Simulating the effect of acoustic treatment types for residential balconies with road traffic noise

Applied Acoustics 79 (2014) 131–140

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Simulating the effect of acoustic treatment types for residential balconies with road traffic noise Daniel A. Naish ⇑, Andy C.C. Tan, F. Nur Demirbilek Queensland University of Technology, George Street, Brisbane, Qld 4000, Australia

a r t i c l e

i n f o

Article history: Received 6 April 2013 Received in revised form 18 December 2013 Accepted 20 December 2013

Keywords: Balcony Road traffic noise Design guide Speech interference

a b s t r a c t Development of design guides to estimate the difference in speech interference level due to road traffic noise between a reference position and balcony position or façade position is explored. A previously established and validated theoretical model incorporating direct, specular and diffuse reflection paths is used to create a database of results across a large number of scenarios. Nine balcony types with variable acoustic treatments are assessed to provide acoustic design guidance on optimised selection of balcony acoustic treatments based on location and street type. In total, the results database contains 9720 scenarios on which multivariate linear regression is conducted in order to derive an appropriate design guide equation. The best fit regression derived is a multivariable linear equation including modified exponential equations on each of nine deciding variables, (1) diffraction path difference, (2) ratio of total specular energy to direct energy, (3) distance loss between reference position and receiver position, (4) distance from source to balcony façade, (5) height of balcony floor above street, (6) balcony depth, (7) height of opposite buildings, (8) diffusion coefficient of buildings and (9) balcony average absorption. Overall, the regression correlation coefficient, R2, is 0.89 with 95% confidence standard error of ±3.4 dB. Crown Copyright Ó 2014 Published by Elsevier Ltd. All rights reserved.

1. Introduction This study aims to produce a relatively simplified method for predicting the difference in speech interference level (SIL) on balconies between the balcony space and a point just outside the balcony. The purpose of this design guide is to assist acoustic practitioners who are involved with residential building design in predicting the acoustic benefits of different balcony acoustic treatments. A result of earlier studies, the effects of balcony acoustic treatments on SIL is demonstrated to be inconsistent across all balcony locations and proximity to the source [1]. Thus, it is important to establish a method which identifies optimised solutions. An optimised solution, which is the least costly balcony acoustic treatment to meet a specified SIL reduction objective, will promote the inclusion of balcony acoustic treatments into building designs. The potential benefits of balcony acoustic treatments have been discussed earlier [2,3] in terms of estimated health cost savings to communities due to potential reductions in exposure to road traffic noise. This study extends studies conducted by others over recent decades into the acoustic effects of residential balconies. Previous studies by others have used a range of methods from full scale

⇑ Corresponding author. E-mail address: [email protected] (D.A. Naish).

measurements [4–8] to scale modelling [9–16] and theoretical models [5,6,9,11–14,17–19]. However, a comprehensive practical design guide remains elusive. To commence building upon these earlier studies, a preliminary investigation into the issues involved in producing design guides identified numerous variables requiring consideration [20]. That study discussed the issues surrounding (i) geometric sensitivity, (ii) temporal sensitivity, (iii) source sensitivity, (iv) compliance testing and (v) path sensitivity. Each of these will be summarised below.

1.1. Geometric sensitivity Geometric sensitivity occurs when the source and receiver locations are such that diffraction and reflection occurrences along the propagation paths leads to relatively higher or lower sound pressure levels than the average of surrounding receiver locations. For example, the probability of strong ceiling reflections to a balcony receiver increases in some balcony locations. The probability of experiencing geometric sensitivity depends on the street width, building heights, source location, balcony type and receiver location inside the balcony space. In calculations, the more sources modelled, the effects of geometric sensitivity are less likely to be observed, particularly if a sufficient number of sources are modelled so that a Leq parameter can be predicted. The negative to

