Paul Doyle MSc Thesis

UNIVERSITY OF SOUTHAMPTON

FACULTY OF ENGINEERING & THE ENVIRONMENT

Institute of Sound & Vibration Research

Sound and Vibration Studies

FEEG6012

Numerical Reverberation Time in Large Rooms

by

Paul Doyle

Thesis for the degree of Master of Science

September 2015

This thesis was submitted for examination in September, 2015. It does not necessarily represent

the final form of the thesis as deposited in the University after examination

Word Count:

19,329 (main body of text only)

23,622 (main body of text and all additional sections)

UNIVERSITY OF SOUTHAMPTON

ABSTRACT

FACULTY OF ENGINEERING & THE ENVIRONMENT

Sound and Vibration Studies

Thesis for the degree of Master of Science

NUMERICAL REVERBERATION TIME IN LARGE ROOMS

Paul Michael Doyle

This dissertation investigates the underestimation of Reverberation Time in large rooms, in

particular sports halls, which have shoebox geometry and large room volumes. Design

constraints mean that acoustic treatment is usually located on the ceiling only. This design

approach has resulted in significant underestimation of the RT compared to measured values,

which creates an uncomfortable acoustic environment for occupants. The aims of the

dissertation are to determine the reasons for the underestimation of RT and to determine

whether software implementing the finite element method (FEM) and discontinuous galerkin

method (DGM) can provide a more accurate prediction method than those currently used.

A literature review has been carried out, related to the behaviour of sound in enclosed spaces

and reasons for RT underestimation. Computer modelling has then been carried out using FEM

DGM software, with the results compared to outputs produced by Sabine calculations and ray-

tracing using CATT Acoustic. A test case room was modelled to ‘calibrate’ the FEM DGM model,

before a specific sports hall was modelled.

The findings from the literature review were that RT underestimation occurs due to the use of

inappropriate calculation methods, the location of acoustic absorption at high level and the

effect of diffusion. The findings from the modelling process were that the Sabine and CATT

Acoustic predictions were similar when absorption was uniformly distributed, but differed with

absorption located non-uniformly on the ceiling. The Sabine formula is not suitable for

predicting the RT in large rooms with non-uniform absorption, significantly underestimating the

RT. The FEM DGM software produced some unusual behaviour; with hard parallel walls, sound

energy propagated similarly to a standing wave. This effect increased with higher ceiling

absorption coefficients. Angling a side wall introduced diffusion, enabling sound energy to reach

the absorptive ceiling, reducing the RT. The results followed the expected trend of RT reduction

but were likely too low. Although the FEM DGM model is 2D, having access to the full field

solution is beneficial as it replicates the real world behaviour of sound more effectively than ray-

tracing and Sabine calculation. Further research is required to expand the model to 3D, allow

for frequency-dependent absorption coefficients and add diffusion to the modelling process.

i

Table of Contents

Table of Contents .......................................................................................................... i

List of Tables ................................................................................................................. v

List of Figures .............................................................................................................. vii

Nomenclature .............................................................................................................. x

List of Accompanying Materials ................................................................................... xii

DECLARATION OF AUTHORSHIP .................................................................................. xiii

Acknowledgements .................................................................................................... xiv

Chapter 1: Introduction ....................................................................................... 1

1.1 Project context - Reverberation Time (RT) in sports halls ....................................... 1

1.2 Design guidance for sports halls .............................................................................. 2

1.3 Acoustic comfort within sports halls ....................................................................... 2

1.4 Current design approach and example sports hall .................................................. 4

1.5 Project purpose ........................................................................................................ 4

1.6 Project aims and objectives ..................................................................................... 5

1.7 Dissertation structure .............................................................................................. 5

1.7.1 Chapter 2: Literature review ...................................................................... 5

1.7.2 Chapter 3: Application of calculations and modelling to sports hall

problem ...................................................................................................... 6

1.7.3 Chapter 4: Results and Discussion ............................................................. 7

1.7.4 Chapter 5: Conclusion ................................................................................ 7

Chapter 2: Literature Review ............................................................................... 8

2.1 Behaviour of sound in enclosed spaces ................................................................... 8

2.1.1 Sound wave propagation ........................................................................... 8

2.1.2 Frequency behaviour of sound waves ....................................................... 9

2.1.3 Wave equation ........................................................................................... 9

2.1.4 Behaviour of sound depending on surface materials .............................. 10

2.1.5 Acoustic absorption ................................................................................. 11

2.1.6 Diffusion and scattering ........................................................................... 12

2.1.7 Diffraction ................................................................................................ 12

ii

2.1.8 Room effects ............................................................................................ 12

2.1.9 Reverberation Time (RT) .......................................................................... 14

2.2 Definition of research problem: RT underestimation in practice .......................... 16

2.2.1 Dane Court Sports Hall............................................................................. 16

2.2.1.1 Stage 1: Initial calculations and measurements .................................... 16

2.2.1.2 Stage 2: Ray-tracing modelling and measurements ............................. 17

2.2.1.3 Stage 3: Final ray-tracing modelling and measurements ...................... 18

2.2.1.4 Stage 4: Introduction of scattering elements into hall ......................... 18

2.2.2 Further examples in sports halls: Arup data set ...................................... 18

2.2.3 Further examples in sports halls: CATT Acoustic example ...................... 19

2.2.4 RT underestimation in non-sports hall - broadcast facility example....... 20

2.3 Reasons for underestimation of RT ....................................................................... 20

2.3.1 Prediction method ................................................................................... 20

2.3.1.1 Diffuse-field calculations ....................................................................... 20

2.3.1.2 Ray-tracing modelling ............................................................................ 21

2.3.2 Location of acoustic absorption .............................................................. 23

2.3.3 Effect of scattering objects ...................................................................... 23

2.3.3.1 Sports hall examples .............................................................................. 23

2.3.3.2 Non-sports hall – broadcast facility example ........................................ 25

2.3.4 Behaviour not accounted for in calculation or modelling processes ...... 27

2.4 Alternative approach – physical design ................................................................. 27

2.5 Room acoustics modelling techniques .................................................................. 28

2.5.1 Ray-tracing and image sources ................................................................ 28

2.5.2 Pseudo Spectral Time Domain (PSTD) method for sports halls .............. 29

2.5.3 Other techniques ..................................................................................... 30

2.5.4 Issues with computer modelling .............................................................. 31

2.6 Modelling method used in this project.................................................................. 32

2.6.1 Finite Element Method (FEM) and Discontinuous Galerkin Method

(DGM)....................................................................................................... 32

2.6.2 FEM DGM modelling process .................................................................. 33

iii

Chapter 3: Application of calculations and modelling to sports hall problem ...... 35

3.1 Test case modelling ................................................................................................ 35

3.1.1 Sabine calculations .................................................................................. 36

3.1.2 Ray-tracing using CATT Acoustic .............................................................. 36

3.1.3 FEM DGM modelling ................................................................................ 38

3.2 Dane Court sports hall modelling .......................................................................... 40

3.2.1 Sabine calculations .................................................................................. 40

3.2.2 Ray-tracing using CATT Acoustic .............................................................. 41

3.2.3 FEM DGM modelling ................................................................................ 43

Chapter 4: Results and Discussion ...................................................................... 46

4.1 Test case model results .......................................................................................... 46

4.1.1 Model 1: Cube-shaped ............................................................................. 46

4.1.1.1 Model 1 octave band behaviour of FEM DGM output data ................. 47

4.1.1.2 Model 1 energy decay curves ................................................................ 48

4.1.1.3 Model 1 wave propagation in 2D environment .................................... 51

4.1.2 Model 2: sloped ceiling and Model 3: angled side wall ........................... 54

4.1.2.1 Model 3 energy decay curves ................................................................ 56

4.1.2.2 Model 3 wave propagation in 2D environment .................................... 59

4.1.3 Test case modelling summary of findings ............................................... 60

4.2 Dane Court sports hall results ................................................................................ 62

4.2.1 Model 1: Absorption at high level only ................................................... 62

4.2.2 Model 2: Absorption at high level with panels at high level ................... 63

4.2.3 Model 3: Absorption at high level with panels at lower level ................. 64

4.2.4 Model 4: Absorptive panels at lower level only ...................................... 64

4.2.5 Model 5: Absorptive ceiling only with angled walls ................................ 65

4.2.6 Dane Court modelling summary of findings ............................................ 66

Chapter 5: Conclusion........................................................................................ 68

5.1 Achievement of project aims and objectives ........................................................ 68

5.2 Further research .................................................................................................... 69

iv

5.2.1 2D modelling ............................................................................................ 69

5.2.2 Non frequency-dependent absorption coefficient.................................. 70

5.2.3 Diffusion and scattering ........................................................................... 70

5.3 Project management ............................................................................................. 71

List of References ....................................................................................................... 72

v

List of Tables

Table 1: Sports hall Tmf RT as a function of floor area (BB93, 2015) .............................................. 2

Table 2: Dane Court Sports Hall - construction materials and absorption coefficients .............. 16

Table 3: Revised absorption coefficients of the 'effective' perforated deck for the calibrated

Odeon model ......................................................................................................................... 17

Table 4: Laboratory tested absorption coefficients for Rockfon Samson tiles ............................ 17

Table 5: Adjusted absorption coefficients for Rockfon Samson tiles .......................................... 18

Table 6: Effect of diffuse reflections on predicted RT using CATT Acoustic ray-tracing software

(James et al, 2012) 1 with beams in ceiling geometry, 2 flat ceiling with high diffusion, 3 auto edge

diffusion ......................................................................................................................... 21

Table 7: Test Case - Absorption and scattering coefficients used for Sabine calculations and ray-

tracing ......................................................................................................................... 36

Table 8: Test Case - Source & Receiver positions for CATT Acoustic ray-tracing modelling ....... 36

Table 9: Test Case - Source & Receiver positions for FEM DGM modelling of 2D vertical sections

......................................................................................................................... 38

Table 10: Dane Court Sports Hall - Absorption and scattering coefficients used for Sabine

calculations and ray-tracing ......................................................................................................... 40

Table 11: Dane Court Sports Hall - Source & Receiver positions for ray-tracing modelling using

CATT Acoustic ......................................................................................................................... 41

Table 12: Dane Court Sports Hall - Source & Receiver positions used for FEM DGM modelling of 2D

Vertical Section - Side Wall 33m x 8.65m .................................................................................... 43


Vertical Section - Rear Wall 18m x 8.65m .................................................................................... 43

Table 14: Test Case Model 1 Option 1 results ............................................................................. 46



vi

Table 17: Test Case Impact of Sloped ceiling and angled side wall on FEM DGM predictions -

Option 1, walls, floor & ceiling α 0.1 ............................................................................................ 54

Table 18: Test Case impact of sloped ceiling and angled side wall on FEM DGM predictions -

Option 2, walls & floor α 0.1, ceiling α 0.5 ................................................................................... 55


Option 3, walls & floor α 0.1, ceiling α 0.9 ................................................................................... 55

Table 20: Dane Court Model 1 results ......................................................................................... 62



Table 23: Dane Court Model 4 results ........................................................................................ 65


vii

List of Figures

Figure 1: Propagation of sound waves in air (Nave, 2012) ............................................................ 8

Figure 2: Spherical radiation of point source and inverse square law (Maury et al, 2015) ........... 9

Figure 3: Behaviour of sound in enclosed spaces when incident upon different materials (Cox &

D'Antonio, 2009) ......................................................................................................................... 10

Figure 4: Acoustic absorption performance of porous materials (Marsh, 1999) ........................ 12

Figure 5: Axial modes (a), tangential modes (b) and oblique modes (c), (Wilmhurst & Thompson,

2012) ......................................................................................................................... 13

Figure 6: Frequency response for small room (Cox & D'Antonio, 2009) ..................................... 14

Figure 7: T20 measurement principle showing extrapolation to T60 (Thompson, 2013) .............. 16

Figure 8: Arup Acoustics data set showing trend of predicted vs. measured Tmf RT for sports halls

(Oeters, 2012) ......................................................................................................................... 19

Figure 9: Example sports hall with non-uniform absorption at ceiling level (James et al, 2012) 19

Figure 10: Single ray in a rectangular room modelled using ray-tracing, showing reflections with

different values for surface scattering coefficient (Rindel, 1995) ............................................... 22

Figure 11: Relationship between surface roughness, D, and wavelength, λ , which illustrates the

frequency dependent behaviour of scattering (James et al, 2012) ............................................. 22

Figure 12: Arup test case, extent of scattering objects in sports hall which resulted in reduction of

1 second in measured Tmf RT, 2.8s down to 1.8s (Oeters, 2012) ................................................. 24

Figure 13: Southbank University, extent of scattering objects in sports hall which resulted in

reduction of 0.9 seconds in measured Tmf RT, 4.0s down to 3.1s, (Oeters, 2012) ...................... 24

Figure 14: Unfurnished broadcast facility during initial measurements following construction,

absorption on soffit and walls ..................................................................................................... 26

Figure 15: Broadcast facility furnished with set constructions during follow up measurements ...

......................................................................................................................... 26

Figure 16: 1/3 octave band RT measurements made by Ion Acoustics in broadcast facility ...... 27

Figure 17: FEM basic modelling process flowchart...................................................................... 32

viii

Figure 18: FEM DGM modelling process flowchart ..................................................................... 33

Figure 19: Test Case Model 1 in CATT Acoustic (10m x 10m x 10m) ........................................... 37

Figure 20: Test Case Model 1 Vertical 2D Section - cube-shaped room ...................................... 39

Figure 21: Test Case Model 2 Vertical 2D Section - sloped ceiling option ................................... 39

Figure 22: Test Case Model 3 Vertical 2D Section - angled wall option ...................................... 39

Figure 23: Dane Court Sports Hall Model 1 - CATT Acoustic (absorptive ceiling only) ................ 41

Figure 24: Dane Court Sports Hall Model 2 - CATT Acoustic (absorptive ceiling with 150m2

additional absorptive panels at high level) .................................................................................. 42


additional absorptive panels at lower level) ................................................................................ 42

Figure 26: Dane Court Sports Hall Model 4 - CATT Acoustic (150m2 absorptive panels at lower level

only, no absorptive ceiling) .......................................................................................................... 42

Figure 27: Dane Court Sports Hall Model 5 - CATT Acoustic (absorptive ceiling with angled side

wall) ......................................................................................................................... 42

Figure 28: Dane Court Sports Hall Side Wall Vertical 2D Section - 33m x 8.65m. Models 1-4 .... 44

Figure 29: Dane Court Sports Hall Rear Wall Vertical 2D Section - 18m x 8.65m. Models 1-4.... 44

Figure 30: Dane Court Sports Hall Side Wall Vertical 2D Section - 33m x 8.65m. Option 5 angled

side wall ......................................................................................................................... 45

Figure 31: Dane Court Sports Hall Rear Wall Vertical 2D Section - 18m x 8.65m. Option 5 angled

rear wall ......................................................................................................................... 45

Figure 32: FEM DGM T20 octave band behaviour for test case Model 1 ..................................... 48

Figure 33: DGM T30 octave band behaviour for test case Model 1 ............................................. 48

Figure 34: Example Energy Decay Plots Model 1 Option 1 (α 0.1 on all surfaces) ...................... 49

Figure 35: Example Energy Decay Plot Model 1 Option 2 (α 0.1 on walls & floor, α 0.5 on ceiling)

......................................................................................................................... 49


......................................................................................................................... 49

ix

Figure 37: Zoomed Energy Decay Plot Model 1 Option 1 (α 0.1 on all surfaces) ........................ 50

Figure 38: Zoomed Energy Decay Plot Model 1 Option 2 (α 0.1 on walls & floor, α 0.5 on ceiling)

......................................................................................................................... 50


......................................................................................................................... 50

Figure 40: Source propagation in 2D, Model 1 Option 1 (α 0.1 on all surfaces) ......................... 51

Figure 41: Source propagation in 2D, Model 1 Option 2 (α 0.1 on walls & floor, α 0.5 on ceiling)

......................................................................................................................... 52

Figure 42: Source propagation in 2D, Model 1 Option 3 (α 0.1 on walls & floor, α 0.9 on ceiling) .

