, so is the denominator of Eq . (9) and

the thermal resistance of the sample is proportional to the coverage. Thus, by

way of Eq . (7), the thermal resistance can be expressed in terms of the sound

insertion loss and the sample thickness. For the more general case where the

installed density is variable and unknown, the density can be estimated from

the sound insertion loss and the thickness. Dividing both sides of Eq . (7) by

i yields, since W = pi,

a = q

o

( 6 )

W = K • i

1_r?

(7)

A — A + Bp + C/p ( 8 )

W

(9)

5
P = K ( 10 )

• (D/i)^

this value of p can be used to compute the denominator of Eq . (9). Thus if the

functional relationship between thermal conductivity and density is known

(i.e., if A, B, and C are known for the example above), the thermal resistance

can be obtained from the measured sound insertion loss and the approximate

sample thickness.

3. Experimental Procedure

3.1 Acoustical Test Chamber

The apparatus designed and constructed for the acoustical measurements is

conceptually similar to a guarded hot plate apparatus used for thermal resistance measurements. Ideally, as indicated in Fig. 2, a sound source projects a plane collimated sound wave upward through the sample to a receiver above the

sample. Measurement of the sound levels at the receiver with the sample

present and with the sample absent enables calculation of the sound insertion

loss (see Eq . (4)). This experimental configuration was achieved using the

components illustrated in Fig. 3. The sound source consisted of a small

loudspeaker located at the focal point of an upward- facing parabolic reflector

used to produce an approximately collimated beam of sound. The insulation

sample was held in a wood-sided basket with a screen bottom to allow passage of

the sound wave. The sound receiver was a condenser microphone located at the

focal point of a downward- facing parabolic reflector.

The test chamber is shown to the right of the photograph in Fig. 4. The two

parabolic reflectors, the source transducer (loudspeaker), the measuring microphone, and a support shelf for the sample baskets were housed inside a cabinet

approximately 0.9 mby 0.9 m by 2.1 m high. The interior walls of the cabinet

were lined with 20-cm by 20-cm by 25-cm deep wedges constructed from fiberglass

board (Owens-Corning Fiberglas Type 703, nominally of 50 kg/m^ density), except

for a nominally 40-cm high section above the sample-basket support shelf (to

allow room inside the enclosure for the insertion of a sample basket or baskets) and certain areas of the walls, e.g., corners, which were not com- pletely covered by the wedges due to geometrical constraints — these portions

were covered with a 5-cm or a 15-cm thick layer of fiberglass board, as appropriate.* The interiors of the floor and ceiling of the cabinet were covered with a 5-cm layer of fine - fiberglass aircraft insulation (Owens-Corning

Fiberglas Type PF-105), which has a much higher sound attenuation coefficient

than does the fiberglass board used for lining the rest of the cabinet.

^Certain trade names and company products are identified in this report in

order to specify adequately the experimental procedures that were followed. In no case does such identification imply recommendation or endorsement by the

National Institute of Standards and Technology, nor does it imply that the

products identified are necessarily the best available for the purpose.

6
;j RECEIVER

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D §°o 0 o

0 o

0 o°o c

°ogSgog5gogogSgc

igSgSgSgSgSgSgSg

" °o 0 o

0 a0 o0 o°o 0 o

3 o°o 0

o

0 o0 o0 o°o OnO„o;o„OnOf ’ogogSgogogSgo ^ogogogogogogo^ogogojo

§2§2§2§2o2§2§2o2§2o2§2J

0 o°o°o 0 o 0 o °o 0 o

0 o

0 o°o

°o 0

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0 o°o

°o 0 n°o 0 o

0 o g§gSgSg§g§

o

0o

o

o

o

o

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o

SOURCE

Fig. 2 Conceptual schematic of an acoustic plane wave traveling

from a sound source through a porous insulation to a sound

receiver

.

Parabolic reflector

\Mesh

Loudspeaker

Parabolic reflector

Fig. 3 Schematic drawing of a compact source projecting sound

downward to a parabolic reflector, upward through the

sample to another parabolic reflector, and then downward

to a measuring microphone.

7
Fig. 4 Photograph of the test chamber with a sample basket

installed. The scientist is measuring the thickness of

another sample, which is resting on a digital balance.

The sample baskets, one of which is shown installed in the test chamber in Fig.

4, had nominal inside dimensions of 53 by 53 cm and nominal heights of 15 or 23 cm. The baskets were constructed from 1.3-cm thick unfinished plywood, were open at the top, and had nylon window screen stretched across the bottom to

hold the material in the baskets (the baskets were transported with a piece of

fiberboard underneath to prevent the screen from sagging in the center of the

basket and thus possibly altering the distribution of material within the

basket). The inside of each of the walls of the baskets was lined with 2.5-cm

thick 50-kg/m^ fiberglass board insulation to reduce acoustical reflections

within the baskets during testing. The sides of the baskets were held together

with glue and metal finishing nails, and the nylon screen was attached to the

outside of the walls of the baskets with metal staples and nylon tape.

Figure 5 is a close-up photograph of the lower half of the test chamber,

showing the loudspeaker, the lower parabolic reflector, and a better view of

the sound absorbing wedges used to minimize unwanted sound reflections inside

8
Fig. 5 Lower half of the test chamber showing the loudspeaker,

the lower reflector, and the sound- absorbing wedges.

the chamber. Figure 6 provides a view of the portion of the test chamber where

the sample baskets are installed in the region between the supporting wires and

the height at which the absorbing wedges begin. The supporting wires prevent

the nylon screen bottom of the sample basket from sagging. The measuring

microphone can be seen near the top of the Fig. 6. The test results given in

this paper are very insensitive to loudspeaker and microphone placement.