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modelling large numbers of sources is the increase in calculation time, thus a balance needs to be established. 1.2. Temporal sensitivity A moving vehicle in a street can be considered as a multitude of moving point sources. Each point source could be located in a place that induces a geometric sensitivity to the balcony receiver. This arises primarily due to the changing diffraction attenuation as the path difference over the dominant diffraction edge is significantly different depending on source location. Temporal sensitivity is also significantly different depending on the location of the receiver in the balcony. Receivers with a greater view of the road will experience less temporal sensitivity than those further into the illuminated zone of the diffracting edge of the balcony. Therefore it is important to conduct predictions with point sources at various places in the street such that temporal sensitivities are smoothed. 1.3. Source sensitivity Micro-dynamics of road traffic noise will demonstrate great variance in sound pressure level for any road as vehicle noise emissions can be significantly different even from similar specification vehicles. The variance is compounded when considering different types of vehicles (cars, trucks), different vehicle speeds, different types of tyre and different driver behaviours. 1.4. Compliance testing Development of a balcony acoustic treatment design guide requires consideration on how a practitioner may use it efficiently, not only for design, but to also confirm compliance with specified criteria. In the case of balcony acoustics, prediction of a specific sound pressure level at a certain location within the balcony space is an onerous task. Rather, it is comprehensively more efficient to assess the effect of the balcony on the sound pressure level, or in other terms, the balconies insertion effect. Measurement is the likely form of compliance testing, and consequently a two microphone measurement procedure is the most appropriate, one microphone at a reference position outside the balcony and one at any other location within the balcony space. This approach is also more acceptable across different jurisdictions that have varying road traffic noise parameters, prediction and measurement locations and criteria. To indicate a possible compliance measurement technique, Fig. 1 shows a dual channel integrating averaging sound level meter (SLM) with two microphones (or alternatively two single channel sound level meters could be used simultaneously). It is essential to locate both the reference microphone outside the balcony space and balcony microphone at a consistently specified position. The SLM should be capable of all standard weighted and unweighted, time based statistical and energy based parameters such as Lmax, Leq, L10 and L90. 1.5. Path sensitivity The sensitivity introduced by the relative levels of energy between the different paths of noise, direct, specular or diffuse also requires consideration in terms of how much calculation effort is required to produce a reasonable design guide. The direct and specular energy paths are the dominant contributors to overall road traffic noise sound pressure levels within balcony spaces. Thus, it is appropriate to reduce the number of diffuse paths included in the calculation to only those most dominant. In this study, only the first order diffuse paths from the street and balcony surfaces are included.

Fig. 1. Possible compliance measurement method schematic showing sound level meter with two microphones (reference and balcony positions).

1.6. Outline of this study A brief description and summary of the theoretical model and the assumptions made in calculations is presented in Section 2. Section 2 also outlines the variables and their derivations used in the development of the design guide prediction model for the various situations assessed. The results including discussion are contained in Section 3 and are followed by conclusions in Section 4. 2. Methodology The methodology implemented in this study is presented in three sections. Firstly the theoretical and computer model specifically developed for this purpose is described. Secondly the development of the design guide is discussed including the indicators and scenarios. Finally the variables used in the design guide are presented in detail. 2.1. Theoretical and computer model The theoretical model used in this investigation is purposefully compiled to assess large numbers of scenarios of road traffic noise on balconies. The model has been used in earlier investigations [1,20,21] and has been validated against measurement data by others [22]. It has also been validated against balcony measurements conducted by the authors, however these results are currently awaiting publication. The details of the theoretical model and its assumptions have been presented elsewhere [1] and so only a very brief outline is provided here. The theoretical model calculates road traffic noise within a balcony space via three main paths (1) direct, (2) specular reflection using the image source technique, and (3) diffuse reflection using the radiosity technique. The entire model calculates in 1/ 3 octave band levels. Vehicles are modelled as single point sources with an adjustable sound power and can be time-lagged to simulate a moving point source above a ground plane. To remove the variability introduced by source sensitivity described above, a reference sound power level of 100 dB in each one third octave band from 20 Hz to 20 kHz is used in the predictions for this study. A reference sound power level allows the prediction of level differences, namely, the difference between the SIL at the reference position to

133

Type 1

Type 2

Type 4

Type 5

Type 3

3.0m

Type 9

0.5m

Type 8

2m or 4m

1.0m

Type 7 1.0m

The primary aim of the design guide is to determine the differences between SIL at a defined reference position outside a balcony and SIL at a position within the balcony space. This is conceptually presented in Fig. 2 which shows a balcony cross-section with two receivers where SIL is calculated to (1) Balcony (SILBalcony), and (2) Façade (SILFacade). SILBalcony is located halfway between the façade and outer edge of the balcony floor (D/2) and is 1.2 m above the balcony floor. The height of 1.2 m has been selected as being the average height of a seated person on the balcony and is likely to be the position where speech interference is most important to the function of the balcony space [1]. SILFacade is located halfway up the façade wall, which is 1.5 m above the floor for a 3.0 m height balcony. Balconies were all set to 3.0 m height in this study as this represents a common floor to floor height for high-rise apartment buildings. Fig. 2 also shows the defined reference position (SILREF) which is located 1.2 m above the balcony floor to be the same as the position for SILBalcony and is 1.0 m outside the front edge of the balcony floor to ensure a measurement position which is feasible to reach. In this figure, four distances are shown as a, b, c and e. These distances are calculated from the most nearest source location only and are explained in more detail below. According to an earlier investigation [1], nine different balcony acoustic treatments are considered important in the development of design guides. These nine types are presented in Fig. 3 and demonstrate a range of options including parapet, ceiling absorption

0.5m

2.2. Design guide development

0.5m

1.0m

Type 6

3.0m

0.5m

1.0m

either of the balcony receiver positions, DSIL. These predictions can be converted to octave band values in the 500 Hz, 1 kHz, 2 kHz and 4 kHz bands which are then used to derive the calculated DSIL. A street canyon and balcony space are constructed with two dimensional specular and diffusely reflecting planes with adjustable absorption coefficients, a, and diffusion coefficients, f. Here, the diffusion coefficient denotes the percentage of incident energy that is non-specularly reflected and does not represent the quality of the scattered energy. Diffraction attenuation around the balcony plane edges is provided through the implementation of standard environmental acoustics barrier attenuating algorithm from ISO9613-2 [23]. The balcony and its receivers can be positioned at any distance and height from the source, enabling a large number of scenarios to be assessed.

