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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