# Acoustic Shell Optimization in Opera Houses for Concert Halls
## 3 The Case Study
### Acoustic Modelling, Measurements and Calibration
In the calibration process, the uncertainty in fly tower modelling was avoided by replacing it with the house curtains; fly tower modelling was also not requested in the simulations (being that the stage area was replaced by the acoustic shell). Furthermore, the well-known absorption coefficients of the house curtains were introduced, having been measured in a reverberation chamber [49], focusing the calibration process only on the theatre hall surfaces. The house curtains' absorption coefficients follow (Table 10):  
The hall absorption coefficients, which remained fixed in the different compared simulations, needed to be identified. The chosen configuration made it possible to start the calibration process, considering the seating area as the main absorption surface of the hall, and allowing, at the beginning, the use of the \"residual absorption coefficients\", i.e., the total absorption, for all the walls, the ceiling, and the balcony fronts, that did not exceed the one proposed by [PERSON] and [PERSON] [50; 51], while the absorption coefficients of the seating area referred to the medium upholstered seats, indicated in the same authors' study [51]. To reduce the uncertainty in comparing the results, the wood panels characteristics were fixed by changing the shell layout, only increasing or decreasing their quantity without changing their acoustic properties. The measured RT and C80 values, for the calibration process referred to the theatre configuration in which the house curtains are closed. The difference between the simulated and the measured values are inside 1 JND [21] (Figure 8). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Material** & \multicolumn{5}{c}{**Centre Frequency of Octave Band [Hz]**} \\ \hline  & 125 & 250 & 500 & 1000 & 2000 & 4000 \\ House curtains & 0.23 & 0.61 & 0.67 & 0.75 & 0.85 & 0.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: House curtain absorption coefficients. In the simulation model, the wood panels' absorption coefficients were taken into consideration. Values from the literature were studied first (Table 11) [52]:  
According to this table, wood panels are generally light partitions, which have their maximum absorption at low frequencies. Therefore, such constructions can make up for the low absorptivity of an audience and thus achieve a more uniform frequency dependence on the reverberation time. Simplified models to predict the reflections from finite objects [53], the diffusion properties for elements with finite dimensions [27], and the attenuation or gain due to panel curvature (Rindel) [53] were also considered. In the end, data obtained in a reverberation chamber were used [49]. The tested panels were made of wood; the areic mass was equal to 13 kg, the dimensions were 1.5 m by 1.5 m each, the radii were equal to 5 m. The panels were screwed onto an aluminum frame, linked to a vertical truss structure. Between the frame and the trusses, neoprene strips, 3 mm thick, were inserted. The measured absorption coefficients follow (Table 12):  
Working in the digital domain, the curved surfaces needed to be discretized in the virtual model, replacing the continuous curves with a succession of straight lines. The scattering coefficients were defined according to the panel radius and the geometry discretization of the curve [46], evaluated as equal to 5% for lower and higher frequencies, and equal to 10% at central frequencies (500 and 1000 Hz). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Material** & \multicolumn{5}{c}{**Centre Frequency of Octave Band [Hz]**} \\ \hline  & 125 & 250 & 500 & 1000 & 2000 & 4000 \\ wood panels & 0.21 & 0.15 & 0.09 & 0.07 & 0.05 & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Wood panels measured absorption coefficients and diffusion. Figure 8: Simulated and measured T30 (**a**) and C80 (**b**) values.