3.0m

D.A. Naish et al. / Applied Acoustics 79 (2014) 131–140

2m or 4m

Fig. 3. Dimensions and characteristics of 9 balcony types.

and ceiling shields. Type 1 balconies are a rare case of balcony without a ceiling but important to quantify the effect of ceiling reflection when compared to Type 2 balconies. Type 2 balconies can be described as the most common balcony or base case. Types 3, 4, 8 and 9 all have solid parapets which increases diffraction attenuation to certain receiver locations within the balcony. Types 1, 2, 5, 6, and 7 do not exhibit any parapet. Types 6, 7, 8 and 9 incorporate a ceiling shield which in some locations provides additional diffraction attenuation and may assist in reducing strong

3 .0 m

SIL Facade

1.0m

1.0m

D 2m or 4m

W

20 m Source

1.2 m

c

H1

e

ζ

H2

P

b

1.5 m

SIL Balcony

SIL REF

a

2m or 4m

= Acoustic absorption, (SILα = 0.75)

Reference Position

Balcony Receiver

Facade Receiver

Fig. 2. Prediction locations, Reference, Balcony and Façade. Note: Distances a, b and c measured similarly for the Façade Receiver.

D.A. Naish et al. / Applied Acoustics 79 (2014) 131–140

2.3. Design guide variables

ζ

As it is the difference in SIL between the reference position and receiver positions that is of interest, two derived values are

(a) Balcony

Receivers

Opposite Buildings

(b)

Direct, Specular & Diffuse Energy

Assume Total Diffuse Energy Constant

Direct & Specular Energy per lane

Diffusion Energy

Time or Distance Direct and Specular Reflection Source Diffuse Source _ Street and Balcony Compartments Fig. 5. Conceptual arrangement of direct and specular module sources and single central diffuse module source in the computer model set up.

calculated from all of the scenarios assessed. These are DSILB calculated using Eq. (1) and DSILF calculated using Eq. (2).

DSILB ¼ SILREF  SILBalcony

ð1Þ

DSILF ¼ SILREF  SILFacade

ð2Þ

After consideration of the available variables from the computer model and scenarios assessed it is deemed that DSILB or DSILF is a function of nine variables (Eq. (3)), being (1) diffraction path difference (DSIL), (2) ratio of total specular energy to direct energy (SDR), (3) distance loss between reference position and receiver position (DDist), (4) distance from source to balcony façade (W), (5) height of balcony floor above street (H1), (6) balcony depth (D), (7) height

ζ

specular reflection off the balcony ceiling. Types 4, 5, 7 and 9 include highly absorptive materials on the ceiling surfaces. Fig. 4 shows the location and scenario configuration of all nine balcony types where SILREF, SILBalcony and SILFacade are calculated. The horizontal distance to the source is 5 m, 10 m, 20 m, 40 m or 100 m and the vertical distance is 3 m, 6 m, 15 m, 30 m, 50 m or 100 m. Thus the locations modelled are spread over a wide area where balcony acoustic treatments are more likely to require design optimisation. The distance from the source to opposite buildings is set to a constant 20 m. Although variable distances could have been modelled, it was necessary to reduce the number of variables to reduce the calculation time for the study. It is considered more important to alter the height of opposite buildings from 0 m, 50 m and 100 m and also the alter the diffusion coefficient of the building facades from 0.1, 0.5 and 0.9. These six combinations for opposite buildings is deemed sufficient to develop the design guides, particularly as it has been previously identified that road traffic noise levels are dominated by direct and specular reflection paths rather than diffuse paths. Two depths of balcony are assessed, being 2.0 m and 4.0 m deep. These two depths are considered to represent the minimum and maximum range of normal residential balcony designs although it is acknowledged that shallower and deeper balconies can be constructed. Finally, the computer model that implements the custom theoretical model is set up as shown conceptually in Fig. 5. A series of point sources is aligned temporally along the axis of the street canyon and only direct and specular reflection paths are calculated at each receiver. Diffuse energy is calculated only from the source nearest to the balcony where it is assumed that diffuse energy from this source is constant temporally. Thus the computer model combines energy from direct, specular reflection and diffuse reflection paths to quantify SILREF, SILBalcony and SILFacde.