3.2 Instrumentation

The instrumentation used to make the acoustic measurements consisted primarily

of a signal generator, filter, and amplifiers to provide the signal to the

loudspeaker. A microphone preamplifier, measuring amplifier, and dynamic

signal analyzer were used to measure the voltages produced by the signal

generator and the measuring microphone.

9
Microphone

Supporting

Wires

Loudspeaker

Sample Space

Fig. 6 Central portion of the test chamber showing the microphone, the region where the sample basket is installed,

the wires that support the sample basket, and the top of

the downward- facing loudspeaker.

The signal used to drive the loudspeaker was a highpass-f iltered swept sine wave that was gated to produce a "chirp" of 1-ms duration. The chirp was repeated every 200 ms. The signal was gated such that the frequency sweeps at

the output of the signal generator began and ended on a positive-going zero- crossing. A trigger circuit was used to synchronize the signal analyzer with

the rest of the measurement instrumentation. The signal generator was com- prised of two function generators (Hewlett Packard Model 3314A) . The first

function generator produced a voltage ramp that was repeated every 200 ms and

drove a voltage-controlled oscillator that was part of a second function

generator. The second function generator was set to produce an integral number

of cycles within each frequency sweep and then gate "off" until receiving the

next trigger from the first function generator. The output of the second

function generator was followed by a wide-band amplifier (Hewlett Packard Model

10
467A) and high-pass filter (consisting of a 200 pF capacitor in series with the

input stage of the amplifier) to shape the spectrum of the "chirp." The

filtered waveform of the test signal was amplified by a power amplifier

(McIntosh Model 7270) that drove the loudspeaker (Analog and Digital Systems

25-mm dome tweeter, Part No. 206-0114, without protective grid).

The output of the measuring microphone (Bruel & Kjaer Type 4165 without

protective grid) was coupled to a preamplifier (Bruel & Kjaer Type 2619) , power

supply (Bruel & Kjaer Type 2801), and measuring amplifier (Bruel & Kjaer Type

2606). The gain of the measuring amplifier was adjusted as needed to match the

input sensitivity of the signal analyzer. The output signal of the measuring

amplifier was time-gated by an electronic switch (General Radio Type 1396-B

Tone-Burst Generator) to prevent undesirable acoustic signals (e.g., delayed

reflections) from occurring during a measurement period. The electronic switch

was triggered by the output of a digital-delay generator (Berkeley Nucleonics

Corp. Model 7010) which was adjusted to provide the proper electronic delay to

compensate for the acoustic delay in the test chamber.

The signal analyzer (Hewlett Packard Model 5420A) was used in a two-channel

mode in which it obtained a transfer function, at 100-Hz intervals up to

25 kHz, for the measurement system between the output of the second function

generator and the output of the electronic switch following the measuring

microphone. The analyzer averaged the results from 100 chirps, or bursts of

sound, obtained with and without the test sample being installed in the test

chamber, and stored these results. The analyzer was later used to take the

complex ratio of the transfer functions obtained with and without the sample

present, thus compensating for the frequency response of the transducers and

instrumentation. A desktop computer (Hewlett Packard Model 9836A) was used to

calculate sound insertion loss, in decibels, and phase shift, in degrees, from

the measurement results. A separate computer (IBM Model XT) was used to

combine the data so as to obtain the average sound insertion losses for the

eleven 1/3-octave band frequencies centered at nominally 2.5, 3.15, 4, 5, 6.3,

8, 10, 12.5, 16, 20, and 25 kHz. Figure 7 shows a representative set of such

data

.

3.3 Test Procedures

The test samples were blown into pre-weighed test baskets to the approximate

desired test density using an "open blow machine" (Unisul Model Volumatic II

No. 1804E2MH) designed specifically for pneumatic application of the materials

tested. The baskets of blown insulation were allowed to come to thermal and

moisture equilibrium with the air in the laboratory module where the acoustic

test apparatus was located. The weight of an empty basket was monitored to

enable tracking the change in the tare weight of the baskets due to varying

moisture content in the wooden sides of the baskets. Jvst prior to acoustic

testing, the filled basket was weighed and the (adjusted) tare weight subtracted to obtain the mass of insulation material. Fiberglass blankets were

tested without baskets and thus their weight was measured directly. The

thickness of each test sample was measured at multiple locations using a pinand-disk depth gage and steel rule [7]. The scientist shown in Fig. 4 is

beginning to make a thickness measurement while the filled sample basket is

located on the digital balance. The coverage [kg/m^] and the installed density

11
30t

0-1 1 1 1 2.5 5 10 20

Frequency. kHz

Fig. 7 An example data set of sound insertion loss versus

frequency for the 1/3-octave bands with center frequencies

from 2.5 to 25 kHz. The sample was blown bonded fiberglass with a coverage of 1.84 kg/m^

[kg/nr] of each test sample were computed from the mass and average thickness

of the sample and the area of the interior of the basket.

After the mass and thickness measurements were completed, the sample was placed

in the test chamber and the acoustic measurements carried out using the

instrumentation and signal described above. The acoustical measurements

required 20 s, of which only 0.1 s was used to acquire data, the rest of the

time being used to assure that the signal captured corresponded to sound that

made a single pass through the sample (i.e., contained negligible reflected

energy) and to protect the source transducer from excessive power input.