......................................................................................................................... 53

Figure 43: Example Energy Decay Plots Model 3 Option 1 (α 0.1 on all surfaces) ...................... 56


......................................................................................................................... 57


......................................................................................................................... 57

Figure 46: Zoomed Energy Decay Plot Model 3 Option 1 (α 0.1 on all surfaces) ....................... 58


......................................................................................................................... 58


......................................................................................................................... 58

Figure 49: Source propagation in 2D, Model 3, Option 2 (α 0.1 on walls & floor, α 0.5 on ceiling)

......................................................................................................................... 59


......................................................................................................................... 60

x

Nomenclature

English Symbols

c Speed of sound (m/s)

C80 Clarity: ratio between early and late sound energy

d Diffusion coefficient

D Surface roughness

D50 Definition: ratio between early and total sound energy

f Frequency (Hz)

𝑓𝑠 Schröeder frequency

G Sound strength (dB)

I Sound intensity

k Wave number

LAeq Steady-state noise level, essentially the energy average of a fluctuating sound level

N Number of time steps

r Reflection coefficient

RT60 Reverberation Time; the time taken for sound to decay by 60dB after excitation

s Scattering coefficient

Tmf Reverberation Time averaged between 500Hz, 1kHz and 2kHz octave bands

T20 Reverberation Time Decay between -5dB and -25dB, extrapolated to a 60dB decay

T30 Reverberation Time Decay between -5dB and -35dB, extrapolated to a 60dB decay

V Volume

W Sound power

xi

Greek Symbols

α Absorption coefficient

�̅� Average absorption coefficient

𝛼𝑤 Weighted absorption coefficient

Δn Time step

λ Wavelength

ω Angular frequency

φ Phi

ρ Density

Sα Absorption area

Acronyms

CFL Courant-Friedrichs-Levy Stability Criterion

DGM Discontinuous Galerkin Method

FEM Finite Element Method

FDTD Finite Difference Time Domain

FVM Finite Volume Method

PSTD Pseudo Spectral Time Domain

SEA Statistical Energy Analysis

2D Two-dimensional

3D Three-dimensional

xii

List of Accompanying Materials

A DVD of Accompanying Materials is provided, which includes the following information:

1. Project Documents: Project plan report, interim report, project presentation and Gantt

charts.

2. Arup Acoustics test case data: GA floor plans for Dane Court sports hall and acoustic

design report.

3. Diffuse-field calculations: Sabine calculations for the test case and Dane Court sports hall

models.

4. CATT Acoustic modelling: Input and output data for test case and Dane Court sports hall

models.

5. FEM DGM modelling: Input and output data for test case and Dane Court sports hall

models.

6. Spreadsheets: Tables used this report, including source and receiver locations for models,

comparisons between Sabine calculation, Catt Acoustic and FEM DGM results.

7. Correspondence: Spreadsheet identifying main project meetings and discussions, and

copies of progress summary documents sent to project supervisor.

xiii

DECLARATION OF AUTHORSHIP

I, Paul Michael Doyle declare that this thesis and the work presented in it are my own and has

been generated by me as the result of my own original research.

Numerical Reverberation Time in Large Rooms.

I confirm that:

1. This work was done wholly or mainly while in candidature for a research degree at this

University;

2. Where any part of this thesis has previously been submitted for a degree or any other

qualification at this University or any other institution, this has been clearly stated;

3. Where I have consulted the published work of others, this is always clearly attributed;

4. Where I have quoted from the work of others, the source is always given. With the exception

of such quotations, this thesis is entirely my own work;

5. I have acknowledged all main sources of help;

6. Where the thesis is based on work done by myself jointly with others, I have made clear

exactly what was done by others and what I have contributed myself;

7. None of this work has been published before submission.

Signed: .............................................................................................................................................

Date: .................................................................................................................................................

xiv

Acknowledgements

I would like to thank my project supervisor, Gwenael Gabard, who has provided technical and

practical advice throughout the duration the project and has guided me throughout the year. I

would also like to acknowledge the help of Vincent Jurdic, who oversaw the project on behalf of

Arup Acoustics. Additional thanks are due to David O'Neill and Gavin Irvine, directors of Ion

Acoustics, who supported me in this endeavour over three years of part-time study.

Chapter 1

1

Chapter 1: Introduction

1.1 Project context - Reverberation Time (RT) in sports halls

The project is based on reverberation time (RT) in large rooms. RT refers to the decay of sound

energy within an enclosed space, and is described further in Section 2.1.9. Rooms which have a

low RT are described as acoustically 'dead' spaces, and include rooms such as recording studios

and critical audio listening rooms. Rooms with a high RT are considered to be acoustically 'lively'

spaces; for example churches, cathedrals and sports halls. In these spaces, a high RT may be

desirable, for example to enhance the effect of choral music. However, in the case of sports halls,

a high RT is not desirable, as speech intelligibility is crucial to ensure effective communication

between staff and students.

Sports halls are of specific interest to this project, and tend to be designed using simple shoebox

geometry. A typical sports hall can have dimensions of 20-30m (length) x 15-20m (width) x 7-9m

(height), which results in large room volumes ranging between 2000 m3 - 5000m3. Materials used

in building sports halls are typically hard and reflective, for example blockwork or timber walls

and flooring and metal ceilings. These materials are used for practical purposes, as they are able

to withstand damage from physical impacts from items such as sports balls.

Building materials can be described in terms of the amount of acoustic absorption they provide;

this refers to the ability of a material to absorb sound energy. The rating of materials in terms of

the level of acoustic absorption they provide is explained in Section 2.1.5. Building materials used

in sports halls provide little acoustic absorption, and the simple geometry of large reflective

surfaces allows sound energy to be reflected back and forth within the room. Parallel side walls

and rear walls create an environment in which room effects such as standing waves and flutter

echoes, which are explained further in Section 2.1.8, can occur. These effects cause a build-up of

reverberant noise levels, creating an uncomfortable acoustic environment for occupants.

One of the most significant impacts is a reduction in speech intelligibility which can result in

reduced control for teaching staff and can exacerbate stress for staff and students. In sports halls,

the metal ceiling usually provides the most significant source of acoustic absorption, as the metal

is perforated with acoustically absorbent mineral fibre located behind the perforations. Sound

energy propagates through the perforations, becoming incident upon the mineral fibre, resulting

in absorption of sound energy. However, as will be discussed in Section 2.3.2, the non-uniform

location of acoustic absorption at ceiling level only can have a negative impact on reducing the RT.

Chapter 1

2

1.2 Design guidance for sports halls

In the UK, the RT in a sports hall is specified as the mid-frequency reverberation time, Tmf, which is

the arithmetic average RT within the 500Hz, 1kHz and 2kHz octave bands. Sport England guidance

(2012) recommends an upper Tmf range between 1.5 and 2.0 seconds. For compliance with UK

Building Regulations, sports halls in educational buildings must achieve the RT targets set out in

Building Bulletin 93 (BB93, 2015), which is also an upper Tmf range between 1.5 and 2.0 seconds,

with the exact Tmf dependent on floor area, as shown in Table 1:

Table 1: Sports hall Tmf RT as a function of floor area (BB93, 2015)

A sports hall with a large room volume which is furnished with reflective materials will therefore

have a high Tmf RT unless additional acoustic absorption is introduced.

1.3 Acoustic comfort within sports halls

Acoustic comfort within an enclosed space can be considered a subjective concept, and it is

difficult to define any objective criteria against which this can be assessed. For sports halls, RT has

historically been used as a primary indicator of acoustic comfort, in addition to speech

intelligibility and internal noise levels. BB93 (2015) sets an internal noise limit of 40dB LAeq in

sports halls, which is the combination of external noise transmitted internally via the building

envelope and mechanical services noise if the building is mechanically ventilated. External noise

transmitted into sports halls via the building envelope can contribute to and exacerbate problems

associated with a high RT, as described by Conetta et al (2012).

The amplitude of internal noise levels depends on the activity taking place, but some activities

generate higher noise levels than others, for example the impact of a basketball bouncing on a

hard floor surface. As Chmelik et al (2012) discuss, the build-up of noise levels may be particularly

disorientating to students or staff with visual impairments, as they will rely on acoustic cues from

effects such as room echoes produced by reflection of sound energy from room surfaces to

localise sound and orient themselves within the hall. The health of teaching staff can also be

adversely affected (Jonsdottir, 2009), as teachers can develop voice problems as a result of raising

their voices to make themselves heard by students.

Chapter 1

3

In addition to RT, several other parameters can be used to indicate the level of acoustic comfort,

such as 'Definition (D50)' and 'Clarity (C80)' as defined by Thiele (1953) and 'sound strength' (G) as

defined by Lehmann (1976). However, these parameters are usually more suited to assessing

room acoustics of performance spaces, radio and television broadcast studios and audio recording

suites. In these spaces, high levels of definition and clarity would be required for speech and

music, and sound strength would be expected to be consistent within the room.

The use of RT as the primary indicator of acoustic comfort in sports halls is a contentious issue in

room acoustics. Tiesler & Lang (2012) agree on the appropriateness of the strategy, but others

such as Nijs and Schuur (2003) argue that the RT is too dependent on room volume, and

specification of a fixed reverberation time may be too onerous a requirement for rooms with very

large volumes. Nijs and Schuur suggest an alternative approach of specifying an average

absorption coefficient (�̅�) across all surfaces within the room. However, as the authors

acknowledge, this approach would be impractical, as the six primary room surfaces will not be

constructed from the same material, and their absorption characteristics will differ.

De Ruiter (2010) accepts the use of RT for assessing the acoustic comfort in spaces such as

concert halls, offices and dwellings, but disagrees regarding its use in sports halls. De Ruiter

argues that while the large volume of these spaces is the main reason for introducing absorptive

materials into the space, RT should not be used as the primary design criterion, and suggests an

amount of acoustic absorption per m2 or per person should be used instead.

Luykx & Vercammen (2012), taking their cue from the work of de Ruiter (2010) suggest that a

measure of sound strength (G) in the hall is more appropriate, as it is the build-up of internal

noise levels which gives rise to uncomfortable acoustic conditions. They believe that the measure

of sound strength is more appropriate as it is not as affected by room effects like standing waves

and flutter echoes, unlike RT measurements. However, they do acknowledge the difficulties

inherent with measuring sound strength, as the test procedure is more complex than that

required than for measuring RT.

In spite of the differing opinions regarding the suitability of RT as the primary indicator of

acoustic comfort in sports halls, current guidance relates to assessment of sports halls in terms of

an upper Tmf RT, and this is the currently accepted approach within acoustic consultancy. This

project is not concerned with the appropriateness of RT as an indicator of acoustic comfort.

Chapter 1

4

1.4 Current design approach and example sports hall

While it is clear that is crucial to provide sufficient acoustic absorption in sports halls, a key

decision is determining the most suitable location for absorptive materials. Absorptive

treatments are generally built into the ceiling construction, as discussed in Section 1.1, and/or at

very high level on the walls. The high vertical position reduces the likelihood of damage to the

usually lightweight absorptive materials. Including the absorptive treatment within the ceiling

itself ensures a convenient solution to introduce a large area of acoustic absorption into the hall.

In acoustic consultancy, RT in sports halls is currently calculated using either a diffuse-field

Sabine calculation (Section 2.3.1.1) or a ray tracing model (Section 2.3.1.2). However, both of

these methods have been shown to underestimate the reverberation time when comparing the

calculated values with real world measurements (Section 2.2).

This project has been carried out with Arup Acoustics, who have provided details of the acoustic

design of a sports hall at Dane Court Grammar School, Kent (Section 2.2.1). Following the

construction of the hall, the measured RT was found to be significantly higher than predictions

made using Sabine calculations and ray tracing modelling. In addition to Dane Court sports hall, a

trend of RT underestimation has been identified by Arup Acoustics, based on 50 sports hall design

projects. RT underestimation can also occur in other large rooms with reflective surface materials

and large volumes. An example of a broadcast facility is provided, based on design work and

physical measurements made by this author within an acoustic consultancy role.

For this project, RT predictions have been made for Dane Court sports hall using Sabine

calculations, ray-tracing modelling using CATT Acoustic and FEM DGM modelling using software

provided by Gwenael Gabard, project supervisor. Results from these processes have been

compared to each other and to measured results obtained by Arup Acoustics during the design.

1.5 Project purpose

The overall purpose of the project is to determine whether FEM and DGM modelling techniques

can be utilised to provide a more accurate reverberation time calculation method than Sabine

calculations or ray tracing modelling. This is achieved by investigating several topics:

Differences between results from Sabine calculations, ray-tracing and measured values.

Differences between modelling using ray-tracing and FEM DGM techniques.

Benefits of having access to the full-field solution from the FEM DGM software.

Whether the 2D FEM DGM model can produce useful results.

Chapter 1

5

1.6 Project aims and objectives

The aims of this project are:

1. To gain an understanding of sports hall design, issues in acoustic consultancy and the

prediction methodologies used in calculating reverberation time.

2. To determine whether FEM software implementing the DGM can provide a more accurate

reverberation time calculation in sports halls.

The objectives of this project are:

1. Identify discrepancies between predicted and measured reverberation time in sports

halls.

2. Evaluate perceived shortcomings of prediction methods, including diffuse-field

calculations and ray-tracing methods.

3. Explore numerical modelling of sports hall 2D sections using FEM DGM software.

4. Compare numerical modelling results to diffuse-field calculations, ray-tracing outputs and

physical measurements.

5. Analyse the effect of introducing scattering elements to the working model.

1.7 Dissertation structure

The structure of this dissertation is divided into several chapters.

Chapter 1: Introduction.

Chapter 2: Literature Review.

Chapter 3: Methodological Processes - Collection of Empirical Data.

Chapter 4: Results & Discussion.

Chapter 5: Conclusions.

The content of Chapters 2-5 is described in more detail in the following sections.

1.7.1 Chapter 2: Literature review

The literature review is based on several topics, which are outlined in the following section:

Section 2.1: Behaviour of sound in enclosed spaces: This section introduces the key concepts of

room acoustics and the behaviour of sound in enclosed spaces. Topics include the wave equation,

reverberation time, absorption, diffusion, and acoustic effects such as standing waves, flutter

echoes, room modes and diffraction.

Chapter 1

6

Section 2.2: Definition of the research problem: This section describes the project focus,

specifically, that current calculation and modelling methods are underestimating the RT in sports

halls compared to measured values. The acoustic design for Dane Court sports hall is described,

along with examples of RT underestimation in sports halls and a broadcast facility.

Section 2.3: Reasons for underestimation of RT: This section seeks to explain why RT

underestimation in sports halls occurs. The primary reasons are likely to be the prediction

method, high vertical location of acoustic absorption within sports halls, the effect of scattering

objects and the influence of acoustic effects such as flutter echoes and standing waves.

Section 2.4: Alternative approach - physical design: This section discusses alternative approaches

which could be considered for sports hall design, which rely on architectural design to provide a

comfortable acoustic environment as opposed to numerical prediction tools.

Section 2.5: Room acoustics modelling techniques: This section describes several techniques

used for room acoustics modelling. These include methods specifically for sports halls such as

geometrical ray-tracing and Pseudo Spectral Time Domain (PSTD) models, and other techniques

such as Statistical Energy Analysis (SEA), Finite Difference Time Domain (FDTD) and hybrid models.

Section 2.6: Modelling method used for this project: The final section provides a description of

the modelling method utilised for this project, the finite element method (FEM) using the

discontinuous galerkin method (DGM). Software has been provided by Gwenael Gabard, project

supervisor, and this section includes a brief description of the modelling process, including pre-

processing and post-processing using MATLAB and identification of user-definable variables.

1.7.2 Chapter 3: Application of calculations and modelling to sports hall problem

This chapter describes the application of Sabine calculations, ray-tracing modelling and FEM DGM

modelling to a sports hall problem. Before Dane Court sports hall could be modelled, a

'calibration' process was carried out, which modelled a simple test case room.

Section 3.1: Test Case Modelling: This section describes the modelling process for a test case

room (10m x 10m x 10m). The test case was used to determine the accuracy of output data from

the FEM DGM software for a simple geometry compared to Sabine calculations and ray-tracing

modelling.

Section 3.2: Dane Court Sports Hall Modelling: The process for the test case has been followed

for the Dane Court Sports Hall, and this section describes the methodology.

Chapter 1

7

1.7.3 Chapter 4: Results and Discussion

This chapter presents the results from all processes used in the project.

Section 4.1: Test Case Results: The results for the test case are presented and compared to

Sabine calculations and ray-tracing modelling outputs for three model options, with varying

degrees of acoustic absorption present on the ceiling. Unusual behaviour in the FEM DGM output

data is discussed and analysed, with a view to understanding how this data has been produced.

Section 4.2: Dane Court Sports Hall Results: The results for Dane Court Sports Hall are presented

and compared to measured values, Sabine calculations, and ray-tracing modelling outputs.

1.7.4 Chapter 5: Conclusion

This chapter concludes the dissertation and discusses the following topics:

Whether the project aims and objectives have been met.

Areas in which the project could be improved.

Further research based on the project findings.

Effectiveness of project management strategies.