Lp

134

Fig. 4. Prediction configuration showing balcony locations, for each 9 balcony types, and 3 façade diffusion types DSIL.

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of opposite buildings (H2), (8) diffusion coefficient of buildings (f) and (9) balcony average absorption ratio (aR). Most of these variables are demonstrated in Fig. 2. Variables W, H1, D, H2 and f do not require further explanation; however the remaining variables are described in detail in the following sections.

DSILBorF ¼ f ðDSIL ; SDR ; DDist ; W; H1 ; D; H2 ; f; aR Þ

ð3Þ

2.3.1. Diffraction path difference, DSIL As SIL is an arithmetic average over a wide frequency range and diffraction attenuation is frequency dependent it is necessary to determine the average diffraction attenuation over the SIL frequencies which is a similar approach taken previously by the first author [24]. This variable is denoted as DSIL and it is calculated according to either form 1 or 2 of Eq. (4) where path difference, X , is from Eq. (5) using the distances a, b and c defined in Fig. 2. This study used Form 2 of Eq. (4). DSIL is only determined for the source that is directly in front of the balcony, and whilst it is recognised that this will often provide the highest path difference of all the direct path sources it is considered that it provides a sufficiently strong correlation towards prediction of DSILB or DSILF. Including a form of average path difference based on spatially and temporally separated point sources would improve overall correlations, however this potentially distracts the aim to produce the most simple design guide. It will be observed that Eq. (4) is a reduced form of the barrier attenuation algorithm from ISO96132 [23] where the second alternative of Eq. (4) uses an average wavelength from 500 Hz to 4 kHz. In order to simplify the design guides the path difference X, has been derived to be calculable from easily identifiable variables (W, D, H1, P) where P is the height of balcony parapet (0 m or 1.0 m in this study). The equations including these variables are slightly different when calculating XBalcony (Eqs. (6)–(8)) and XFacade (Eqs. (9)–(11)).

DSIL ¼

    kHz 1 4X 20 10Log10 3 þ X or 10Log10 ð3 þ 98XÞ 4 500 Hz k

X¼aþbc

ð4Þ ð5Þ

For XBalcony: 1

a ¼ ððW  DÞ2 þ ðH1 þ PÞ2 Þ2

b¼

c¼

!12  2 D 2 þ ð1:2  PÞ 2

ð6Þ

ð7Þ

!12  2 D 2 W þ ðH1 þ 1:2Þ 2

a variable derived from the ratio of total specular energy in the SIL frequencies to the direct energy SIL is used, SDR, which is shown in Eq. (12). The further derivation of SDR is found in the results section.

SDR ¼

DDist ¼ 20Log10

b ¼ ðD2 þ ð1:5  PÞ2 Þ

ð13Þ

e 1

ð14Þ

2.3.4. Ratio of average absorption, aR The variable aR is a function of an (Eq. (15)), where ‘n’ is balcony types 2 to 9 inclusive; which is the average absorption in the balcony space and its ratio with the average absorption estimate for a Type 1 balcony. Variable a is calculated using standard Sabine room acoustics theory from the internal surface area of the balcony space, ST, and the surface area of each individual balcony surface component, Sc, and its respective average absorption coefficient, ac, across the speech frequencies 500 Hz to 4000 Hz (Eq. (16)). To simply the calculation for this study as the width of all balconies has been set to P 4.0 m, ST can be devolved to Eq. (17)and Scac can be determined through the use of Eq. (18). In Eq. (18), four new variables are included, V1,V2,V3 and V4 which represent ceiling absorption, parapet height, presence of ceiling shields and ceiling shield absorption respectively and their constant values are found in Table 1.

aR ¼ a¼

an where n ¼ 2 to 9 a1

ð15Þ

P

Sc a c ST

ð16Þ

ST ¼ 14D þ 24 ð8Þ

X

ð9Þ ð10Þ

1

c ¼ ðW 2 þ ðH1 þ 1:5Þ2 Þ2

c 

e ¼ ððW  ðD þ 1ÞÞ2 þ ðH1 þ 1:2Þ2 Þ2

1

1 2

ð12Þ

2.3.3. Distance loss reference to receiver, DDist A possibly unexpected variable is the difference in decibels introduced by the change in distance between the reference location and the balcony receiver location, DDist, Eq. (13). This is important when distances to the source are comparable to the distance between the two receivers. Similar to the previous variables, to assist the purpose of the design guide, the calculation of this variable is reduced to easily identifiable variables (W, D, H1). It requires calculation of distance, e, shown in Fig. 2 through the use of Eq. (14). The distance, c, is calculated from either Eqs. (8), (11).