3.4 Test Samples

This study benefitted greatly by being able to "piggyback" on the round-robin

tests [8] of the apparent thermal conductivity of several loose-fill insulations carried out recently under the auspices of the ASTM C16.30 Task Group on C687 Loose-Fill Testing. Materials from the same lots as those used for this

12
round robin were made available to NIST for the acoustic tests described in the

present paper. The test materials investigated were a fiberglass blanket (the

only material not blown), a bonded fiberglass, an unbonded fiberglass, a rockwool, and a cellulose. The reader is referred to Ref. 8 for more complete

descriptions of these materials.

Samples were blown at densities within 10 percent of the target densities for

the round robin tests referenced above. Additional samples for this study were intentionally blown to smaller or larger densities than those specified in the

round robin instructions. For each of the four blown materials, at least one sample was tested at its as-blown density and then compressed and acoustically

measured at two higher densities.

Table 1 gives the thickness, coverage, and density of the samples used for the

acoustical measurements reported in this paper. The entries with an asterisk

following the sample thickness correspond to further compression of the

proceeding sample. The fiberglass blanket samples of different thicknesses

were obtained by stacking individual blankets. The samples with a dagger

following the thickness correspond to the two previous sample boxes being

stacked one upon the other in the acoustic test chamber.

4. Experimental Results

Acoustical data were taken over the frequency range from 2.5 to 25 kHz.

However, with the exception of the data on the direct effects of sample

compression, shown in Figs. 12-15 below, only data at 10 kHz are included in

the present paper. This frequency was selected to enable treating the various

materials and thicknesses on a common basis.

4.1 Coverage

Figure 8 shows the measured values of coverage (mass per unit area in the test

basket) plotted versus the measured sound insertion loss at 10 kHz for the

samples of bonded fiberglass blanket and of blown bonded fiberglass. The

straight lines drawn from the origin through the data are seen to fit the

experimental data very well and the slopes of the two lines only differ by 2.4

percent. Figure 9 shows the same quantities plotted for the blown unbonded

fiberglass. The data are reasonably well fitted by the straight line but not

so well as in the previous figure. The three data points for a coverage of

1.99 kg/m^ (see Table 1) correspond to the same sample at three different

thicknesses, obtained by further compression; the fact that the same coverage

does not produce the same sound insertion loss indicates that the coverage is

not simply proportional to the sound insertion loss so that, in Eq . (7), rj is

not equal to one. It should also be noted that the slope of the line in Fig. 9 is very different from the slopes of the lines in Fig. 8. For a given coverage, the finer-fiber unbonded glass produces almost twice the sound attenuation

produced by the larger-fiber bonded material.

Figure 10 is a plot of the coverage of blown rockwool plotted versus the

measured sound insertion loss at 10 kHz. There is considerable scatter in the

13
Table 1 Thickness, coverage, and density of the test

samples. (The tabulated densities may, due to

rounding errors, differ slightly from values

computed from the tabulated thickness and

coverages .

)

Sample Material Thickness

m

Coverage

kg/m2

Density

kg/m 3

Fiberglass blanket 0.278 3.11 11.2

0.248 2.78 11.2

0.310 3.44 11 .

0.184 2.11 11.5

Blown bonded glass wool 0.184 1.84 9.9

0.186 1.87 10.1

0.370f 3.70 10.0

0.233 1.73 7.5

0 . 183* 1.73 9.5

0.128* 1.73 13.6

0.188 1.37 7.3

0.220 2.35 10.7

Blown unbonded glass wool 0.169 1.69 10.0

0.168 1.75 10.4

0.337j 3.44 10.2

0.229 1.99 8.7

0.178* 1.99 11.2

0.119* 1.99 16.7

0.191 1.52 7.9

0.207 2.14 10.4

Blown rockwool 0.165 5.41 32.7

0.225 5.44 24.2

0.180* 5.44 30.2

0.117* 5.44 46.3

0.162 5.39 33.3

0.189 6.47 34.3

0.184 6.43 34.9

0.173 3.69 21.3

0.169 3.64 21.5

Blown cellulose 0.169 7.15 42.4

0.399 8.04 40.3

0.183 6.94 37.9

0.188 7.79 41.4

0.147* 7.79 52.9

0.115* 7.79 67.6

f Two samples stacked

* Compressed

14
Fig. 8 Measured coverage versus sound insertion loss at 10 kHz

for the bonded fiberglass samples (both the blanket and

the blown materials). The equations define the leastsquares straight lines fitted to the data and passing

through the origin.

15
Fig. 9 Measured coverage versus sound insertion loss at 10 kHz

for the blown unbonded fiberglass samples. The equation

defines the least-squares straight line fitted to the data

and passing through the origin.

16
Fig. 10 Measured coverage versus sound insertion loss at 10 kHz

for the blown rockwool samples. The equation defines the

least-squares straight line fitted to the data and passing

through the origin.

17
results and the data deviate considerably from the straight line fitted to

them. This scatter should not, however, be too surprising. Rockwool typically

contains a significant percentage of "shot" and fused fibers that are too large

to contribute to sound absorption but which may constitute up to 40 percent of

the mass. One would expect to have statistical variations in the percentage of

shot in different samples, even from the same lot of material. Furthermore,

when samples of different density are produced by differences in blowing

technique, one would expect systematic variations in shot content.

The coverage-versus - insertion loss data for cellulose are shown in Fig. 11.

The sound insertion loss at 10 kHz for the highest density sample (the last

entry in Table 1) was too high to be measured accurately and hence is not shown

in Fig. 11. This fact, plus the observation that the two samples that have a coverage of 7.79 kg/m^ have rather different insertion losses indicates that r? differs from unity for the cellulose samples as well.

