Computer Computer Modeling of a Modeling of a

Large Fan-Shaped Large Fan-Shaped AuditoriumAuditorium

Heather SmithHeather SmithTimothy W. LeishmanTimothy W. Leishman

Acoustics Research GroupAcoustics Research GroupDepartment of Physics & AstronomyDepartment of Physics & Astronomy

Brigham Young UniversityBrigham Young University

Auditorium Auditorium CharacteristicsCharacteristics• Large Large

• Seats 21,000 peopleSeats 21,000 people• Volume = 11,400,000 cu. ftVolume = 11,400,000 cu. ft

• Fan-shapedFan-shaped• Curved and concavely oriented surfaces Curved and concavely oriented surfaces

toward the rear of the hall based primarily toward the rear of the hall based primarily on one center of curvatureon one center of curvature

• Coupled SpacesCoupled Spaces• Large cavity behind the rostrumLarge cavity behind the rostrum• Large cavity above the canopy ceilingLarge cavity above the canopy ceiling

• Transparent surfacesTransparent surfaces• Façade side wallsFaçade side walls• Façade ceilingFaçade ceiling

• Large skylightsLarge skylights

Challenges in Modeling this Challenges in Modeling this AuditoriumAuditorium

• Large number of facesLarge number of faces• Curved surfaces approximated with planar surfacesCurved surfaces approximated with planar surfaces

• Sensitive to absorption & scattering Sensitive to absorption & scattering coefficientscoefficients• Large surfacesLarge surfaces• ““If in doubt, try with both high and low values [for If in doubt, try with both high and low values [for

scattering coefficients] and see if the results are scattering coefficients] and see if the results are sensitive or not (it depends on the hall shape and sensitive or not (it depends on the hall shape and the absorption distribution and is very difficult to the absorption distribution and is very difficult to know in advance).” know in advance).” - Bengt-Inge Dalenbäck - Bengt-Inge Dalenbäck (CATT user’s web page)(CATT user’s web page)

• Coupled room Coupled room • Transmission coefficients for some surfacesTransmission coefficients for some surfaces

Absorption CoefficientsAbsorption Coefficients• Used published absorption coefficients Used published absorption coefficients

when possiblewhen possible• Otherwise estimated values using similar Otherwise estimated values using similar

materials or rough averaging materials or rough averaging • Used cumulative absorption curves to Used cumulative absorption curves to

determine contributions of surfaces to determine contributions of surfaces to total absorptiontotal absorption

• Because of their contributions to total Because of their contributions to total absorption, larger surfaces are very absorption, larger surfaces are very sensitive to absorption coefficient choicessensitive to absorption coefficient choices

Absorption Curves

0

5000

10000

15000

20000

25000

30000

100 1000 10000

Frequency

Ab

sorp

tio

n (

Sab

ins)

Carpet

Med Uph Seats

Wood Floors

Avg Owens andGlass

2" Owens

1/2" Gypsum

Heavily UphSeats

4" Owens

Canopies

Organ Pipes

Concrete

Façade

Ceiling

EstimatedUpper Room

PlywoodPaneling

Avg Carpet &Plywood

Avg Wood &1/2" Gypsum

Avg Concrete &2" Owens

Unglazed Brick

CeilingTreatment

TotalAbsorption

Measured TotalAbsorption

Scattering CoefficientsScattering Coefficients• Little or no published data on scattering Little or no published data on scattering

coefficients for surfacescoefficients for surfaces• Approximating scattering coefficientsApproximating scattering coefficients

• Use approximations suggested by various authorsUse approximations suggested by various authors• Measure surface dimensions and compare to the Measure surface dimensions and compare to the

wavelengthwavelength

• Limitations of approximationsLimitations of approximations• Do not specify which three-dimensional surface Do not specify which three-dimensional surface

dimension(s) to usedimension(s) to use• Vague in assignment of scattering coefficient Vague in assignment of scattering coefficient

values based on the wavelength/surface dimension values based on the wavelength/surface dimension ratioratio

ComparisonsComparisons

C-50C-50 C-C-8080

STSTII

MeasureMeasuredd

-2.89-2.89 --0.80.811

0.40.477

CATTCATT -.21-.21 2.82.8 0.50.588

EASEEASE -3.45-3.45 --0.10.188

0.50.577

CATT Model

EASE Model Measur

ed

Early Decay Time

0

0.5

1

1.5

2

2.5

3

3.5

100 1000 10000Frequency

EDT

(s)

Measured

CATT

EASE

T-30

0

0.5

1

1.5

2

2.5

3

3.5

4

100 1000 10000

Frequency

T-3

0 (s

)

MeasuredCATTEASE

Source: Omnidirectional loudspeaker

Receiver: KEMAR manikin with microphones at opening of artificial ear canal

Refining Absorption in Refining Absorption in the Modelthe Model

• Experimentally measure absorption Experimentally measure absorption coefficients for surfaces that have a coefficients for surfaces that have a large effect on total absorption large effect on total absorption • SeatsSeats• Seated Audience Seated Audience • Ceiling treatmentCeiling treatment

Refining Scattering in Refining Scattering in the Modelthe Model

• Work to obtain better scattering coefficient values Work to obtain better scattering coefficient values for important surfaces (i.e., seats, seated audience)for important surfaces (i.e., seats, seated audience)• ExperimentalExperimental

•Measure scattering coefficients in reverberation Measure scattering coefficients in reverberation chamber using proposed standard ISO/DIS chamber using proposed standard ISO/DIS 17497-117497-1

• NumericalNumerical•Use BEM package to predict scattering Use BEM package to predict scattering

coefficients coefficients • AnalyticalAnalytical

•Solutions for arrays of simple scatterers (e.g. Solutions for arrays of simple scatterers (e.g. spheres)spheres)

ConclusionsConclusions• It appears to be feasible to model a It appears to be feasible to model a

very large hall using commercial very large hall using commercial geometric acoustics packagesgeometric acoustics packages

• Models need more refining in order Models need more refining in order to better match the measured resultsto better match the measured results

• Additional work is needed to Additional work is needed to determine more accurate values for determine more accurate values for scattering and absorption scattering and absorption coefficients of surfacescoefficients of surfaces