For XFacade:

a ¼ ððW  DÞ2 þ ðH1 þ 1Þ2 Þ2

Direct SIL Specular SIL

ð11Þ

2.3.2. Direct/specular energy ratio, SDR A significant path in the arrival of road traffic noise to a balcony space is reflection off the ceiling plane. Consequently, a design guide must take account of the potential for strong reflections from the ceiling. This potential path is possibly the most geometrically and temporally sensitive path of all the possible pathways. To account for ceiling reflection and other paths of specular reflection,

Sc ac ¼

ð17Þ

4Dð1 þ V 1 Þ 100 ð2D þ 4ÞðV 2 þ 12 V 3 V 4 þ 100ð3  V 2  12 V 3 ÞÞ þ 100 þ 0:12

ð18Þ

Table 1 P Constants for use in Eq. (18) to determine Scac for all balcony types. Balcony type

V1

V2

V3

V4

1 2 3 4 5 6 7 8 9

100 1 1 75 75 1 75 1 75

0 0 1 1 0 0 0 1 1

0 0 0 0 0 1 1 1 1

1 1 1 1 1 1 1 1 75

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(b) 25

20

ΔSIL Calculated

ΔSIL Calculated

(a) 25 15 10 5 0

20 15 10 5 0

1

2

3

4

5

6

7

8

9

1

2

3

4

Balcony Type

5

6

7

8

9

Balcony Type

Fig. 6. Statistical distribution of calculated DSIL for (a) balcony and (b) façade.

3. Results and discussion In total, the results database contains 9720 scenarios, which is 4860 scenarios for SILBalcony and SILFacade and 540 cases for each balcony type per balcony receiver. This number of cases is considered an appropriate sample size on which to compute regression when balanced against the greatly increased study calculation time if significantly more scenarios were to be investigated. Overall statistical distribution of calculated DSIL is presented in Fig. 6 in the form of quartile plots (minimum, 25th percentile, arithmetic mean, 75th percentile, maximum) for each balcony type and receiver position within the balcony (balcony receiver or façade receiver). These quartile plots demonstrate the large range of DSIL that can be expected from any balcony type. Types 1, 4, 5, 7 and 9 have the largest ranges due to either no ceiling, or ceiling

25

with absorption. This effect is also observed when comparing no parapet Type 1 and Type 5 balconies that have very similar statistical distributions and mean indicating that the ceiling absorption of the Type 5 balcony effectively converts a Type 2 balcony into a Type 1. Comparing parapet balconies Type 3 and 4 and their statistical distributions show the significant increase in DSIL mean and widening of the range between the 25th and 75th percentiles due to the introduction of ceiling absorption. The effect of ceiling shields on balconies is demonstrated by comparing Type 2 with Type 6 balconies, Type 3 with Type 8 balconies and Type 4 with Type 9 balconies; where it appears that ceiling shields alone have a limited effect on a small number of scenarios. Ceiling shields appear to be more effective in increasing DSILB rather than DSILF which is an interesting finding and is observed by comparing the mean DSILB for Types 4 and 9 balconies. As expected it is the Type

25

(a)

20

20

15

15

10

10

5

5

0

(b)

0 0

25

50

75

100

0

25

50

W, m 25

75

100

H1, m 25

(c)

20

20

15

15

10

10

5

5

0

(d)

0 -5

5

15

DSIL

25

0

1

2

Δ Dist

Fig. 7. Scatter plots of DSILB or DSILF for (a) W, (b) H1, (c) DSIL and (d) DDist.

3

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D.A. Naish et al. / Applied Acoustics 79 (2014) 131–140

25

Specular greater

25

Direct greater

20

20

15

15

10

10

5

5

0

Specular greater

Direct greater

0 0

0.5

1

1.5

0

R

25

0.5

1

1.5

R

Specular greater

25

Direct greater

20

20

15

15

10

10

5

5

Specular greater

Direct greater

0

0 0

0.5

1

1.5

0

R

0.5

1

1.5

R

Fig. 8. Scatter plots of SDR against DSILB or DSILF for balconies (a) Type 1, (b) Type 2, (c) Type 3 and (d) Type 9.

9 balcony with the greatest level of acoustic treatment that has the highest 25th percentile, mean, 75th percentile and maximum DSIL. However, the Type 4 balcony would, in many circumstances, be the more cost effective balcony acoustic treatment in terms of DSILB. The remainder of this section firstly conducts an inspection on the correlation of some of the continuous variables to DSIL, largely to show that individually variables have limited to no correlation to DSIL. Secondly, it is demonstrated how the direct to specular ratio variable, SDR, is generated for further use in the compiled design guide. Finally, the compiled design guide is developed and presented.