Chapter 2

8

Chapter 2: Literature Review

2.1 Behaviour of sound in enclosed spaces

2.1.1 Sound wave propagation

Sound waves disturb the medium in which they propagate, creating periodic pressure fluctuations

above and below the steady-state atmospheric pressure. It is not the sound waves that

propagate through the medium, but the pressure disturbances, as they move in the direction of

travel of the sound waves in backwards and forwards motion. When sound intensity increases,

more air molecules are moved. Figure 1 shows sound wave propagation in air (Nave, 2012).

Figure 1: Propagation of sound waves in air (Nave, 2012)

The speed of sound in air, c, depends on the air temperature, and can be calculated at any

temperature using (1). The speed of sound in air at a temperature of 20°C is 343m/s.

c = 331.4 + 0.6Tcelcius (1)

A point source propagates spherically, with sound power W. The area over which the sound

energy propagates can be thought of as an imaginary sphere (Maury et al, 2015). At the surface

of the imaginary sphere, the source intensity, I, will be spread over the area of the sphere,

becoming = 𝑊

4𝜋𝑟2 . As the distance, r, from the point source increases, the source intensity will be

spread over a greater area, and will reduce according to the inverse square law, i.e. by 1

𝑟2. This

principle is illustrated in Figure 2 (Maury et al, 2015).

Chapter 2

9

Figure 2: Spherical radiation of point source and inverse square law (Maury et al, 2015)

2.1.2 Frequency behaviour of sound waves

The behaviour of sound waves in enclosed spaces is frequency-dependent, and relies on the

wavelengths, λ, of individual frequencies, which can be calculated using (2):

λ =𝑐

𝑓 (2)

where c is the speed of sound in m/s, and f is frequency. Low frequencies have longer

wavelengths than high frequencies. For example, for c = 343m/s, frequencies of 50Hz, 500Hz and

5kHz will have a wavelengths of 6.9m, 0.69m and 0.07m respectively.

For room acoustics analysis, frequencies are divided into octave bands, instead of individual

frequencies. Octave bands spread the frequency content of a noise source into low, mid and high

octave bands, with each successive octave band being approximately double the value of the

previous band. The octave bands generally used in room acoustics are 63Hz, 125Hz, 250Hz,

500Hz, 1kHz, 2kHz, 4kHz and 8kHz.

2.1.3 Wave equation

The equations in this section are based on an ISVR6117 Architectural and Building Acoustics

lecture by Fazi (2013). The propagation of sound in an enclosed space is defined by the wave

equation (3), which is a 2nd order partial differential equation (PDE).

∇2𝑝(�⃗�, 𝑡) − 1

𝑐2 𝜕2 𝑝(𝑥,𝑡)

𝜕𝑡2 = 0 (3)

The wave equation is satisfied by the homogeneous Helmholtz equation (4) and the Neumann

boundary condition for rigid walls (5):

∇2𝑃(�⃗�) + 𝑘2𝑃(�⃗�) = 0 (4)

∇𝑃(�⃗�). �⃗⃗� = 0 (5)

Chapter 2

10

This results in the eigenvalue problem (6):

−∇2𝑃(�⃗�) = 𝑘2𝑃(�⃗�) (6)

which has eigenvalue solution (7) and eigenfunction solution (room modes) (8):

𝑘𝑛 = 𝜔𝑛

𝑐 (7)

𝜑𝑛 (�⃗�) (8)

2.1.4 Behaviour of sound depending on surface materials

When sound energy encounters a surface, it will either be absorbed, reflected or scattered,

depending on the surface material characteristics, as shown in Figure 3 (Cox & D'Antonio, 2009).

Figure 3: Behaviour of sound in enclosed spaces when incident upon different materials (Cox &

D'Antonio, 2009)

As Figure 3 shows, when sound waves encounter an absorptive material, the sound energy

reflected back into the room is attenuated in comparison to the initial sound. When sound waves

encounter a flat, reflective material, sound energy will be reflected back into the room in a

specular manner. When sound waves encounter a diffuse material, sound energy will be

'scattered' back into the room, in a non-specular, more random manner.

Chapter 2

11

2.1.5 Acoustic absorption

The absorption of a material is defined by the absorption coefficient, α, which describes the

ability of the material to absorb sound energy incident on its surface. Random-incidence α values

can be measured in a laboratory, according to BS EN ISO 354 (2003), and is specified as a value

between 0 and 1 , where 0 indicates no absorption and 1 indicates absorption of all sound energy.

Energy reflected back into a room can be determined by the reflection coefficient, r, which is

calculated simply as 1-α.

α values are specified by manufacturers in octave bands between 125Hz and 4kHz. Absorptive

materials are rated in terms of a single Absorption Class, according to BS EN ISO 11654 (1997),

which rationalises the octave band absorption behaviour into a single value, αw. For example,

Absorption Class A is rated at αw 0.9 to 1.0 and Absorption Class E is rated at 0.15 to 0.25.

Acoustic absorbers are commonly constructed from porous materials, which allow sound energy

to be absorbed by the material surface. When sound energy becomes incident the material, the

sound energy is converted into heat energy and dissipated. However, as absorption coefficients

are frequency dependent, materials do not absorb sound energy uniformly across the entire

frequency range. Norton and Karczub (2003) note that porous materials provide very good

acoustic absorption from 1kHz upwards, but very little at frequencies below 250Hz. This is due to

the fact that low frequency sound waves have much longer wavelengths, λ, than high frequency

sound waves, and cannot physically travel through the material easily.

As Norton and Karczub (2003) explain further, the ability of a porous material to absorb sound

effectively is governed by the particle velocity of the sound wave. The maximum particle velocity

occurs at λ

4 and

3λ

4, and this is where a porous material absorbs sound energy most effectively.

The distance from the wall to the porous material or the thickness of the material itself if located

close to the wall must match the value of λ

4 or

3λ

4 for particular frequencies to be absorbed.

For 63Hz, a wavelength of λ

4 is 1.35m, which is the thickness required for the material to absorb

frequencies of 63Hz. For 125Hz, a wavelength of λ

4 is 0.68m, which is the thickness required for

the material to absorb frequencies of 125Hz. Therefore, porous materials will not absorb low

frequencies effectively, unless they are very thick materials, or unless they are placed far away

from the wall. Figure 4 (Marsh, 1999) illustrates this principle.

Chapter 2

12

Figure 4: Acoustic absorption performance of porous materials (Marsh, 1999)

2.1.6 Diffusion and scattering

Diffusion is the ability of a surface material to scatter sound, and is a ratio between the scattered

sound energy and total reflected sound energy (Rindel, 1995). Until very recently, it was not

possible to quantify the scattering provided by surface materials. However, relatively recent

research (D'Antonio & Rife, 2011) has resulted in the production of a standard, BS ISO 1749-1

(2004) + A1 (2014), which allows the random incidence scattering coefficient, s , of a material to

be measured. The s values can then be used for room acoustics modelling . The directional

diffusion coefficient, d , can also be measured, using BS ISO 1749-2 (2012), and is intended for use

by manufacturers to aid in the design of diffusing materials.

2.1.7 Diffraction

Diffraction occurs when sound waves 'bend' or 'wrap' around the edge of a surface or an obstacle

(Kuttruff , 2009). Diffraction can occur at any frequency, but is more prevalent at low frequencies,

when the wavelengths, λ, are longer than the room dimensions. However, in sports halls with flat

surfaces and room dimensions in excess of 30m (side walls) and 15m (rear walls), diffraction

would not be considered to be problematic. It is worth noting however, that geometric modelling

techniques such as ray-tracing do not take diffraction into account, and therefore are not an

entirely accurate representation of real-life environments (Kutruff, 2009).

2.1.8 Room effects

Room modes occur when sound waves reflect off wall surfaces (Kuttruff , 2009) The three types

of room mode are shown in Figure 5 (Wilmhurst & Thompson, 2012). Axial modes occur when

sound is reflected between two surfaces; tangential modes occur where sound is reflected

between four surfaces, and oblique modes occur where sound is reflected between six surfaces.

Chapter 2

13

As the number of reflective surfaces increases, the amplitude of the modes decreases; axial

modes have the highest amplitude and oblique modes have the lowest amplitude.

Figure 5: Axial modes (a), tangential modes (b) and oblique modes (c), (Wilmhurst & Thompson,

2012)

For a rectangular room with dimensions Lx, Ly and Lz, the wave numbers can be calculated using

(9), from Fazi (2013):

𝑘2𝑛𝑥,𝑛𝑦,𝑛𝑧

= (𝑛𝑥𝜋

𝐿𝑥)

2+ (

𝑛𝑦𝜋

𝐿𝑦)

2

+ (𝑛𝑧𝜋

𝐿𝑧)

2 (9)

The modes can be calculated using (10):

𝜑𝑛𝑥,𝑛𝑦,𝑛𝑧 (�⃗�) = cos (

𝑛𝑥𝜋𝑥

𝐿𝑥) 𝑐𝑜𝑠 (

𝑛𝑦𝜋𝑦

𝐿𝑦) 𝑐𝑜𝑠 (

𝑛𝑧𝜋𝑧

𝐿𝑧) (10)

Standing waves occur when a sound source is excited and a sound wave travels towards a

parallel surface, with the reflected wave propagating back in the direction of the source (Kuttruff ,

2009). The reflected sound has the same frequency content as the initial sound, and at intervals

of the shared harmonic, the waves interfere with one another, causing a periodic increase in

amplitude. Standing waves can be caused by axial room modes and can be controlled by

provision of diffusive materials on adjacent surfaces.

Figure 6 shows a typical frequency response for a small room (Cox & D'Antonio, 2009), which

shows distinct modes at lower frequencies, with overlapping modes at higher frequencies.

Chapter 2

14

Figure 6: Frequency response for small room (Cox & D'Antonio, 2009)

The Schröeder frequency, fs, (Schröeder & Kuttruff, 1962) is the frequency at which a room is

dominated by individual modes instead of overlapping modes, and is calculated using (11):

𝑓𝑠 = 2000 √𝑇60

𝑉 (11)

The Schröeder frequency is considered to be an indicator of the point at which results from

geometrical modelling methods such as ray-tracing become inaccurate.

Flutter echoes can occur in spaces with simple geometry and large flat surfaces, as sound energy

reflects and forth between the parallel walls, following an excitation of a sound source (Cox &

D'Antonio , 2009). After the initial excitation, successive repetitions are audible as distinct echoes

of the original sound. As the parallel walls are hard and reflective, sound energy is not absorbed

effectively, and sound energy reflections occur in a regular pattern. Flutter echoes can be

controlled with provision of acoustic absorption or diffusion to one or more of the parallel walls,

or with angling of one or more of the side walls.

2.1.9 Reverberation Time (RT)

Reverberation Time (RT), denoted as RT60, is the time it takes for sound energy to decay by 60dB

after excitation. RT can be calculated using the Sabine formula (12), which originated in 1898,

from experiments conducted by Wallace Clement Sabine in the Fogg Lecture Hall at Harvard

University as documented in Sabine (1922):

𝑅𝑇60 = 0.161 𝑉

𝐴 (12)

where V is the volume of the room in cubic metres, A is Sα ̅where S is the total surface area

within the room, and �̅� is the average absorption coefficient of all surfaces in the room, calculated

by (13):

Chapter 2

15

�̅� =1

𝑆∑ 𝛼𝑖𝑆𝑖𝑖 (13)

where 𝑆 = ∑ 𝑆𝑖𝑖 , i.e. the summed area of all surfaces within the room.

The Sabine formula has long been used by acousticians for estimating the RT in enclosed spaces,

including sports halls. The Sabine formula relies on a diffuse-field assumption, meaning that

sound energy is equal in all locations within an enclosed space, and also relies on absorption

being uniformly distributed. Therefore, the Sabine formula is only accurate in reverberant rooms,

where the absorption of surfaces within the space is low and similar for different surfaces. There

are a number of additional RT formulae, which have built upon Sabine's initial findings, which are

summarised in Sheaffer (2007) and discussed below.

Erying (1930) introduced an alternative formula (14) for calculating RT, which is based on the

mean free paths between the reflections in a diffuse field:

𝑅𝑇60 = 55.3 𝑉

−𝑐𝑆 𝑙𝑛(1−�̅�) (14)

where V is the volume of the room in cubic metres, c is the speed of sound in air (343m/s), S is

the total surface area within the room and �̅� is the average absorption coefficient of all surfaces

in the room, calculated using (13). The Erying formula is used for rooms where �̅� is higher, but

also relies on a uniform absorption distribution.

Subsequent equations were suggested by Millington (1932) and Sette (1933), which relied on

variations in the manner in which absorption coefficients were averaged. A more advanced

formula was produced by Fitzroy (1959), which took the geometrical sound field into account in

addition to the absorption characteristics within the room (15).

RT60 = 55.3𝑉

𝑐𝑆2 [−𝑆𝑥

𝑙𝑛(1−𝑎𝑥) +

−𝑆𝑦

𝑙𝑛(1−𝑎𝑦) +

−𝑆𝑧

𝑙𝑛(1−𝑎𝑧)] (15)

where Sx, Sy and Sz are the total surface areas of two opposing boundaries and ax, ay and az are

the average absorption coefficients of each pair of opposing boundaries.

As Neubauer (2000) explains, the Fitzroy formula is based on the principle that a sound field in a

rectangular enclosed space may enter into a pattern of oscillation along the rooms x, y and z axes.

The Erying formula relies on the assumption that the absorption in the space will be equal in all

directions, but the Fitzroy formula allows for differences in absorption that may be present in the

different axes, which is more indicative of reality in rectangular rooms such as sports halls. The

Fitzroy formula is best suited to rooms in which the absorption is located non-uniformly.

Chapter 2

16

Although RT is specified as decay of 60dB, it is difficult to physically measure this in a room.

Measurements are usually made of the decay between -5dB and -25dB (T20), as shown in Figure 7

(Thompson , 2013), or between -5dB and -35dB (T30), with the T60 extrapolated from these values

Figure 7: T20 measurement principle showing extrapolation to T60 (Thompson, 2013)

2.2 Definition of research problem: RT underestimation in practice

2.2.1 Dane Court Sports Hall

An example sports hall has been provided by Arup Acoustics, based on a project involving a sports

hall at Dane Court Grammar School, Kent. The hall has the dimensions 33m (l) x 18m (w) x 8.65m

(h) with a volume of 5138m3. The design process is described in the following sections:

2.2.1.1 Stage 1: Initial calculations and measurements

Initial calculations were made using the Sabine and Fitzroy formulae. The construction materials

and absorption coefficients used are shown in Table 2.

Table 2: Dane Court Sports Hall - construction materials and absorption coefficients

As Table 2 shows, the α values assigned to the floor and walls are low, ranging between 0.05 and

0.15, depending on the octave frequency band. The main source of absorption was the

perforated metal deck on the soffit. The Sabine calculation indicated a Tmf RT of 2.1 seconds and

the Fitzroy calculation indicated a Tmf RT of 3.2 seconds.

Floor - Wood 5% 0.15 0.15 0.11 0.10 0.07 0.06 0.07

Door - Wood 5% 0.14 0.14 0.10 0.06 0.08 0.10 0.10

Window - Glass 5% 0.10 0.10 0.07 0.05 0.03 0.02 0.02

Walls - Concrete 5% 0.10 0.10 0.05 0.06 0.07 0.09 0.08

Soffit - Perforated metal deck 30% 0.40 0.40 0.36 0.41 0.48 0.47 0.45

400050063 125 250 1000 2000

Absorption coefficient (α) in octave frequency bands (Hz)Surface & Material Scattering

Chapter 2

17

Once the sports hall was built, the Tmf RT was measured as 3.8 seconds, which is 1.7 seconds

higher than the Sabine calculation and 0.6 seconds higher than the Fitzroy calculation, and much

higher than the design target of 1.5 -2.0 seconds outlined in Sport England and BB93 guidance. In

the case of the Sabine calculation, this represents a major underestimation.

2.2.1.2 Stage 2: Ray-tracing modelling and measurements

In Stage 1, only calculations were considered, and no computer modelling was carried out. For

Stage 2, a ray-tracing model using Odeon software was created. The aim of the modelling process

was to determine the reduction of the Tmf RT which could be achieved by introducing additional

acoustic absorption into the hall. Before the improvement could be determined, the model was

'calibrated' to the existing condition. The approach chosen was to significantly reduce the α

values for the perforated ceiling deck; as shown in Table 3, to three decimal places to highlight

the reduction. Scattering values of 30% were applied to the ceiling and 5% to all other surfaces.

Table 3: Revised absorption coefficients of the 'effective' perforated deck for the calibrated

Odeon model

Once the model was ‘calibrated’ to the measured Tmf RT of 3.8 seconds, an area of 150m2 of

Rockfon Samson tiles (600mm x 600mm x 40mm) was applied to the walls. The tiles are rated as

a Class A absorber (𝛼𝑤 > 0.9), and have the laboratory-tested α values shown in Table 4. A

scattering value of 5% was assigned to these tiles.