The sound insertion loss data obtained with the same samples compressed to

different thicknesses provide information as to the values of the exponent r\ for the different materials at different sound frequencies. Figures 12-14 show

the percentage change in insertion loss, versus frequency, for the four types

of blown material. Restricting attention to the results at 10 kHz, it is seen

that the blown bonded fiberglass and the blown rockwool samples exhibited very

little dependency of insertion loss on thickness, indicating that for these

samples the value of r? appears to be very near to unity. For the finer-fiber

unbonded glass material and, particularly, for the cellulose material which has

very small pores, the insertion loss increased as the sample was compressed,

indicating a value for r\ that is significantly different from unity.

In order to further explore the effectiveness of using a value of r? different

from unity, a non-linear least squares software package was used to fit

equations of the form of Eq . (7) to the experimental data of coverage versus

sound insertion loss and sample thickness for the various blown materials. For

the two fiberglass materials, the proportionality constant, K, was forced to be

the same but the bonded and unbonded materials were allowed to have different

values for r? . The measured coverage is plotted versus the predicted coverage

in Fig. 16. For the bonded fiberglass, the value obtained for rj was 1.0285,

with 95 percent confidence limits of ±0.0013, while for the unbonded fiberglass

rj = 0.8652 ±0.0037. The residual standard deviations were 0.016 kg/rcr and

0.052 kg/m^ for the bonded and unbonded fiberglass, respectively.

A similar procedure applied to the data for rockwool yielded the results

plotted in Fig. 17. There is some improvement in comparison to the simple

proportionality of Fig. 10 but the value obtained for r) is not reasonable in

terms of the results of the compression test (Fig. 14). In an attempt to

predict coverage with less uncertainty, several different equations with linear

coefficients were fitted to the experimental data. One of the more successful

equations was W = K • D(1 + bD +cD'), where K, b, and c are constants to be

determined and D' is the slope of the sound insertion loss versus the logarithm

of sound frequency, evaluated at 10 kHz (see Fig. 7). The results of this curve - fitting attempt are shown in Fig. 18. Clearly there is a marked improvement but at the expense of one more constant to be determined.

18
10t

Fig. 11 Measured coverage versus sound insertion loss at 10 kHz

for the blown cellulose samples. The equation defines the

least-squares straight line fitted to the data and passing

through the origin.

19
15t

+»c

0) o

Q. 10

CD

CDO

c

o- 5

c

0)

0)c

0)o>c

(0 r

o

-5

Blown bonded fiberglass

©—© 27 percent compression

• • 83 percent compression

2.5 10 20

Frequency. kHz

Fig. 12 Percentage change in insertion loss, plotted versus sound

frequency, due to compressing a blown bonded fiberglass

sample to two different thicknesses.

20
15t

Frequency. kHz

Fig. 13 Percentage change in insertion loss, plotted versus sound

frequency, due to compressing a blown unbonded fiberglass

sample to two different thicknesses.

21
15t

c®

o

§. 10

m

too

c

10

J

u

-5

Blown rockwool

P——

25 percent compression

91 percent compression

2.5 10 20

Frequency, kHz

Fig. 14 Percentage change in insertion loss, plotted versus sound

frequency, due to compressing a blown rockwool sample to

two different thicknesses.

22
50t

c

®

u

c

0) a

40"

0)m° 30+

co

Blown cellulose

28 percent compression

63 percent compression

0-1 «— 2.5

-+5

_l 1 1 1 h 10 20

Frequency. kHz

Fig. 15 Percentage change in insertion loss, plotted versus sound

frequency, due to compressing a blown cellulose sample to

two different thicknesses.

23
Predicted coverage. kg/m*#2

Fig. 16 Measured coverage plotted versus predicted coverage for

the blown fiberglass samples, both bonded and unbonded.

The prediction equations were of the form of Eq . (7) with

a fixed value of K but different values of r? for the two

types of material.

24
Predicted coverage. kg/m#*2

Fig. 17 Measured coverage plotted versus predicted coverage for

the blown rockwool samples. The prediction equation was

of the form of Eq. (7).

25
Predicted coverage. kg/m#*2

Fig. 18 Measured coverage plotted versus predicted coverage for

the blown rockwool samples. The prediction equation is

discussed in the text.

26
For future work of this nature, it is recommended that the value of rj be

determined directly by compression of a number of samples rather than just one of each material as was done here. It also would be very useful to measure the

shot content of each sample after completion of the acoustic tests.

4.2 Thermal Resistance

The apparent thermal conductivities at 23.9 °C for some samples of the roundrobin materials were measured using the NIST 1-meter line-heat-source guarded

hot plate. The results of these measurements for the blown materials are illustrated in Figs. 19 and 20. The curves shown are of the form of Eq. (8)

and were fitted to the experimental data, yielding values for the constants A,

B, and C. These equations were used to compute the thermal resistance of each

acoustical test sample from its measured density and thickness.

As indicated following Eq . (9), if the density of the material were constant,

the thermal resistance would be simply proportional to the coverage so that if

the density were constant and r? equal to unity, the thermal resistance would

simply be proportional to the sound insertion loss. The limited usefulness of

such a relationship is evidenced by the results shown in Figs. 21 and 22.