3.1. Inspection of the variables It is found, largely as expected, that there is little to no correlation between DSIL and other continuous variables (DSIL, DDist, W, H1). Fig. 7 shows the scatter plot diagrams of each of these four variables versus DSILB and DSILF combined where it is observed there is no obvious trend in the data. The scatter plots of W (Fig. 7(a)) and H1 (Fig. 7(b)) confirm horizontal and vertical distances away from the source are, by themselves, inappropriate variables for the development of design guides. (Fig. 7(c)) appears to have the highest correlation of these four variables where a

Table 2 Coefficients and exponents for each balcony type and receiver for use in Eq. (19).

*

Position

Balcony type

XpA

XpB

XpC

CA

CB

CC

R2

SE*

Balcony

1 2 3 4 5 6 7 8 9

0.0105 0.6682 0.2526 0.6222 0.8626 0.6446 0.8644 0.3218 0.8401

0.3218 0.4596 0.3531 0.0928 0.9520 0.4604 0.9467 0.3571 0.9538

0.1011 0.0680 0.1201 0.0380 0.0292 0.0613 0.0262 0.0844 0.0389

0.9476 0.0086 0.1525 0.0084 0.0013 0.0097 0.0012 0.0864 0.0022

0.0191 0.0422 0.0847 0.4080 0.0016 0.0397 0.0014 0.0835 0.0015

0.0950 1.1152 0.9121 1.4929 1.0560 1.1126 1.0517 1.0207 1.0418

0.997 0.996 0.992 0.996 0.997 0.994 0.997 0.993 0.995

±0.104 ±0.120 ±0.161 ±0.126 ±0.110 ±0.145 ±0.114 ±0.154 ±0.137

Facade

1 2 3 4 5 6 7 8 9

0.9016 0.9046 0.8364 0.9615 0.8866 0.8983 0.8844 0.7853 0.9855 0.0105

0.9233 0.5584 0.2410 0.1637 0.9591 0.5671 0.9526 0.3031 0.2155 0.3218

0.0253 0.0342 0.0375 0.0175 0.0048 0.0414 0.0062 0.0493 0.0258 0.1011

0.0002 0.0019 0.0042 0.0009 0.0007 0.0023 0.0007 0.0057 0.0010 0.9476

0.0004 0.0310 0.2136 0.5210 0.0017 0.0276 0.0014 0.1355 0.3718 0.0191

1.0193 1.1061 1.2772 0.6155 1.0420 1.1042 1.0403 1.2059 0.7672 0.0950

0.998 0.997 0.995 0.996 0.997 0.995 0.997 0.995 0.996 0.997

±0.096 ±0.106 ±0.125 ±0.121 ±0.112 ±0.132 ±0.111 ±0.130 ±0.130 ±0.104

95%CI.

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Table 3 Coefficients, exponents and constants for each balcony type and receiver for use in Eq. (20).

*

Position

Variable

Balcony Type 1

2

3

4

5

6

7

8

9

Balcony

C1 X1 Xp1 Xc1 C2 X2 Xp2 Xc2 C3 X3 Xp3 Xc3 C4 X4 Xp4 Xc4 C5 X5 Xp5 Xc5 R2 SE*

1.458 1.000 0.785 0.003 0.112 1.000 0.998 0.002 0.000 1.000 1.000 0.000 0.010 1.000 0.994 0.000 0.313 1.000 0.999 0.001 0.954 ±3.8

1.424 0.979 0.542 2.494 2.945 0.993 0.794 0.238 0.307 0.978 2.453 1.087 0.007 1.000 0.754 0.003 0.016 1.000 0.964 0.081 0.986 ±1.1

28.518 1.001 0.087 0.558 5.105 1.016 0.968 0.195 9.553 1.000 0.337 0.213 0.004 1.000 0.970 0.000 0.133 1.000 1.000 0.005 0.915 ±4.6

2.677 1.000 0.622 0.005 4.647 1.000 1.011 0.011 1.278 1.000 0.980 0.011 0.002 1.000 1.000 0.000 0.082 1.000 1.000 0.001 0.986 ±2.9

1.001 0.995 0.810 0.536 16.977 0.960 1.624 0.711 3.095 0.965 0.486 0.960 0.010 1.000 0.886 0.002 0.073 1.000 0.972 0.063 0.977 ±2.4

5.563 1.000 0.235 0.007 1.816 1.000 0.991 0.009 0.964 1.000 0.994 0.003 0.001 1.000 0.999 0.000 0.063 1.000 1.000 0.001 0.955 ±2.2

0.971 0.998 0.814 0.360 20.376 0.987 1.652 0.701 4.654 0.990 0.371 0.537 0.009 1.000 0.918 0.001 0.051 1.000 0.984 0.034 0.976 ±2.6

8.877 0.987 0.334 0.439 5.652 0.979 1.874 1.064 0.065 0.990 2.523 0.347 0.003 1.000 0.962 0.000 0.111 1.000 1.005 0.016 0.941 ±4.7