Table 4: Laboratory tested absorption coefficients for Rockfon Samson tiles

As Table 4 shows, the 𝛼 values of 0.2 at 63Hz and 125Hz are relatively low, but the 𝛼 values from

500Hz are very high, which is in line with the expected performance, as discussed in Section 2.1.3.

Results from the Odeon model indicated that the predicted Tmf RT was 2.3 seconds, a reduction

of 1.5 seconds compared to the existing Tmf RT. Following the modelling, 150m2 of the Rockfon

Samson tiles were then installed in the hall, and the re-measured Tmf RT was 3.0 seconds, which is

0.7 seconds higher than the Odeon prediction.

'Effective' perforated deck 30% 0.000 0.001 0.025 0.060 0.120 0.120 0.050

63 125 250 1000 2000

Absorption coefficient (α) in octave frequency bands (Hz)Material Scattering

4000500

Rockfon Samson wall panels

(600 x 600 x 40)5% 0.20 0.20 0.50 0.90 1.00 1.00 1.00

Surface & MaterialAbsorption coefficient (α) in octave frequency bands (Hz)

Scattering500 400063 125 250 1000 2000

Chapter 2

18

2.2.1.3 Stage 3: Final ray-tracing modelling and measurements

Further modelling took place for Stage 3, and the effective absorption coefficients of the Rockfon

Samson tiles were reduced (Table 5), to reflect the higher measured Tmf RT of 3.0 seconds, and to

‘calibrate’ the model to the re-measured Tmf RT.

Table 5: Adjusted absorption coefficients for Rockfon Samson tiles

Once the Odeon model was ‘calibrated’, an additional 150m2 of Rockfon Samson tiles were

added to the soffit, and the Tmf RT was predicted as 2.0 seconds. With the additional 150m2 of

tiles installed on the soffit of the sports hall, the re-measured Tmf RT was 2.8 seconds, a reduction

of only 0.2 seconds on the previously measured value. It is noted that the additional 150m2 of

Rockfon Samson tiles was applied to the soffit: this would have replaced the already installed

perforated metal deck, which was providing some degree of acoustic absorption. In light of this, it

is not so surprising that the improvement was only minimal at 0.2 seconds.

2.2.1.4 Stage 4: Introduction of scattering elements into hall

Stage 4 involved the introduction of nets into the sports hall. The re-measured Tmf RT was 2.0

seconds. The presence of the nets resulted in a much greater deal of scattering being present in

the space, which would have diverted the sound energy up to higher level, instead of the sound

energy building up at low level and not being incident upon the absorption. In the case of Dane

Court sports hall, the standard Sabine calculations and ray tracing modelling have significantly

underestimated the Tmf RT.

2.2.2 Further examples in sports halls: Arup data set

In addition to Dane Court sports hall, as Oeters (2012) describes, Arup Acoustics have

accumulated a data set of over 50 sports halls with predicted and measured Tmf RTs. Predictions

were made using calculations based on the Sabine, Erying and Fitzroy formulae and using ray-

tracing software such as CATT Acoustic and Odeon. The study was not designed to indicate which

specific prediction method was least accurate when compared to measured values, but to identify

a trend in the data set. Figure 8 shows the trend determined by this study, and it is apparent that

the predicted Tmf RT is generally lower than the measured Tmf RT.

'Effective' Rockfon Samson wall

panels (600 x 600 x 40)5% 0.03 0.08 0.40 0.55 0.55 0.45 0.35

MaterialAbsorption coefficient (α) in octave frequency bands (Hz)

63 125 250 500 2000 40001000Scattering

Chapter 2

19

Figure 8: Arup Acoustics data set showing trend of predicted vs. measured Tmf RT for sports halls

(Oeters, 2012)

2.2.3 Further examples in sports halls: CATT Acoustic example

James et al (2012) describe an example sports hall (Figure 9) in which the RT has been significantly

underestimated using CATT Acoustic ray-tracing software implementing the Sabine formula. The

sports hall dimensions are 43m x 23m x 7m (Volume 6923 m3). The design considered non-

uniform absorption, with absorption on 50% of the ceiling, and an average absorption coefficient,

�̅� ,of 0.43 over the entire ceiling area. Remaining surfaces were constructed from hard materials.

Figure 9: Example sports hall with non-uniform absorption at ceiling level (James et al, 2012)

The predicted Sabine RT at 1kHz was 1.9 seconds, but following construction, the T30 at 1kHz was

measured at 5.7 seconds. This example illustrates the inappropriateness of using the Sabine

formula in large spaces with non-uniform absorption at high level. It is noted that the authors

specify the T30 at 1kHz from CATT Acoustic as 5.1 seconds for a detailed model (ceiling beams

included in geometry) and 5.9 seconds for a simplified model (flat ceiling), both of which are

relatively close to the measured value of 5.7 seconds. It is possible that although CATT Acoustic is

not accurate when implementing the Sabine formula, it may be accurate for the T20 and T30

parameters.

Chapter 2

20

2.2.4 RT underestimation in non-sports hall - broadcast facility example

This author has been involved in the acoustic design for a large room at a broadcast facility, where

the use of the Sabine formula has underestimated the RT compared to measured values. The

room has a volume of approximately 5130m3, and is used for filming purposes. The design

criterion was 0.55 seconds (averaged between 250Hz and 4kHz in 1/3 octave bands). Calculations

were made using the Sabine formula, and it was recommended to treat the entire soffit with a

proprietary absorptive quilt (𝛼𝑤 0.9) and Class A absorptive panels (𝛼𝑤 0.9) to cover 2/3 of the

wall area. It was recommended to place the wall panels at head height, to prevent flutter echoes

between the parallel hard walls. Following construction, the RT250Hz-4kHz, 1/3 octaves was measured as

1.03 seconds. However, the room was unfurnished at the time of testing, and .the introduction of

scattering elements reduced the RT significantly, as will be discussed in Section 2.3.3.

2.3 Reasons for underestimation of RT

2.3.1 Prediction method

2.3.1.1 Diffuse-field calculations

Calculations made using the Sabine formula rely on two assumptions: that the room is a diffuse

field and that absorption is uniformly distributed. As the average absorption coefficient, �̅�,

increases, the RT will not tend to zero for the Sabine formula. The Erying formula also relies on

the absorption being uniformly distributed, but the RT will tend to zero as �̅� increases.

As Hodgson (1996) discusses, in addition to these, the accuracy of diffuse-field formulae depends

on additional factors including room shape, surface reflections and fitting density, meaning the

Sabine and Erying formulae are only accurate under specific conditions. Hodgson suggests that

results obtained using these formulae should not be considered reliable unless the conditions are

met. Sabine is accurate only in cases where �̅� is low, but Erying is accurate with any �̅� value. In

rooms with low absorption and smooth, non-diffuse surfaces, specular reflections will be

prominent, and the room must be a cubic shape with uniform absorption for the Erying formula

to be effective. As the Sabine and Erying formulae rely on a uniform distribution of absorption,

neither are suitable for sports halls in which the absorption is located on the soffit alone. The

Fitzroy formula (15) accounts for non-uniform absorption, but is not commonly used by acoustic

consultants when designing sports halls. Effects such as room modes, standing waves and flutter

echoes are also not taken into account into any of these calculations. It is the responsibility of the

consultant to consider these effects and advise on strategies to prevent their occurrence.

Chapter 2

21

Stauskis (2012) compared results using the Sabine, Erying and Fitzroy formulae, among others,

using a sample sports hall (13.6m x 10.7m x 7m, Volume 1018m3). The main findings were:

When all surfaces had a low α value, but the absorption was uniformly distributed, there

was little difference between the results.

With higher α values, but with the absorption uniformly distributed, the Fitzroy and

Erying formulae produced higher RT values than the Sabine formula.

When non-uniform α values were used for different surfaces, the Fitzroy formula

produced higher RT values than the Erying formula.

2.3.1.2 Ray-tracing modelling

It will be shown in Section 2.3.3 that diffusion has a significant impact on reducing the RT in

enclosed spaces. The Sabine, Erying and Fitzroy formulae do not account for diffusion but this is

accounted for in ray-tracing modelling. Diffuse reflections can be modelled as simple specular

reflections from a surface, or a combination of specular and scattered edge reflections. Using the

sports hall example from Section 2.2.3, as James et al (2012) show in Table 6, the nature of the

diffuse reflections can have an impact on the predicted RT.

Table 6: Effect of diffuse reflections on predicted RT using CATT Acoustic ray-tracing software

(James et al, 2012) 1 with beams in ceiling geometry, 2 flat ceiling with high diffusion, 3 auto edge

diffusion

As Table 6 indicates, for the detailed model, a lower scattering coefficient, s , was used, as the

geometry of the ceiling was more complex, but surface edge diffusion was included for the ceiling

beams. A higher s value was used for the simple model, with no surface edge diffusion. Both

models produced an RT at 1kHz between 5-6 seconds. When the s values for both models are set

to zero, reflections will be specular only, and no diffusion will occur. The predicted RT is between

12-13 seconds for the models, and it is evident that implementing specular reflections only is

inappropriate for ray-tracing modelling.

Chapter 2

22

Figure 10 shows the effect of increased scattering coefficients on the behaviour of a single ray in

a simple rectangular room using Odeon ray-tracing software (Rindel, 1995).

Figure 10: Single ray in a rectangular room modelled using ray-tracing, showing reflections with

different values for surface scattering coefficient (Rindel, 1995)

As Figure 10 shows, when the s value of all surfaces is zero, the ray propagates in a specular

manner, with early and late reflections essentially identical. With an s value as low as 0.02, this

behaviour begins to break down, and late reflections become less uniform. With an s value of 0.2,

the ray is reflected at random angles and a reasonable diffuse field is produced. In the extreme

case of an s value of 1, the behaviour of the reflections is random.

Choosing a suitable diffuse reflection method in addition to an appropriate scattering coefficient

for surfaces is crucial in ensuring the accuracy of output RT data from ray-tracing modelling.

However, further knowledge is required related to the frequency dependent nature of scattering

coefficients. Figure 11 (James et al, 2012) shows the relationship between surface roughness, D ,

and wavelength, λ.

Figure 11: Relationship between surface roughness, D, and wavelength, λ , which illustrates the

frequency dependent behaviour of scattering (James et al, 2012)

Chapter 2

23

As Figure 10 shows, when λ is much smaller than D, i.e. at high frequencies, diffusion is effective;

when λ is identical to D, significant diffusion occurs; when λ is much larger than D, i.e. at low

frequencies, less diffusion occurs. Therefore, diffusion is more prevalent at high frequencies than

low frequencies, but this depends on the dimensions of the surface roughness, D.

2.3.2 Location of acoustic absorption

Zander et al (2013) conducted a study which analysed the effect of the quantity and distribution

of acoustic absorption within sports halls. The study involved ray-tracing modelling using CATT

Acoustic, and used two different sized halls as example cases. The dimensions were as follows:

Hall 1 (45m x 27m x 7.15m, Volume = 8,687m3) & Hall 2 (27m x 15m x 5.65m, Volume = 2,288m3).

The design requirements for these halls were for the T30 at 1kHz not to exceed 2.0 seconds,

according to the German standard DIN 18041. For both halls, predictions were made using two

options. Option 1 represented the standard approach of applying acoustic absorption to the soffit

only, with the remaining walls and floor surfaces reflective. Option 2 involved applying acoustic

absorption uniformly to the soffit and four walls, with the only reflective surface being the floor.

Scattering for all surfaces was set at 10% across all frequencies, as all surfaces were flat.

Results indicated that for the non-uniform absorption layout, while there was an adequate

absorption area, �̅� , to meet the RT requirements, the target was not met. For the uniform

absorption layout, the RT target was met, with the same 𝑆�̅� as the non-uniform case. In the case

of Hall 2, the predicted T30 at 1kHz was 2-4 times higher in the non-uniform case. In the case of

Hall 1, the volume and absorption area was larger, and the variation was more significant.

2.3.3 Effect of scattering objects

2.3.3.1 Sports hall examples

Oeters (2012) makes the observation that for non-uniform absorption distribution in sports halls,

sound energy is primarily propagating in the horizontal plane and is not 'seeing' the absorption

located at high level. The proposed solution is to introduce scattering elements into the space,

which will ‘disrupt’ the horizontal-travelling sound energy and ‘re-direct’ the sound energy to the

absorption at high level. Oeters provides two examples where the introduction of scattering

elements into existing sports halls has resulted in a significant reduction of the Tmf RT compared to

measurements made in the unfurnished hall. The first example was an Arup test case, in which

the initial Tmf RT was measured at 2.8 seconds. When scattering elements (Figure 12) were

introduced, the measured Tmf RT reduced to 1.8 seconds, a significant reduction of 1 second.

Chapter 2

24

Figure 12: Arup test case, extent of scattering objects in sports hall which resulted in reduction of

1 second in measured Tmf RT, 2.8s down to 1.8s (Oeters, 2012)

The second example involved a sports hall at Southbank University, in which the Tmf RT was

measured at 4.0 seconds. The introduction of scattering elements (Figure 13) resulted in a

measured Tmf RT of 3.1 seconds, a significant reduction of 0.9 seconds.

Figure 13: Southbank University, extent of scattering objects in sports hall which resulted in

reduction of 0.9 seconds in measured Tmf RT, 4.0s down to 3.1s, (Oeters, 2012)

It is noted that the second example at Southbank University is still significantly above the RT

range of 1.5 to 2.0 seconds advised by BB93 (2015)and Sport England (2012). The Arup test case

had an additional 150m2 of acoustic absorption applied to the walls, which accounts for the initial

Tmf RT being lower than the Southbank University hall. Oeters concludes by noting that up to a

30% reduction in Tmf RT can be achieved with the introduction of scattering elements such as

benches, gym mats, nets or table tennis tables.

Chapter 2

25

Hosoien (2014) describes the impact of scattering objects on the predicted RT in a Norwegian

study based on two gymnasia and three sports halls, which were refurbished with the aim of

improving room acoustics by reducing RT. The gymnasia had relatively low room volumes (840m3

and 2410m3), while the sports halls were larger (9,467m3, 9,310m3 and 6,747m3). RT

measurements were made in each space, before a ray-tracing model using Odeon software was

used to attempt to replicate the measured RT. The ray-tracing models had relatively simple

shoebox shaped room geometry. The accuracy of the ray-tracing modelling in replicating the

measurement results relied heavily on the choosing of appropriate scattering coefficients for the

room surfaces. As the study sample size was small, the validity of observed trends is not as robust

as studies involving a larger sample, but there are some useful conclusions:

Increasing the scattering coefficients reduced the predicted RT to a similar range to the

measured RT. However, there was a larger deviation from the measured RT values at

lower octave bands and less deviation in the mid and high octave bands.

In cases where the total sound absorption area, 𝑆�̅� , was small, increasing the scattering

coefficient had no significant effect on the predicted RT.

In the opposite case, i.e. where 𝑆�̅� was large, the RT reduced with increased scattering,

but this was only in cases with non-uniform absorption. Where absorption was uniformly

distributed, the RT actually increased with increased scattering. This behaviour could be

attributed to room effects such as flutter echoes, which were observed during the RT

measurements for one of the halls in this study.

Scattering coefficients of 0.15, 0.20 and 0.25 gave the best results in terms of predicting

the RT. These scattering coefficients are not high, but the outcome is agreeable with the

effect of relatively low scattering coefficients discussed in Section 2.3.1.2.

It is clear from these studies that scattering objects can have an impact on reducing RT in sports

halls. As previously discussed, correct specification of scattering coefficients requires specialist

knowledge of material properties in addition to experience which cannot be readily gained.

2.3.3.2 Non-sports hall – broadcast facility example

As discussed in Section 2.2.4, this author has been involved in the acoustic design of a large room

for broadcast facility, where the RT was underestimated using the Sabine formula. The design

criterion was an onerous 0.55 seconds, averaged between 250Hz and 4kHz in 1/3 octave bands.

Measurements were made with a target launcher firing 0.22 blanks; a total of ten measurements

were made during the initial measurement, spread around the room. The measured RT250Hz-4kHz, 1/3

octaves was 1.03 second, with no furnishings in the room, as shown in Figure 14.

Chapter 2

26

Figure 14: Unfurnished broadcast facility during initial measurements following construction,

absorption on soffit and walls

The RT was re-measured with scattering elements introduced into the room, which included

several set constructions, as shown in Figure 15. Although the sets would have introduced

additional absorption into the room, this was negligible, as the sets were made from hard

materials such as wood and metal. With the sets in place, the RT was re-measured, with the

target launcher firing 0.22 blanks as the noise source; a total of six measurements were made.