Figures 23, 24, and 25 show the thermal resistance (obtained, as described

above, from density and thickness) plotted versus the predicted thermal

resistance for blown fiberglass, rockwool, and cellulose, respectively. The

predicted thermal resistance was obtained from the measured sound insertion

loss and thickness using Eq . (9), with W obtained by the best method of the

previous section, p obtained from that value of W divided by the measured

sample thickness, and A, B, and C being the values obtained for the curves in

Figs. 19 and 20. The predictions are seen to be very good for fiberglass, not

bad for cellulose, and only fair for rockwool. The agreement between observation and prediction for rockwool might have been better if the density of the

material has been known exclusive of shot content for both the thermal and the

acoustical measurements.

5. Prospects for Field Use

Based upon the results presented above, the use of sound insertion loss

measurements to predict the coverage or the thermal resistance of loose-fill

insulations appears promising, particularly for fiberglass materials. The

extension of the above-described laboratory work to field conditions will be

challenging but there do not appear to be any insurmountable difficulties. (It

should be noted that regardless of whether a circular cutter, a thermal

technique, or an acoustical technique is used, variations in installed thick- ness and coverage will require measurements at a large number of locations in

order to achieve statistical reliability.)

Two different approaches [9] appear feasible for using sound waves for in-situ

evaluation of attic insulation coverage and thermal resistance. One approach,

shown in Fig. 26, would be to position a transducer above the insulation and measure the (pulsed) signal that has passed downward through the insulation,

27
Thermal

conductivity.

W/m

Fig. 19 Thermal conductivity versus installed density for the two

types of blown fiberglass material. The data were obtained in the NIST 1-meter, line-heat-source guarded hot

plate. The curves (of the form of Eq . (8)) were used to

estimate, from measured densities, the thermal conductivities of the samples used in the acoustic tests. For

bounded fiberglass, the equation of the curve is A = 0.0270 — 0.000272 p + 0.319/p, in the units shown in the

figure. For unbonded fiberglass, the curve is described

by A = 0.0053 + 0.000623p + 0.378/p.

28
Thermal

conductivity,

W/m

0 . 055t

rockwool

0 . 050”

0 . 045"

0 . 040"

cellulose

0.035+-

25 —i 1 1 1

1 30 35 40 45 50

Density. kg/m**3

Fig. 20 Thermal conductivity versus installed density for blown

rockwool and blown cellulose. The data were obtained in

the NIST 1-meter, line-heat-source guarded hot plate. The

curves, of the form of Eq . (8), were used to estimate,

from measured densities, the thermal conductivities of the

samples used in the acoustic tests. For rockwool, the

equation of the curve is A = —0.0110 + 0.000475p + 1.382/p, in the units shown in the figure. For cellulose,

the curve is described by A = —0.0452 + 0.000878p + 2.112/p.

29
Fig. 21 Thermal resistance versus sound insertion loss, at 10 kHz,

for the blown bonded and unbonded fiberglass samples.

Each line fitted to the data represents the least-squares

straight line passing through the origin.

30
Fig. 22 Thermal resistance versus sound insertion loss, at 10 kHz,

for the blown rockwool and cellulose samples. Each line

fitted to the data represents the least-squares straight

line passing through the origin.

31
Predicted thermal resistance. m*#2 K/W

Fig. 23 Thermal resistance computed from density and thickness

versus thermal resistance predicted from sound insertion

loss and thickness for the blown bonded and unbonded

fiberglass samples.

32
Predicted thermal resistance. m##2 K/W

Fig. 24 Thermal resistance computed from density and thickness

versus thermal resistance predicted from sound insertion

loss and thickness for the blown rockwool samples.

33
Predicted thermal resistance. m#*2 K/W

Fig. 25 Thermal resistance computed from density and thickness

versus thermal resistance predicted from sound insertion

loss and thickness for the blown cellulose samples.

34
SOURCE/RECEIVER

oococcccccccooccccoccocccccccccccccoccoooococcccooooocoococcoocccccccec dooococccccccccccccoccooooooccocccooooooocooccccooocooooccococccccccccc:

OOOOOOOOOOOCCCCCCOCOOOOCCOOCOOOOCCOOOCCOOCCOCOOOOOOOCOOOOOOCOOCCGCCCCCC

DOOCOOOOOCOOCCOOOOOOCOCCOOCCOOCCCOOOOCCOOOCGOOOOOOOOOOOOOOOOOOOOOCCCCCC: OOOOOOOOOCCOOOOOOOOCCCOOCOOOOOCOOCCCCCOCCOCCGOOOOOOOOOOOCOOCOOOCCCCCC: r )OOOOOOOOOOOOOOOCOOOCCCCCCOOOOOOOOOOOOOOOOOOOOOOOOOCOOCOCOOCOOOCCOCGCC:

'

OOOOOOOOOOOOGCCCOOCOCCOCCGOOOOOCOOOOOOCOOOCCCOCCOOOOOOOOOCCCOOOCOOCCCCC JOOOOOOOOOOOOOOOOCOOCCOCCCCCOCCCCOCOOOCOOOCCCiCCCOOOOOOOCOOCCOOCOCCrCCC

OOOOOOOOCOCOCOOCOOCOCOOCCCGCCCCCCCCOCOOOOOCOCOCCOOCOOCOOOCCOCOOCCCCCCCC DOOOOOOOOOOOCCCCOCCCCCCCCCCCCn

OOOOOOOOOCCOCCOCCCGCCCrCCOCCCCCCCCCCC JOOOOOOOOOOOCCOOOOCOCCCCCC'iy^l IS Jk VIAM ococcoooooocgccocoocccccc c c: : OOOCCCOCCCOOOOCOOOCCCCOOCC||iQULM I lUN'OOOOOOOOOOOCOOCCOOCCCCCCCCCC

300000 CCCCCCOCOOOOCCOOCCCCl w, .^.....ooooooooooocccocococcccccccc

.