2.948 1.000 0.634 0.004 5.645 1.000 1.010 0.011 1.317 1.000 0.985 0.007 0.002 1.000 1.000 0.000 0.218 1.000 1.000 0.001 0.987 ±3.1

Facade

C1 X1 Xp1 Xc1 C2 X2 Xp2 Xc2 C3 X3 Xp3 Xc3 C4 X4 Xp4 Xc4 C5 X5 Xp5 Xc5 R2 SE*

3.123 0.983 0.509 2.200 50.904 1.031 2.069 0.992 0.000 1.000 1.000 0.000 0.019 1.000 0.804 0.003 v0.474 1.000 1.065 0.147 0.918 ±5.6

6.853 1.000 0.150 0.021 5.970 1.000 1.072 0.079 0.189 1.000 0.866 0.097 0.002 1.000 0.996 0.000 0.069 1.000 0.996 0.011 0.967 ±1.8

6.604 0.998 0.274 1.121 2.069 1.001 1.090 0.232 0.589 1.000 0.041 0.334 0.007 1.000 0.870 v0.001 0.034 1.000 0.998 0.007 0.956 ±2.9

1.913 0.995 0.670 0.389 15.037 0.953 1.678 0.835 0.510 0.996 0.686 0.162 0.002 1.000 0.999 0.000 0.437 1.000 1.010 0.034 0.983 ±3.2

3.831 0.981 0.320 0.905 21.471 0.959 2.926 0.883 0.558 1.001 0.936 0.131 0.024 1.000 0.657 0.000 0.495 1.000 1.040 0.014 0.963 ±3.4

9.191 1.000 0.104 0.016 7.639 0.988 1.667 0.690 10.321 0.994 0.025 0.413 0.000 1.000 0.997 0.000 0.073 1.000 0.994 0.021 0.954 ±2.3

2.843 1.012 0.363 1.133 23.713 1.043 3.054 1.059 0.415 1.000 0.882 0.104 0.050 1.000 0.508 0.000 0.551 1.000 1.076 0.015 0.964 ±3.4

12.888 1.000 0.204 0.352 4.316 1.002 0.928 0.139 5.892 1.000 0.481 0.121 0.002 1.000 0.990 0.000 0.016 1.000 0.999 0.003 0.938 ±4.2

2.152 0.996 0.614 0.416 20.069 0.958 1.747 0.864 1.235 0.996 0.642 0.167 0.003 1.000 0.997 0.000 0.570 1.000 1.013 0.043 0.980 ±3.6

95%CI.

direct relationship is emerging; however variability is too high to be relied upon solely to predict DSILB or DSILF. Finally, DDist, (Fig. 7(d)) shows no potential relationship with DSILB or DSILF. Consequently, it is necessary to combine a number of different variables in order to obtain a suitable prediction algorithm to support the development of the intended design guide. The remaining sections demonstrate how this is achieved. 3.2. Generating SDR variable To develop a theoretical form of SDR to be used in the design guides, the calculated data was analysed through the use of multivariable linear regression with power indices. SDR is calculated from the predicted data using Eq. (12) where a value less than one indicates overall specular energy is greater than the direct path energy. Three variables, (W, D, H1), are linearly regressed with SDR with exponents as per the general form in Eq. (19). Each balcony type and receiver location is assessed separately. X

SDR ¼ C A ðW X pA Þ þ C B ðDX pB Þ þ C C ðH1 pC Þ

ð19Þ

It is useful to inspect visually the relationships between SDR and DSILB and DSILF and comparing these relationships across balcony types. To do this, Types 1, 2, 3 and 9 balconies are selected to compare the extremes between balcony acoustic treatment levels and the results are shown in Fig. 8. It is observed in Fig. 8 that SDR is significantly different between balcony types and depends strongly on the presence of parapets and/or ceiling absorption. The presence of parapet and ceiling absorption has been excluded from the regression due to each balcony type being assessed independently. The Type 1 balcony (Fig. 8(a)) exhibits a narrow range of SDR over a wide range of DSILB or DSILF. Locations where SDR < 1 are those where the leading floor edge provides diffraction attenuation significant enough to reduce direct energy below specular reflections from the opposite buildings. The high concentrations of SDR  1 occurs due to strong first order specular reflections off the ground plane being similar to the direct path energy, which may or may not include diffraction attenuation. A Type 2 balcony (Fig. 8(b)) has significantly less distribution in DSILB or DSILF than a Type 1 balcony due to reflection from the ceiling plane alone. The strong first order specular reflections from the ceiling plane ensures a relative concentration of low SDR correlated with low DSILB