Figure 15: Broadcast facility furnished with set constructions during follow up measurements

The re-measured RT250Hz-4kHz, 1/3 octaves was 0.59 seconds, which was closer to the target of 0.55

seconds, and 0.44 seconds lower than the initial RT in the unfurnished room. Figure 16 shows the

1/3 octave band RT measured for the unfurnished and furnished scenarios.

Chapter 2

27

Figure 16: 1/3 octave band RT measurements made by Ion Acoustics in broadcast facility

2.3.4 Behaviour not accounted for in calculation or modelling processes

In addition to the location of acoustic absorption and the degree of scattering within sports halls,

other acoustic effects can adversely affect the RT. Luykx and Vercammen (2012) suggest that

flutter echoes can be potentially disturbing in sports halls. Flutter echoes are not taken into

account in diffuse-field calculations and it is likely that they are not modelled accurately using ray

tracing methods, as no phase information or individual ray interactions are modelled.

Flutter echoes can be dealt with relatively easily; Cox & D'Antonio (2009) suggest applying

acoustic absorption to at least one of the two parallel walls to reduce the sound energy.

Alternatively, diffusers could be mounted to one or more of the walls, to control the spread of

sound energy within the room. However, these may not be practical solutions, due to the

sensitivity of absorptive and diffusive materials to impact from items such as sports balls. An

alternative approach suggested by Barron (2009) and Blauert & Xlang (2009) is to angle or tilt

both of the parallel walls by 5° or greater. Diffraction is also not considered in ray-tracing (as

discussed in Section 2.1.8), or in diffuse-field calculations.

2.4 Alternative approach – physical design

Acoustic comfort in sports halls can also be improved by modification of the architectural design.

Pavcekova et al (2012) are of the opinion that during the design process, an architect will rarely

consider how the physical design of a space will impact on the acoustic comfort experienced by its

occupants. Pavcekova et al conducted a study of a sports hall in Poprad, Slovakia, with a volume

of 9,379m3, which had not been designed to the standard shoebox shape. The sports hall was

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

Re

ve

rbe

rati

on

Tim

e (

s)

Frequency (Hz)

Broadcast FacilityReverberation Time Measurements by Ion Acoustics (2015)

Unfurnished condition

Furnished condition

Chapter 2

28

constructed primarily from concrete, with an audience seating area. The primary source of

acoustic absorption was acoustic baffles mounted on the soffit. Side walls were angled to prevent

flutter echoes, and to ensure a reduction of noise levels. The intent of the study was to

determine whether the standard approach of applying acoustic absorption at soffit level only

would yield satisfactory results if the hall was designed using a non-shoebox configuration.

Predictions of RT were made using the Sabine and Erying formulae, and using CATT Acoustic ray

tracing software. The findings of the study were that altering the architectural design of the side

walls in addition to the standard approach of applying absorption to the soffit would result in a

satisfactory RT, a reduction of noise levels and an increase in speech intelligibility. It is likely that

the design eliminated the occurrence of flutter echoes, which helped in reducing the RT.

2.5 Room acoustics modelling techniques

Ray-tracing has been discussed several times in this report, and has been used for this project, to

enable a comparison between measured values, Sabine calculations and FEM DGM modelling.

The basic principles of the ray-tracing modelling technique are described, and several alternative

methods which could be considered for modelling sports halls are briefly discussed.

2.5.1 Ray-tracing and image sources

Ray-tracing is a geometrical modelling technique and one of the most commonly used in acoustic

consultancy. The technique was first described by Krokstad et al (1968) in a paper which

described a method for calculating the impulse response of an enclosed space. In its simplest

form, an omnidirectional point source sends a collection of individual rays into a room; and the

rays interact with the room surfaces. The manner in which the rays interact depends on the

absorption and diffusing properties of the surface material, as discussed in Sections 2.1.5 and

2.1.6. The rays which reach the receiver point (s) are used to calculate a variety of room acoustics

metrics, including RT.

Although ray-tracing can be considered a simple system, there are many user-definable variables

to consider, which relate to surface material characteristics, including absorption and scattering

coefficients, and diffuse reflection behaviour (Section 2.3.1.2). Earlier ray-tracing software did not

include diffuse reflection behaviour, so only specular reflections were considered, but modern

software (e.g. CATT Acoustic and Odeon) allows diffuse reflections to be modelled. Ray-tracing is

useful in large rooms where wavelengths are small in comparison to the room dimensions, even

at lower frequencies depending on the room size, but is not as useful for small rooms, where low

frequency effects such as room modes can adversely affect the results.

Chapter 2

29

The image source method (Allen & Berkeley, 1979) is a technique which models all reflections

from surface materials using individual image sources. Early reflections are therefore modelled

more accurately than in the ray-tracing method (Vörlander, 1989). For rooms with simple

geometry, a reasonable amount of image sources are created, but for rooms with complex

geometry, this can produce significant numbers of sources, which requires significant

computational power (Rindel, 1995). Scattering is not taken into account in the image source

model. Many software packages now combine both methods, where early reflections are

calculated using the image source method and later reflections are calculated using the ray-

tracing method (Vörlander, 1989). The accuracy of results produced by these techniques will be

limited by the Schröeder frequency (11), so very low frequency behaviour may not be modelled

accurately.

2.5.2 Pseudo Spectral Time Domain (PSTD) method for sports halls

Hornikx et al (2014) introduced a modelling approach based on a Fourier pseudo spectral time

domain method (PSTD). This method allows the computation of sound propagation by solving

linearised Euler equations, taking the surface material impedance into account. The study

involved modelling two sports halls (Hall 1: 8,400m3 and Hall 2: 10,000m3) using the PSTD

method, ray tracing method and Sabine calculations. It is noted that Hall 2 had more acoustic

absorption present than Hall 1, and also had a balcony area, which would have provided diffusion.

The purpose of the study was simply to compare the three different methods and gain an

understanding of the accuracy of each when compared to physical measurements.

The authors are of the opinion that the diffuse-field and geometrical methods used in acoustic

consultancy are too 'approximative' and less accurate at lower frequency ranges, where 'wave

effects' such as room modes occur. The authors make the point that as geometrical methods are

only valid above the Schröeder frequency, low frequency behaviour such as diffraction would not

be accounted for, but concede that including diffraction to the geometrical method would

increase computational demands significantly. The PSTD method does take behaviour such as

diffraction into account. The authors point to the skill of the operator of ray-tracing software as

being important in the choosing of representative scattering coefficients. Results from the three

methods were compared to physical measurements; the main findings for Hall 1 were:

PSTD: Comparable with measurements. Higher RT values were obtained in the upper two

octave bands, with lower values at the 125Hz octave band. The standard deviation of the

results was comparable with the standard deviation of the measured values, but the

Chapter 2

30

difference in modelled and measured values by receiver position was significant, with

little correlation.

Geometrical method (CATT Acoustic): RT was higher than measured values in upper two

octave bands, but not by a significant margin. CATT Acoustic over-predicted the RT at

125Hz, where the PSTD under-predicted. Higher standard deviation than the measured

results.

Diffuse-field (Sabine calculation): RT significantly under-predicted when compared to

measured values, especially at the upper two octave bands.

The main findings for Hall 2 were:

PSTD and CATT Acoustic agree with measured values better for the lowest two octave

bands. Both methods under-predict the RT at 500Hz.

The Sabine calculation under-predicts the RT significantly, similarly to the result for Hall 1.

The PSTD and ray-tracing methods perform similarly well for Hall 2 and not for Hall 1. The

presence of additional absorption and scattering from the balcony is likely to be responsible for

this behaviour. The PSTD method appears to be a useful method to use for modelling the

acoustics of sports halls, and performed the best in terms of replicating the measured values.

However, the study was limited to the low frequency range in 1/3 octave bands from 50Hz to

630Hz, and it is therefore only applicable to this low frequency range. This technique would need

to be adapted to include a higher frequency range to be used in assessing sports halls, or would

need to be used in a hybrid scenario with additional techniques.

2.5.3 Other techniques

Statistical Energy Analysis (SEA), was introduced by Nilsson (1992), and is used for modelling

spaces with non-uniform absorption distribution. The technique considers the transmission of

energy through a room by splitting the sound field into room modes. As Wilmhurst & Thompson

(2012) describe, the technique can be modified to consider axial, tangential and oblique room

modes in conjunction with the room dimensions, to determine 'loss factors' caused by damping

and coupling, to enable the uneven distribution of absorption to be more accurately modelled.

The Finite Difference Time Domain (FDTD) method is used to simulate low-frequency and mid-

frequency sound propagation in enclosed spaces and is useful for simulating large room volumes

(Botteldooren, 1995). However, as Sheaffer et al (2012) discuss, there are issues concerning the

accuracy of the sound source in replicating real-world behaviour, and limited literature related to

this topic. As Murphy et al (2014) further discuss, while current research related to frequency

Chapter 2

31

dependent absorption and scattering coefficients has increased the potential for FDTD to become

more accurate, this will lead to an increased demand on computer processing power.

As Vörlander (2012) discusses, several hybrid techniques exist for room acoustics modelling,

including the previously discussed ray-tracing/image source method, techniques which implement

'wave-based' methods for low frequency content and additional methods for the remaining

frequency content. For example, Oxnard & Murphy (2013) describe a 2D technique combining

FDTD and a multi-plane model, which is comparable to a 3D hybrid FDTD/ray-tracing model in

terms of accuracy.

2.5.4 Issues with computer modelling

The accuracy of output data from computer modelling will depend greatly on the skill and

knowledge of the user. Many of the techniques implement complex mathematical solutions and

their operational interfaces will include several user-definable variables. As Vörlander (2012)

discusses, there can be difficulties in defining input data for complex models, in particular

boundary conditions such as absorption and scattering characteristics of surfaces, for which there

is a lack of information regarding the uncertainty of such data.

Kang & Neubauer (2014), when discussing RT prediction in rooms with non-uniform absorption,

highlight the importance of selecting appropriate scattering coefficients for surfaces. They also

discuss the importance of the reflective behaviour of surface boundaries, as ray-tracing modelling

using 'geometrically reflecting' and 'diffusely reflecting' methods will produce different

reverberation time results. Predicted RTs will be higher when implementing specular reflections

instead of diffuse reflections, as discussed in Section 2.3.1.2.

The computational demands of computer modelling software remain relevant, despite

improvements in modern processing power. As Lam (2004) discusses, numerical wave-based

modelling techniques are useful for predictions at lower frequencies, but as the frequency range

being considered extends, the processing power required becomes so significant that the

software cannot be operated simply. Siltanen et al (2010) agree with this opinion and suggest

that wave-based techniques are used for low frequency only, with image source techniques used

for the mid and high frequency early reflections, and a relatively new technique called radiance

transfer for the late reflections.

Chapter 2

32

2.6 Modelling method used in this project

2.6.1 Finite Element Method (FEM) and Discontinuous Galerkin Method (DGM)

The finite element method (FEM) is a numerical method used to generate approximate solutions

to differential equations (Hutton, 2004). In its most basic form, the FEM splits an object into a

number of discrete triangular finite elements connected by nodes. The finite elements generate

an overall mesh which represents the room geometry. In 3D, the mesh will represent the entire

room, but in 2D, the mesh should be considered as a 'slice' or section of the 3D environment.

FEM can be used to model sound propagation in enclosed spaces using the wave equation,

which is solved at each node, with boundary conditions and variables specified for the calculation

process. Solutions for each element are stored in a global matrix, which is then solved to provide

a solution at the nodes. The solutions produced by FEM can be high order. The basic FEM

process is shown in Figure 17 below.

Figure 17: FEM basic modelling process flowchart

The FEM can be used to model complex geometries, but for the purposes of this project the

geometry is a simple 2D section. The finite volume method (FVM) allows the differential equation

to be solved locally (Yücel, 2012). The discontinuous galerkin method (DGM) is considered to

combine the advantages of FEM and FVM and allows high order solutions which are solved locally.

Chapter 2

33

The DGM can be used for simulating the propagation of acoustic waves in the time domain, as

described by Lähivaara et al (2008), with comparable results to measured data. The DGM has

been implemented in the software provided for this project, and the full-field solution allows the

interaction between individual sound waves to be observed, even in a 2D model.

2.6.2 FEM DGM modelling process

The FEM DGM modelling process is illustrated in Figure 18.

Figure 18: FEM DGM modelling process flowchart

Chapter 2

34

As Figure 18 shows, pre-processing is performed within MATLAB. The ‘geometry.m’ file allows

the FEM mesh to be defined by creation of vertices coordinates. The ‘pre.m’ file writes the nodes

(‘square.n’ file), elements (‘square.e’ file), allows the microphone coordinates to be determined

for the receiver positions and stored in the ‘microphones.bin’ file. The ‘pre.m’ file also creates

coordinates in which to plot the output solution (‘image.bin’ file). The size of each individual FEM

triangle element can also be set in the ‘pre.m’ file, using the variable ‘Hmax’. Additional pre-

processing is performed using the ‘square.prb’ file which includes several user-definable variables,

the most important of which are described below.

Number of steps (N): Indicates the number of time steps (Δn) required for the

calculation. The length of the output signal is determined by delta Δn x N.

CFL: Refers to the Courant -Freidrichs-Levy criterion, which is used to limit the time step

(Δn) to ensure stability of the system (Schär, 2012). The CFL governs the length of time

for each individual time step (Δn).

Calculation order: A higher order can improve the accuracy of calculations, but requires

greater computational processing power. Although using a lower calculation order will

require less processing power and will therefore take less time to produce an output, the

accuracy of the output may be compromised.

Additional variables include ρ (density of air, 1.2 kg/m3), c (speed of sound in air, 343 m/s),

absorption value for wall elements (non-frequency dependent, 0 to 1), source type (acoustic

pulse), source width (a narrower width of 0.2 produces a higher frequency range of up to 4kHz

than a width of 0.5, which only generates frequencies up to 2kHz) and source amplitude (0 to 1).

Chapter 3

35

Chapter 3: Application of calculations and modelling to

sports hall problem

RT output data has been produced using three primary processes:

Spreadsheet-based calculations implementing the Sabine formula (12).

Ray-tracing modelling using CATT Acoustic software.

Numerical modelling using FEM DGM software.

Before the Dane Court sports hall was modelled, it was decided to model a simple test case room

(10m x 10m x 10m), to allow a 'calibration' process to be carried out for the FEM DGM software.

As will be discussed in Section 4.1, the FEM DGM produced unrealistic results with increased

absorption on the ceiling, which was due to a lack of diffusion in the model. There was no

variable included in the model for diffusion, so reflections were specular. In order to try to

introduce an element of diffusion, the physical principle of angling a surface (as discussed in

Section 2.4) was implemented in the model, to see if this would reduce the RT. This was

investigated using two additional models, incorporating a sloped ceiling and angled side wall

respectively. The sloped ceiling had little effect on the RT but the angled side wall reduced the RT

and scattered the sound energy more effectively within the 2D section.

Once the calibration process was complete, Dane Court sports hall was modelled for five

different scenarios, to enable a comparison between the prediction methods and measured data

where available. The initial design with high level absorption only was replicated, then additional

absorptive panels were added on the walls. Further modelling was carried out to determine the

impact of the location of the absorption on the RT output data, as this was determined to be one

of the primary reasons for RT underestimation. Additional FEM DGM modelling was then carried

out to determine the effect of an angled wall on the RT outputs, to determine whether the

reduction in RT shown for the test case occurred for Dane Court sports hall.

3.1 Test case modelling

The three test case models (Model 1: cube-shaped, Model 2: pitched roof, Model 3: angled wall)

were modelled using the following options, which have different absorption coefficients (α):

Option 1: α 0.1 on walls, floor and ceiling.

Option 2: α 0.1 on walls and floor, α 0.5 on ceiling.

Option 3: α 0.1 on walls and floor, α 0.9 on ceiling.

Chapter 3

36

The cube-shaped room (Model 1) was modelled using Sabine, ray-tracing and FEM DGM. Rooms

with a sloped roof (Model 2) and angled wall (Model 3) were modelled using FEM DGM only.

3.1.1 Sabine calculations

Sabine calculations were made using an Excel spreadsheet implementing the Sabine formula (12).

Frequency dependent α values would normally be used, but for the purposes of the test case

analysis, a uniform α value has been used for the room surfaces to enable a direct comparison

with the FEM DGM outputs; these are shown in Table 7. The same α values were used for the

ray-tracing modelling, so the scattering value of 10% for all surfaces is also indicated.

Table 7: Test Case - Absorption and scattering coefficients used for Sabine calculations and ray-

tracing

3.1.2 Ray-tracing using CATT Acoustic

Ray-tracing was carried out using CATT Acoustic (version 9.0a). The basic geometry of the test

case room was drawn in Google Sketchup and exported to CATT Acoustic using the SU2CATT plug-

in. The sound source was an omnidirectional white noise source, located in an off-centre

position. Six receivers were positioned around the room. The source and receiver positions were

all at a height of 1.5m above the floor level and are shown in Table 8.