CEILING

Fig. 26 One experimental configuration for field measurements of

the coverage or thermal resistance of blown- in-place attic

insulation. A pulse of sound from a transducer above the

insulation passes downward through the insulation,

reflects off the upper side of the ceiling, and returns

through the insulation to the transducer.

35
ATTIC AIR

)CCCCCOOOOCOCOCOOOCOOOOOCCOOCOOOOOOOOOOOOOOOOOOOOOOOOOCCOCCCCOCOCCOCCCCCC'CCC CCCCCCCCCCCCCOOCCOOOOCCCCCCOOOOOOOOCCOOCOOOOOOOOOOOCOCCOCOOOCOCOOOGCCCCCCCCCC iccococcocccccoooocoooooooooooGcoooocococooooooooooooooooooccoooccooccccccccc OCCCCCCCCGCOCGOOOOOOOOOOCOOOOOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOCOOOOOOOOOOCC CC C

' lOCCOCCCCCCOCCCOOOOOOCOOOOOOOOOOOOOOCOOOOOOOOOOOOOOOOOOOOOOCCOOCCOOOCCOCCCCC c CCOOCCCOCCCOCCOOOOCCCOOCOCCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOGCCCCCCC : 'COOCCOOOOOOOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOCOOOOOOCOOCCCCCCC

CCGCCCCCOOOOCOOOOOOOOCOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOCOCCCCCCCC OCCCOCOCOOOCOOOOOOOOOOCOOOOOOOOOOOOOCOOOOOOOOOOOOOOOOGCOOOOOOOOOOOCCCGCCCCCC

ccccocoococoocoocooocooooocooooooooocoooooooooooooooooooooooooooooocccccccccc )CCOCOCCCOOOOOCOOOOOO OO OOOOOOOOOOOOOOOGOOOOOOOOOOOOOOOOOOOOOOOOOOOOGCCOC CCC CC occcccoooocooccooco do ocoooooooooooooooooooooooooooooooooooooooooooccccccccc fCOCOGCOOOOCOCOOOOOCacflfcOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOCC CGC c c c COOOOOOOOOOOCC O OP c okc akp OOOOOOOOOOOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOC CC CCC c 'CCOOOOOOOOOOCCq COCCCGOCCCOCCOC

'CCOOOOOOOOOOOOI OCCOCCCOOGCOOOC

)CCCOCOCCOCCOCO< CCCGCCGOOCOOCOC CCCCCCCCCCCOCGC

>CCCCCCCCCCCOOO( COCCCCOOCCCCOCC

'ccocc:cccoccco( ccccccccccccccc

)oocccc:ccoooco( cococcoccocoooc

;ccccoccooooooo( OCGOCCCC COOOGOC GCOOOCCCCOCCCOCI

:cccccccccccooo

ccc: crccccccoo CCC occcccococooooooooooooooccooooooocoooo ZZZZZZ1 ZZZZZZZ2ZZZZZZZZ&

C ooccocoooooooooooooooooooooooooo

c CoA

: go ccoo€ooooccocoocooooocooooooooooooooooooo

rooooooooococoooooooooooooooooooooooooooo

oooooooooooocooooooocoooooocooooooooooooc

:CCOCOOCOOOOOOCCOOOOOOOOGOOOOOOOOOOOOOOOO CCCCGOCOOCCCCOOOOOCOOOOOOOOOOCOCOOOOOOOOO CCOOOCOCCCCOCCCOGCOOOOOOOOOOOGOOOOOOOOOO

CCOCCCOCCCGC A TlOkl ° O ° 0 ° G O O ° ° O O :coccccccccc IrlOULn I lUli^oooooocoooc GCCOOOCOCCCCvw., w v. oooooooooooo :cococcoooccocoocccoocoooooooooooooocooooc CCCCOOCCOOOOGCOOCCOOOOOOOOOOOOOOOOOOCOOOO

rcccoooooooooooooooooooooooooocooooooooooe ccccoooooooooooooooocoooooooooooooooooooo CCOOOOCOOOOCOOCOOOCGOOOOOCOOOOOOOOOOOOOO

CEILING

coooooocccccoccc

cocoooooccccccccc

IGOOCOOOOCCCCC ccc ccooooocccccc ccc c

: coocooccccc c :c:c ccooooocccccccccc icoococcccoococcc

ccccccocccc ccc c c c

: c ccccccccccc cccc ccccoooococcccccc

rooccooccoccccccc ooooccocccccccccc

'COOCOOOGCCCCCCCC CCCOOOOOOCCCCCCCC

rOOCOOOOOCGCCCCCC CCCCOCOOCCCCGCCCC

:gooooocccooccgcc ccoooooogococccc

: ccoooooocccccccc cocccooococccoccc

:cccooocgoocccccc cccocoocccocooccc

Fig. 27 Experimental configuration for field measurements of the

density or thermal conductivity of blown- in-place attic

insulation when it is not practical to enter the attic

space. A sound source probe and a sound receiving probe

are each inserted through small holes in the ceiling and

measurements made as described in the text.

36
reflected from the top of the ceiling, and passed upward through the insulation

and back to the transducer. The source/receiver shown in Fig. 26 could include

a parabolic reflector, as used in the present study, or could simply be an extended transducer. A second approach, illustrated conceptually in Fig. 27,

would be to position a transmitter and a receiver a fixed distance apart within

the insulation.

The technique of using a vertically oriented system such as depicted in Fig.