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or DSILF. A Type 3 balcony (Fig. 8(c)) demonstrates a similar trend to a Type 2 balcony; however the inclusion of a parapet increases DSILB or DSILF for a number of scenarios resulting in a wider range of SDR > 1. The parapet is not influential in many scenarios where SDR  1 similar to many Type 2 scenarios. The Type 9 balcony (Fig. 8(d)) has a similar spread of data to the Type 1; however the presence of a ceiling, albeit absorptive, concentrates many scenarios where SDR < 1 and DSILB > 12 or DSILF > 12. Similar to earlier findings, this again indicates the importance of absorption being placed on balcony ceilings in order to increase DSILB or DSILF. The coefficients and exponents with the highest derived correlation for each balcony type and receiver are shown in Table 2. These values were obtained by iteration of each coefficient and exponent such that the highest R2 correlation coefficient is determined. The R2 is above 99% with average 95% confidence interval standard errors, SE, of ±0.12 dB for all balcony types and receivers which is a highly correlated result. Thus Eq. (19) using coefficients and exponents in Table 2 is deemed suitable for inclusion into the design guide to predict SDR.

X

SILP ¼ C 1 ðX 1 ðDSIL þ DDist ÞX p1 þ X c1 Þ þ C 2 ðX 2 SDR p2 þ X c2 Þ X

X

þ C 3 ðX 3 aR p3 þ X c3 Þ þ C 4 ðX 4 H2 p4 þ X c4 Þ þ C 5 ðX 5 fX p5 þ X c5 Þ

ð20Þ

The minimum R2 = 0.915 occurs for Type 3 DSILB, the maximum R2 = 0.987 occurs for Type 9 DSILB and the mean across all balcony types and receivers is R2 = 0.961. The least prediction accuracy ±5.6 dB occurs for Type 1 DSILF, the highest prediction accuracy ±1.1 dB occurs for Type 2 DSILB and the mean prediction accuracy across all balcony types and receivers is ±3.2 dB. A scatter plot of all 9720 scenarios of DSILB or DSILF versus DSILP is shown in Fig. 9 where it can be observed that a direct linear relationship has been obtained from the study. Direct linear regression of Fig. 9 determines a satisfactory correlation coefficient, R2 = 0.89, and prediction accuracy of ±3.4 dB which is also satisfactory. Thus it is considered that Eq. (20) in combination with the coefficients, exponents and constants in Table 3 provides a reasonable level of accuracy in prediction of the effects of various balcony types and scenarios on differences in speech interference level.

3.3. DSIL regression Multivariate linear regression is conducted in order to derive an appropriate design guide equation for each balcony type. Regression on the entire dataset including all balcony types combined did not return a reasonable correlation which is to be expected as there are vast differences between the balcony types. The relative weight of each variable in predicting DSIL also differs depending on balcony type and location, so each variable is considered to follow the same modified exponential form (y = a(x)b + c). The overall equation to predict DSIL follows the form in Eq. (20) where the relevant coefficients are presented in Table 3. Like SDR, these values were obtained by iteration of each coefficient, exponent and constant such that the highest R2 correlation coefficient is determined. Each balcony type and receiver location achieves an independent correlation coefficient, R2, and 95% confidence interval standard error, SE, which are also presented in Table 3.

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4. Conclusions This study has explored the development of potentially simple application of a design guide algorithm to predict the difference in speech interference level depending on balcony type, acoustic treatment and location within a street canyon. Through the use of a combined direct, specular reflection and diffuse path theoretical and computer model along with simplifying assumptions, many scenarios have been calculated and used to develop this proposed design guide. There are a number of limitations in the study which need to be noted, specifically in the scenarios that are not currently included in the results database, such as (i) balconies with less width, (ii) balconies with larger depths than 4 m, (iii) balconies with heights other than 3.0 m, (iv) comparisons with multiple sources (simultaneous or time-lagged) and (v) variable distance between source and opposite facades. Future work in this area should focus on increasing the numbers of scenarios and also aiming to develop design guide algorithms which have higher accuracy than that presented above. Regardless of the above-mentioned limitations, a satisfactorily strong correlation between the proposed design guide predictions and the calculated values is obtained, thus suggesting that the design guide algorithm can be used to promote the use of balcony acoustic treatments in the building design profession. The proposed design guide is also likely to assist acoustic professionals in optimising selection and location of balcony acoustic treatments to reduce SIL and also overall road traffic noise sound pressure level and its effects on people on residential balconies. An additional benefit of the design guide is an improved ability to predict SIL on balcony facades, which can be translated into improved optimised selection of building façade sound transmission loss performance. This may assist acoustic professionals to meet specified internal road traffic noise criteria, thus reducing other potentially harmful effects on people caused by road traffic noise, such as sleep disturbance. Finally, it is concluded that balcony acoustic treatments have a significant effect on speech interference levels on residential balconies that are subject to road traffic noise.

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References Fig. 9. Scatter plot of DSILB or DSILF versus DSILP where DSILP is calculated from Eq. (20) using the coefficients, exponents and constants from Table 3 (R2 = 0.89, ±3.4 dB).

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