Table 8: Test Case - Source & Receiver positions for CATT Acoustic ray-tracing modelling

Several user-definable variables exist within the CATT Acoustic modelling environment, and are

discussed briefly. Three options are included to model diffuse reflections; they can either be 'off',

'surface' or 'surface and edge'. The 'surface and edge' option is intended for use in rooms with

Floor, walls & Model 1 ceiling 10% 0.10 0.10 0.10 0.10 0.10 0.10 0.10

Model 2 ceiling 10% 0.50 0.50 0.50 0.50 0.50 0.50 0.50

Model 3 ceiling 10% 0.90 0.90 0.90 0.90 0.90 0.90 0.90

Surface & Material2000 4000

Absorption coefficient (α) in octave frequency bands (Hz)

63 125 250 500

Scattering (ray-

tracing)

Test Case

1000

Description x (m) y (m) z (m)

Source 4.5 4.8 1.5

Receiver 1 2.5 3.0 1.5

Receiver 2 2.2 5.1 1.5

Receiver 3 3.0 8.9 1.5

Receiver 4 6.5 7.9 1.5

Receiver 5 8.6 2.3 1.5

Receiver 6 8.8 5.5 1.5

Chapter 3

37

more complex geometry and smaller objects which may provide diffusion at their edges, and is

not intended for use in shoebox shaped rooms. Room temperature was set at 20°C, humidity at

50% and air density at 1.20 kg/m3. A relatively low scattering coefficient of 0.10 (10%) was

applied to all surfaces, and diffuse reflections were enabled. The model generated output data in

eight octave bands, from 125Hz to 16kHz, and included several room acoustic parameters

including T20, T30 and Sabine RTs.

When running a model, the number of rays per octave generated by the source can be set; there

is a balance between the number of rays and the accuracy of the output RT data. An excessive

number of rays will increase computational demands and may not yield more accurate results.

The setting represents the number of initial rays sent out by a sound source, and each individual

ray then interacts with the room geometry before being sampled at the receiver positions. For six

receiver positions, 10,000 rays per octave would result in the model sending out 80,000 rays for

each receiver. For 20,000 rays this increases to 160,000 rays. CATT Acoustic documentation

includes an 'auto' setting which estimates the number of rays required based on the model

complexity. When engaging this setting, the suggested number of rays was between 12,000 and

24,000, so a value of 20,000 was implemented for all the test case modelling.

The truncation time refers to the length of the Impulse Response (IR) output. The desired length

of the IR should be the length of the T60 entire decay. The 'Interactive RT Estimation' setting

estimates the T60 decay before running a model, and the truncation time is set in terms of the

highest RT value in any single octave. This tool was used before running all model options, so the

truncation time varies for the different models. An image of the cube-shaped test case model 1 in

CATT Acoustic is shown in Figure 19.

Figure 19: Test Case Model 1 in CATT Acoustic (10m x 10m x 10m)

Chapter 3

38

3.1.3 FEM DGM modelling

Pre-processing for the test case FEM DGM model was carried out in MATLAB, as described in

Section 2.6.2. The basic geometry was set up in the 'geometry.m' file, which also defined the

mesh size and shape, and several variables were defined in the 'pre.m', 'square.prb' and

'job_WaveEq2D' files. The following settings were used:

h size (triangles in mesh): 0.5.

Number of steps (N): 250,000.

Time step (Δn): 1.2 x 10-5.

CFL: 1.5.

ρ0: 1.2 kg/m3.

c0: 343 m/s.

Calculation order: 9.

Absorption value for wall elements: Option 1 – α 0.1 for all surfaces; Option 2 - α 0.1 for

floor and side walls & α 0.5 for ceiling, Option 3 - α 0.1 for floor and side walls & α 0.9 for

ceiling.

Source type: acoustic pulse.

Source width: 0.2.

Source amplitude (A): 1.0.

Source and receiver positions used for all FEM DGM modelling of the test case are shown in

Table 9. As the sections were 2D, they represented a vertical 'slice' of the 3D environment. The

2D vertical section for the cube-shaped room (Model 1) is shown Figure 20; the section used for

the sloped ceiling (Model 2) is shown in Figure 21 and the section used for the angled wall (Model

3) is shown in Figure 22.

Table 9: Test Case - Source & Receiver positions for FEM DGM modelling of 2D vertical sections

Description x (m) y (m)

Source 4.8 1.5

Receiver 1 2.5 1.5

Receiver 2 2.2 1.5

Receiver 3 3.0 1.5

Receiver 4 6.5 1.5

Receiver 5 8.6 1.5

Receiver 6 8.8 1.5

Chapter 3

39

Figure 20: Test Case Model 1 Vertical 2D Section - cube-shaped room

Figure 21: Test Case Model 2 Vertical 2D Section - sloped ceiling option

Figure 22: Test Case Model 3 Vertical 2D Section - angled wall option

Post-processing was carried out in MATLAB. For each of the six receiver positions the following

data was generated: T20 and T30 RT data in octave bands from 125Hz to 4kHz, energy decay plots

and time step plots showing the sound source propagating in the 2D model.

Chapter 3

40

3.2 Dane Court sports hall modelling

The Dane Court Sports Hall was modelled using the following 5 options:

Model 1: Absorptive ceiling only.

Model 2: Absorptive ceiling & 150m2 absorptive wall panels located at high level.

Model 3: Absorptive ceiling & 150m2 absorptive wall panels located at lower level.

Model 4: 150m2 absorptive wall panels at lower level only (no absorptive ceiling).

Model 5: Absorptive ceiling only with angled side wall and rear wall options.

All options were modelled using Sabine calculations, ray-tracing and FEM DGM. Models 2,3 and

4 investigated the effect of the quantity and location of absorption on the RT outputs. Model 5

investigated whether an angled wall would reduce the RT output, as seen for the test case model.

3.2.1 Sabine calculations

The Sabine calculations have considered the frequency-dependent absorption coefficients used

by Arup Acoustics during the design stage, as discussed in Section 2.2.1. Although the design

included reductions of the α values to represent what Arup Acoustics considered to be the

'effective' α values of the perforated deck ceiling and wall panels, the α values were not modified

for this study, as the ray-tracing modelling was carried out using a different software package.

The α and scattering values used for the Dane Courts sports hall are shown in Table 10, and are

the same as those used in the Arup Acoustics design. For the wall panels, the α value is 1

between 1kHz and 4kHz; this value was used for the Sabine calculations, but was reduced to 0.95

for the ray-tracing modelling, as unusual results were produced when using this extreme value.

Table 10: Dane Court Sports Hall - Absorption and scattering coefficients used for Sabine

calculations and ray-tracing

Floor - Wood 5% 0.15 0.15 0.11 0.10 0.07 0.06 0.07

Door - Wood 5% 0.14 0.14 0.10 0.06 0.08 0.10 0.10

Window - Glass 5% 0.10 0.10 0.07 0.05 0.03 0.02 0.02

Walls - Concrete 5% 0.10 0.10 0.05 0.06 0.07 0.09 0.08

Soffit - Perforated metal deck 30% 0.40 0.40 0.36 0.41 0.48 0.47 0.45

Rockfon Samson wall panels

(600x600x40)5% 0.20 0.20 0.50 0.90 1.00* 1.00* 1.00*

Dane Court Sports Hall

* α = 1.00 used for Sabine calculations, but reduced to 0.95 for ray-tracing modelling to prevent unusual results

Surface & MaterialScattering (ray-

tracing)

Absorption coefficient (α) in octave frequency bands (Hz)

63 125 250 500 1000 2000 4000

Chapter 3

41

3.2.2 Ray-tracing using CATT Acoustic

The ray-tracing modelling for Dane Court sports hall was carried out in an identical manner to the

test case. Diffuse reflections were enabled, with the room temperature set at 20°C, humidity at

50% and air density at 1.20 kg/m3. 20,000 rays per octave were implemented for the sound

source, with the 'Interactive RT Estimation' setting to determine the appropriate truncation time.

The source and receiver positions used are shown in Table 11.

Table 11: Dane Court Sports Hall - Source & Receiver positions for ray-tracing modelling using

CATT Acoustic

Images of the models for Dane Court sports hall within CATT Acoustic are shown in Figure 23

(Model 1), Figure 24 (Model 2), Figure 25 (Model 3), Figure 26 (Model 4) & Figure 27 (Model 5).

Figure 23: Dane Court Sports Hall Model 1 - CATT Acoustic (absorptive ceiling only)

Description x (m) y (m) z (m)

Source 15.0 8.5 1.5

Receiver 1 3.0 10.4 1.5

Receiver 2 7.0 2.4 1.5

Receiver 3 8.5 14.1 1.5

Receiver 4 19.1 3.1 1.5

Receiver 5 27.0 9.5 1.5

Receiver 6 28.7 15.4 1.5

Chapter 3

42


additional absorptive panels at high level)


additional absorptive panels at lower level)

Figure 26: Dane Court Sports Hall Model 4 - CATT Acoustic (150m2 absorptive panels at lower level

only, no absorptive ceiling)

Figure 27: Dane Court Sports Hall Model 5 - CATT Acoustic (absorptive ceiling with angled side

wall)

Chapter 3

43

3.2.3 FEM DGM modelling

Pre-processing for the Dane Court Sports Hall FEM DGM models was carried out in MATLAB, as

described in Section 2.6.2. The α values assigned to the wall elements are shown below.

Model 1: α 0.1 for walls and floor, α 0.4 for ceiling.

Model 2: α 0.1 for walls and floor, α 0.4 for ceiling, α 0.9 for locations with absorptive

panels at high level.

Model 3: α 0.1 for walls and floor, α 0.4 for ceiling, α 0.9 for locations with absorptive

panels at lower level.

Model 4: α 0.1 for walls, floor and ceiling, α 0.9 for locations with absorptive panels at

lower level.

Model 5: α 0.1 for walls and floor, α 0.4 for ceiling.

The source and receiver positions used for the FEM DGM modelling are shown in Table 12 and

Table 13, for the side wall and rear wall 2D 'slices' of the 3D environment.


Vertical Section - Side Wall 33m x 8.65m


Vertical Section - Rear Wall 18m x 8.65m


Source 15.0 1.5

Receiver 1 3.0 1.5

Receiver 2 7.0 1.5

Receiver 3 8.5 1.5

Receiver 4 19.1 1.5

Receiver 5 27.0 1.5

Receiver 6 28.7 1.5


Source 8.5 1.5

Receiver 1 10.4 1.5

Receiver 2 2.4 1.5

Receiver 3 14.1 1.5

Receiver 4 3.1 1.5

Receiver 5 9.5 1.5

Receiver 6 15.4 1.5

Chapter 3

44

The 2D sections used for Models 1-4 are identical, and are shown in Figure 28 (side wall) and

Figure 29 (rear wall).

Figure 28: Dane Court Sports Hall Side Wall Vertical 2D Section - 33m x 8.65m. Models 1-4

Figure 29: Dane Court Sports Hall Rear Wall Vertical 2D Section - 18m x 8.65m. Models 1-4

The 2D sections used for Model 5 with angled walls are shown in Figure 30 (side wall) and Figure

31 (rear wall).

Chapter 3

45

Figure 30: Dane Court Sports Hall Side Wall Vertical 2D Section - 33m x 8.65m. Option 5 angled

side wall

Figure 31: Dane Court Sports Hall Rear Wall Vertical 2D Section - 18m x 8.65m. Option 5 angled

rear wall

Post-processing was carried out using in MATLAB, with T20 and T30 RT data, energy decay plots

and time step plots showing the sound source propagation in the 2D section.

Chapter 4

46

Chapter 4: Results and Discussion

4.1 Test case model results

Results from the test case modelling are shown in the following sections. Initially, the results for

Model 1 (cube shaped room) are shown, with the results from Sabine calculations, ray-tracing and

FEM DGM modelling compared to each other. Results for the additional models are then shown,

to determine the impact of a sloped ceiling (Model 2) and an angled wall (Model 3) on the RT

output data from FEM DGM modelling only.

4.1.1 Model 1: Cube-shaped

The results for Model 1 with absorption options 1-3 are shown in Tables 14, 15 and 16

respectively, in terms of RT in octave bands from 125Hz to 4kHz and single Tmf RT values.

Table 14: Test Case Model 1 Option 1 results



With α 0.1 on all surfaces (Table 14), RT outputs from the Sabine calculations and CATT Acoustic

T20/T30 are very similar, in terms of single Tmf and octave band values, with only a small difference

of 0.1-0.2 seconds between the predicted values. FEM DGM RT outputs are lower than those

125 250 500 1000 2000 4000

Sabine calculation 2.7 2.7 2.6 2.5 2.3 1.9 2.5

CATT Acoustic T20 2.5 2.5 2.5 2.4 2.2 1.8 2.4 very close to Sabine

CATT Acoustic T30 2.5 2.5 2.5 2.4 2.2 1.8 2.4 very close to Sabine

DGM T20 2.1 2.0 2.0 1.9 2.0 2.1 2.0 lower than Sabine & CATT


Model 1, cube-shaped room.

Option 1: Wall & ceiling α 0.1Tmf (sec) Comment

Reverberation Time in Octave Band Frequency (Hz)

125 250 500 1000 2000 4000


CATT Acoustic T20 1.6 1.6 1.6 1.6 1.5 1.3 1.5 identical to Sabine

CATT Acoustic T30 1.6 1.6 1.6 1.6 1.5 1.3 1.5 identical to Sabine


DGM T30 2.0 2.3 1.6 1.4 1.3 0.9 1.4 close to Sabine & CATT

Tmf (sec) CommentModel 1, cube-shaped room.

Option 2: Wall α 0.1, ceiling α 0.5


125 250 500 1000 2000 4000


CATT Acoustic T20 1.3 1.3 1.3 1.2 1.2 1.0 1.2 higher than Sabine

CATT Acoustic T30 1.4 1.3 1.3 1.3 1.3 1.1 1.3 higher than Sabine

DGM T20 2.8 2.5 1.7 2.2 1.7 0.0 1.9 higher than Sabine & CATT

DGM T30 2.4 3.1 2.5 1.9 2.1 0.2 2.2 higher than Sabine & CATT

Model 1, cube-shaped room.

Option 3: Wall α 0.1, ceiling α 0.9

Reverberation Time in Octave Band Frequency (Hz)Tmf (sec) Comment

Chapter 4

47

from Sabine and CATT Acoustic, by between 0.4 and 0.5 seconds, in single Tmf and octave band

values. There is no major difference between the FEM DGM T20 and T30 outputs. It is not easy to

determine which result is 'correct', as there is no measured data to compare the predictions to.

The similarity of the Sabine and CATT Acoustic results suggests that the Sabine formula is suited

to rooms with uniform absorption distribution. It is expected that as the absorption becomes

non-uniform, the Sabine calculation will begin to produce lower RT values than the other

methods.

With α 0.1 on the walls & floor, and α 0.5 on the ceiling (Table 15), RT outputs from the Sabine

calculations and CATT Acoustic T20/T30 are identical. The absorption has become non-uniform, so

it is surprising that the Sabine and CATT Acoustic outputs are agreeable. The FEM DGM T20 is

lower than the Sabine and CATT Acoustic outputs, and while the T30 is very close in terms of the

Tmf, the octave band behaviour is quite different, with higher RT's at lower frequencies and lower

RT's at higher frequencies. It is not clear why the FEM DGM data is lower than the other

methods. The Sabine formula has been shown to underestimate the RT for non-uniform

absorption, so the Sabine output data would be expected to be lower than the FEM DGM data.

With α 0.1 on the walls & floor, and α 0.9 on the ceiling (Table 16), the CATT Acoustic outputs are

slightly higher than Sabine, by between 0.1 and 0.2 seconds. This indicates that the Sabine

formula is finally beginning to produce the expected behaviour of under-predicting the RT with

non-uniform absorption. The FEM DGM T20 and T30 outputs are higher than all other predictions,

and are displaying the unusual behaviour of increasing with a higher α value. The T30 output is in

fact higher than the T30 with α 0.1 on all surfaces. Although the FEM DGM outputs were expected

to be higher than the Sabine outputs, there is clearly some unusual behaviour taking place in the

2D model, as the output data directly contradicts the expected trend of reduced RT with

increased absorption.

4.1.1.1 Model 1 octave band behaviour of FEM DGM output data

In order to appreciate the increases in RT in the FEM DGM model, it is useful to plot the octave

band behaviour of the T20 (Figure 32) & T30 (Figure 33) RT for Model 1, absorption options 1, 2 & 3.