26 , with the transducer in the attic space operating in a send-receive , or pulse -echo, mode, would have the advantage of requiring no penetration holes in

the ceiling. It has the disadvantage, however, of requiring access to the

attic space, with the probe suspended from a "fishing pole" operated from the access hole or the operator actually entering the attic. A further complication with this technique is the large attenuation associated with the sound

passing twice through a large thickness of insulation; this difficulty can be

dealt with by using sound of lower frequency than is reported in the present

study

.

The technique of using two probes inserted through small holes in the ceiling

to the same height within the insulation, so that the sound waves travel parallel to the ceiling, has several advantages. It should be possible to determine

the insulation depth by monitoring the signal as the probe pair is moved upward

through the insulation layer. When the signal matched a pre-calibrated value

established for an open air path, the boundary between the upper surface of the

insulation and the attic air would be determined. By measuring the signal as the probes are moved upward through the insulation, the insulation density as a function of elevation (depth) could be determined. This technique would have

the disadvantage of requiring that two small holes be drilled through the

ceiling at each location where the density profile and the depth of the

insulation need to be ascertained. However, these holes would be very small

and could easily be repaired upon completion of measurements.

It is important to reiterate the need to know the relationship between sound

insertion loss and coverage for the particular material that is installed in an attic. If the insulation is, for example, a virgin glass wool of known origin,

it should be possible to use "standard" parameters for that material. For

unknown materials, or materials that exhibit considerable variability, the

appropriate parameters should be determined for the particular lot of material.

Probably the easiest way to obtain the appropriate parameters, when access to

the attic is possible, would be to measure the sound insertion loss at a few

locations near the access hole to the attic, both with the insulation at its

installed thickness and with the insulation compressed to, say, half its

installed thickness. A circular-cutter and depth gage could then be used to

determine the coverage and thickness at the same locations where the acoustical

measurements were made. From these data, the parameters K and r) in Eq . (7)

could be obtained for the specific installed insulation.

The acoustical technique could then be used to map the sound insertion loss at

a large number of locations in the attic. These data (plus the nominal thickness, since W is only weakly dependent upon i) could then be used to compute

the coverage at each location where sound insertion loss was measured. In this

37
way the coverage could be mapped without the destructive effects of taking

numerous circular-cutter samples throughout the attic.

If it is desired to obtain the thermal resistance as well as the coverage, it

would be necessary to know the relationship between thermal conductivity and

density for the particular type of insulation. Usually such data should be

available from the insulation manufacturer.

6. Conclusions

It is shown that the coverage, W, of installed insulation in an attic is

related to the sound insertion loss, D, and thickness, £, by the expression

W = K • i

1

"

17

, ( 11 ) where K and r/ are material - dependent constants. The parameter 77 will have a value not too different from unity so that £ need not be known very accurately

in order to obtain W. For the special case where r? = 1, this equation reduces

to W = K • D, i.e., the coverage is proportional to the sound insertion loss.

The thermal resistance, R, of installed insulation in an attic is related to

the sound insertion loss, the thickness, the density, p, and the thermal

conductivity, A = A (p) , by the expression

£ = _W

= K » l

1

'

77

A pX p A

( 12 )

If the density of the sample is constant so is the denominator of Eq . (12) and

the thermal resistance is proportional to the coverage. For the special case where the density is constant and, also, rj = 1 , the thermal resistance is

proportional to the sound insertion loss. For the case where the installed

density is variable and unknown, the density can be estimated from

P = K • (D/i)'? ; (13)

this value of p can be used to obtain the denominator of Eq . (12), provided the

dependence of thermal conductivity on density is known for the particular type

of insulation. In this manner the thermal resistance can be related to the

measured sound insertion loss and the approximate sample thickness.

An apparatus was designed and constructed to carry out laboratory measurements

of the sound insertion loss of samples of blown insulation. In this apparatus

the insulation sample is held in a wood-sided basket with a screen bottom to

allow passage of the beam of sound through a central region of the sample. The

instrumentation used provided measurements of sound insertion loss as a function of frequency from 2.5 to 25 kHz.

In addition to data on sound insertion loss, data were obtained on the coverage, density, and thickness of the insulation blown into each sample basket.

The test materials investigated were a fiberglass blanket (the only material

38
not blown), a bonded fiberglass, an unbonded fiberglass, a rockwool, and a cellulose. For each material, samples were prepared of varying thickness,

coverage, and density. For one sample of each of the blown insulations, a value of r) was obtained by measuring sound insertion loss as the sample

material was compressed to different thicknesses.

The experimental data for each material were analyzed to examine the relationship between coverage and sound insertion loss at 10 kHz. For the blown

fiberglass samples, the coverage was found to be reliably predicable from sound

insertion loss and sample thickness, using Eq. (11) with a single value of K

but with different values of r] being used for the two types of fiberglass. The

correlation between W and D was found to be poor for the rockwool samples,

presumably because rockwool includes a rather large component of shot and fused

fiber that affects W but not D. For cellulose, the correlation between W and D was much better than for rockwool but not so good as for fiberglass.

A limited number of measurements were made of the thermal conductivity of each

material as a function of density. Empirical equations fitted to these data were used to estimate, from measured density and thickness, the thermal

resistance of the other samples on which acoustical, but no thermal, measurements were made. The thermal resistance was also predicted, using Eqs . (12)

and (13), from the measured sound insertion loss and sample thickness, also

using coefficients from the empirical equations fitted to the experimental data

for thermal conductivity versus density. The correlation between thermal

resistance (as computed from measured thickness and density) and the predicted

(from sound insertion loss and thickness) thermal resistance was found to be

very good for fiberglass, not bad for cellulose, and only fair for rockwool.

