Computer Modeling of a Large Fan-Shaped Auditorium Heather Smith Timothy W. Leishman Acoustics Research Group Department of Physics & Astronomy Brigham Young University

Auditorium Characteristics LargeLarge 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 toward the rear of the hall based primarily on one center of curvatureCurved and concavely oriented surfaces toward the rear of the hall based primarily on 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 Auditorium Large number of facesLarge number of faces Curved surfaces approximated with planar surfacesCurved surfaces approximated with planar surfaces Sensitive to absorption & scattering coefficientsSensitive to absorption & scattering coefficients Large surfacesLarge surfaces “If in doubt, try with both high and low values [for scattering coefficients] and see if the results are sensitive or not (it depends on the hall shape and the absorption distribution and is very difficult to know in advance).” - Bengt-Inge Dalenbäck (CATT user’s web page)“If in doubt, try with both high and low values [for scattering coefficients] and see if the results are sensitive or not (it depends on the hall shape and the absorption distribution and is very difficult to know in advance).” - Bengt-Inge Dalenbäck (CATT user’s web page) Coupled roomCoupled room Transmission coefficients for some surfacesTransmission coefficients for some surfaces

Absorption Coefficients Used published absorption coefficients when possibleUsed published absorption coefficients when possible Otherwise estimated values using similar materials or rough averagingOtherwise estimated values using similar materials or rough averaging Used cumulative absorption curves to determine contributions of surfaces to total absorptionUsed cumulative absorption curves to determine contributions of surfaces to total absorption Because of their contributions to total absorption, larger surfaces are very sensitive to absorption coefficient choicesBecause of their contributions to total absorption, larger surfaces are very sensitive to absorption coefficient choices

Scattering Coefficients Little or no published data on scattering coefficients for surfacesLittle or no published data on scattering coefficients 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 wavelengthMeasure surface dimensions and compare to the wavelength Limitations of approximationsLimitations of approximations Do not specify which three-dimensional surface dimension(s) to useDo not specify which three-dimensional surface dimension(s) to use Vague in assignment of scattering coefficient values based on the wavelength/surface dimension ratioVague in assignment of scattering coefficient values based on the wavelength/surface dimension ratio

Comparisons C-50C-80STI Measured CATT EASE CATT Model EASE Model Measured

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

Refining Absorption in the Model Experimentally measure absorption coefficients for surfaces that have a large effect on total absorptionExperimentally measure absorption coefficients for surfaces that have a large effect on total absorption SeatsSeats Seated AudienceSeated Audience Ceiling treatmentCeiling treatment

Refining Scattering in the Model Work to obtain better scattering coefficient values for important surfaces (i.e., seats, seated audience)Work to obtain better scattering coefficient values for important surfaces (i.e., seats, seated audience) ExperimentalExperimental Measure scattering coefficients in reverberation chamber using proposed standard ISO/DIS Measure scattering coefficients in reverberation chamber using proposed standard ISO/DIS NumericalNumerical Use BEM package to predict scattering coefficientsUse BEM package to predict scattering coefficients AnalyticalAnalytical Solutions for arrays of simple scatterers (e.g. spheres)Solutions for arrays of simple scatterers (e.g. spheres)

Conclusions It appears to be feasible to model a very large hall using commercial geometric acoustics packagesIt appears to be feasible to model a very large hall using commercial geometric acoustics packages Models need more refining in order to better match the measured resultsModels need more refining in order to better match the measured results Additional work is needed to determine more accurate values for scattering and absorption coefficients of surfacesAdditional work is needed to determine more accurate values for scattering and absorption coefficients of surfaces