Chapter 4

48

Figure 32: FEM DGM T20 octave band behaviour for test case Model 1

Figure 33: DGM T30 octave band behaviour for test case Model 1

As Figure 32 shows, the predicted T20 is behaving as expected when comparing Options 1 & 2, in

that the RT reduces with a higher α value on the ceiling. However, for Option 3, the expected

behaviour breaks down, with the RT increasing significantly and producing higher RT values than

Options 1 & 2 at all octave bands. As Figure 33 shows, this behaviour is similar for the T30, but

Option 2 is now also showing an increase at 250Hz compared to Option 1.

4.1.1.2 Model 1 energy decay curves

Further investigation is required to understand the unusual behaviour occurring within the FEM

DGM model, and it is useful to plot energy decays to enable comparison. Figures 34, 35 and 36

show the energy decay curves for Microphone 1 for absorption options 1, 2 and 3 respectively.

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

125 250 500 1000 2000 4000

Re

ve

rbe

rati

on

Tim

e (

se

c)

Frequency (Hz)

Test Case Model 1 FEM DGM T20 Octave band predictions

Option 1-wall abs 0.1, ceiling abs 0.1



0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

125 250 500 1000 2000 4000

Reve

rbe

rati

on

Tim

e (

se

c)

Frequency (Hz)

Test Case Model 1FEM DGM T30 Octave band predictions




Chapter 4

49

Figure 34: Example Energy Decay Plots Model 1 Option 1 (α 0.1 on all surfaces)



The decay for option 1 is relatively smooth, but later reflections are evident in the plots for

Options 2 and 3. These plots show the entire signal decay, so further plots are shown in Figures

37, 38 and 39 for absorption options 1, 2 and 3, which focus in on the region between 0.9 and 1.0

seconds to compare the behaviour of reflections over a narrower time range.

Chapter 4

50

Figure 37: Zoomed Energy Decay Plot Model 1 Option 1 (α 0.1 on all surfaces)



It is clear that for this narrow time frame, the decay for option 1 is still quite steady, but options

2 and 3 are displaying some distinct periodic reflections, which are attributable to the reflective

side walls assigned an α value of 0.1. The sound source in the 2D FEM DGM model is propagating

between parallel surfaces, showing standing wave type behaviour.

Chapter 4

51

4.1.1.3 Model 1 wave propagation in 2D environment

A series of time steps can be plotted showing the wave propagation within the 2D FEM DGM

model. Figures 40, 41 and 42 show some sample time steps for absorption options 1, 2 and 3, to

illustrate how the acoustic pulse source is propagating within the model. Further plots are

provided in the Accompanying Materials on the supplied DVD, but these plots give a good

indication of the source propagation behaviour.

Figure 40: Source propagation in 2D, Model 1 Option 1 (α 0.1 on all surfaces)

Chapter 4

52

As Figure 40 shows, after initial excitation, the pulse source propagation generates a reasonable

diffuse field, with the sound energy spread out quite evenly. This is as expected for an α value of

0.1 assigned to all surfaces, as all reflections should be similar in terms of amplitude.


As Figure 41 shows, after initial excitation, sound energy is absorbed by the ceiling with an α

value of 0.5, but the energy propagating between the two hard side walls remains at greater

amplitude. The energy has been reflected back from the semi-absorptive ceiling in a diffuse

Chapter 4

53

manner. However, the wave propagation is displaying distinct standing wave behaviour between

the identical parallel walls, with the sound energy reflecting back and forth periodically.


As Figure 42 shows, with the ceiling assigned an α value of 0.9, the majority of the sound energy

incident on the ceiling is absorbed. The standing wave behaviour observed in the plots is just as

pronounced as the plots with the ceiling assigned an α value of 0.5 and the sound field is

dominated by the periodic reflections between the side walls.

Chapter 4

54

As previously discussed, the FEM DGM model does not allow diffusion to be specified for any

room surfaces, so all reflections are specular. At this point in the project, it was clear that it

would be beneficial to attempt to disrupt the sound energy travelling between the two parallel

walls, to determine whether the physical design approach discussed in Section 2.4 would be

useful in reducing the RT.

4.1.2 Model 2: sloped ceiling and Model 3: angled side wall

The results for Model 2 (sloped ceiling) and Model 3 (angled side wall) with absorption options 1-

3 are shown in Tables 17, 18 and 19 respectively, in terms of RT in octave bands from 125Hz to

4kHz and single Tmf RT values. The results for Model 1 are also shown to enable a comparison

between the three models.


Option 1, walls, floor & ceiling α 0.1

As Table 17 shows, with all surfaces assigned an α of 0.1, there is a minor difference of between

0.1 and 0.2 seconds between predictions from the cube shaped room and the sloped ceiling and

angled side wall. The highest values of 2.2 seconds are produced by the angled side wall; the T20

and T30 results show little variation for this model. It is likely that the sloped ceiling is simply too

far away from the sound source to have any impact on the RT.

125 250 500 1000 2000 4000

Model 1 (cube-shaped)

T20 2.1 2.0 2.0 1.9 2.0 2.1 2.0

T30 2.2 2.1 2.0 2.0 2.0 2.0 2.0

Model 2 (sloped ceiling)

T20 2.2 2.2 2.1 2.0 2.0 2.0 2.0

T30 2.2 2.2 2.1 2.1 2.0 2.0 2.1

T20 2.2 2.2 2.3 2.1 2.1 2.1 2.2

T30 2.3 2.3 2.3 2.1 2.1 2.1 2.2

Reverberation Time in Octave Band Frequency (Hz)Tmf (sec)

Option 1:

Wall & ceiling α 0.1

Model 3 (angled side wall)

Chapter 4

55

Table 18: Test Case impact of sloped ceiling and angled side wall on FEM DGM predictions -

Option 2, walls & floor α 0.1, ceiling α 0.5

As Table 18 shows, as the ceiling α value increases to 0.5, the behaviour becomes less

predictable. With the sloped ceiling, the RT increases with the higher α values, this is similar

behaviour to that observed for the results for the cube-shaped model. It is likely that for the

geometry being assessed, changing the slope of the ceiling will not introduce any significant

degree of diffusion, as the ceiling is simply too far away at 8.5m from the source height. With an

angled side wall, the RT reduces significantly, which means that the angled wall is more efficient

at physically directing the sound energy to the acoustic absorption at high level. However, it is

noted that the predicted T20 and T30 values of 0.9 seconds are still below the 1.5 seconds

predicted for the Sabine and CATT Acoustic outputs with this degree of absorption in the room, so

it is likely that the RT is still being under-predicted by the FEM DGM.


Option 3, walls & floor α 0.1, ceiling α 0.9

125 250 500 1000 2000 4000

T20 1.8 1.3 1.1 1.1 1.1 0.0 1.1

T30 2.0 2.3 1.6 1.4 1.3 0.9 1.4

T20 1.9 2.4 1.9 1.5 1.3 0.8 1.6

T30 2.0 2.4 2.7 2.1 1.6 1.1 2.1

T20 1.0 0.9 0.9 0.9 0.9 0.8 0.9

T30 1.0 0.9 0.9 0.9 0.9 0.9 0.9

Option 2:

Wall α 0.1, ceiling α 0.5





125 250 500 1000 2000 4000

T20 2.8 2.5 1.7 2.2 1.7 0.0 1.9

T30 2.4 3.1 2.5 1.9 2.1 0.2 2.2

T20 2.3 2.9 2.6 1.7 1.7 0.1 2.0

T30 2.3 2.6 3.0 2.6 1.9 1.4 2.5

T20 0.7 0.5 0.4 0.3 0.3 0.0 0.4

T30 0.7 0.7 0.6 0.5 0.4 0.4 0.5




Option 3:

Wall α 0.1, ceiling α 0.9


Chapter 4

56

As Table 19 shows, as the ceiling α value increases further to 0.9, the behaviour retains the same

pattern as seen with a ceiling α value of 0.5, but with more pronounced effects. The sloped

ceiling option is predicting higher values than with the ceiling at α 0.1, and the angled side wall

option is producing a much lower RT than the other two models. The angled wall option is

producing the expected trend in the data; that the RT will reduce with increased absorption and

effective diffusion, but the predictions are again likely too low.

4.1.2.1 Model 3 energy decay curves

The energy decay plots for Model 2 (sloped ceiling) are very similar to those observed for the

cube-shaped room, in that they display a relatively linear slope with α 0.1 on the ceiling, and

increased later reflections with α 0.5 and 0.9 on the ceiling. As the sloped ceiling option has not

reduced the RT and is similar to the cube shaped room, these decays have not been plotted, but

are included in the Accompanying Materials for reference.

However, it is useful look at the behaviour of the energy decay curves for Model 3, with the

angled wall, as this model has resulted in a reduction in RT with increased absorption to the

ceiling and increased diffusion. Example decay plots are shown in Figures 43, 44 and 45 for

absorption options 1, 2 and 3.

Figure 43: Example Energy Decay Plots Model 3 Option 1 (α 0.1 on all surfaces)

Chapter 4

57



It is clear from the plots that they display a linear slope which gets steeper with increased

absorption on the ceiling, and the late reflections observed for the other models are not

apparent.

Once again, it is useful to focus in on a region of the decay to observe the behaviour of

reflections: Figures 46, 47 and 48 show the decay between 0.4 and 0.5 seconds for Options 1, 2

and 3. A different range has been chosen to the previous plots, as the RT predictions are lower.

Chapter 4

58

Figure 46: Zoomed Energy Decay Plot Model 3 Option 1 (α 0.1 on all surfaces)



Comparing Figures 46 and 47, the behaviour of the later reflections is much more consistent as

the α value of the ceiling increases from 0.1 to 0.5, and the periodic reflections observed in Model

1 are not evident. As Figure 48 shows, as the α value of the ceiling increases to 0.9, distinct

reflections become more apparent, but these are lower in amplitude than with the α value of 0.5.

Chapter 4

59

4.1.2.2 Model 3 wave propagation in 2D environment

The wave propagation with an α value of 0.1 on all surfaces shows similar diffuse-field behaviour

to the plot in Figure 40; these plots have not been shown but have been included in the

Accompanying Materials.

Figure 49 shows the acoustic pulse source propagating within the 2D model with an α value of

0.5 on the ceiling.


As Figure 49 shows, the standing wave behaviour is not noticeable with the angled wall, and the

plot resembles a diffuse field.

Figure 50 shows the acoustic pulse source propagating within the 2D model and an α value of 0.9

on the ceiling.

Chapter 4

60


As Figure 50 shows, although there is some standing wave type behaviour evident earlier on, the

sound energy scatters relatively quickly and is absorbed by the ceiling. It is therefore concluded

that by angling the side walls, diffusion is introduced into the FEM DGM model, and the standing

wave type behaviour does not dominate the sound field.

4.1.3 Test case modelling summary of findings

The Sabine and CATT Acoustic predictions are similar, with minor differences in RT for an

α value of 0.1 on all surfaces. This is as expected, as the Sabine formula assumes a diffuse

field with uniform absorption.

The Sabine and CATT Acoustics predict the same RT with a ceiling α value of 0.5, which is

not as expected, as the absorption is non-uniform. However, with the ceiling α value at

0.9, Sabine predictions are lower than those from CATT Acoustic, which does follow the

expected behaviour.

For a cube shaped room, with increased absorption on the ceiling, standing wave

behaviour dominates the FEM DGM RT output data, and causes the RT to increase with

Chapter 4

61

higher absorption coefficients assigned to the ceiling. This is due to the lack of diffusion in

the FEM DDM model and the specula reflections.

For the FEM DGM modelling, the RT does not reduce with a sloped ceiling, primarily

because the geometry of the room has the ceiling height at 10m, so the source is too far

away from the ceiling surface.

For the FEM DGM modelling, angling the side wall has resulted in an increase in the RT

with all surfaces assigned an α value of 0.1 compared to the cube shaped room. As the

ceiling absorption increases in the angled wall model, the RT reduces. This is attributable

to the angled side wall disrupting the standing wave pattern, angling the sound energy to

the absorption at high level and introducing diffusion into the room.

The FEM DGM predictions with the angled wall are certainly too low, but the trend of the

model behaviour is as expected, in that the RT is reducing with increased absorption to

the ceiling and increased diffusion in the room. Angling the wall is a somewhat extreme

design approach, but the results highlight the need for diffusing elements to be added

into the FEM DGM modelling process.

The full-field solution produced by the FEM DGM model is useful in that it allows the

wave propagation to be observed directly, in particular the interaction between different

sound waves. This is not possible in the Sabine calculations. CATT Acoustic does allow

the source propagation to be observed, but this only indicates the location of reflections

and does not show the interactions between individual rays.

Having access to the full-field solution highlights the occurrence of room effects such as

standing waves, which are not represented in Sabine calculations or CATT Acoustic

modelling.

The 2D modelling environment is restrictive in that it does not replicate the real-world

behaviour of sound in a 3D space, but nevertheless is still considered to be useful, as it

has replicated room effect behaviour which has been attributed to increases of RT in

sports halls.

The test case has considered a cube-shaped room, and as the side wall and rear wall

sections are the same, it does not matter which section is used for analysis. In a non cube-

shaped room, it may not be clear which section is most representative of the room.

Chapter 4

62

4.2 Dane Court sports hall results

The results from the Dane Court Sports Hall modelling are shown in the following sections.

As described in Section 2.2.1, the design process carried out by Arup Acoustics involved

spreadsheet-based calculations, ray-tracing modelling using Odeon software and physical

measurements. It has not been possible to receive the full details and data outputs from the

design process except for the details described in Section 2.2.1. Octave band data has been

provided for the final measurements with scattering elements introduced into the hall, but this

includes absorptive panels on the walls and on the ceiling, which partially obscure the initial

absorptive ceiling. This scenario has not been replicated in the modelling for this project, so has

not been used for comparison purposes.

For Model 1, with an absorptive ceiling only, the modelled values are compared to the measured

Tmf RT of 3.8 seconds. For Model 2, with the absorptive ceiling and additional 150m2 of absorptive

panels on the walls, the modelled values are compared to the measured Tmf RT of 3.0 seconds.

Model 3 and Model 4 are intended to show the effect of the location of absorption on the RT,

while Model 5 has been used to determine the effect of angling the side wall on the output data.

4.2.1 Model 1: Absorption at high level only

The results for Model 1 are shown in Table 20, in terms of RT in octave bands from 125Hz to 4kHz

and single Tmf RT values.

Table 20: Dane Court Model 1 results

As Table 20 shows, the Sabine calculation is under-predicting the Tmf RT by a considerable

margin; the calculated Tmf of 2.0 seconds is just below the prediction of 2.1 seconds made by Arup

Acoustics, as described in Section 2.2.1.1. The CATT Acoustic T20 and T30 outputs are very close to

the measured RT. There is a slight difference between the CATT Acoustic T20 and T30, which is

noticeable in the lower octave bands, between 125Hz and 500Hz.

125 250 500 1000 2000 4000

Measured RT

(Arup Acoustics)- - - - - - 3.8

Sabine calculation 2.0 2.5 2.2 2.0 1.9 1.6 2.0 much lower than measured Tmf

CATT Acoustic T20 3.3 4.3 3.9 3.5 2.8 2.2 3.4 close to measured Tmf

CATT Acoustic T30 3.4 5.0 4.4 3.5 2.9 2.2 3.6 very close to measured Tmf

DGM side wall T20 2.5 3.5 4.4 5.8 4.2 1.4 4.8 higher than measured Tmf


DGM rear wall T20 2.1 2.7 3.2 3.1 1.7 1.1 2.6 lower than measured Tmf

DGM rear wall T30 2.2 2.8 3.4 4.1 3.6 1.3 3.7 very close to measured Tmf

Model 1, absorptive ceiling

only


Chapter 4

63

The FEM DGM predictions for the side wall section are higher than the measured RT for the both

the T20 and T30, by 1 to 1.3 seconds. While this may not appear to be overly accurate, it is noted

that the model does not include any diffusion, unlike the CATT Acoustic model, and as has been

previously shown in the test case, the RT is expected to reduce with diffusion introduced into the

space. The FEM DGM outputs for the rear wall are lower than the measured RT for the T20, but

almost the same for the T30. The rear wall RT is lower than the side wall in general, which is not

surprising as the rear wall area is smaller than the side wall.

4.2.2 Model 2: Absorption at high level with panels at high level


and single Tmf RT values.


As Table 21 shows, the Sabine calculation is once again significantly under-predicting the Tmf RT,

but the CATT Acoustic T20 and T30 outputs are very close to the measured RT. This is a useful

result, and although this project is more concerned with the potential use of the FEM DGM

software for sports hall design, it is clear from the results from Models 1 and 2 that CATT Acoustic

software would have been suitable for the design of Dane Court sports hall. Although there is

only a small degree of scattering (5%) attributed to the wall surfaces, it is likely that this is

sufficient to divert the sound energy to the absorption at ceiling level. As discussed in Section

2.2.1.2, Arup Acoustics predicted a Tmf of 2.3 seconds using the Odeon ray-tracing software

package, which is not as accurate as the CATT Acoustic outputs compared to the measured RT.

