Computer Modeling of a Large Fan-Shaped Auditorium

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Computer Modeling of a Large Fan-Shaped Auditorium

• Heather Smith
• Timothy W. Leishman

Acoustics Research Group Department of Physics
Astronomy Brigham Young University
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Auditorium Characteristics

• Large
• Seats 21,000 people
• Volume 11,400,000 cu. ft
• Fan-shaped
• Curved and concavely oriented surfaces toward the
  rear of the hall based primarily on one center of
  curvature
• Coupled Spaces
• Large cavity behind the rostrum
• Large cavity above the canopy ceiling
• Transparent surfaces
• Façade side walls
• Façade ceiling
• Large skylights

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Challenges in Modeling this Auditorium

• Large number of faces
• Curved surfaces approximated with planar surfaces
• Sensitive to absorption scattering coefficients
• Large 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 users web page)
• Coupled room
• Transmission coefficients for some surfaces

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Absorption Coefficients

• Used published absorption coefficients when
  possible
• Otherwise estimated values using similar
  materials or rough averaging
• Used 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 choices

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Scattering Coefficients

• Little or no published data on scattering
  coefficients for surfaces
• Approximating scattering coefficients
• Use approximations suggested by various authors
• Measure surface dimensions and compare to the
  wavelength
• Limitations of approximations
• Do not specify which three-dimensional surface
  dimension(s) to use
• Vague in assignment of scattering coefficient
  values based on the wavelength/surface dimension
  ratio

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Comparisons
CATT Model
EASE Model
C-50 C-80 STI
Measured -2.89 -0.81 0.47
CATT -.21 2.8 0.58
EASE -3.45 -0.18 0.57
Measured
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Source Omnidirectional loudspeaker
Receiver KEMAR manikin with microphones at
opening of artificial ear canal
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Refining Absorption in the Model

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

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Refining Scattering in the Model

• Work to obtain better scattering coefficient
  values for important surfaces (i.e., seats,
  seated audience)
• Experimental
• Measure scattering coefficients in reverberation
  chamber using proposed standard ISO/DIS 17497-1
• Numerical
• Use BEM package to predict scattering
  coefficients
• Analytical
• Solutions for arrays of simple scatterers (e.g.
  spheres)

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Conclusions

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