The agreement might have been better for rockwool if the density of each sample

had been known exclusive of shot content for both the acoustical and the

thermal measurements.

Based on the results presented in this report, it is concluded that the use of

sound insertion loss measurements to predict the coverage or thermal resistance

of insulation appears promising, particularly for fiberglass materials. The

extension of this technique to field measurements will be challenging but there

do not appear to be any insurmountable difficulties. Two different approaches

are described for in-situ acoustical measurements, one approach that yields

coverage and R-value and another approach that is more closely tied to density

and thermal conductivity. For either of these techniques it is necessary to

know the relationship between coverage (or density) and sound insertion loss

for the particular material that is installed. If it is desired to obtain

thermal resistance (or thermal conductivity) , it is necessary to know the

relationship between thermal conductivity and density for the particular type

of insulation.

7. Acknowledgments

We thank H. G. Woten, President of Unisul Inc., for the loan of the blowing

machine; R. S. Graves of Oak Ridge National Laboratory for sharing his ex- perience in the use of the blowing machine; R. D. Adams of Owens Corning Fiberglas Corp. for arranging the availability of the ASTM round robin materials and

39
for providing us with data on fiber diameters; W. M. Edmunds of Owens Corning

Fiberglas Corp . and J. F. Kimpflen of Certain-teed Corp. for arranging to provide guidance on blowing and handling of loose-fill insulations; T. A. Somers

of the NIST Center for Building Technology (CBT) for carrying out the thermal

conductivity measurements; and R. R. Zarr of CBT for supervising the thermal

conductivity measurements and assisting with blowing the test samples.

8. References

[1] Private communication between Michael Baum, of NIST, and Eunice Baros and

Nicky Clark, of the Florida Attorney General's Office of Consumer Affairs,

April 1987.

[2] Private communication between Michael Baum, of NIST, and Bill Cloud of the

Georgia Governor's Office, April 1987.

[3] ASTM C687-85, Standard Practice for Determination of the Thermal Resistance of Loose-fill Building Insulation (American Society for Testing and

Materials, Philadelphia, 1985).

[4] Letter, dated December 7, 1984, from Kenneth D. Mentzer, Staff Vice President of the Mineral Insulation Manufacturers Association, to Ernest

Ambler, Director of the National Bureau of Standards.

[5] Delany, M. E. and Bazley, E. N., "Acoustical Properties of Fibrous Absorbent Materials," Appl. Acoustics 3, 105-116 (1970).

[6] Bies, D. A., "Acoustical Properties of Porous Materials," pp . 245-269 in

Noise and Vibration Control, L. L. Beranek, Ed. (McGraw-Hill, New York,

1971) .

[7] ASTM C167-82, Standard Test Methods for Thickness and Density of Blanket

or Batt Thermal Insulation (American Society for Testing and Materials,

Philadelphia, 1982).

[8] Adams, R. D. and Hust, J. G., "An Intralaboratory Comparison of the ASTM

C-687 Loose Fill Insulation Test Procedure," in Proc . Symposium on Insulation Materials, Testing and Applications, ASTM STP 1030, D. L. McElroy and J. F. Kimpflen, Eds. (American Society for Testing and Materials, Philadelphia, in press).

[9] Blessing, G. V., and Flynn, D. R. , "Acoustic Evaluation of Thermal

Insulation," U.S. Patent 4,672,851, June 16, 1987.

40
NBS-114A (REV. 2-80

U.s. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

4. TITLE AND SUBTITLE

1. PUBLICATION OR 2 REPORT NO.

NISTIR 88-3882

. Performing Organ. Report NoJ 3. Publication Date j April 1989

An Acoustical Technique for Evaluation of Thermal Insulation

5. AUTHOR(S)

Daniel R. Flynn, David J. Evans, Thomas W. Bartel

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

1. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Mineral Insulation Manufacturers Assoc. Office of Buildings & Community Systems

1420 King Street Building Systems Division

Alexandria, VA 22314 U.S. Dept, of Energy

Germantown, MD 20874

Under Caatract DE-ACQ5-84QB71 40D

10. SUPPLEMENTARY NOTES with Martin Marietta Energy Systems Inc

; ~j Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bl iogrophy or literature survey, mention it here) A laboratory apparatus has been constructed that enables rapid measurement of the sound

insertion loss of a sample of insulation as a function of frequency. An extensive

series of measurements of the sound insertion losses associated with blown samples of

fiberglass, rockwool, and cellulose has been completed; the results of these acoustical

measurements are highly correlated with coverage (mass per unit area) and thermal

resistance (R-value) . An investigation is planned to extend the acoustical techniques

used in the laboratory apparatus to in-situ determination of the sound transmission

loss through thermal insulation installed in attics. Two possible approaches to such

field measurements are described.

12. KEY WORDS (Six to twelve entries ; alphabetical order; capitalize only proper names; and separate key words by semicolons)

acoustics; attic insulation; heat flow; heat transfer; insulation; non-destruction

evaluation; non-destructive testing; sound attenuation; sound propagation; thermal

conductivity; thermal insulation; thermal resistance

13. availability 14. NO. OF

PRINTED PAGES

[X~ Uni imited 46

j

| For Official Distribution. Do Not Release to NTIS

] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

' 15. Price 20402.

TxOrder From National Technical Information Service (NTIS), Springfield, VA. 22161 $12.95

USCOmm-DC 6043-P60