The FEM DGM predictions for the side wall section are again higher than the measured RT for

the both the T20 and T30, by 1.5 to 1.7 seconds. This is a significant overestimation compared to

the measured RT, and is attributable to the absorption being located at such a high vertical

position. Observing the wave propagation plots (provided in Accompanying Materials), the

standing wave type behaviour observed for the test case modelling is still occurring due to the

hard parallel wall surfaces, and as with Model 1, the lack of diffusion is likely to be responsible for

125 250 500 1000 2000 4000

Measured RT

(Arup Acoustics)- - - - - - 3.0

Sabine calculation 1.9 2.1 1.7 1.5 1.4 1.3 1.5 much lower than measured Tmf





DGM rear wall T20 2.2 2.8 3.3 3.6 2.2 0.7 3.0 identical to measured Tmf

DGM rear wall T30 2.3 2.8 3.2 3.8 3.6 1.4 3.5 higher than measured Tmf


& 150m2 panels at high level


Chapter 4

64

the higher RT values. The FEM DGM outputs for the rear wall follow the trend seen in Model 1, in

that they are lower than those for the side walls, and are close to the measured RT; the T20 is in

fact identical to the measured RT, but the T30 is higher.

4.2.3 Model 3: Absorption at high level with panels at lower level


and single Tmf RT values. These results are compared to those from Model 2, as they are

concerned with the effect of the location of absorption on the RT.


The Sabine calculation results are the same as for Model 2, due to the fact that the calculation

relies on an assumption of uniformly distributed absorption and does not take the location of

absorption into account. The CATT Acoustic predictions have reduced compared to Model 2, by

between 0.2 seconds (T20) and 0.6 seconds (T30), showing that there is a reduction achieved by

placing acoustic absorption lower down in the room.

The DGM FEM outputs are showing a significant reduction in the predicted Tmf compared to

model 2. The side wall section RT Tmf has reduced by approximately 3 seconds for both the T20

and T30, and the rear wall section Tmf has reduced by 1.5 seconds (T20) and 1.9 seconds (T30). This

suggests that the behaviour of the FEM DGM software depends highly on the location of

absorption, and although the predicted Tmf values of between 1.5 seconds and 1.7 seconds are

likely lower than what the Tmf would be in reality, the reduction in RT is more in keeping with the

expected behaviour of the RT in a real rectangular room, albeit on an exaggerated scale.

4.2.4 Model 4: Absorptive panels at lower level only


and single Tmf RT values. These results are compared to those from Model 3, with the purpose of

determining the effect of the absorptive ceiling on reducing the RT.

125 250 500 1000 2000 4000

Sabine calculation 1.9 2.1 1.7 1.5 1.4 1.3 1.5 identical Tmf to Model 2

CATT Acoustic T20 2.6 2.8 2.7 2.7 2.4 1.9 2.6 reduction in Tmf compared to Model 2


DGM side wall T20 1.3 1.4 1.4 1.6 1.7 1.3 1.6 significant reduction in Tmf compared to Model 2


DGM rear wall T20 0.9 1.1 1.4 1.7 1.5 0.8 1.5 significant reduction in Tmf compared to Model 2



& 150m2 panels at lower

level


Chapter 4

65


The Sabine calculation values have increased, which is as expected due to the area of acoustic

absorption, Sα, being reduced and the dependence of the Sabine formula (12) on this variable.

Compared to Model 3, the CATT Acoustic predictions have not changed for the T20, and have

increased by only 0.4 seconds for the T30. The location of the absorption at lower level only

means that more sound energy is absorbed by the side and rear walls before it gets an

opportunity to propagate within the room, which reduces the amount of later reflections and the

RT. It is likely that the absorptive ceiling is not effective when acoustic absorption is located on

the walls; if sound energy does become incident on the ceiling, it will already have been reduced

in intensity by the wall panels, and the ceiling in any case does not provide a great degree of

acoustic absorption.

The FEM DGM output data has increased for both the side wall and rear wall sections, but only

by 0.6 seconds (side wall T20 and T30) and 0.5 seconds (rear wall T20 and T30). As with the CATT

Acoustic outputs, this suggests that the contribution of absorption from the wall panels is much

more significant than the ceiling absorption.

It is noted that the predictions have accounted for only 150m2 of wall panels; in order to meet

the design requirements of BB93 (Section 1.4), an increased area of wall panels would need to be

provided.

4.2.5 Model 5: Absorptive ceiling only with angled walls


and single Tmf RT values. Model 5 is essentially the same as Model 1, with absorption located on

the ceiling only, but the wall has been angled to determine whether this will reduce RT, as seen

previously for the test case modelling.

125 250 500 1000 2000 4000

Sabine calculation 3.3 3.9 2.9 2.7 2.4 1.9 2.6 increase in Tmf compared to Model 3

CATT Acoustic T20 3.2 3.7 2.8 2.7 2.4 1.9 2.6 Tmf identical to Model 3

CATT Acoustic T30 3.5 4.1 3.0 2.7 2.3 1.9 2.6 small increase in Tmf compared to Model 3

DGM side wall T20 2.4 2.4 2.2 2.2 2.2 2.2 2.2 increase in Tmf compared to Model 3

DGM side wall T30 2.4 2.5 2.4 2.4 2.3 2.1 2.3 increase in Tmf compared to Model 3

DGM rear wall T20 2.1 2.0 1.9 2.0 1.9 1.8 2.0 increase in Tmf compared to Model 3

DGM rear wall T30 2.1 2.1 2.1 2.1 2.1 1.8 2.1 increase in Tmf compared to Model 3

Tmf (sec) CommentModel 4, 150m2 panels at

lower level only


Chapter 4

66


As Table 24 shows, the Sabine calculation values are the same as those for Model 1, as the room

volume has remained the same, and the Sabine formula (12) relies heavily on this variable.

The CATT Acoustic outputs have reduced compared to Model 1, by 0.5 seconds (T20) and 0.2

seconds (T30). The scattering values assigned to the wall and floor surfaces were quite low, at 5%,

so the angled wall has introduced an additional degree of diffusion into the model, which

accounts for the small reduction in RT.

The FEM DGM outputs follow the behaviour seen for the test case, in that the RT has reduced

significantly for the side wall and rear wall sections. The angled wall has directed the sound

energy towards the absorption at high level, due to the fact that the angled wall has introduced

some much needed diffusion into the model. As with the results for Model 3, the general

behaviour of RT reduction is as expected, but the predicted RT values may be under-predicted

compared to reality. There is little variation between the side wall and rear wall predictions,

unlike Model 1, which had significant differences between the different sections.

4.2.6 Dane Court modelling summary of findings

Sabine predictions are much lower than measured RT values. This is as expected based

on the findings of the literature review, and is attributable to the assumptions of uniform

absorption distribution and a diffuse field.

CATT Acoustic predictions are similar to the measured RT values for Model 1 (absorptive

ceiling) and Model 2 (absorptive ceiling & wall panels at high level). This is a useful result

and shows that there is a potential for some ray-tracing software packages to be useful in

the acoustic design of sports halls. It is noted that the predictions made by Arup

Acoustics using Odeon software under-predicted the RT compared to the measured

values and CATT Acoustic predictions. This highlights that differences can still be inherent

in software packages designed to serve the same purpose. It is possible that there are

additional user-definable variables in the Odeon software interface which were set up

125 250 500 1000 2000 4000

Sabine calculation 2.0 2.5 2.2 2.0 1.9 1.6 2.0 identical Tmf to Model 1


CATT Acoustic T30 3.3 4.4 4.0 3.4 2.7 1.9 3.4 slight reduction in Tmf compared to Model 1






only, angled walls


Chapter 4

67

differently than in CATT Acoustic. As discussed in Section 2.5.4, the skill of the user of

such software is crucial to output data accuracy.

FEM DGM rear wall outputs are closer to the measured RT values for Model 1 and Model

2, and side wall outputs are generally higher than the rear wall outputs for these models.

This is likely to be due to the fact that the sound field is dominated by the sound energy

propagating in the horizontal plane, between the two adjacent hard wall surfaces.

Moving the wall absorption lower down only reduces the CATT Acoustic outputs by a

small degree, but has a significant impact on the FEM DGM outputs. When the

absorption is all located at high level, sound energy does not get an opportunity to be

absorbed as the absorption is simply too far away, and the model is still producing the

standing wave type behaviour seen in the test case. However, moving the absorption

lower down means this behaviour is broken up more quickly and the RT reduces.

Removing the absorptive ceiling and retaining the wall panels at low level has a minor

impact on the CATT Acoustic and FEM DGM outputs, with both models showing small

increases in RT. This shows that the absorptive ceiling is not as effective when there is

absorption on the walls at low level. However, if this design approach were considered,

additional wall panels may be necessary in order to meet the design criteria outlined in

BB93 (2015).

Altering the room design by angling a wall reduces the CATT Acoustic RT outputs slightly;

as the scattering values used are quite low, the angled wall is introducing another small

amount of diffusion which is lowering the RT.

The angled wall significantly reduces the RT outputs for the FEM DGM model. As seen in

the test case model, this is due to the fact that the angled wall adds diffusion into the

room. This result illustrates the need for diffusion to be included as a user-definable

variable in the FEM DGM software.

As seen for the test case, having access to the full-field solution produced by the FEM

DGM software is useful, as it shows that the standing wave type behaviour is occurring in

the Dane Court model also. The model is successful in replicating a real-world behaviour

that Sabine calculations and CATT Acoustic modelling cannot.

While the 2D model has been shown to be useful in replicating some real-world

behaviour, it is not clear which 2D section best represents the physical layout of the hall.

The solution provides two different Tmf RT values for the same room, and while this is

useful for observing physical behaviour of sound energy in these planes, further research

is required to accurately understand the results in the context of a 3D room.

Chapter 5

68

Chapter 5: Conclusion

5.1 Achievement of project aims and objectives

The aims of this project were:

1. To gain an understanding of sports hall design, issues in acoustic consultancy and the

prediction methodologies used in calculating reverberation time.

2. To determine whether FEM software implementing the DGM can provide a more accurate

reverberation time calculation in sports halls.

The achievement of these aims was dependent on achieving the following objectives:

1. Identify discrepancies between predicted and measured reverberation time in sports

halls.

2. Evaluate perceived shortcomings of prediction methods, including diffuse-field

calculations and ray-tracing methods.

3. Explore numerical modelling of sports hall 2D sections using FEM DGM software.

4. Compare numerical modelling results to diffuse-field calculations, ray-tracing outputs and

physical measurements.

5. Analyse the effect of introducing scattering elements to the working model.

The objectives have been achieved, and form the basis of this dissertation. A variety of data has

have been referred to which illustrates the underestimation of reverberation time in sports halls

and other large rooms. The underestimation of RT in sports halls has been attributed to several

reasons, including the prediction method, location of acoustic absorption, effect of scattering

objects and other room effects.

The prediction methods used in acoustic consultancy are primarily diffuse-field calculations

based on the Sabine formula and ray-tracing software packages. It has been concluded that the

Sabine formula is not suitable for use in the prediction of RT in sports halls and large rooms, due

to the assumptions of a diffuse-field and the uniform distribution of acoustic absorption. While

there is published data which highlights the inaccuracies of ray-tracing modelling packages, it has

been found in this study that CATT Acoustic software produces accurate single figure Tmf RT values

when compared to measured data for Dane Court sports hall. Unfortunately no octave band data

was available, so the comparisons have only been made to Tmf RT values. It is clear from the

research that user-definable variables play an important role in the accuracy of output data from

Chapter 5

69

ray-tracing models. Arup Acoustics underestimated the RT using Odeon software, but the CATT

Acoustic software has been reasonably successful in replicating measured data.

It has been shown that the FEM DGM software is potentially useful for predicting the RT in large

rooms such as sports halls. When the absorption is located at high level only, the software is

over-predicting the RT, but the wave propagation plots are showing standing wave type behaviour

between the reflective parallel wall surfaces. Identification of this behaviour in the output data is

extremely useful, and the DGM FEM code has replicated a room effect which is believed to be

responsible for high RT in sports halls.

The FEM DGM software produces a full-field solution, which is based on the physical

characteristics of sound wave propagation, so interactions between individual sound waves are

modelled. This is not the case for Sabine calculations and ray-tracing software, so in this respect

the FEM DGM software is very useful for observing the behaviour of a sound source in an

enclosed space.

The FEM DGM software is more sensitive to changing the location of acoustic absorption than

the CATT Acoustic model, and a potentially useful conclusion is that applying absorption to the

walls at a lower height only may be sufficient and may negate the need for absorption at ceiling

level. Introducing scattering elements into the model by angling the side walls produces the

expected behaviour of reducing the RT with increased absorption, and although the reduction is

rather severe compared to the RT produced by the CATT Acoustic model, this serves to highlight

the importance of providing diffusion in sports halls.

5.2 Further research

There are several areas of research which could improve upon the existing FEM DGM software,

which are discussed below.

5.2.1 2D modelling

The FEM DGM model is only operational in 2D at present. This approach requires the user to

visualise a 2D section as a 'slice' of a 3D environment. The primary limitation of this approach is

that the sound source will only propagate in a simple, box-shaped environment, and many of the

complex interactions which occur in 3D will not be modelled. Despite this limitation, this project

was carried out in the first instance to determine whether the FEM DGM method is a viable

modelling approach worth pursuing. The intent is for the project to be carried on either by

Chapter 5

70

another MSc student, or by Arup Acoustics, and it is likely that the model will be converted to 3D,

although this will require significant additional computer programming.

Another consideration when analysing the data produced by the 2D sections is determining

which section to base conclusions on. It has been observed that larger side wall sections generally

produce higher RT values than the smaller rear wall sections, and in some cases the rear wall

sections are generating results comparable to measured values. However, the rear wall sections

do not represent the entire sound field comprehensively enough and do not factor in the large

room volume of the room as a whole. Therefore, further research is required to match the 2D

results to the 3D environment.

5.2.2 Non frequency-dependent absorption coefficient

The absorption coefficient of wall surfaces is defined as a single value in the FEM DGM model.

This is not indicative of real-world construction materials, which have variable absorption

coefficients across octave bands. Many materials will have low absorption coefficients at the

lower frequency range (63Hz to 125Hz), due to the physical limitations of the material (e.g.

mineral fibre, as discussed in Section 2.1.5). Using a single absorption coefficient value simplifies

the calculation process, but compromises the accuracy of the output RT results. Also, for Dane

Court sports hall, predictions made using the Sabine formula and CATT Acoustic have used

frequency-dependent absorption coefficients, so the comparison of these predictions to those

from the FEM DGM software is flawed. Ideally, the FEM DGM software would be modified to

allow a frequency-dependent absorption coefficient to be specified.

5.2.3 Diffusion and scattering

As discussed in Section 2.3.3, scattering objects can have a significant impact on reducing the RT

in sports halls and other large rooms. It has been shown from the literature review that there are

several cases in which the RT has reduced simply by introducing scattering elements into the

room. The FEM DGM model does not account for diffusion, and the higher RT outputs observed

for the Dane Court Model 1 scenario with absorption at ceiling level only are likely attributable to

this. Angling the walls has essentially introduced diffusion into the model, which has reduced the

RT, so it is likely that including diffusion as a user-definable variable would be beneficial. This

would require additional computer programming.

Chapter 5

71

5.3 Project management

This project has been carried out in conjunction with a part-time role in acoustic consultancy, and

has taken place over approximately ten months. Time management has been a crucial aspect of

the project, and required a balance between academic and professional commitments.

A Project Plan document was produced in November 2014, which set out the project

background, research methods, communication methods, project objectives and timescale in the

form of a Gantt chart. An Interim Report was submitted in March 2015, which further clarified

the project aims and objectives, described a summary of the literature review and empirical data

collection methods, a risk assessment and an updated Gantt chart. A project presentation took

place in July 2015, which allowed an opportunity to explain the purpose of project and summarise

the findings to date. A third revision of the Gantt chart was produced for the presentation. The

Project Plan, Interim Report and presentation slides and all Gantt chart revisions are provided in

the Accompanying Materials.

Over the duration of the project, correspondence has taken place between Gwenael Gabard,

project supervisor and Vincent Jurdic of Arup Acoustics. The correspondence has been carried

out through several face-to-face meetings, emails, and Lync/phone conversations. A spreadsheet

detailing the key meetings is provided in the Accompanying Materials.

List of References

72

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